f(0) = ( f(k) +f(-k) ) / 2
f(0) = (16 - 4) / 2
f(0) = 12 / 2
f(0) = 6 → ANSWER
*Remember that f(0) = m(0) + n = n
If we have f(x) = mx + n, then:
f(k)= mk + n and f(-k)= -mk + n
If we add them:
f(k) + f(-k)
= mk + n -mk + n
= 2n
= 2f(0)
So we conclude that:
f(0) = [f(k) + f(-k)] / 2
1-Rodrigo spent $1.47 to buy 3 red balloons. The balloons all had the same price. How much did each balloon cost?
Answer:49 cents
Step-by-step explanation:
U have to divide the 1.47 into 3
Find the equation of the quadratic function in vertex form, with vertex (-1, 8) that has a y-
intercept of 4 (which means it passes through the point (0,4)).
Answer:
The equation of the quadratic function is y = -4(x + 1)² + 8
Step-by-step explanation:
The vertex form of the quadratic function is y = a(x - h)² + k, where
a is constant(h, k) are the coordinates of the vertex of its graph∵ The vertex of the graph of the quadratic function is (-1, 8)
∴ h = -1 and k = 8
→ Substitute the values of h, k in the form of the equation above
∵ y = a(x - -1)² + 8
∴ y = a(x + 1)² + 8
→ To find a substitute x and y of the equation by the coordinates
of a point lies on the graph of the function
∵ The y-intercept is 4
→ That means the graph intersect the y-axis at point (0, 4)
∴ x = 0 and y = 4
∵ 4 = a(0 + 1)² + 8
∴ 4 = a(1)² + 8
∴ 4 = a(1) + 8
∴ 4 = a + 8
→ Subtract 8 from both sides
∵ 4 - 8 = a + 8 - 8
∴ -4 = a
→ Substitute the value of a in the equation
∴ y = -4(x + 1)² + 8
∴ The equation of the quadratic function is y = -4(x + 1)² + 8
If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
If m< EBC = 3y+10 and m< ABE = 2y-20, the value of m< EBF is 56 degrees
How to solve for the angleThe questions says that If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
We have to solve this using the rule of supplementary angles that says that
m<EBC + m<ABE = 180 degrees
This would be written as
3y+10 + 2y-20 = 180
collect like terms
3y + 2y + 10 - 20 = 180
5y - 10 = 180
5y = 180 + 10
5y = 190
then y = 190/5
y = 38 degrees
We have to put the value of y in 2y-20
= 2 * 38 - 20
= 76 - 20
= 56
Given that
m< ABE = m< EBF
Then the value of m< EBF = 56
12. we have < EBF = < ABE - < ABF
then 2b - (7b - 24)
when we open the bracket
< EBF = -5b + 24
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help meh then i give you sum huge amount of points!
Answer:
It's D
Step-by-step explanation:
10 divided by 20
i hate school okokokokokok
Answer:
Thanks for the free points...
I love school by the way
Answer:
hey
can you give me a brainliest
Step-by-step explanation:
what is x in 4x²-12x+ 9 = 0
Answer: x = √9/8
answer is x = square root of 9/8
Step-by-step explanation:
PLEASE HELP
Are the triangles shown at the right congruent? Explain. (picture of triangle below)
A. Yes, by SSA.
B. Yes, by the HL Theorem.
C. No; SSA cannot be used because there is only one pair of congruent corresponding sides.
D. No; the HL Theorem cannot be used because there is only one pair of congruent legs.
Answer:
A
Step-by-step explanation:
they look the same to me :D
PLZ HELP ASAP! MARKING BRAINLIEST AS WELL!
Three hens lay 3 eggs in 3 days.
(1) How many hens would lay 12 eggs in 12 days?
(2) How many hens would lay 3 eggs in 9 days?
