the distance is 13 length units
Final answer:
Using the Pythagorean Theorem, we calculate the distance between the points (5, -2) and (-7, 3) to be 13 units.
Explanation:
To find the distance between two points on a coordinate plane, we use the Pythagorean Theorem. Given points (5, -2) and (-7, 3), we calculate the difference in the x-coordinates and y-coordinates separately and then square each result.
d² = (5 - (-7))² + (-2 - 3)²
= (5 + 7)² + (-5)²
= 12² + (-5)²
= 144 + 25
= 169
Now, taking the square root of both sides to calculate the distance:
d = √(169)
= 13
Therefore, the linear distance between the two points, often denoted as 'PQ', is 13 units.
10 mm
4 mm
u What is the volume of the cone to the nearest whole number?
Answer:
V=167.5 cubic mm
Step-by-step explanation:
Volume of the Cone is given with the formula
[tex]V=\frac{1}{3} \pi r^2h[/tex]
though we are not specified what is radius and which one is the height , we are assuming that ,
Height = 10 mm
Radius = 4 mm
Substituting these values in the formula we get
[tex]V=\frac{1}{3} \pi 4^2 \times 10[/tex]
[tex]V=\frac{1}{3} \pi 160[/tex]
[tex]V=\frac{160 \times 3.14}{3}[/tex]
[tex]V=\frac{160 \times 3.14}{3}[/tex]
[tex]V=\frac{502.40}{3}[/tex]
[tex]V=167.5[/tex]
The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?
A) 14°
B) 16°
C) 18°
D) 20°
Answer:
Option C.
The measure of the complement angle is [tex]18\°[/tex]
Step-by-step explanation:
Let
x-----> the angle
we know that
The complement of an angle is equal to [tex](90-x)\°[/tex]
The supplement of an angle is equal to [tex](180-x)\°[/tex]
we have
The complement of an angle is one-sixth the measure of the supplement of the angle
[tex](90-x)\°=(1/6)(180-x)\°[/tex]
solve for x
[tex](540-6x)\°=(180-x)\°\\ (6x-x)=(540-180)\°\\ (5x)=(360)\°\\ x=72\°[/tex]
Find the measure of the complement angle
[tex](90-x)\° ----> (90-72)=18\°[/tex]
Answer:
Option C. 18
Step-by-step explanation:
Let x be the given angle. 1 6 (180 − x) = (90 − x) 30 − 1 6 x = 90 − x 5 6 x = 60 x = 72° The supplement angle to 72° is 108°. The complement angle to 72° is 18°.A. A frog is climbing out of a well that is 8 feet deep. The frog can climb 4 feet per
hour but then it rests for an hour, during which it slips back 2 feet. How long will
it take for the frog to get out of the well?
B. What if the well was 40 feet deep, the frog climbs 6 feet per hour, and it slips back
1 foot while resting?
Answer:
A: 5 hrs. B: 14 hrs. and 40 min.
Step-by-step explanation:
too long to explain.
In the first scenario, the frog takes 4 hours to get out of the 8-feet deep well. In the second scenario, it takes the frog 8 hours to get out of the 40-feet deep well.
Explanation:The question is about calculated frog’s movement to get out of a well involving both climbing rate and slip-back rate during rest which brings us into the realm of simple arithmetic and mental math. Let's take each case one at a time.
A. 8 Feet Deep Well
The frog climbs 4 feet per hour but then slips back 2 feet. Therefore, effectively, the frog climbs only 2 feet per hour (4-2=2). After 3 hours, the frog would have climbed 6 feet (3*2=6). In the fourth hour, the frog would climb another 4 feet reaching a total of 10 feet, but since the well is only 8 feet deep, he would have already climbed out. Therefore, it would take the frog 4 hours to climb out of the well.
B. 40 Feet Deep Well
The frog climbs 6 feet per hour and slips back 1 foot, therefore effectively climbs 5 feet per hour (6-1=5). After 7 hours, the frog would have climbed 35 feet (7*5=35). In the eighth hour, the frog would climb additional 6 feet, reaching a total of 41 feet. Again, considering the well is only 40 feet deep, he would have climbed out at this point. So, it would take 8 hours for the frog to climb out of a 40 feet deep well.
Learn more about Time calculation here:https://brainly.com/question/34080240
#SPJ11
The point (4, 3) is reflected across the y-axis. What are the coordinates of the new point?
a) 4,3
b) 4,-3
c)-4, 3
d)-4,-3
helpppppp!!!!!
The answer is (-4,3) so C
Answer:
[tex]\boxed{\text{c) (-4, 3)}}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign: it becomes (-x, y).
Thus, if a point A, say, (4, 3) is reflected across the y-axis, its reflection A' is at
[tex]\boxed{\textbf{(-4, 3)}}[/tex]
Eudora transferred a balance of $6400 to a new credit card at the beginning
of the year. The card offered an introductory APR of 7.8% for the first 3
months and a standard APR of 26.5% thereafter. If the card compounds
interest monthly, what will Eudora's balance be at the end of the year?
(Assume that Eudora will make no payments or new purchases during the
year, and ignore any possible late payment fees.)
Final answer:
Eudora's balance at the end of the year will be $7,750.03.
Explanation:
To calculate Eudora's balance at the end of the year, we need to calculate the interest for each period separately and then add them together. The credit card offers an introductory APR of 7.8% for the first 3 months, so we will calculate the interest for this period first.
Step 1: Calculate the interest for the introductory period:
Interest = Balance * Introductory APR * (Introductory Period / 12) = $6400 * 0.078 * (3/12) = $156.00
Since the card compounds interest monthly, we need to calculate the interest for each month of the remaining 9 months at the standard APR of 26.5%:
Step 2: Calculate the interest for each month of the remaining 9 months:
Interest for each month = Balance * Standard APR / 12 = $6400 * 0.265 / 12 = $139.67
Step 3: Add up the interest for the introductory period and the remaining 9 months:
Total interest = Interest for the introductory period + (Interest for each month * Number of months) = $156.00 + ($139.67 * 9) = $1,350.03
Step 4: Calculate the final balance at the end of the year:
Final balance = Balance + Total interest = $6400 + $1,350.03 = $7,750.03
Therefore, Eudora's balance at the end of the year will be $7,750.03.
In which quadrant is the number –14 – 5i located on the complex plane?
Answer:
3rd Quadrant
Step-by-step explanation:
The "i" in complex numbers behave same as the y in real numbers, so basically this number translated in real would be same as (-14,-5).
To graph this, we have to go -14 units in x direction and -5 units in y direction. Basically, 14 units to the left and then 5 units down. That will place us in 3rd quadrant.
Hence, -14 -5i will fall in the 3rd quadrant of the complex plane.
Answer:
C. III
Step-by-step explanation:
-3x + 8 <15 find the solution set of the inequality
Subtract 8 from both sides
-3x < 15 - 8
Simplify 15 - 8 to 7
-3x < 7
Divide both sides by -3
= x > -7/3
Answer:
x > - 2 1/3
Step-by-step explanation:
- 3x + 8 < 15
- 3x < 7
x > - 2 1/3
Which is a counterexample for the conditional statement shown?
If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function.
The points have the same x-coordinate value.
The points have the same y-coordinate value.
The points follow the rule (x, y) (–x, –y).
The points follow the rule (x, y) (–y, –x).
Answer: First Option
The points have the same x-coordinate value.
Step-by-step explanation:
By definition, a relation is considered a function if and only if for each input value x there exists only one output value y.
So, the only way that the line that connects two points in the coordinate plane is not a function, is that these two points have the same coordinate for x.
For example, suppose you have the points (2, 5) and (2, 8) and draw a line that connects these two points.
The line will be parallel to the y axis.
Note that the value of x is the same x = 2. But when x = 2 then y = 5 and y = 8.
There are two output values (y = 8, y = 5) for the same input value x = 2.
In fact all the vertical lines parallel to the y-axis have infinite output values "y" for a single input value x. Therefore, they can not be defined as a function.
Then the correct option is:
The points have the same x-coordinate value.
