Answer:
option d.
Step-by-step explanation:
We have the following set of data:
x 0 1 2 3 4
f (x) 18 14 10 6 2
Let's assume the function is linear, then, the equation of the line would ne:
(y - y0) = m(x-x0)
where m= (y1-y0) / (x1-x0)
And (x1, y1) = (1, 14)
(x0, y0) = (0, 18)
You can choose any of the points given in the set of data.
Then,
m = (14-18)/(1-0) = -4.
Then the equation of the line is:
(y - 18) = -4x
y = -4x + 18.
If the function is linear, then all the points given in the set of data will satisfy the function. Let's try:
(2, 10):
10 = -4(2) + 18.
10 = 10
SATISFIES THE EQUATION
(3, 6):
6 = -4(3) + 18.
6 = 6
SATISFIES THE EQUATION
(4, 2)
2 = -4(4) + 18.
6 = 6
SATISFIES THE EQUATION
So, the function is linear. And the correct option is option d.
Answer:
D. Line.ar; -4x + 18
Step-by-step explanation:
Hi I would really iike if someone helped me with this homework that I have I don't understand. an aquarium in the shape of a parallelepiped ABCDEFGH length AB = 80cm, width AD = 40cm, height DH = 50cm. a) we put HM = x cm give a frame for x b) give, according to x, the volume of water contained in the aquarium. This volume will be expressed in cm ^ 3 then in liters.
170^3 this is the answer just make sure you do you're work.
Hannah is saving money for a car. She earns $160 each week working part time after school and on the weekends at Papa's Pizza. Hannah currently has $1,280 in savings. Her parents put $50 in her savings account each week and she saves one-half of her paycheck each week. Which expression represents the situation? (n represents the number of weeks) A) 1,280 + 130n B) 1,280 + 160n + 50n C) 1,280 + 160n 2 D) 1,280 + 160n + 50n 2
Answer:
it is A
Step-by-step explanation:
find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.
Let [tex]z=-\sqrt3+i[/tex]. Then
[tex]|z|=\sqrt{(-\sqrt3)^2+1^2}=2[/tex]
[tex]z[/tex] lies in the second quadrant, so
[tex]\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6[/tex]
So we have
[tex]z=2e^{i5\pi/6}[/tex]
and the fourth roots of [tex]z[/tex] are
[tex]2^{1/4}e^{i(5\pi/6+k\pi)/4}[/tex]
where [tex]k\in\{0,1,2,3\}[/tex]. In particular, they are
[tex]2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}[/tex]
[tex]2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}[/tex]
[tex]2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}[/tex]
[tex]2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}[/tex]
Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v ≤ π.
Compute the surface element:
[tex]\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv[/tex]
[tex]\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}[/tex]
[tex]\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}[/tex]
So the integral is
[tex]\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)[/tex]
[tex]=\dfrac23(37^{3/2}-1)[/tex]
1. Malia thinks she and her friends should sell the wristbands for $2.50 each. She sells 4 wristbands on the first day of the fundraiser.
a. How can the amount Malia earns be represented as an addition sentence?
b. What is the sum, and what does it mean in this situation?
c. Show the sum on a number line.
The amount Malia earns can be shown as an addition sentence by multiplying the price of the wristbands by the quantity sold. The sum of this addition is $10, which is what Malia earned on the first day of the fundraiser. This sum can be visualized on a number line with four equal jumps of $2.50 leading to a sum of $10.
Explanation:a. The amount Malia earns can be represented as an addition sentence by multiplying the price of the wristbands ($2.50) by the number of wristbands sold (4). The addition sentence would look like this: $2.50 + $2.50 + $2.50 + $2.50.
b. The sum of the addition sentence above is $10. This means that Malia has earned $10 on the first day of the fundraiser by selling 4 wristbands at $2.50 each.
c. The sum on a number line can be shown by marking off four equal jumps of $2.50 starting from zero, which leads you to the total sum of $10 at the fourth jump.
Learn more about Addition Sentence here:https://brainly.com/question/33833194
#SPJ2
Can someone please help me on this question.
