Answer:
true
Step-by-step explanation:
vertical angles are congruent
What is the equation of the following line written in general form? (The y-intercept is 7.)
Answer:
3x - y + 7 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:
[tex]1=-2m+7[/tex] subtract 7 from both sides
[tex]-6=-2m[/tex] divide both sides by (-2)
[tex]3=m\to m=3[/tex]
We have the equation:
[tex]y=3x+7[/tex]
Convert it to the general form [tex]Ax+By+C=0[/tex]:
[tex]y=3x+7[/tex] subtract 3x and 7 from both sides
[tex]-3x+y-7=0[/tex] change the signs
[tex]3x-y+7=0[/tex]
Find the interquartile range for each set of data.
Set 1: 21, 5, 14, 10, 8, 17, 2
Answer:
12.
Step-by-step explanation:
First arrange in ascending order:
2 5 8 10 14 17 21
The median is 10.
the lower quartile is the middle number of 2 5 and 8 which is 5.
Similarly the upper quartile is 17.
IQR = 17 - 5 = 12.
Answer:
12
Step-by-step explanation:
An angle with its vertex at the center of a circle intercepts an 80° arc of that circle.
What is the measure of the angle?
let's recall that, arc's angle measures come from the central angle they're in.
if this intercepted arc is 80°, and is intercepted by an angle stemming from the center, namely a central angle, then the angle is also 80°. Check the picture below.
If angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is 80°.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that angle with its vertex at the center of a circle intercepts an 80° arc of that circle
We have to find the measure of the angle.
When an angle is formed at the center of a circle, it intercepts an arc of the circle that is equal in measure to the angle.
Since the given angle intercepts an 80° arc of the circle, we know that its measure is also 80°. so the measure of the angle is 80°.
Hence, if angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is 80°.
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Chase and Alonzo stand next to each other and throw baseballs in the air.
The path of Chase's ball is described by the equation y = - 4x2 + 5x + 7. The
path of Alonzo's ball is shown by the graph.
Answer:
Alonzo baseball
Your question is incomplete and lacks a graph. Please check below for the full content.
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
The misssing graph is shown below.
The correct option is option C: Alonzo's baseball
What is a quadratic equation?The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.
Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.
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The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:
A scientist measures the angle x and the distance y between the Sun and the moon. Using complete sentences, explain how the scientist can
use only these two measurements to calculate the distance between the Earth and the moon.
Answer:
The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x
Step-by-step explanation:
Let
EM -----> the distance between the Earth and the Moon.
y -----> the distance between the Sun and the Moon.
we know that
In the right triangle of the figure
The sine of angle x is equal to divide the opposite side to angle x (distance between the Earth and the Moon.) by the hypotenuse ( distance between the Sun and the Moon)
so
sin(x)=EM/y
Solve for EM
EM=(y)sin(x)
therefore
The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x
Last year, your team bought 11 baseball caps for $55. This year, the cost per cap is the same. Write a
proportion that gives the cost c of buying 15 baseball caps.
To find the cost of buying 15 baseball caps, we set up a proportion using the information about the cost per cap from last year. The cost of buying 15 caps is $75.
Explanation:To write a proportion that gives the cost of buying 15 baseball caps, we can use the fact that the cost per cap is the same as last year. Let c represent the cost of buying 15 caps. We can set up the proportion as follows:
11 caps / $55 = 15 caps / c
To solve for c, we can cross-multiply and solve for the unknown variable:
11c = 15 * $55
c = (15 * $55) / 11 = $75
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To find the cost of buying 15 baseball caps, set up a proportion of 11 caps for $55 and 15 caps for (c). Solve for (c) by cross multiplying and dividing by 11. The cost of buying 15 baseball caps would be $75.
Explanation:To write a proportion that gives the cost (c) of buying 15 baseball caps, we can set up the ratio of the number of caps to the cost of the caps in two scenarios: 11 caps for $55 and 15 caps for (c). Since the cost per cap is the same in both scenarios, the proportion would be:
11/55 = 15/(c)
To solve for (c), we can cross multiply:
11 * c = 15 * 55
Dividing both sides of the equation by 11, we find:
c = 15 * 55 / 11 = 75
Therefore, the cost of buying 15 baseball caps would be $75.
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If a Canada goose completes a $2400$-mile migration in exactly $13$ days and $8$ hours, then what was her average speed for the whole trip in miles per hour?
Enter your answer as a fraction or as a decimal, without units.
Answer:
Her average speed = 7.5 miles/hour
Explanation:
First, since the required speed unit is miles/hour, we need to make sure that all units given are in miles (for distance) and hour (for time)
We are given that:
Distance covered = 2400 miles
Times taken = 13 days and 8 hours
We know that 1 day has 24 hours
Therefore:
13 days = 13 x 24 = 312 hours
Time taken = 13 days and 8 hours = 312 + 8 = 320 hours
Now, average speed is calculated as the total distance divided by the total time
This means that:
[tex]Average Speed=\frac{Total Distance}{Total Time} = \frac{2400}{320}=7.5[/tex] miles/hour
Hope this helps :)
To find the average speed, convert the total migration time of 13 days and 8 hours to hours, which is 320 hours. Then divide the total distance, 2400 miles, by the total time to get an average speed of 7.5 miles per hour.
Explanation:To calculate the average speed of the Canada goose on its $2400$-mile migration completed in $13$ days and $8$ hours, we must first convert the total time into hours. There are $24$ hours in a day, so $13$ days is equal to $13 \times 24 = 312$ hours. Adding the additional $8$ hours, we have a total travel time of $320$ hours. The average speed is then calculated by dividing the total distance by the total time.
The average speed of the goose is:
Divide the total distance of $2400$ miles by the total time of $320$ hours.Calculate $2400 \div 320$ to find the average speed in miles per hour.The average speed is $\frac{2400}{320} = 7.5$ miles per hour.
Slade draws triangle PQR. He then constructs a perpendicular bisector from vertex P that intersects side QR at point T. What can Slade conclude, based on his drawing? QT = RT TP = RQ PQ = PR PT = PQ
Answer:
QT = RT
Step-by-step explanation:
When drawing triangle PQR the perpendicular bisector cuts the triangle in half, which results in two sides that are congruent. This makes QT and RT congruent.
Based on the triangle QPR option C) PQ = PR and A) QT = RT
A) QT = RT B) TP = RQC) PQ = PR D) PT = PQWhat is congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In QPR
∠Q = ∠R (∵ PT is a bisector)
∴QT = RT (∵ PT is a bisector of QR)
PT is a common between PQT and RQT
∴PQ = PR ( by congruent part of congruent triangle)
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Which describes the difference between the two sequences?
First Sequence: 5, 10, 20, 40..
Second Sequence: 8, 15, 22, 29, ...
The first sequence is geometric because there is a common ratio of 2. The second sequence is arithmetic because there
is a common difference of 7.
The first sequence is geometric because there is a common difference of 2.
The second sequence is arithmetic because there is a common ratio of 7
The first sequence is geometric because there is a common difference of 7. The second sequence is arithmetic because
there is a common ratio of 2.
The first sequence is arithmetic because there is a common difference of 2. The second sequence is geometric because
there is a common ratio of 7.
NEEDD THE ANSWER ASAP IMA MARK BRAINLIS! 1st one answer
Answer:
its a)the first sequence is geometric bc of the common ratio of 2. the second sequence is arithmetic bc of the common difference of 7.
Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
What is a number pattern?Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.
For the given situation,
First sequence: 5, 10, 20, 40..
Second sequence: 8, 15, 22, 29, ...
Now consider the first sequence: 5, 10, 20, 40..
Here, when we divide the second number by first number, we get the common ratio as 2.
⇒ [tex]\frac{10}{5}=2[/tex]
⇒ [tex]\frac{20}{10}=2[/tex]
⇒ [tex]\frac{40}{20}=2[/tex]
Thus the first sequence follows a geometric progression with common ratio 2.
Now consider the second sequence: 8, 15, 22, 29, ...
Here, when we subtract the first term is subtracted from the second term, the common difference is 7.
⇒ [tex]15-8=7[/tex]
⇒ [tex]22-18=7[/tex]
⇒ [tex]29-22=7[/tex]
Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
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PLEASE I NEED HELP!!!! What is the type of two-dimensional solid created by a vertical cross section of the cone that passes through the apex? What is the area of the cross section?
triangle; area = 45 ft2
triangle; area = 90 ft2
circle; area = 36π ft2
circle; area = 144π ft2
Answer:
triangle; area = 90 ft2
Step-by-step explanation:
THe type of two dimensional solid created by a vertical cross section of the cone that passes through the apex is a triangle, as you can see in the picture, if you draw a line that cuts the cone in half passing through the apex it would just be a triangle, and the area of the cross section is given by the formula:
[tex]a=\frac{b*h}{2}[/tex]
Since you have the radius of the base of the cone, you need the diameter to calculate the area, the diameter is given by the next formula:
[tex]D=2r[/tex]
[tex]D=2(6)[/tex]
[tex]D=12[/tex]
Now you just put your values into the formula of the triangle:
[tex]a=\frac{(12)(15)}{2}[/tex]
[tex]a=\frac{(180}{2}[/tex]
[tex]a=90[/tex]
So the area of the triangle formed is:
[tex]90ft^{2}[/tex]
Answer:
B
Step-by-step explanation:
correct on ed2020
i need help asap thank you marking brainliest
Answer:
[tex]a_{20} = 12+3(20-1)[/tex]
Step-by-step explanation:
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
_____<√32<_____
Answer:
5 < √32 < 6.
Step-by-step explanation:
√25 = 5 and √36 = 6 so
5 < √32 < 6.
I’ve tried it many times but I can’t seem to get it can someone please help please please help I really do need help
A) -4
B) -1/4
C)4
D)1/4
Answer:
-1/4
Step-by-step explanation:
You can find the slope from a graph several ways.
Here are two ways of doing it.
Method 1. Slope formula
Find two points, then apply the slope formula, m = (y2 - y1)/(x2 - x1)
We read two easy to read points of the graph: (0, -2) and (4, -3)
m = (y2 - y1)(/(x2 - x1) = [-3 - (-2)]/(4 - 0) = (-3 + 2)/4 = -1/4
Method 2. Rise/Run
Slope = m = rise/run
Pick two points. Start at one point and go to the other point by going vertically (rise) and horizontally). The vertical distance is the rise, and the horizontal distance is the run. Up is positive, and down is negative. Right is positive, and left is negative.
Pick points (0, -2) and (4, -3).
Start at (0, -2). To go to (4, -3), move 1 unit down. That is a rise of -1. Now go horizontally 4 inits to the right. That is a run of 4.
slope = rise/run = -1/4
What do exponential functions model in the real world? How does the
standard equation form of the exponential equation change in each
situation?
Exponential functions model growth patterns such as population growth under ideal conditions, while the logistic model accounts for resource limits. The standard exponential equation is Y=abˣ, while logistic growth has a more complex form that includes the carrying capacity.
Exponential functions model various real-world phenomena in which growth occurs at a rate proportional to the current amount. For example, in natural populations, exponential growth is observed when resources are abundant and organisms can reproduce without constraints.
The standard form of an exponential function is Y = abx, where 'a' is the initial amount, 'b' is the growth factor, and 'x' represents time or another independent variable. In the context of population growth, 'a' would be the initial population size, 'b' is the growth rate per time period, and 'x' is the time elapsed.
Logistic growth is another pattern that is observed when resources become limited. It starts off similar to exponential growth but eventually slows down as the population reaches the carrying capacity of the environment.
Environmental conditions represented by the exponential growth model imply unlimited resources and space, whereas the logistic growth model includes the effects of limiting factors such as space, food, and other resources.
What is the equivalent expression 3m + (m + 5)
Answer:
[tex]\large\boxed{3m+(m+5)=4m+5}[/tex]
Step-by-step explanation:
[tex]3m+(m+5)=3m+m+5\qquad\text{combine like terms}\\\\=(3m+m)+5=4m+5[/tex]
Please please answer this correctly
Answer:
it should be 1/2
Step-by-step explanation:
because the sequence is going down by 0.05 each time;
7/10= 0.70
13/20= 0.65
3/5= 0.6
11/20= 0.55
so to continue the pattern,
1/2= 0.5
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If segment AD = 3 cm, what is the smallest diameter of wrapper that will fit the candy bar?
a.3
b.4
c.5
d.6
Answer:
6
Step-by-step explanation:
Because AD and BC Are congruent so when you add them that would equal the diameter of the rapper.
Option D is correct. The smallest diameter of wrapper that will fit the candy bar is 6
According to the attached figure - the cross-sectional view of candy bar ABC. If a cylindrical container is created from the cross-section, then the diameter of the cylindrical container formed from the cross-section will be the side AC.
From the figure, AD = DC and AC = AD + DC
Given the segment AD = 3cm
AC = AD + AD (Since AD = DC)
AC = 2AD
AC = 2(3)
AC = 6
This shows that the smallest diameter of wrapper that will fit the candy bar is 6. Option D is correct
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Please answer this correctly
Answer:
Step-by-step explanation:
the answer is 4/5
Because there are 5 section and the blueberry takes up 4 of the sections it is 4/5
Answer:
4/5
Step-by-step explanation:
So he divided something into 5 sections.
He fills one section with graph jelly and 4 sections with blueberry jelly.
Since there are 5 sections and 4 are filled with blueberry, then 4/5 is the fraction of the table he filled will blueberry.
8. Factor 12y2 + 5y - 2 completely.
A. (6y - 1)(2y + 2)
B. (4y - 2)(3y + 1)
C. (4y - 1)(3y + 2)
D. (4y + 1)(3y - 2)
Answer:
C. (4y -1)(3y+2)
Step-by-step explanation:
12 y^2 + 5 y - 2
12 y^2 + (-3+8) y - 2
12 y^2 - 3y + 8y - 2
3y(4y-1)+2(4y-1)
(4y-1)(3y+2)
Determine if the ordered pair (6, 4) is a solution to the inequality
[tex]y < \frac{3}{4}x - 3[/tex]
A.No, because (6, 4) is above the line
B.Yes, because (6, 4) is below the line
C.Yes, because (6, 4) is on the line
D.No, because (6, 4) is on the line
Answer:
A
Step-by-step explanation:
all we need to do is to plug the point (6,4) in the inequality and see if it satisfies it :
pay attention that here we have x=6 y=4
4<[tex]\frac{3}{4} (6) - 3[/tex]
we simplify we get :
4<4.5-3
4<1.5 which is incorrect so (6,4) is not a solution. moreover
notice that 4 is > than 1.5 so the point lies above the line
thus the answer is : A
you can also solve this problem by graphing the line [tex]y= [/tex][tex]\frac{3}{4} x-3[/tex] and plotting the point (6,4) and hence you will notice that the point is above the line
Answer:
A. No, because (6, 4) is above the lineStep-by-step explanation:
[tex]y<\dfrac{3}{4}x-3\\\\\text{Put the coordinates of the point and check the inequality:}\\\\(6,\ 4)\to x=6,\ y=4\\\\4<\dfrac{3}{4}\cdot6-3\\\\4<\dfrac{18}{4}-3\\\\4<4.5-3\\\\4<1.5\qquad\bold{FALSE}\\\\\text{Therefore your answer is NO, because (6, 4) is above the line.}[/tex]
[tex]\text{Other mathod:}\\\\\text{Show this inequality in the coordinate system.}\\\\\text{Draw the dotted line}\ y=\dfrac{3}{4}x-3.\\\\for\ x=0\to y=\dfrac{3}{4}(0)-3=0-3=-3\to(0,\ -3)\\\\for\ x=4\to y=\dfrac{3}{4}(4)-3=3-3=0\to(4,\ 0)\\\\\text{shaded region below the line}\\\\\text{Mark point (6, 4) and check if it lies in the shaded region.}[/tex]
help me on my home work
what is 2*2*2*2*0=
Answer:
0
Step-by-step explanation:
Anything multiplied by 0 gives you an answer of 0, therefore 2*2*2*2*0=0
Answer:
0
Step-by-step explanation:
In most cases, zero times anything is zero.
Here we have 2*2*2*2 = 2^4 = 16. Thus,
2*2*2*2*0 = 16(0) = 0
Find measure of angle that is complementary to a 28•angle (•=degree)
14•
28•
62•
152•
WHAT IS A COMPLEMENTARY ANGLE?
Complementary comes from the word complement. When two angles sum a total of 90°, they 'complement' each other. A complementary angle is a combination of two angles whose sum is equal to 90°.
BACK TO THE QUESTION
The question is asking what the measure of the other angle is. The given angle is 28°.
HOW TO FIND YOUR ANSWER
When you're given the measure of one of the angles, it's easy to find the other. All you have to do is subtract the measure of the angle from 90°.
In this question, you are given that the angle is 28°. That means you have to subtract 28 from 90.
[tex]90\°-28\°=62\°[/tex]
a. 14° ✘
b. 28° ✘
c. 62° ✓
d. 152° ✘
The answer to your question is 62°, also known as choice c.
There are 20 squid and 36 eels in a fish tank. What is the ratio of squids to eels? What is the rate of squids to eels? What about the simplified ratio and unit rate?
Answer:
Ratio: 20:36
Rate: 20 squids per 36 eels
Simplified ratio:
[tex] = \frac{20}{36 } = \frac{10}{18} = \frac{5}{9} [/tex]
Unit ratio:
20/36 squids per eel (dividing by 36)
Please mark Brainliest if this helps!
Answer:
Step-by-step explanation:
Number of squid in the tank = [tex]20[/tex]
Number of eels in the tank = [tex]36[/tex]
Rate of squids to eels will be obtained by creating a fraction of number of squids over number of eels
Rate of squid to eels = [tex]\frac{20}{36}[/tex]
also ratio of squid to eels will be written as [tex]20:36[/tex]
Simplified ratio = [tex]\frac{20}{36} = \frac{5}{9} = 5:9[/tex]
Unit rate will be defined as number of squid per eels
Unit rate = [tex]\frac{20}{36} = 0.55[/tex]
A line passes through (9,-9) and (10,-5).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
y-9 = 46% + 9); -4x + y = 45
y + 9 = 4(x + 9); -4% + y = -45
Y + 9 = 4(-9); -4x + y = -45
y - 9 = 40%-9); -4% + y = 45
[tex]\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-9)}{10-9}\implies \cfrac{-5+9}{1}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-9)\implies y+9=4(x-9) \\\\\\ y+9=4x-36\implies y=4x-45\implies \stackrel{\textit{standard form}}{-4x+y=-45}[/tex]
just a quick note
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
now, however the inappropriate choices here, do have it with a negative "x".
Answer:
y + 9 = 4(x - 9); -4x + y = -45
Step-by-step explanation:
According to the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so put the coordinates into their correct positions, depending on the signs. In the equation, there is a 9 in it [-(-9) = 9], according to the formula. By the way, this is its y-coordinate. The x-coordinate is 9, which is normal, according to the formula (see part of above answer in parentheses). So now, this is how your work will look:
y + 9 = 4x - 36 [Point-Slope Form]↷
- 9 - 9
----------------
y = 4x - 45 [Slope-Intercept Form]↷
-4x -4x
------------
-4x + y = -45 [Standard Form]
Here we are at this second equation.
I am joyous to assist you anytime.
Find the radius of the circle whose equation is (x² - 10x + 25) + (y² - 16y + 64) = 16. 4 8 16
Answer:
Radius of circle is 4
Step-by-step explanation:
The standard equation of circle is
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and r is the radius.
We are given:
(x² - 10x + 25) + (y² - 16y + 64) = 16
we know that a^2-2ab+b^2 =(a-b)^2
Using the above formula and converting the given equation into standard form, we get:
(x-5)^2+(y-8)^2=(4)^2
So, radius of circle is 4.
What is the area of a trapezoid with bases of 15.8 yd and 21.8 yd and a height of 11.7 yd?
439.92 yd2
219.96 yd2
127.53 yd2
92.43 yd2
Add the bases together, divide that by 2 then multiply by the height.
15.8 + 21.8 = 37.6
37.6/2 = 18.8
18.8 x 11.7 = 219.96 yd^2
Answer:
B) 219.96 yd2
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
(a + b) /2*h
Now you would plug in the numbers
(15.8 + 21.8) /2*11.7
Now solve this in order of operations
(15.8 + 21.8) /2*11.7
37.6/2*11.7
18.8*11.7
219.96
What is the number pie
You meant pi, pi is a irrational number, but they use 3.14 for approximation, so that is your answer.
Hope this helped!
Nate
[tex]\pi-\bold{pi}\\\\\pi\ \text{it's the ratio of a circle's circumference to its diameter}\\\\\pi=\dfrac{\text{circumference of a circle}}{\text{circle diameter}}\\\\\pi\ \text{it's irrarional number}\\\\\pi=3.14159265358979323846264338327...\\\\\text{Approximation of}\ \pi:\\\\\pi\approx3.14\\\\\pi\approx\dfrac{22}{7}\\\\\pi\approx\dfrac{355}{113}[/tex]
The number pi occurs when calculating the surface area or volume of the rotational solids.
Cylinder:
[tex]S.A.=2\pi r^2+2\pi rH\\\\V=\pi r^2H[/tex]
Cone:
[tex]S.A.=\pi r^2+\pi rl\\\\V=\dfrac{1}{3}\pi r^2H[/tex]
Sphere:
[tex]S.A.=4\pi R^2\\\\V=\dfrac{4}{3}\pi R^3[/tex]
The number pi occurs when calculating the area and the circumference of a circle.
[tex]C=\pi d=2\pi r\\\\A=\pi r^2[/tex]
It is also used to convert angle measure in degrees to radians.
[tex]x^o=\dfrac{x\pi}{180}\ rad[/tex]
which of the following equations of a line perpendicular to the line y=-1/3x+1 , passing through the point (2,7)?
Answer:
y=3x+1 (slope-intercept form)
-3x+y=1 (standard form)
3x-y=-1 (another version of standard form)
y-7=3(x-2) (point-slope form)
Step-by-step explanation:
y=mx+b is slope intercept form where m is slope and b is y-intercept.
The slope of perpendicular lines are opposite reciprocals.
The opposite reciprocal of -1/3 is 3.
So we are looking for a line of the form y=3x+b going through (2,7)
y=3x+b with (x,y)=(2,7)
7=3(2)+b
7=6+b
7-6=b
1=b
b=1
So the equation is y=3x+1.
Now you can also put it in standard form:
Subtract 3x on both sides:
-3x+y=1
You can also multiply both sides by -1:
3x-y=-1
ax+by=c is standard form.
We can also use point slope form.
y-y1=m(x-x1) where (x1,y1) is a point contained by our line and m is the slope.
We have m=3 and (x1,y1)=(2,7)
y-7=3(x-2)
Which quadratic equation is equivalent to (x^2-1)^2-11(x^2-1)+24=0
Answer:
The correct answer is first option
u² - 11u + 24 = 0
When u = (x² - 1)
Step-by-step explanation:
It is given that,
(x² - 1)² - (x² - 1) + 24 = 0
To find the correct answer
Substitute u = x² - 1
The equation becomes,
u² - 11u + 24 = 0 Where u = (x² - 1)
Therefore the correct answer is first option
u² - 11u + 24 = 0
When u = (x² - 1)
Answer:
u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0
Step-by-step explanation:
(x²-1)² - 11(x²-1) + 24 = 0
Evaluate each equation by substituting the value of u to match the equation above.
1) u² - 11u + 24 = 0 where u = (x² - 1)
(x²-1)² - 11(x²-1) + 24 = 0
This equation matches (x²-1)² - 11(x²-1) + 24 = 0
2) (u²)² - 11(u²) + 24 where u = (x² - 1)
[(x²-1)²]² - 11(x²-1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
3) u² + 1 - 11u +24 = 0 where u = (x² - 1)
(x² - 1)² + 1 - 11(x²-1) + 24 = 0
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)
[(x²-1)²-1]² - 11(u² - 1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.
!!
if two cylinders are similar and the ratio between the lengths of the radii is 3:4 what is the ratio of their surface area
Answer:
that the linear scale factor is 4:3 which can be written as 4/3
the volume scale factor will be:
(4/3)^3
D. 64:27
Step-by-step explanation: