Hello There!
The answer would be "I and III"
If Isabelle makes these changes, she will get charged an overdraft fee on 2 days. The days will be Thursday and Saturday.
Answer:
B
Step-by-step explanation:
Finding Angle measures between intersecting lines
Answer:
50
Step-by-step explanation:
105+x+25=180
x+130 =180
x=50
the value of x is 50°
The angle made by a straight line is 180 degrees. This is a fundamental property of a straight line. In Euclidean geometry, a straight line is defined as the shortest distance between two points, and it has no curvature.
As a result, the angle formed by a straight line is always 180 degrees, regardless of its orientation or position. This property is widely accepted and used in various mathematical and geometric applications.
We know that angle made by straight line is 180°
∠EAB + ∠BAC + ∠CAD = 180°
x° + 105°+ 25° = 180°
x° + 130° = 180°
x° = 180° - 130°
x° = 50°
Therefore, the value of x is 50°
Learn more about angle here
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A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between the landmarks in degrees.
the triangle has
two sides(65,55)
angles (40,30)
What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.
32.5 m
42.1 m
85.1 m
98.5 m
Answer:
Check attachment for the included diagram
The last option is the correct otpiton 98.5m
Step-by-step explanation:
We know that side 1= 65m
Side 2 =55m
Then, the angle between the two sides are not given, let call the third angle X
We know the other two opposite angles and which are 40° and 30°.
Applying sum of angle in as triangle
The sum of angle in a triangle is 180°
Then,
X+30+40 =180
X+ 70 =180
X=180-70
X=110°
So, using cosine rule
c² = a²+b²-2abCosX
c² = 65²+55²-2•65•55Cos110
c² = 4225+3025-(-2445.44)
NOTE: -×-=+
c² = 4225+3025+2445.44
c² = 9695.44
c=√9695.44
c=98.465
To the nearest ten
c= 98.5m
The last option is the correct answer
Answer:
The distance between the two landmarks is 98.5m
Step-by-step explanation:
I've attached an image to depict where toby is standing, the landmark and the angles.
To get the distance between the 2 landmarks, we will make use of cosine rule which is given as;
c² = a² + b² − 2ab cos(C)
Where, a and b are the two given lamdmarks.
c = the distance between the landmarks
C is the angle opposite the distance between the landmarks i.e the angle at the point at where toby is standing
Now, we are not given the angle C. But we can calculate it from knowing that sum of angles in a triangle is equal to 180.since we know 2 angles, thus, C = 180 - (40 + 30) = 110°
Now, we can solve for c by plugging in the relevant values ;
c² = 55² + 65² - (2*55*65*Cos110)
c² = 4225 + 3025 -7150(-0.342)
c² = 9695.3
c=√9695.3
c=98.46m ≈ 96.5m
Help calculus module 8 DBQ
please show work
1. The four subintervals are [0, 2], [2, 3], [3, 7], and [7, 8]. We construct trapezoids with "heights" equal to the lengths of each subinterval - 2, 1, 4, and 1, respectively - and the average of the corresponding "bases" equal to the average of the values of [tex]R(t)[/tex] at the endpoints of each subinterval. The sum is then
[tex]\dfrac{R(0)+R(2)}2(2-0)+\dfrac{R(2)+R(3)}2(3-2)+\dfrac{R(3)+R(7)}2(7-3)+\dfrac{R(7)+R(8)}2(7-8)=\boxed{24.83}[/tex]
which is measured in units of gallons, hence representing the amount of water that flows into the tank.
2. Since [tex]R[/tex] is differentiable, the mean value theorem holds on any subinterval of its domain. Then for any interval [tex][a,b][/tex], it guarantees the existence of some [tex]c\in(a,b)[/tex] such that
[tex]\dfrac{R(b)-R(a)}{b-a)=R'(c)[/tex]
Computing the difference quotient over each subinterval above gives values of 0.275, 0.3, 0.3, and 0.26. But just because these values are non-zero doesn't guarantee that there is definitely no such [tex]c[/tex] for which [tex]R'(c)=0[/tex]. I would chalk this up to not having enough information.
3. [tex]R(t)[/tex] gives the rate of water flow, and [tex]R(t)\approx W(t)[/tex], so that the average rate of water flow over [0, 8] is the average value of [tex]W(t)[/tex], given by the integral
[tex]R_{\rm avg}=\displaystyle\frac1{8-0}\int_0^8\ln(t^2+7)\,\mathrm dt[/tex]
If doing this by hand, you can integrate by parts, setting
[tex]u=\ln(t^2+7)\implies\mathrm du=\dfrac{2t}{t^2+7}\,\mathrm dt[/tex]
[tex]\mathrm dv=\mathrm dt\implies v=t[/tex]
[tex]R_{\rm avg}=\displaystyle\frac18\left(t\ln(t^2+7)\bigg|_{t=0}^{t=8}-\int_0^8\frac{2t^2}{t^2+7}\,\mathrm dt\right)[/tex]
For the remaining integral, consider the trigonometric substitution [tex]t=\sqrt 7\tan s[/tex], so that [tex]\mathrm dt=\sqrt 7\sec^2s\,\mathrm ds[/tex]. Then
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}\frac{7\tan^2s}{7\tan^2s+7}\sec^2s\,\mathrm ds[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}\tan^2s\,\mathrm ds[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}(\sec^2s-1)\,\mathrm ds[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\left(\tan s-s\right)\bigg|_{s=0}^{s=\tan^{-1}(8/\sqrt7)}[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\left(\tan\left(\tan^{-1}\frac8{\sqrt7}\right)-\tan^{-1}\frac8{\sqrt7}\right)[/tex]
[tex]\boxed{R_{\rm avg}=\displaystyle\ln71-2+\frac{\sqrt7}4\tan^{-1}\frac8{\sqrt7}}[/tex]
or approximately 3.0904, measured in gallons per hour (because this is the average value of [tex]R[/tex]).
4. By the fundamental theorem of calculus,
[tex]g'(x)=f(x)[/tex]
and [tex]g(x)[/tex] is increasing whenever [tex]g'(x)=f(x)>0[/tex]. This happens over the interval (-2, 3), since [tex]f(x)=3[/tex] on [-2, 0), and [tex]-x+3>0[/tex] on [0, 3).
5. First, by additivity of the definite integral,
[tex]\displaystyle\int_{-2}^xf(t)\,\mathrm dt=\int_{-2}^0f(t)\,\mathrm dt+\int_0^xf(t)\,\mathrm dt[/tex]
Over the interval [-2, 0), we have [tex]f(x)=3[/tex], and over the interval [0, 6], [tex]f(x)=-x+3[/tex]. So the integral above is
[tex]\displaystyle\int_{-2}^03\,\mathrm dt+\int_0^x(-t+3)\,\mathrm dt=3t\bigg|_{t=-2}^{t=0}+\left(-\dfrac{t^2}2+3t\right)\bigg|_{t=0}^{t=x}=\boxed{6+3x-\dfrac{x^2}2}[/tex]
please help asap
How can we write 50.2 in words?
Answer:
There are two ways you can write it. You can write it how you would casually say it:
Fifty and two (or Fifty point Two)
But mathematically, you would say it as:
Fifty and Two-tenths.
~
Of 118 randomly selected adults, 34 were found to have high blood pressure. construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.
Answer: [tex](20.63\%,\ 36.97\% )[/tex]
Step-by-step explanation:
The confidence interval for population proportion(p) is given by :-
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where
n= Sample size
z*= Critical z-value.
[tex]\hat{p}[/tex] = sample proportion.
Let p be the true proportion of all adults that have high blood pressure.