What does x^4-7x+10 equal
Answer:
7
Step-by-step explanation:
The answer is A right?
Answer:
C. 42
Step-by-step explanation:
PEMDAS
1. Parentheses: (4 + 2) = 6
6² + 3 • 2
2. Exponents: 6² = 36
36 + 3 • 2
3. Multiplication/Division: 3 • 2 = 6
36 + 6
4. Addition/Subtraction: 36 + 6 = 42
42
Helppp????? Answer????
Answer:
No. of sweets Sue has = (18-x) -5
No. of sweets Tony has = (18+x)/2
Step-by-step explanation:
Sue has sweets = 18
Tony has sweets = 18
Sue give Tony sweets = x
Sweets left for Sue = 18 - x
Sweets for Tony = 18 + x
Sue eats 5 sweets = (18-x) -5
Tony eat half of his sweets = (18 +x)/2
No. of sweets Sue has = (18-x) -5
No. of sweets Tony has = (18+x)/2
Give the terms that best describes arc BC
Answer:
Option D. minor arc
Step-by-step explanation:
we know that
In a circle the measure of minor arc plus the measure of major arc is equal to 360 degrees
The measure of minor arc is less than 180 degrees
The measure of major arc is greater than 180 degrees
In this problem
Arc BDC is a major arc
Arc BC is a minor arc
a bottle contains 2.360 ml of a liquid. the total mass of the bottle and liquid together is 6.160g. The mass of the empty bottle is 4.850 g. what is the density of the liquid?
A) 2.610 ml
B) 1.802 ml
C) 0.555 ml
D) 2.055 ml
Answer:
C.) 0.555
Step-by-step explanation:
This is annoying because we're dealing with decimals.
So, we need to know how density works. Density works by dividing mass (g) by volume (ml).
Since the empty bottle has a mass of 4,850g and the bottle + the liquid have a total mass of 6.160g, we'll subtract the bottle's mass from the total mass, giving us 1.310g. Again, we divide mass by volume to obtain density (which should be listed as g/ml).
1.310 ÷ 2.360 = ~0.555
Therefore, your answer is 0.555
The density of the liquid in the bottle is calculated by dividing the mass of the liquid (found by subtracting the mass of the empty bottle from the total mass when full) by its volume. The correct answer is C) 0.555 ml.
Explanation:The subject here is density, which is a physical property of a substance that can be calculated by its mass over its volume. In your case, you are being asked to find the density of the liquid inside the bottle. This can be done by first, finding the mass of the liquid alone, then dividing that by the volume of the liquid given in the question.
The mass of the liquid can be found by subtracting the mass of the empty bottle from the total mass of the bottle when full (6.160g - 4.850g = 1.310g). The volume of the liquid is already given as 2.360 ml.
Finally, you compute the density by dividing the mass of the liquid by its volume (1.310g / 2.360 ml = 0.555 g/ml).
So, the correct choice is C) 0.555 ml.
Learn more about Density here:https://brainly.com/question/34199020
#SPJ2
Help me.. ASAP just number 10 pls
use the bar graph to find the experimental probability of the event
10 ~ Spinning A 3
I hope this helps!~ I tried
Honestly I feel like it is 10.
Math 3: First question on the attached file
Step-by-step explanation:
cos 330°=cos ( 360 -30)
In fourth quad the value of cos A is positive .
All angles when subtracted by multiple of 180° or (π) the function remain same
cos (30°)=√3/2
Also-
Cos(330)=Cos(360–30)
since Cos(360-x)=cos(x) where x is in degree
Cos(330)=Cos(30)= √ 3 /2 ~ 0.866
Answer:
Answer:
cos ( 330 º ) = √ 3 /2
Explanation:
Remember that
cos ( a − b ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b )
and that
330 º = 360 º − 30 º , so
cos ( 330 º ) = cos ( 360 º − 30 º ) = cos ( 360 º ) cos ( 30 º ) + sin ( 360 º ) sin ( 30 º )
The cosine, sine, tangent and secant of 360º equal the cosine, sine, tangent and secant of 0º respectively. We know that
sin 0 º is 0, and that cos 0 º = 1 so
cos ( 330 º ) = 1 ⋅ cos ( 30 º ) + 0 ⋅ sin ( 30 º )
cos ( 330 º ) = √ 3 /2
Hope This Helps! Have A Nice Day!!
A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Explain your reasoning.
Answer:
Part A) The slope is undefined
Part B) The equation of the line is [tex]x=p[/tex]
Part C) None y-intercept
Part D) The slope of a line perpendicular to the given line is equal to zero
Step-by-step explanation:
we have that
Describe
A) slope of the line
B) equation of the line
C) y-intercept
D) slope of a line perpendicular to the given line
Part A) slope of the line
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](p,a)\ (p,-a)[/tex]
Substitute the values
[tex]m=\frac{-a-a}{p-p}[/tex]
[tex]m=\frac{-2a}{0}[/tex] -----> the slope is undefined
Its a vertical line (parallel to the y-axis)
Part B) Equation of the line
we know that
The equation of a vertical line is equal to the x-coordinate of the points through which the line passes.
so
[tex]x=p[/tex]
Part C) The y-intercept
The y-intercept is the value of y when the value of x is equal to zero
The vertical line not intercept the y-axis
so
None y-intercept
Part D) slope of a line perpendicular to the given line
A line perpendicular to the given line is a horizontal line (parallel to the x-axis)
therefore
The slope is equal to zero
Which is the graph of the function f f(x)=(x-4)(x+4)?
Answer:
4th bubble
Step-by-step explanation:
First FOIL: f(x) = x² + 3x - 4. Then convert from Standard Form [y = Ax² + Bx + C] to Vertex Form [y = A(X - H)² + K], where (h, k) is the vertex and -h gives the OPPOSITE terms of what they really are. So, you do this by completing the square [½B]²:
2¼ = [½(3)]² [then figure out figure out how much you need to get to -4 (k)]2¼ - 6¼ = -4Your vertex formula is y = (x + 1½)² - 6¼.Remember, -h gives the OPPOSITE terms of what they really are, so your vertex is (-1½, -6¼).
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
What is the domain of the square root function graphed below?
Answer: all real numbers
Step-by-step explanation: the domain for any function is always , all real numbers or in other words, negative infinity to positive infinity.
Answer:
c. x >= 0
Step-by-step explanation:
Let f(x) = 3x2 - 6x + 2. Find f(-2).
A) 20
B) 22
C) 24
D) 26
Answer:
D) 26
Step-by-step explanation:
f(x) = 3x^2 - 6x + 2
Let x = -2
f(-2) = 3(-2)^2 - 6(-2) + 2
=3(4) +12+2
= 12 +12+2
=26
For this case we have a function of the form [tex]y = f (x).[/tex]
Where:
[tex]f (x) = 3x ^ 2-6x + 2.[/tex]
We must find the value of the function when [tex]x = -2.[/tex]
Substituting we have:
[tex]f (-2) = 3 (-2) ^ 2-6 (-2) +2\\f (-2) = 3 * 4 + 12 + 2\\f (-2) = 12 + 12 + 2\\f (-2) = 26[/tex]
Thus, the value of the function is 26.
Answer:
26
Option D
What is 3 2/3 + 5 11/24?!
[tex]\text{Hey there!}[/tex]
[tex]\text{What is 3}\frac{2}{3}\ + 5\frac{11}{24}[/tex]
[tex]\text{3}\frac{2}{3}\rightarrow 3\times3=9\rightarrow9+2=11\rightarrow\ \rightarrow\frac{11}{3}[/tex]
[tex]5\frac{11}{24}\rightarrow5\times24=120\rightarrow120+11=131\rightarrow\ \rightarrow\frac{131}{24}[/tex]
[tex]\text{Your problem becomes:}\frac{11}{3}+\frac{131}{24}[/tex]
[tex]\text{Solve that}\uparrow\text{and your should come up to}\rightarrow[/tex] [tex]\frac{73}{8}\ or\ 9\frac{1}{8}[/tex]
[tex]\boxed{\boxed{\bf{Answer:\frac{73}{8}\ or \ 9\frac{1}{8}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Ms. Donaldson earns $18.80 per hour for the first 40 hours she works in a week . She earns 1 1/2 times that amount per hour for each hour beyond 40 hours in a week. Last week Ms. Donaldson worked 45.5 hours. How much money did she earn?