Answer:
Step-by-step explanation:
[tex]3x^{2} + 5x-12=0[/tex]
[tex]-12=-5x-3x^{2}[/tex]
[tex](-12=-5x-3x^{2} ) * -1[/tex]
[tex]\sqrt{12=5x+3x^{2}[/tex]
Anna's scores for a video game are 670, 575, 400, 575, 1250, 720, and 885. Which statement about the data is correct?
Answer:
Step-by-step explanation:
what are the statements about the data?
Answer
C) The mean is greater than the median.
Step-by-step explanation:
To find the median, order the scores from LEAST to GREATEST.
400, 575, 575, 670, 720, 885, 1250.
The mean is the middle number, which is 670.
To find the mean, average the scores:
400 + 575 + 575 + 670 + 720 + 885 + 1250
7
= 725
725 > 670; therefore, the mean is greater than the median.
A set of 36 cards is numbered with the positive integers from 1 to 36. If the cards are shuffled and one is chosen at random, what is the probability that the number on the card is a multiple of both 4 and 6?
Answer:
1/12.
Step-by-step explanation:
The numbers divisible by 6 are 6, 12, 18, 24, 30 and 36.
Of these 12, 24 and 36 are also divisible by 4.
So the required probability is 3/36
= 1/12.
a toy company's total payment salaries for the first two months of 2005 is $21, 894. write and solve an equation to find the salaries for the second month if the first month's salaries are $10,205.
Solution: Second month = m
The equation is
m + 10205 = 21894
m = 11689
So the second month will be $11,894. :)
To solve for the second month's salaries, subtract the first month salary from the total for two months. The solution to the equation $21,894 - $10,205 gives this salary: $11,689.
Explanation:The subject of this problem is a toy company's salary expenses over a course of two months. Let's denote the salary expenses for the second month as X. We know from the problem that the total salary expenses for the first two months (January and February) are $21,894. Furthermore, we know that the salary expenses for January are $10,205.
We can write an equation to express these facts as follows: X (which is the salary expenses for February) is equal to the total salary for the two months minus the salary for January, or in mathematical notation, X = $21,894 - $10,205.
We solve this math equation by subtracting $10,205 from $21,894, giving us X = $11,689. Therefore, the second month's salaries total $11,689.
Learn more about Salary Expenses here:https://brainly.com/question/33557398
#SPJ3
Graph y = | x | + 5
Answer:
(0,5) (0,-5)
Step-by-step explanation:
Answer:
Step-by-step explanation:
The basic (parent) function here is y = |X|, the absolute value function.
This function has a v-shape that opens up and has its vertex at (0, 0).
Each leg is at a 45° angle to the x - axis. Draw this.
Then translate the entire graph upward by 5 units. The result will be the graph of y = | x | + 5.
Determine the critical? value(s) for a? left-tailed test of a population mean at the alphaequals0.01 level of significance based on a sample size of nequals15.
Answer: 2
Step-by-step explanation:
A bag of lollipops contains red lollipops and purple lollipops. 80% of the lollipops in the bag are red. A number generator simulates selecting 10 lollipops from the bag. The number generator is used 10 times and the number or red lollipops in each simulated trial is shown in the dot plot. Which description is correct about the number generator?
Answer:
The number generator is fair. It picked the approximate percentage of red lollipops most of the time.
Step-by-step explanation:
The other answer choices represent various misinterpretations of the nature of the experiment or the meaning of the numbers generated.
___
A number generator can be quite fair, but give wildly varying percentages of red lollipops. Attached are the results of a series of nine (9) simulations of the type described in the problem statement. You can see that the symmetrical result shown in the problem statement is quite unusual. A number generator that gives results that are too ideal may not be sufficiently random.
Option D is correct as it indicates that the number generator picked a percentage of red lollipops close to the expected 80% most of the time, reflecting fairness and random sampling variability.
Let's analyze the question regarding the fairness of the number generator. We know that 80% of the lollipops in the bag are red.
Option A: The number generator picked red lollipops 90% of the time in 3 experiments. This slight variation could be due to sampling variability, not necessarily unfairness.
Option B: States the correct percentage of red lollipops was not chosen at all, which might suggest the generator is faulty, but without more data, it's inconclusive.
Option C: Indicating the generator picked red lollipops half the time is incorrect as it would be inconsistent with the given information.
Option D: The generator picked the approximate percentage of red lollipops most of the time. This is plausible as the results can vary slightly due to random sampling.
Based on this analysis, Option D seems to be the most accurate description, assuming the observed percentages are close to the theoretical 80% on average, reflecting a fair and random selection process.
Employees earn vacation pay at the rate of one day per month. during the month of july, 25 employees qualify for one vacation day each. their average daily wage is $100 per day. what is the amount of vacation benefit expense to be recorded for the month of july? multiple choice $25 $100 $250
i’m petty sure you add them all up
Answer:
$2,500
Step-by-step explanation:
The situation states that the employees earn vacation pay at the rate of one day per month and their daily wage is $100. Also, it states that in july 25 employees qualify for one vacation day. So, in order to determine the amount of vacation benefit expense for july, you need to multiply the daily wage for the number of employees that got the benefit:
$100*25= $2,500
Easy and Fun Math review questions.
Use Pascal’s triangle to expand each binomial.
(a+b)^5
Answer:
Step-by-step explanation:
You need the 6th row of Pascal's triangle which contains the numbers 1, 5, 10, 10, 5, 1
Fill in the expansion as follows, using those numbers and the fact that a = 1 and b = 1:
[tex]1(1a)^5(1b)^0+5(1a)^4(1b)^1+10(1a)^3(1b)^2+10(1a)^2(1b)^3+5(1a)^1(1b)^4+1(1a)^0(1b)^5[/tex]
That simplifies down nicely to
[tex]a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5[/tex]
Those are fun! Pascal's triangle is one of the coolest things ever!
To expand (a+b)^5 using Pascal's Triangle, we can use the Binomial Theorem. The expansion can be written as (a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + (b^5).
To expand the binomial (a+b)^5 using Pascal's Triangle, we will use the Binomial Theorem. According to the theorem, the expansion of (a+b)^n can be written as:
(a+b)^n = (nC0)(a^n)(b^0) + (nC1)(a^(n-1))(b^1) + (nC2)(a^(n-2))(b^2) + ... + (nCn)(a^0)(b^n)
For (a+b)^5, the expansion would be:
(a+b)^5 = (5C0)(a^5)(b^0) + (5C1)(a^4)(b^1) + (5C2)(a^3)(b^2) + (5C3)(a^2)(b^3) + (5C4)(a^1)(b^4) + (5C5)(a^0)(b^5)
Simplifying further, we get:
(a+b)^5 = (a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + (b^5)
what is the cube root of 64i
a) 4 cis 30 degrees, 4 cis 150 degrees, 4 cis 270 degrees
b) 4 cis 60 degrees, 4 cis 180 degrees, 4 cis 300 degrees
c) 1, -1, -i
d) 4 cis 0 degrees, 4 cis 120 degrees, 4 cis 240 degrees
Answer:
c
Step-by-step explanation:
To find √8342 , use the logarithmic equation:
log 4,171
√log8342
log 8,342 - log 1/2
1/2log8,342
Answer:
Step-by-step explanation:
1/2log8,342 is almost correct. Should enclose that "1/2" inside parentheses. The "1/2" stems from our needing to find the value of the square root of 8342.
Answer: The required answer is [tex]\dfrac{1}{2}\log 8342.[/tex]
Step-by-step explanation: We are given to use the logarithmic equation to find [tex]\sqrt{8342}.[/tex]
We will be using the following logarithmic property :
[tex]\log a^b=b\log a.[/tex]
Let us consider that
[tex]x=\sqrt{8342}~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Applying logarithm on both sides of equation (i), we have
[tex]\log x=\log{\sqrt{8342}\\\\\Rightarrow \log x=\log(8342)^\frac{1}{2}\\\\\Rightarrow \log x=\dfrac{1}{2}\log 8342.[/tex]
Thus, the required answer is [tex]\dfrac{1}{2}\log 8342.[/tex]
in the triangle below what ratio is sec H
For this case we have that by definition:
[tex]Secant (A) = \frac {1} {Cosine (A)}[/tex]
Then, we find the cosine of the angle H, this will be given by the leg adjacent to H on the hypotenuse of the triangle.
[tex]Cos (H) = \frac {g} {f}[/tex]
So, the secant of H is given by:[tex]Sec {H} = \frac {1} {\frac {g} {f}}\\Sec {H} = \frac {f} {g}[/tex]
Answer:
Option C
A box without a top is to be made from a rectangular piece of cardboard, with dimensions 11 in. by 16 in., by cutting out square corners with side length x and folding up the sides
Answer:
• V = x(11 -2x)(16 -2x)
• x ≈ 2.1 in
Step-by-step explanation:
a) The volume of the box is the product of its depth (x), width (11 -2x) and length (16 -2x). The equation can be simply ...
v(x) = x(11 -2x)(16 -2x)
__
b) A graphing calculator can plot this equation directly. All that is needed is to enter it into the appropriate space provided by the calculator. The value of x that gives the greatest volume is the value that makes the function have a local maximum between x=0 and x=5.5 (where the volume is again zero).
That value of x is about 2.1 inches.
Please please help please
Answer:
130.5 in²
Step-by-step explanation:
The area (A) of a regular pentagon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 8.7 × 5 ← pentagon has 5 sides
= 43.5 in
A= 0.5 × 43.5 × 6 = 130.5 in²
Using the image below, please match the correct trigonometric function with the correct value.
sin (α) =
csc(α) =
tan(α) =
sec(α) =
cos(α) =
cot(α)=
Options:
1. 8/17
2. 15/17
3. 8/15
4. 15/8
5. 17/15
6. 17/8
ANSWER
See explanation
EXPLANATION
The given triangle is a right angle triangle.
We use the mnemonics SOH CAH TOA.
The given angle is
[tex] \alpha [/tex]
The opposite is 8 units, the adjacent is 15 units and the hypotenuse is 17 units.
[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} = \frac{8}{17} [/tex]
[tex] \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } = \frac{17}{8} [/tex]
[tex]\tan( \alpha ) = \frac{opposite}{adjacent} = \frac{8}{11} [/tex]
[tex] \cot( \alpha ) = \frac{1}{ \tan( \alpha ) } = \frac{15}{8} [/tex]
[tex]\cos( \alpha ) = \frac{adjacent}{hypotenuse} = \frac{15}{17} [/tex]
[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } = \frac{17}{15} [/tex]
In a right-angled triangle ABC, the trigonometric functions based on the given sides equate to: sin(α) = Option 3, csc(α) = Option 4, cos(α) = Option 5, sec(α) = Option 2, tan(α) = Option 1, and cot(α) = Option 6.
In a right-angled triangle, the Trigonometric Functions can be calculated based on the sides of the triangle.
For your problem, in triangle ABC, given that AB = 15 (hypotenuse), BC = 8 (opposite α) and AC = 17 (adjacent to α), we can compute the values as follows:
sin(α) = opposite/hypotenuse = BC/AB = 8/15 = (Option 3)
csc(α) = 1/sin(α) = 15/8 = (Option 4)
cos(α) = adjacent/hypotenuse = AC/AB = 17/15 = (Option 5)
sec(α) = 1/cos(α) = 15/17 = (Option 2)
tan(α) = sin(α)/cos(α) = (BC/AB) / (AC/AB) = BC/AC = 8/17 = (Option 1)
cot(α) = 1/tan(α) = 17/8 = (Option 6)
Learn more about Trigonometric Functions here:
https://brainly.com/question/28483432
#SPJ3
The probable question may be:
In Right angle triangle ABC, Angle ABC is 90 degree, Angle BAC is α , side AB= 15, side BC=8 and side AC=17.
please match the correct trigonometric function with the correct value.
sin (α) =
csc(α) =
tan(α) =
sec(α) =
cos(α)=
cot(α)=
Options:
1. 8/17
2. 15/17
3. 8/15
4. 15/8
5. 17/15
6. 17/8
A rectangular prism has a volume of 2320.5 in.? a width of 12.75 inches and a height of 14 inches what is the length?
Answer:
13
Step-by-step explanation:
Volume = length x width x height
2320.5 = l x 12.75 x 14
2320.5 = l x 178.5
2320.5/178.5 = l
l = 13
Please help me
thanks!!
Answer:
Step-by-step explanation:
Question One
Multiply through by 2
2*1/2 * (2x + y ) = 21/2 * 2
Combine
2x + y = 21
Subtract 2x from both sides
y = 21 - 2x
Now equate the two given equations
y = 21 - 2x
y = 2x
Add 2x to both sides
2x = 21 - 2x
2x + 2x = 21
4x = 21
x = 21/4
x = 5 1/4
or
x = 5.25
Question 2
[tex]\dfrac{2x + 6}{(x + 2)^2} - \dfrac{2}{(x + 2)}[/tex]
multiply numerator and denominator of the second fraction by (x + 2)
[tex]\dfrac{2x + 6}{(x + 2)^2} - \dfrac{2(x + 2)}{(x + 2)*(x + 2)}[/tex]
Remove the numerator brackets in the right hand fraction. Look out for the minus sign.
[tex]\dfrac{2x + 6}{(x + 2)^2} - \dfrac{2(x + 2)}{(x + 2)^2}\\\\\dfrac{2x + 6- 2x - 4}{(x + 2)^2}}\\\\\dfrac{2}{(x + 2)^2}[/tex]
Answer: [tex]\bold{x=\dfrac{21}{4}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{2}(2x+y)=\dfrac{21}{2}\\\\\text{Multiply both sides by 2 to clear the denominator:}\\2x + y = 21\\\\\text{Now, the system is:}\bigg\{{2x+y=21\atop{y=2x}}\\\\\text{Substitute y in the first equation with 2x to solve for x:}\\2x + y = 21\\2x + 2x = 21\\.\qquad 4x=21\\\\.\qquad \large\boxed{x=\dfrac{21}{4}}[/tex]
Answer: a = 2
Step-by-step explanation:
[tex].\quad \dfrac{2x+6}{(x+2)^2}-\dfrac{2}{x+2}\bigg(\dfrac{x+2}{x+2}\bigg)\\\\\\=\dfrac{2x+6}{(x+2)^2}+\dfrac{-2(x+2)}{(x+2)^2}\bigg\\\\\\\\=\dfrac{2x+6-2x-4}{(x+2)^2}\\\\\\=\dfrac{2}{(x+2)^2}\implies \large\boxed{a=2}[/tex]
You purchase 5 pounds of apples and 2 pounds of oranges for $9.Your friend purchases 5 pounds of apples and 6 pounds of oranges for $17. Write and solve a system of linear equations that represents this situation
Answer:
x = 1 and y = 2
Step-by-step explanation:
Let apples are represented by x
and let oranges are represented by y
You purchase 5 pounds of apples and 2 pounds of oranges for $9. This line in equation format can be written as:
5x + 2y = 9
Your friend purchases 5 pounds of apples and 6 pounds of oranges for $17.
This line in equation format can be written as:
5x + 6y = 17
Now we have two equations:
5x + 2y = 9 -> eq (i)
5x + 6y = 17 -> eq(ii)
We can solve these equations to find the value of x and y.
Subtracting eq(i) from eq(ii)
5x + 6y = 17
5x + 2y = 9
- - -
_________
0+4y= 8
=> 4y = 8
y= 8/4
y = 2
Now, putting value of y in eq (i)
5x + 2y = 9
5x +2(2) = 9
5x +4 = 9
5x = 9-4
5x = 5
x = 1
so, x = 1 and y = 2
Please help!!!!!!!!!!
Answer:
Step-by-step explanation:
65 - Acute
72 - Acute
96 - Obtuse
Answer:
(a)
Step-by-step explanation:
Given 3 sides of a triangle a, b and c where c is the longest side, then
• If a² + b² = c² ⇒ triangle is right
• If a² + b² > c² ⇒ triangle is acute
• If a² + b² < c² ⇒ triangle is obtuse
Here a = 65, b = 72 and c = 96
65² + 72² ? 96²
4225 + 5184 ? 9216
9409 > 9216 ⇒ triangle is acute
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
An organization of berry farmers releases a study reporting that people who eat blueberries every day have a lower cholesterol level.
Which statement describes the best conclusion to draw from the study?
Answer:
C
Step-by-step explanation:
I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.
The best conclusion from the study is that the consumption of blueberries might be associated with lower cholesterol levels. However, it's important to note that correlation does not mean causation and other factors could be at play.
Explanation:The statement that comes closest to an appropriate conclusion from the study is that the possible consumption of blueberries might be associated with lower cholesterol levels. However, it is important to remember that correlation does not necessarily imply causation. While the organization of farmers showed a connection between eating blueberries and lower cholesterol, this does not necessarily mean eating blueberries directly causes lower cholesterol. Other factors could be involved. For instance, those who eat blueberries daily might generally lead healthier lifestyles, contributing to lower cholesterol levels.
Learn more about Blueberries and cholesterol levels here:https://brainly.com/question/27024225
#SPJ2
If B=26° and b=18 then find c (picture provided)
Answer:
c. 41.1
Step-by-step explanation:
To find a, we'll use the Law of Sines that says:
[tex]\frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex]
And we'll isolate c to get:
[tex]c = \frac{sin(C) * b}{sin(B)}[/tex]
Then we will plug-in the information we already have :
[tex]c = \frac{sin(90) * 18}{sin(26)} = 41.06[/tex]
So, let's round it to 41.1 to match the answer number C.
Answer:
The correct answer is option C. 41.1
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Sin θ = opposite side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of c
It is given that, B=26° and b=18
Sin26 = opposite side/Hypotenuse = b/c
c = 18/Sin26 = 41.1
Therefore the correct answer is option c. 41.1
Solve the quadratic equation by factoring. 9x^2+24x+20=4
A. x=4/3
B. x=-3/4
C. x=4
D. x=-4/3
D. -4/3
Let's solve your equation step-by-step.
9x2+24x+20=4
Step 1: Subtract 4 from both sides.
9x2+24x+20−4=4−4
9x2+24x+16=0
Step 2: Factor left side of equation.
(3x+4)(3x+4)=0
Step 3: Set factors equal to 0.
3x+4=0 or 3x+4=0
x= −4 /3
Hope This helps
Answer:
D. x = [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
Step 1: Subtract 4 from both sides.
9x^2 + 24x + 20 − 4 = 4 − 4
9x^2 + 24x + 16 = 0
Step 2: Factor left side of equation.
(3x+4)(3x+4) = 0
Step 3: Set factors equal to 0.
3x+4=0 or 3x+4=0
x = [tex]-\frac{4}{3}[/tex]
I hope this helps your assignment! Anyways, have a fantastic day! :D
Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the ground to the floor of the porch, which is 2 1/2
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.
What length board should Jessica buy if she uses the maximum angle of incline?
Enter your answer in the box. Round only your final answer to the nearest tenth.
The board must be about 4.4 ft long
Answer:
Length of board should Jessica buy is 4.4 feets.
Step-by-step explanation:
Height of the ramp = [tex]2\frac{1}{2} ft=\frac{5}{2} ft[/tex]
Distance of the porch from the ground = x
Inclination of the ramp,θ = 35°
In triangle ABC,
AB = [tex]\frac{5}{2} ft[/tex]
AC = x
θ = 35°
According trigonometric ratios:
[tex]\sin \theta =\frac{Perpendicular}{hypotenuse}[/tex]
[tex]\sin 35^o =\frac{AB}{AC}[/tex]
[tex]0.573576=\frac{\frac{5}{2} ft}{x}[/tex]
[tex]x=4.3586 ft\approx 4.4 ft[/tex]
Length of board should Jessica buy is 4.4 feets.
What is "theoretical probability"? What is "experimental probability"? What's the difference?
Theoretical probably is what you would expect to happen.
Example, flipping a coin has a 50% chance of landing on heads, so if you flipped a coin 100 times, theoretically the coin would land on heads 50 times ( 50%).
Experimental probablity is what actually happens. Using the coin example, flipping the coin 100 times, it could actually land on heads 100 times or any number of times from 0 to 100.
Hello There! Theoretical probability deals with events happening in theory. It is what is expected t happen.
Experimental probability is a little different. This is based on the number of repeated trials during an experiment.
The difference is Theoretical probability is what you expect to happen
Experimental probability is what actually ends up happening.
Given the similarity statement ΔDEF ∼ ΔXYZ, which angle corresponds with ∠Z?
A. ∠F
B. ∠Y
C. ∠E
D. ∠D
Answer:
F
Step-by-step explanation:
In congruent triangles, or similar triangles, the letters in the same place will also be congruent
Answer:
the answer is A
Step-by-step explanation: