To expand an expression, use FOIL method.
F - FirstMultiply the first term in each expression inside the parentheses.-7y and y are the first terms in each expression.
(-7y)(y) = -7y²
O - Outside Next is to multiply the terms outside. (The first term in the first expression and the last term in the second expression)-7y is the first term in the first expression
-4 is the last term of the second expression
(-7y)(-4) = 28y
I - InsideThe next step is to multiply the terms inside. (The last term in the first expression and the first term in the last expression)-8 is the last term in the first expression
y is the first term in the second expression
(-8)(y) = -8y
L - LastLast step is to multiply the last term in each expression.-8 is the last term of the first expression
-4 is the last term of the second expression
(-8)(-4) = 32
Combine all simplified terms.
-7y² + 28y - 8y + 32-7y + 20y + 32Answer:
-7y + 20y + 32Wxndy~~
3. Find sin A and cos B exactly.
B
a
C
6
4
A
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{6^2 - 4^2}=a\implies \sqrt{36-16}=a\implies \sqrt{20}=a\implies 2\sqrt{5}=a \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies sin(A)=\cfrac{\sqrt{5}}{3} \\\\\\ cos(B )=\cfrac{\stackrel{adjacent}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies cos(B)=\cfrac{\sqrt{5}}{3}[/tex]
question 14, thank you
The parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
Path of the parametric equations
The given parametric equation can be expressed as follows;
x = 3 + cosθ
y = 2sinθ
From the given options, a plot of the various equation can be used to determine the paths of the equation.
For; x = 3 + cos(2θ) and y = 2sin(2θ), its parametric plots is same as original equation since the equation [3 + cos(2θ) and y = 2sin(2θ)] changed at equal rate of the angles.
Thus, the parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
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Classify the triangle by its angles and sides
A. Right scalene
B. Obtuse isosceles
C. Acute scalene
D. Right isosceles
Mariano is standing at the top of a hill when he kicks a soccer ball up into the air. The height of the hill is h feet, and the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of the hill after t seconds is given by the polynomial −16t2 + vt + h. Find the height of the ball after 4 seconds if it was kicked from the top of a 25 foot tall hill at 72 feet per second.
Answer:
57 f
Step-by-step explanation:
-16t² + vt + h
-16(4 s)² + (72 f/s)(4 s) + (25 f)
-256 + 288 + 25 = 57
What is the x-intercept of this function?
Answer:
(3,0)
Step-by-step explanation:
Need help with this fast
Answer:
C
Step-by-step explanation:
Formula for the volume of a cone :
Volume (cone) = 1/3πr²h
===========================================================
Given :
⇒ r = 4 units
⇒ h = 21 units
============================================================
Solving :
⇒ Volume (cone) = 1/3 × π × (4)² × 21
⇒ Volume (cone) = 16 × 7 × π
⇒ Volume (cone) = 112π units²
Answer:
[tex]\sf C. \quad 112 \pi \:units^2[/tex]
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
radius = 4 unitsheight = 21 unitsSubstituting the given values into the formula:
[tex]\implies \sf Volume=\dfrac{1}{3} \cdot \pi \cdot 4^2 \cdot 21[/tex]
[tex]\implies \sf Volume=112 \pi \:units^2[/tex]
Solve for D: 70D + 6 - 9D= 35 + 4D - 20.
Answer:
The answer is D = 9/57
Step-by-step explanation:
Get the variable D by itself as stated to solve for D.
I got the other numbers to the other side.
70D + 6 - 9D = 35 + 4D - 20.
(70D - 9D - 4D) = (35 - 20 - 6)
57D = 9
D = 9/57
SOMEBODY PLEASE JUST HELP ME I DON'T KNOW
Answer:
Step-by-step explanation:
B is at (-3,-2) Multiply by 3: (-9,-6)
O is at (2,-1) Multiply by 3: (6,-3)
T is at (-3,3) Multiply by 3: (-9,9)
Hope this helps!!
A family plan for a cell phone has a monthly base price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) (in $) of a family for x additional family members added is C(x)=
The linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
How to get the linear equation?
Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.
Then if there are x family members added, the cost will be:
$75 + $10.99*x
Then the linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
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y= -x - 8x - 16 how many solutions
Answer:
1 solution
Key:
Assume x is the the range x > 0 ≥ 1, in other words, assume x is equal to 1.
Step-by-step explanation:
[tex]y = -x - 8x - 16\\= -x - 8x\\= 9x\\= 9x - 16[/tex]
The equation of a curve is y = x³ + 4x. Show that the value of y increases when x increases. ² is a decreasing function.
We will see that f'(x) > 0, which means that f(x) is an increasing function.
How to prove that the function is increasing?
For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.
Here we have the cubic function:
f(x) = x³ + 4x
If we differentiate this, we get:
f'(x) = df(x)/dx = 3x² + 4.
And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.
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Please show your work! I'll give brainliest as well, thanks in advance!
The area of a circle is defined as [tex]\pi(r^{2})[/tex], where r = 4.3 here. 4.3^2 ≅ 18.49, so the area of the full circle is 18.49π.
The shaded section covers 12 degrees of the full 360 degrees in a circle, or 1/30th of the area. Therefore, the area of the shaded section is equal to [tex]\frac{18.49\pi}{30}[/tex], or about 1.936. In this question's context, that would be 1.936[tex]in^{2}[/tex].
i needs help please
Answer:
Step-by-step explanation:
calculates the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100
The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
How to calculate arithmetic progression?The first term of an arithmetic progression can be calculated using the following expression:
Sn = n/2 [2a + (n − 1)d]
Where;
a = first termUn = sumn = no of termsd = common ratio100 = 2 [2a + (4 - 1)4]
100 = 4a + 24
4a = 100 - 24
a = 76/4
a = 19
Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
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PLEASE HELP TIMER!!!!!!!!!!!!!
Answer:
Answer: -3/2
Step-by-step explanation:
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In the diagrams, the pre-image is shown with a dashed line and the image is shown with a solid line. Which
transformation represents a dilation?
5
543-11-
4 5 X
Save and Exit
Next
Submit
Mark this and return
Answer:d
Step-by-step explanation:
Solve for N:
A_-21
B_21
C_-96
D_96
Step-by-step explanation:
n + 5 = -16
n = -21
The correct option is -21
Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5+ 1.25x
X=the number of weeks that have passed
Y = the height of the plant
How tall will with plant be after 7 weeks?
After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 2.5 + 1.25x
Plug x = 7 weeks
y = 2.5 + 1.25(7)
y = 11.25 units
Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
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Which of the following is equivalent to:
(2x³ + 2) + (5x³ + 3)
Answer:
Step-by-step explanation:
2x^3 + 5x^3 + 2 + 3 = 7x^3 + 5
Write the logarithmic expression as a single logarithm with coefficient , and simplify as much as possible. Assume that all variable expressions represent positive real numbers.
1/2ln(b^2+1)-1/2ln(b+1)
Answer:
hope you can understand
if x²+y²=20 and x-y=6 how is x.y?
Answer:
xy = - 8
Step-by-step explanation:
note that
(x - y)² = x² + y² - 2xy , that is
6² = 20 - 2xy
36 = 20 - 2xy ( subtract 20 from both sides )
16 = - 2xy ( divide both sides by - 2 )
- 8 = xy
[tex](x-y)^2=x^2-2xy+y^2[/tex]
Therefore
[tex]6^2=20-2xy\\36=20-2xy\\2xy=-16\\xy=-8[/tex]
Polygon ABCD is plotted on a coordinate plane and then rotated 90° clockwise about point C to form polygon A′B′C′D′. Match each vertex of polygon A′B′C′D′ to its coordinates.
Graph of rigid functions on a coordinate plane. A quadrilateral vertices are plotted at A (4, 6), B (5, 3), C (4, 2), and D (1, 2) in quadrant 1. Interior are of quadrilateral is shaded.
The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)
How to match the vertices of the polygon?The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.
The vertices of polygon ABCD are given as:
A = (4, 6)
B = (5, 3)
C = (4, 2)
D = (1, 2)
The rule of rotation about point C is:
(x,y) = (a + b - y, x + b - a)
Where:
(a, b) = (4, 2) --- the point of rotation.
So, we have:
(x,y) = (4 + 2 - y, x + 4 - 2)
(x,y) = (6 - y, x + 2)
The above means that:
A' = (6 - 6, 4 + 2) = (0,6)
B' = (6 - 3, 5 + 2) = (3,7)
C' = (6 - 2, 4 + 2) = (4,6)
D' = (6 - 2, 1 + 2) = (4,3)
Hence, the image of the rotation and their vertices (i.e. coordinates) are:
A' = (0,6)
B' = (3,7)
C' = (4,6)
D' = (4,3)
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Find the value of x and y
Answer:
x = 1
y = -3
Step-by-step explanation:
cos(pi) = -1
so many ways :
sqrt(0.5/2) = sqrt(0.5/2 × 8/8) = sqrt(4/16)
= sqrt(0.5/2 × 18/18) = sqrt(9/36)
= sqrt(1/4) = 1/2
"nicest" approach (all integers) :
3x² = sqrt(9)
3x² = 3
x² = 3/3 = 1
x = 1
2y = sqrt(36)
2y = 6
y = 6/2 = 3
one of them has to be negative (because cos(pi) = -1), so it has to be y, because 3x² cannot be negative with real numbers.
so, y = -3
-1 × 3×1²/(2×-3) = sqrt(0.5/2) = 1/2
-1 × 3/-6 = 1/2
3/6 = 1/2
1/2 = 1/2
correct
Which expression is equivalent to…
Answer:
the 3rd one ez clapppppppp
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write the expression for the number of sweets Sue and Tony now have
Answer:
Sue : 13 - x Tony : x/2 + 9Step-by-step explanation:
Sue Tony_________________________________________________
initial number of sweets | 18 | 18
| |
Sue gives Tony x sweets | 18 - x | 18 + x
| |
Sue ,eats 5 of her sweets. and | 18 - x - 5 = | (18 + x)/2 =
Tony ,eats half of his sweets | 13 - x | 9 + x/2
What is the average collection period??
Answer:
an accounting metric used to represent the average number of days between a credit sale date and the date when the purchaser remits payment.
The price of a 7-minute phone call is $1.75. What is the price of a 13 minute phone call?
Answer:$3.25
Explanation:
Since the 7 min phone call is at 1.75, that means that one minute of phone call time is 0.25. 13 minutes would be 0.25*13=3.25
hope this helps
You roll two number cubes.
Let event A = You roll an even number on the first cube.
Let event B= You roll a 6 on the second cube.
Are the events independent or dependent? Why?
O A. Dependent, because 6 is an even number.
о B. Dependent, because both cubes have six sides.
O C. Independent, because they have no outcomes in common.
D. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
Answer:
Step-by-step explanation:
If you roll an even number it doesn't just get rid of the number off the cube, it still exists
Events A and B are independent.
These events have no outcomes in common,
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Events A and B are independent because the outcome of one event does not affect the probability of the other event.
The fact that 6 is an even number is not relevant to the independence of the events.
Event A is the event of rolling an even number on the first cube, which has three even and three odd numbers.
Event B is the event of rolling a 6 on the second cube, which has one 6 and five non-6 numbers.
These events have no outcomes in common, and the outcome of the first roll does not affect the outcome of the second roll.
Therefore,
Events A and B are independent.
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In an urn there are 6 red balls, 4
blue balls and 10 yellow balls.
What is the probability of
choosing a yellow ball?
Answer:
1/2 / 50% chance
Step-by-step explanation:
There are 10 yellow out of 20 (6 + 4 + 10 = 20) balls.
So, the probability is 10 / 20
Or, 1 / 2 (which is the same thing as 50% chance)
(chance = probability)
Which of the following are not trigonometry identities? Check all that apply
Answer:A
Step-by-step explanation:
Good luck on the exam!