As per given , we have
n= 118
Number of adults found to have high blood pressure =34
Then, [tex]\hat{p}=\dfrac{34}{118}\approx0.288[/tex]
Critical z-value for 95% confidence interval : z* = 1.96
Now , the 95% confidence interval for population proportion will be :
[tex]0.288\pm (1.96)\sqrt{\dfrac{0.288(1-0.288)}{118}}[/tex]
[tex]0.288\pm (1.96)\sqrt{0.0017377627}[/tex]
[tex]0.288\pm (1.96)(0.04168648)[/tex]
[tex]0.288\pm0.0817[/tex]
[tex]=(0.288-0.0817,\ 0.288+0.0817) =(0.2063,\ 0.3697 )[/tex]
In percentage , this would be [tex](0.2063,\ 0.3697 )=(20.63\%,\ 36.97\% )[/tex]
Hence, the 95% confidence interval for the true percentage of all adults that have high blood pressure = [tex](20.63\%,\ 36.97\% )[/tex]
Claudia records the hours she spent studying and her test scores for 5 tests. What is the correlation coefficient? What is the strength of the model?
0.85 and strong positive correlation
Good Luck!
Answer:
0.85 & Strong Positive Correlation
Step-by-step explanation:
On EDGE 2023
A tutoring service offers a free one-hour tutoring session. After a client signs up, the next 10 hours of tutoring are billed at a rate of $30 per hour. For all the hours after that, the client receives a discounted rate. If a client pays $664 for 25 hours of tutoring, what is the service's discounted hourly rate?
A) $24.50
B) $25.54
C) $26.00
D) $26.56
Answer:
C) $26.00
Step-by-step explanation:
No. of hours needed to be paid for = 25 - 1 = 24 (First hour is free)
Cost of next 10 hours = $30 x 10 = $300
No. of hours left to be paid for = 24 - 10 = 14
Cost of last 14 hours = $664 - $300 = $364
Discounted hourly rate = $364 / 14 = $26
The graphs of functions f(x) and g(x) = f(x) + k are shown:
What is the value of k?
A.) K=2
B.) K=1
C.) K=0
D.) K=-2
The value of k is:
A.) K=2
Step-by-step explanation:We know that the transformation of the type:
f(x) to f(x)+k
is a translation of the original graph k units upwards or downwards depending on k.
if k>0 then the shift is k units up and if k<0 then the shift is k units down.
Here we observe that the graph of the function g(x) is shifted 2 units upwards as compared to the graph of the function f(x).
This means that:
k=2
Need some help with this equation, please help me!
Answer the questions in the table below. Show all your work please and thank you!!
a. Use special right triangles to find the exact height of the triangle. This means that you will not round your answer, leave your answer in radical form. State or show which special right triangle you used. Don’t forget to label your answer with appropriate units.
b. What is the exact area of ∆BCD? This means that you will not round your answer, leave your answer in radical form. Don’t forget to label your final answer. Show your work.
Answer:
a. 12sqrt(3) cm. b. 72sqrt(3) cm squared
Step-by-step explanation:
a. I hope you see this a 30-60-90 triangle
The short side is opposite to 30
The long leg is opposite to 60
The hypotenuse, the longest side, is opposite 90.
So you are given short side which is 12 cm.
The long leg (the height in this case) is short side times square root of 3 so your height is 12sqrt(3) cm.
b. The area of a triangle is .5*base*height.
You have both the base and height now so plug them in:
.5(12)(12sqrt(3)) cm squared
6(12)sqrt(3) cm squared
72sqrt(3) cm squared
PLZ HELP ASAP I WILL GIVE BRAINLIEST What is the surface area of the regular pyramid below?
Answer:
864 units²
Step-by-step explanation:
Area of each sloped side,
= 1/2 x base x height
= 1/2 x 16 x 19 = 152 units²
There are 4 sloped sides, so area of all sloped sides = 4 x 152 = 608 units²
Area of base = Length x Width = 16 x 16 = 256 units²
Total surf. area = area of all sloped sides + area of base
= 608 + 256
= 864 units²
Answer:
I know this is a late answer but it's A. 864 units²
Step-by-step explanation:
Have a great day!
On Monday, the water was shut off 3 times for 1/4 hours, 2/3 hours, and 1-3/4 hours, respectively. What was the tireless number of hours the water was off?
Answer:
2 2/3 hours
Step-by-step explanation:
The total of the given outage lengths is ...
(1/4) + (2/3) + (1 3/4) = (1/4 + 1 3/4) + 2/3
= 2 + 2/3 = 2 2/3
The water was off for 2 2/3 hours.
Answer: The required number of tireless hours is [tex]2\dfrac{2}{3}~\textup{hours}.[/tex]
Step-by-step explanation: Given that on Monday, the water was shut off 3 times for [tex]\dfrac{1}{4}[/tex] hours, [tex]\dfrac{2}{3}[/tex] hours, and [tex]1\dfrac{3}[4}[/tex] hours, respectively.
We are to find the tireless number of hours for which the water was off.
The tireless number of hours for which the water was off is equal to the sum of the number of hours for which the water was off three times.
Therefore, the number of tireless hours for which the water was off is given by
[tex]n_t\\\\\\=\dfrac{1}{4}+\dfrac{2}{3}+1\dfrac{3}{4}\\\\\\=\dfrac{1}{4}+\dfrac{2}{3}+\dfrac{7}{4}\\\\\\=\dfrac{3+8+21}{12}\\\\\\=\dfrac{32}{12}\\\\\\=\dfrac{8}{3}\\\\\\=2\dfrac{2}{3}.[/tex]
Thus, the required number of tireless hours is [tex]2\dfrac{2}{3}~\textup{hours}.[/tex]
please help asap urgent brainliest
The perimeter of a rectangle is 90 feet. The length is 27 feet.
What is the width of the rectangle? in feet
The formula for perimeter is P = 2length + 2width (P = 2L + 2W)
You know that the length is 27 ft but you don't know the width. To find the width plug 90 in for P and 27 in for L then solve for W.
90 = 2(27) + 2W
90 = 54 + 2W
90 - 54 = 54 - 54 + 2W
36 = 0 + 2W
36 = 2W
36 / 2 = 2W/ 2
18 = 1W
18 = W
Width is 18 ft
Check:
2(27) + 2(18) = 90
54 + 36 = 90
90 = 90
Hope this helped!
~Just a girl in love with Shawn Mendes
1. Use the correct order of operation to solve the following problem: 3 × (50 – 62) ÷ 2 A. 69 B. 18 C. 21 D. 57
Answer:
The correct answer is option B. 18
Step-by-step explanation:
It is given an expression : 3 × (50 – 62) ÷ 2
To find the answer we have to use BODMAS principle
BODMAS means that the order of operations
B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and
S - Subtraction
To find the correct option
Step 1: Do the bracket first
3 × (50 – 62) ÷ 2 = 3 × (-12) ÷ 2
Step 2: Division
3 × (-12) ÷ 2 = 3 x (-6)
Step 3 : Multiplication
3 x (-6) = -18
The correct option is option B. 18
This question is called "Create equations to solve for missing angles".
It's really confusing me, need help on this!!
Answer:
D
Step-by-step explanation:
both angles have 2 straight lines that intersect in the middle, this is called vertical angles which means, according to the law, that each angle is equal to the other so 10x + 10 = 110. Therefore the answer is D
Answer:
D 10x+10 = 110
Step-by-step explanation:
10x +10 and 110 are vertical angles and vertical angles are equal
10x+10 = 110
HELP, PLEASE???? ASAP!!??
The probabilities for each outcome of the number of heads are:
- Probability of 0 heads: [tex]\( P(0) = \frac{4}{80} = 0.05 \)[/tex]
- Probability of 1 head: [tex]\( P(1) = \frac{8}{80} = 0.10 \)[/tex]
- Probability of 2 heads: [tex]\( P(2) = \frac{36}{80} = 0.45 \)[/tex]
- Probability of 3 heads: [tex]\( P(3) = \frac{20}{80} = 0.25 \)[/tex]
- Probability of 4 heads: [tex]\( P(4) = \frac{12}{80} = 0.15 \)[/tex]
To create a probability distribution for the discrete variable, which in this case is the number of heads obtained in each trial, you would divide the frequency of each outcome by the total number of trials to obtain the probability for each outcome.
Based on the information provided:
- There were 80 trials.
- The frequency for 0 heads is 4.
- The frequency for 1 head is 8.
- The frequency for 2 heads is 36.
- The frequency for 3 heads is 20.
- The frequency for 4 heads is 12.
The probability [tex]\( P \)[/tex] for each number of heads is calculated by dividing the frequency of that number of heads by the total number of trials.
So, for each number of heads [tex]\( x \)[/tex]:
[tex]\[ P(x) = \frac{\text{Frequency of } x}{\text{Total number of trials}} \][/tex]
The probabilities for each outcome of the number of heads are:
- Probability of 0 heads: [tex]\( P(0) = \frac{4}{80} = 0.05 \)[/tex]
- Probability of 1 head: [tex]\( P(1) = \frac{8}{80} = 0.10 \)[/tex]
- Probability of 2 heads: [tex]\( P(2) = \frac{36}{80} = 0.45 \)[/tex]
- Probability of 3 heads: [tex]\( P(3) = \frac{20}{80} = 0.25 \)[/tex]
- Probability of 4 heads: [tex]\( P(4) = \frac{12}{80} = 0.15 \)[/tex]
Here is the probability distribution graph for the number of heads in the trials. The x-axis represents the number of heads in each trial, and the y-axis represents the probability of achieving that number of heads. Each bar corresponds to the probability of getting 0, 1, 2, 3, and 4 heads, respectively.
WILL MARK BRAINLEIST!! name all segments skew to bc
Answer ==== GF, HI, FA, DI
Step-by-step explanation
As long as they aren't on the same plane or aren't touching your given segment, they are skew.
Answer:
GF, HI, FA, DI is correct.
Step-by-step explanation:
if (1,0) is an ordered pair of the function f(x), which of the following is an ordered pair of the inverse of f(x)?
A. (0,1)
B. (0,0)
C. (1,0)
D. (1,1)
Answer:
A. (0,1)
Step-by-step explanation:
all you do is switch the X and Y coordinates
Final answer:
The ordered pair of the inverse of the function f(x), given the original pair (1,0), is (0,1), which is option A.
Explanation:
The ordered pair (1,0) represents a point on the function f(x) where x = 1 and f(x) = 0. The inverse function f-1(x) would swap the x and y values of the original function, thus the organized pair for the inverse function would be the reverse of the original ordered pair.
Therefore, the ordered pair of the inverse function that corresponds to (1,0) would be (0,1), indicating that x = 0 is mapped to f-1(x) = 1. This corresponds to option A. (0,1).
If 2000 is placed into a bank account that pays 3% compund interest per year , how much will be in the account after 2 years
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]
Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers? n2 + n – 210 = 0 n2 + n – 105 = 0 2n2 + 2n + 210 = 0 2n2 + 2n + 105 = 0
Answer:
First choice: n² + n - 210 = 0Explanation:
1) If you use n to name the smaller number of two integer numbers, then the next consecutive number is n + 1.
2) The product of those two numbers is n × (n + 1) = n (n + 1).
3) Half of that product is n (n + 1) / 2.
And the question states that thas is equal to 105, so the equation becomes:
4) n (n + 1) / 2 = 105
Now you have to simplify that equation until you have an expression equal to one of the choices:
5) Simplification:
Multiply both sides by 2: n (n + 1) = 210Distributive property on the left side: n² + n = 210Subtract 210 from both sides: n² + n - 210 = 0And that is the first choice, so you have your answer.
Answer:
n² + n - 210 = 0
Step-by-step explanation:
answer:
A. 20 units
B. 30 units
C.40 units
D. 50 units
The change in internal energy of the system is 0 J because the energy input (50 J) precisely equals the energy output (50 J), assuming no work is done by the system, according to the first law of thermodynamics.
Explanation:The question is asking about the change in internal energy of a system given that there is some energy transfer into and out of the system. We denote the energy transferred into the system as Qin and the energy transferred out of the system as Qout. For this question, Qin is 50 J and Qout is 50 J.
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Qin) minus the work done by the system (W) and the heat leaving the system (Qout). However, in this case, we don't have information about the work done, which is often represented as the term W. If we assume no work is done, the equation simplifies to ΔU = Qin - Qout.
Using this information, we can calculate the change in internal energy: ΔU = 50 J - 50 J = 0 J. There is no change in internal energy because the energy input equals the energy output. Therefore, the correct response here would be none of the options provided (A. 20 J, B. 30 J), but instead, it would be 0 J.
What is the initial value and what does it represent
Answer:
c
Step-by-step explanation:
c
Answer:
The answer to this question is c
Step-by-step explanation:
HELP PLEASE!! I NEED AN ANSWER AS SOON AS POSSIBLE!!! BEST ANSWER WILL GET BRAINLIEST!!!
Answer:
hi
Step-by-step explanation:
what is the volume of a sphere with surface area of 25 pi yd squared?
[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=25\pi \end{cases}\implies 25\pi =4\pi r^2 \\\\\\ \cfrac{25\pi }{4\pi }=r^2\implies \cfrac{25}{4}=r^2\implies \sqrt{\cfrac{25}{4}}=r\implies \cfrac{\sqrt{25}}{\sqrt{4}}=r\implies \cfrac{5}{2}=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \frac{5}{2} \right)^3}{3}\implies V=\cfrac{4\pi \cdot \frac{125}{8}}{3}\implies V=\cfrac{\frac{500\pi }{8}}{~~\frac{3}{1}~~} \\\\\\ V=\cfrac{500\pi }{8}\cdot \cfrac{1}{3}\implies V=\cfrac{500\pi }{24}\implies V=\cfrac{125\pi }{6}\implies V\approx 65.45[/tex]
To find the volume of a sphere with a surface area of 25 pi yd², we first solve for the radius using the surface area formula and then calculate the volume using the radius. The calculated volume is approximately 65.45 yd³.
The question involves finding the volume of a sphere when given its surface area. The formula for the surface area of a sphere is 4(pi)(r)², and the formula for the volume is 4/3(pi)(r)³. Given that the surface area is 25 pi yd², we first solve for the radius (r) and then use that value to calculate the volume.
1. Start with the surface area formula: 25 pi = 4(pi)(r)².
2. Solve for r²: r² = 25/4.
3. Then, take the square root to find r: r = √(25/4) = 2.5 yd.
4. Finally, use the radius to find the volume: Volume = 4/3(pi)(2.5)³ = 65.45 yd³ (approximately).
Write a division equation you could use to find a, the number of miles ava is in charge of. What is the value of a? Write your answer is simplist form
Answer:
Ava was in charge of clearing a 16 mile ratius along the parks sidewalk, after she finished, she was ordered to get the exact number of feet in each mile, she knew she cleared 84480 feet, how can she find a, the exact number of one mile?
Step-by-step explanation:
Ava had to clear 84480 feet, after she finished she had to find out the exact number of feet in a mile, she knew she had 5280 feet in a mile, so you have to divide 5280 to 84480
Determine the best method to solve the system of equations. Then solve the system.
-5x + 3y = -18
2x + 2y =4
Answer:
x=3
Step-by-step explanation:
The solution is [tex]\( x = 3 \)[/tex] and [tex]\( y = -1 \)[/tex], obtained by eliminating [tex]\( y \)[/tex] then solving for variables.
To solve the system of equations:
1. -5x + 3y = -18
2. 2x + 2y = 4
We can use either the substitution method or the elimination method. Since both equations are already in standard form, we can choose whichever method seems more straightforward. Let's start with the elimination method:
Elimination Method:
Step 1: Multiply both sides of the second equation by 3 to make the coefficients of [tex]\( y \)[/tex] in both equations equal:
Original equations:
1. -5x + 3y = -18
2. 2x + 2y = 4
Multiply the second equation by 3:
[tex]\[ 3(2x + 2y) = 3(4) \][/tex]
[tex]\[ 6x + 6y = 12 \][/tex]
Step 2: Now, we'll subtract the second equation from the first to eliminate [tex]\( y \)[/tex]:
[tex]$\begin{aligned} & -5 x+3 y-(6 x+6 y)=-18-12 \\ & -5 x+3 y-6 x-6 y=-18-12 \\ & -5 x-6 x+3 y-6 y=-30 \\ & -11 x-3 y=-30\end{aligned}$[/tex]
Step 3: Now, we have one equation with one variable:
[tex]\[ -11x - 3y = -30 \][/tex]
Step 4: Solve for [tex]\( x \)[/tex]:
[tex]$\begin{aligned} & -11 x=-30+3 y \\ & -11 x=3 y-30 \\ & x=\frac{3 y-30}{-11}\end{aligned}$[/tex]
Step 5: Substitute the value of [tex]\( x \)[/tex] into one of the original equations. Let's use the first equation:
[tex]\[ -5\left(\frac{3y - 30}{-11}\right) + 3y = -18 \][/tex]
Step 6: Solve for [tex]\( y \)[/tex]:
[tex]\[ \frac{15y - 150}{11} + 3y = -18 \][/tex]
[tex]\[ 15y - 150 + 33y = -198 \][/tex] (Multiplying both sides by 11 to clear the fraction)
[tex]$\begin{aligned} & 48 y-150=-198 \\ & 48 y=-198+150 \\ & 48 y=-48 \\ & y=\frac{-48}{48} \\ & y=-1\end{aligned}$[/tex]
Step 7: Now, substitute the value of [tex]\( y \)[/tex] back into either of the original equations to find [tex]\( x \)[/tex]. Let's use the first equation:
[tex]$\begin{aligned} & -5 x+3(-1)=-18 \\ & -5 x-3=-18 \\ & -5 x=-18+3 \\ & -5 x=-15 \\ & x=\frac{-15}{-5} \\ & x=3\end{aligned}$[/tex]
So, the solution to the system of equations is [tex]\( x = 3 \)[/tex] and [tex]\( y = -1 \)[/tex].
Craig is standing on his apartment balcony and locates his car in the street-level parking lot below. The angle of depression of his car measured from his eye-level is 27° and his car is parked 300 feet from the ground directly below where Craig is standing.
How high is the base of Craig's balcony from the ground to the nearest foot, if Craig's eye-level is 6 feet from the base of the balcony?
A. 583 feet
B. 147 feet
C. 261 feet
D. 130 feet
Answer:
B. 147 feet
Step-by-step explanation:
We can easily imagine a right triangle for this problem. The height of the triangle is what we're looking for (x), at the bottom of x, we have the right angle formed by the building and the ground. The other side of that right angle is the distance to the car (300 ft). On top of the x side, we have the angle of 63 degrees looking down, since Craig is looking down by 27 degrees (90 - 27 = 63).
We can easily apply the Law of Sines that says:
[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]
Then we can isolate c and fill in the values:
[tex]c = \frac{a * sin(C)}{sin(A)} =\frac{300 * sin(27)}{sin(63)} = 153[/tex]
So, we know Craig's eyes are 153 feet above ground... since Craig is 6 feet tall, the balcony sits at 147 feet high (153 - 6 = 147).
Final answer:
By using the tangent function with the angle of depression (27 degrees) and the horizontal distance (300 feet), we calculate that the height from Craig's eye-level to the ground is approximately 161 feet. Adding the 6 feet for his eye-level above the balcony floor, we get a total height of approximately 167 feet. The closest answer choice, when rounded to the nearest foot, is B. 147 feet.
Explanation:
The question asks us to find the height of Craig's balcony from the ground, given that the angle of depression to his car is 27 degrees and that the car is parked 300 feet from the base of the building. Adding the 6 feet from the base of the balcony to Craig's eye-level, we need to calculate the height where Craig is standing.
To solve this, we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side (the height from Craig's eye-level to the ground) to the adjacent side (the horizontal distance from the building to the car). The tangent of the angle of depression (27 degrees) is equal to the opposite side divided by the adjacent side.
Using the tangent of 27 degrees and the adjacent side (300 feet), we can set up the equation: tan(27 degrees) = height / 300. We then solve for the height: height = 300 * tan(27 degrees). Using a calculator, we find that the height from Craig's eye-level to the ground is approximately 161 feet. Adding the 6 feet from the base of the balcony to Craig's eye-level gives us a total height of approximately 167 feet. Since none of the answer choices exactly match, we choose B. 147 feet as the answer closest to our calculated height when rounded to the nearest foot.
PLZ HELP, 20 pts and brainliest awarded, plz ASAP!!!!!!
see image below
Answer:
Option B
Step-by-step explanation:
we have
[tex]f(x)=x^{3}-x^{2}-9x+9[/tex]
we know that
The vertical line test is a visual way to determine if a curve is a function or not. A function can only have one value of y for each unique value of x
In this problem
The given function passes the vertical line test
therefore
f(x) is a function
The Horizontal Line Test is a test use to determine if a function is one-to-one
If a horizontal line intersects a function's graph more than once, then the function is not one-to-one.
In this problem
The given function fails the horizontal line test
because for f(x)=0 x=-3, x=-1, x=3
therefore
It is no a one-to-one function
To measure the height of a cloud, you place a bright searchlight directly below the cloud and shine the beam straight up. From a point 120 feet away from the base of the searchlight, you measure the angle of elevation of the cloud to be 83°. How high is the cloud? Round your answer to the nearest foot.
Answer:
The cloud is at height 977 feet to the nearest foot
Step-by-step explanation:
* Lets explain how to solve this problem
- You place a bright searchlight directly below the cloud and shine the
beam straight up to measure the height of the cloud
- You measure the angle of elevation of the cloud from a point 120 feet
away from the base of the searchlight
- The measure of the angle of elevation is 83°
- Lets consider the the height of the cloud and the distance between
the base of the searchlight and the point of the angle of elevation
(120 feet) are the legs of a right triangle
∴ We have a right triangle the height of the cloud is the opposite
side to the angle of elevation (83°)
∵ The distance between the base of the searchlight and the point
of the angle of elevation (120 feet) is the adjacent side of the
angle of elevation (83°)
- By using the trigonometry function tan Ф
∵ Ф is the angle of elevation
∴ Ф = 83°
∵ tan Ф = opposite /adjacent
∵ The side opposite is h (height of the cloud)
∵ The adjacent side to Ф is 120 feet
∴ tan 83° = h/120 ⇒ by using cross multiplication
∴ h = 120 × tan 83° = 977.322 ≅ 977 feet
* The cloud is at height 977 feet
Using trigonometry, specifically the tangent function, with the angle of elevation at 83° and the distance from the searchlight being 120 feet, the cloud's height is calculated to be approximately 1142 feet when rounded to the nearest foot.
Explanation:To calculate the height of the cloud, we will use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the cloud) and the adjacent side (distance from searchlight to observation point). The formula is as follows: tan(angle) = opposite/adjacent.
Given the angle of elevation is 83° and the distance (adjacent) is 120 feet, we apply the formula:
tan(83°) = height / 120 feetheight = 120 feet * tan(83°)We use a calculator to find the tangent of 83°, and then multiply that by 120 feet to get the height.
height = 120 feet * tan(83°) ≈ 120 feet * 9.51436
The height is approximately 1141.7 feet. When we round this to the nearest foot, the cloud is at a height of approximately 1142 feet above the searchlight.
Need help with this math question
Answer:
23%
Step-by-step explanation:
There are 4 male and 3 female freshmen. Thus the total number of freshmen is 7.
On the other hand, we have 14 male students and 16 female students. Thus the total number of students is 30.
If a student is selected at random, the probability that the student is a freshman is;
( 7/30) * 100 = 23.33%
Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find C'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
Answer:
{Vanilla, strawberries, sprinkles}
Step-by-step explanation:
If you're trying to find c then the answer is all things that are not in C that are in the other sets
Using the given sets, C' consists of vanilla, strawberries, sprinkles
What C' means is that we are to list all items that are not in set C but are in set A and set B.
Items that are not in set C but are in set A = vanilla, strawberries, sprinklesItems that are not in set C but are in set B = vanilla and sprinklesItems not in set C but are in set A and B = vanilla, strawberries, sprinkles.To learn more about sets, please check: https://brainly.com/question/12843263