Answer:
1 hen lays 1 egg in 3 days
Basically, in 3 days 1 hen lays 1 egg
1 hen lays 4 eggs in 12 days
Therefore, 3 hens lay 12 eggs in 12 days ******************
1 hen lays 3 eggs in 9 days ******************
Step-by-step explanation:
Find the equation of the line.
Use exact numbers.
y = __x + __
Answer: y= x-5
Step-by-step explanation:
It already gave you the y-intercept, which is on the y-axis. It is: (0,-5)
So your equation is: y = mx-5
Now you find your slope by using the two points it gives us: (0,-5) and (5,0)
-5 - 0= -5(from the two y- coordinates) and 0 - 5 = -5(from the two x-coordinates)
That is -5 divided by -5 so the answer would be 1
Your equation is: y = 1x-5
But you don't have to put the 1 because the x itself counts as 1
One number is 4 times as large as another. The sum of their reciprocals is ½. What is the sum of the numbers? i need asap answer plssss
Answer:
The sum of the two numbers is 12.5
Step-by-step explanation:
First we write a system of equations.
One number is 4 times larger than the other.
y = 4x
The sum of their reciprocals is 1/2
1/x + 1/y = 1/2
Substitute
1/x + 1/4x = 1/2
1 + 1/4 = 1/2x
x = 2.5
Solve for other number
y = 4(2.5)
y = 10
The inverse of x is 2/5 or 4/10, and the inverse of y is 1/10. When added the sum is 5/10 or 1/2.
A carpenter wishes to make a rain gutter with a rectangular cross-section by bending up a flat piece of metal that is 18 feet long and 44 inches wide. The top of the gutter is open. What values of x, length of metal bent up, will give a cross-sectional area of at most 50 square inches? Round your answer to three decimal places.
Answer:
x = 20.996 , 1.002 square inches.
Step-by-step explanation:
We assume that the sides are bent at right angles
Dimensions of the given metal sheet are
Length = 18feet = 216 inches
Width = 44 inches
When we will bend the width part of the given metal sheet
let the bent length be x
so the cross sectional dimensions will be
width = 44-2x
length = x
Area = x(44-2x)
The given are should be at most 50 square inches
so the equation becomes
x(44-2x)[tex]\leq 50[/tex]
-2x^2 + 44x [tex]\leq 50[/tex]
[tex]2x^2 -44x +50\geq 0[/tex]
[tex]x^2 -22x +25\geq 0[/tex] (dividing the equation by 2)
upon solving the above quadratic equation we get
x = 20.996 , 1.002
both the solutions are possible.
Therefore we have the are using the values of x as 20.996 and 1.002 are
42.159968 and 42.079992 which is less than 50 square inches.
PLEASE HURRY!!
Juan's cell phone company charges $35 a month for phone service plus $0.50 for each
text message. How many text messages does Juan send in a month if his bill was $52?
1.
Define the variable:
2.
Determine the constant:
3
What is the rate:
4
Write the equation and solve:
Juan sent 34 text messages.
First, you have to subtract 35 from 52. The answer you should get is 17. If you divide 17 by $.50 you should get 34.
Please help!
How do you find the slope of this equation
y = 7x-3
Answer:
Step-by-step explanation:
H
Answer:
The slope is 7
Step-by-step explanation:
y = mx + b
m is the slope and as we can see in the equation, 7 is there instead of m, therefore 7 is the slope
is 3x+4y=1 written in slope intercept form?
Answer:
no
Step-by-step explanation:
if you want it in slope intercept form it would be :
y= -3/4 + 1/4
A triangle has sides of lengths 12, 14, and 19. Is it a right triangle?
Answer:
a^2 + b^2 = c^2
C should equal to the longer side, which would be 19.
Plug in other two numbers for A and B.
12^2 + 14^2 = 19^2
Now see if it's correct. If it is, then it's a right triangle, if it's not then it isn't a right triangle.
144 + 196 = 361
340 = 361
It's not a right triangle.
Step-by-step explanation:
Because I know it. Can You mark me as a brainliest?
Carlos purchased four pounds of oranges for $3.20. He later realized he needed nine pounds.
How much more money will he need to spend to bring his total up to nine pounds?
Answer: 5.8
Step-by-step explanation:
To find the answer to this question, you need to find the difference between the two numbers. To find the difference between the two numbers you have to subtract.
9 - 3.20 = 5.8
Answer:
$4
Explanation
3.20 / 4 = .80 .80 x 9 = 7.20 7.20 - 3.20 = 4
Laura's yard is in the shape of a square and a half-circle. She just got a puppy named Sprinkles for her birthday. In order to keep him safe, she wants to line the perimeter of her yard with a fence. How much fencing will she need to enclose the entire yard and keep Sprinkles from running away?
Answer:
The total perimeter she would need to fence would be:
4L + πr
Step-by-step explanation:
Since her yard is a square and half a circle, and she wants to fence the whole distance around the square and the half circle, then she needs to know the perimeter of a square and semicircle.
The perimeter of a square which is the distance around the square is given by 4L where L is the side length.
The perimeter of a circle, which is the circumference of a circle is 2πr, where r is the radius of the circle Therefore, half a circle would be 2πr/2 = πr.
The total perimeter she would need to fence would be:
4L + πr.
pls pls plssss helppOOOOoo
Which graph represents the function f(x) = |x|?
Answer:
Graph 1
Step-by-step explanation:
Does the table below represent a proportional relationship?
x 1 2 3 4
y -4 -8 -12 -16
A.
Yes, because all the ratios of y to x are equal to -2.
B.
No, because the table has negative numbers.
C.
Yes, because all the ratios of y to x are equal to -4.
D.
No, because the ratios of y to x are not equal.
Answer:
C
Step-by-step explanation:
Here, we want to know if the table represents a proportional relationship
Looking at the table, if we multiply the x-terms by -4, we get the y-terms
So the answer here is that Yes, because all the ratios of y to x are equal to -4
Find the inverse of the following function: f(x)=√(2x +3) - 4
Determine the domain for which this inverse function will be defined. Write your answer as an inequality.
I have this question for GMM and I got the inverse right, but I don't know how to get the domain. I thought it was x<(or equal to) 3/2 but it says it's wrong
The domain of the inverse function in inequality is written as x ≥ √3 -4.
What is domain and range ?
The is the set of possible input values, and the range is the set of all possible output values of the graph.
Here, the given function is :
f(x) = √(2x +3) - 4
and it is already found that its inverse is :
f⁻¹(x) = {(x+4)² - 3}/ -2
Therefore, to find the domain of this inverse function we equate the numerator to greater then equals to zero that is :
(x+4)² - 3 ≥ 0
(x+4)² ≥ 3
(x+4) ≥ √3
x ≥ √3 -4
Therefore, the domain of the inverse function in inequality is written as x ≥ √3 -4.
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At King Kong High School, the average weight of senior boys is 168 lbs. with a standard deviation of 7 lbs. The average weight for senior girls is 117 lbs. with a standard deviation of 5 lbs. Suppose a new distribution is created by adding the boys' weights and the girls' weights together. Assuming that the weights for boys and girls are independent, which of the following is true?
I. The mean of this new distribution is 168 + 117.
II. The standard deviation of this new distribution is 5+ 7.
III. The variance of this new distribution is 52 + 72
A) I only
B) II only
C) I and II only
D) I and III only
E) I, II, and III
Answer:
I and III only. Got it correct on Stats test.
Thus, the mean of this new distribution is 168 + 117 and the standard deviation of this new distribution is 5+7. Therefore, option C is the correct answer.
Given that, at King Kong High School, the average weight of senior boys is 168 lbs.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Here, a new distribution is created by adding the boys' weights and the girls' weights together.
So, the new average weight of senior boys and girls
= 168+117
= 285 lbs
The new standard deviation is 5+7
= 12 lbs
Thus, the mean of this new distribution is 168 + 117 and the standard deviation of this new distribution is 5+7. Therefore, option C is the correct answer.
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HELPPPPPPPP PLEASEEEEEEEE
help again! algebra 1
Answer: maybe c?
Step-by-step explanation:
from eqn. 1
3x + 2y = 23
2y = 23 - 3x
y = 23/2 - 3/2x
sub into eqn. 2
1/2x - 4 = 23/2 - 3/2x
1/2x + 3/2x = 23/2 + 4/1
2x = 23/2 + 8/2
2x = 31/2
x = 31/4
sub into eqn. 1
31/4 + 2y = 23
2y = 23 - 31/4
2y = 92/4 - 31/4
2y = 61/4
y = 61/8 or 7 5/8
ummm i got something wrong but try c?
Answer:
C . 31/4,-1/8
Step-by-step explanation:
1. sub the given value of y
into 3x + 2 (1/2x -4) 23
2. slove for x = 31/4
3.sub the given value of x into 1/2x - 4 =y
4. solve the equation for y
5. y = -1/8
6. ordered pair to (x,y) = 31/4,1,8
Crystal pls help again
Answer:
I think its 63 degrees.
Answer:
63
Step-by-step explanation:
In a triangle, all interior angles add up to 180
47+70+x=180
x=63
Use the provided ruler to measure the length of the segment. What is the length of the segment to the nearest tenth of a centimeter?
The length of the segment is {Blank} centimeters.
The length of the segment to the nearest tenth of a centimeter is 105.0 cm
What is the length of the segment to the nearest tenth of a centimeter?The given parameter is the line segment
When the line segment is measured by a meter rule, we have the length to be
Length = 105 cm
When approximated to the nearest tenth, we have:
Length = 105.0 cm
Hence, the length of the segment to the nearest tenth of a centimeter is 105.0 cm
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Name any 2 supplementary angles that equal 180 degrees
Answer:
100 degrees and 80 degrees
Step-by-step explanation:
Supplementary angles are two angles that add up to 180 degrees when combined.
Answer:
angle B= 95
angle D= 85
Step-by-step explanation:
Solve using substitution and show your work:
-3x-3y=3
y=-5x-17
Answer:
Step-by-step explanation:
Isolate any variable, x or y, but since y has already been isolated, use y to solve for x.
Substitute y into the first equation -3x-3y=3
This equals -3x - 3 (-5x - 17) = 3
Distribute to get -3x + 15x + 51 = 3
Then bring like terms together. -3x + 15x = 3 - 51
12x = -48
Solve for x
x = -4
Substitute -4 for x in the equation: y = -5x - 17
y = − 5x − 17
y = (−5) (−4) − 17
y = 20 - 17
y = 3 ( Simplify both sides of the equation)
Answer:
x = − 4 and y = 3
A principle of 5,350 is placed in an account that earns 3.5% interest. If the interest is compounded annually, how much money will be in the account at the end of 5 years?
Answer:
6,354.12
Step-by-step explanation:
what is seven not an example of
The correct option is (C) variable.
Seven is not an example of variable.
What is a variable ?A variable can be taken as a letter or number or a symbol which is not fixed that mean its value may be change any time .
What is an expression?An expression is consist of multiple symbols, letters or numbers .Expression is a proper mathematical statement consist of single letter or may be multiple letter combine with some operators.
What is a term?It can be a constant or a variable or both.
What is a constant?A constant is a letter or symbol whose value is fixed always.
In the given question,
As, Seven is a single digit number therefore it is a fixed value which can not change. Thus it is clear that seven is a constant . Also, seven is a term and an expression as well , as it denotes the mathematical value.
Thus, seven is not an example of variable.
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The complete question is :
Seven is not an example of _____.
A) an expression B) term C) variable D) constant
What is the slope of the segment with end points at (300, -2) and (500,6)
Answer:
The answer is A: 1/25