Answer: You take $18.80 divide by 2 =$9.40 then $18.80+$9.40=$28.20
$28.20 x's 5.5=$$155.10
$18.80 x's 40=$752.00
then add 752.00+155.10=$907.10
Step-by-step explanation:
Look at the table of values below.
Which equation is represented by the table?
A.y = 2x + 1
B.
y = 3x + 2
c.
y = 4x - 1
D. y = 5x - 3
Answer:
Your answer will be C. y= 4x-1
Step-by-step explanation:
On the x value side, the numbers represent what to fill in x with, and y should be the output of it.
For example :
4(1) = 4 - 1 = 3
4(2) = 8 - 1 = 7
4(3) = 12 -1 = 11
Hope this helps and was correct
This y = 4x-1, equation is represented by the table
How the equation is represented by the table:On the x value side, the numbers represent what to fill in x with, and y should be the output of it.
For example :
4(1) = 4 - 1 = 3
4(2) = 8 - 1 = 7
4(3) = 12 -1 = 11
The correct answer is option C.
Learn more about how can we can use table of values to calculate an equation, refer:
https://brainly.com/question/11804354
#SPJ2
The population of a village has a constant growth of 5% every year. If its present population is 1,04,832, what was the population two years ago?
Answer:
95086
Step-by-step explanation:
We let the population one year ago be x, the relationship between x and the present population is;
(105/100)*x = 104832
This is because the present population exceeds the population one year ago by 5%.
therefore,
1.05*x = 104832
x = 99840
We now let the population two years ago be y, the relationship between y and the population one year ago is;
(105/100)*y = 99840
This is because the population one year ago exceeds the population two years ago by 5%.
Therefore,
1.05*y = 99840
y = 95085.7
Rounding to the nearest whole number;
95086
What are the zeros of the function f(x)= x^2-x-12/ x^2+x-12
Answer:
x=-3 ; x= 4
Step-by-step explanation:
zeros of the function are the value of x at which the function becomes zero. Or graphically when the graph line crosses the x-axis those values of x are the zeros of the function.
Finding zeros of given function f(x)= x^2-x-12/ x^2+x-12 by substituting f(x)=0
0= x^2-x-12/ x^2+x-12
0= (x+3)(x-4)/(x-3)(x+4)
(x+3)(x-4)=0
(x+3)=0 ; (x-4)=0
x=-3 ; x= 4
the zeros of the function f(x)= x^2-x-12/ x^2+x-12 are at point x=-3 and x= 4 !
Answer:
-3,4
Step-by-step explanation:
A.P.E.X
In a unit circle, what is the length of an arc that subtends an angle of
π/4 radians?
A unit circle has radius 1, and thus circumference [tex]2\pi[/tex].
Since an angle of [tex]\frac{\pi}{4}[/tex] is one eighth of a whole turn, the length of an arc that subtends an angle of [tex]\frac{\pi}{4}[/tex] radians will be one eighth of the whole circumference:
[tex]l = \dfrac{2\pi}{8} = \frac{\pi}{4}[/tex]
In fact, the radians have the property that, in the unit circle, the length of the arc is exactly the measure of the angle. In general, you have
[tex]l = r\cdot\alpha[/tex]
where l is the length of the arc, r is the radius and [tex]\alpha[/tex] is the angle in radians. So, if [tex]r=1[/tex], you have [tex]l=\alpha[/tex]
The length of an arc in a unit circle that subtends an angle of π/4 radians is simply π/4, because in a unit circle, the length of an arc is the angle (in radians) multiplied by the radius (which is 1).
Explanation:In Mathematics, particularly in the study of a unit circle, an interesting concept to learn is the length of an arc that subtends an angle. Here, the given angle is π/4 radians. In a unit circle, the length of an arc can be calculated by simply multiplying the angle (in radians) by the radius of the circle. In this case, since the radius is 1 (as it's a unit circle), the length of the arc is simply the measurement of the angle in radians, which is π/4.
Learn more about Arc length in unit circle here:https://brainly.com/question/2193394
#SPJ3
Rolling probability of 2
The answer is 25%
If you roll 20 times in total and you land on two 5 times 5/20 = .25
Hope this helps!
Which two points in the graphed function have an average rate of change of 5?
Answer:
B. points A and B
Step-by-step explanation:
"Rate of change" is just a fancy name for slope.
The question asks for points on the graph having a slope of 5. We know a slope of 5 is a positive (goes up from left to right) and it's quite steep.
By looking at the graph, we see that to have a slope of 5, it has to take place in the first half of the graph.
Let's look at the possible options:
A. Points D and F: From point D to point F, you're going down, so the slope is negative. NO
B. Points A and B: goes up, pretty steep. Let's calculate the slope.
Point A: (2,1), Point B: (3,6)
Slope = (6 - 1) / (3 - 2) = 5 / 1 = 5
We found it!
C. Points B and C: goes up, pretty steep too. Let's calculate the slope:
Point B: (3,6) , Point C: (4,9)
Slope = (9 - 6) / (4 - 3) = 3 / 1 = 3, NO, not the slope we're looking for
D. Points C and E: goes down, NO, not what we want.
in a cirlce of radius 5 cm, what is the length in cm of an arc subtended by a central angle measuring 2 radians?
Answer:
The length L is 10 cm
Step-by-step explanation:
We need to find the length of the arc subtended by a central angle of 2 radians and the circle has radius of 5cm.
So, the formula used will be:
l = r Θ
Where L= length of arc
r= radius of circle
and Θ is angle
In The given question
L=?
r = 5 cm
Θ = 2 radians
Putting values in formula:
L = r Θ
L = 5 * 2
L = 10 cm
So, the length L is 10 cm
Final answer:
The length of the arc subtended by a central angle of 2 radians in a circle of radius 5 cm is 5 cm.
Explanation:
The length of an arc subtended by a central angle can be found using the formula:
Length of arc = (central angle / 2π) × circumference of the circle
In this case, the central angle is 2 radians and the radius of the circle is 5 cm. The circumference of the circle is given by 2πr, where r is the radius. So, the length of the arc can be calculated as:
Length of arc = (2 / 2π) × (2π × 5) = 5 cm
A cube has a volume of 216 cubic centimeters. What can be concluded about this cube? Check all that apply.
Recall the formula: Cube V= s^3
The side length, s, can be found using the equation 3s=216
This is a perfect cube.
The side length is 72 centimeters.
The side length is 6 centimeters.
Taking the cube root of the volume will determine the side length.
If you multiply the volume by three, you can determine the side length.
Answer:
Second option: This is a perfect cube.
Fourth option: The side length is 6 centimeters.
Fifth option: Taking the cube root of the volume will determine the side length.
Step-by-step explanation:
You know that the volume of a cube can be calculated with:
[tex]V=s^3[/tex]
Where s is the lenght of any side of the cube.
Since you know the volume of this cube, you can calculate the side lenght by solving for "s". You can make this taking the cube root of the volume.
Therefore, you get that the side lenght of this cube is:
[tex]s=\sqrt[3]{216cm^3}[/tex]
[tex]s=6cm[/tex]
(Since it has exact cube root, it is a perfect cube)
Answer:
B,D,E
Step-by-step explanation:
50 points!
For which rational expression is -5 an excluded value of x?
A) x-5/6
B) x+5/6
C) 6/x-5
D) 6/x+5
Answer:
D
Step-by-step explanation:
An excluded value is any value of x that makes the denominator of the rational expression zero as this would make the expression undefined.
Consider expression D
[tex]\frac{6}{x+5}[/tex]
This will be undefined when
x + 5 = 0 ⇒ x = - 5 ← excluded value → D
Answer:
D) 6/x+5
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
In this example, we will use D
x + 5 = 0 ⇒ x = - 5 ( Excluded value )