The vertex (0,2) of the parabola's vertex shape, which can expand upward or downward, equals (x - 0)² + 2.
What is parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
What is a vertex form of an equation?
An equation's conventional vertex form is written as:
f(x) = (x-h)² + k where;
(h, k) is the vertex
Vertex (0,2) should be replaced in the equation's vertex form.
f(x) = (x - 0)² + 2
As a result, vertex (0,2) of the parabola with an opening up or down is equal to (x - 0)² + 2.
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Write the coordinates of the vertices after a reflection over the line y=-5.
The coordinates of the vertices after a reflection over the line y = -5 is given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
How to obtain the coordinates of the vertices after the reflection?The vertices of the original quadrilateral are given as follows:
T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).
The reflection line y = -5 is an horizontal line, meaning that after the reflection:
The x-coordinate remains constant.The y-coordinate will be equidistant to y = -5, however in an opposite direction.For example, the distance of the y-coordinate of the vertex U from -2 is of:
2 units above.
Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:
U'(2,-7).
Applying this rule for all the other vertices, they will be given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
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x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
JKLM is a parallelogram.
What is the measure of ZKLJ?
Enter your answer in the box.
Theres no point 'Z', so i'm gussing you want the angle of <KLJ?
<K and <M are the same, therefore <M = 130
<J + <K + <M + <L = 360
130 + 130 = 260, 360 - 260 = 100
<J and <L are the same
<MJK = 50 and <KLM = 50
<KLM/2 = <KLJ
50/2 = 25
Geometry Suppose that a pizza must fit into a box with a
base that is 12 in. long and 12 in. wide. You can use the
quadratic function A Tr² to find the area of a pizza in
terms of its radius.
a. What values of r make sense for the function?
b. What values of A make sense for the function?
c. Graph the function. Round values of A to the
nearest tenth.
Question 39
The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
How to determine the Radius of the circle?You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box
The quadratic function reads
A= πr²
Where A= Area of circle,
π = 22/7
and r= radius of the circle
A= (22/7)*6
Width of the box is 12
Therefore 12/2 = r=6
A= (22*6*6)/7
A=113.1 in²
In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
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d) if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg
When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.
A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.
Given,
Mean of the weights = 102.4 kg
Standard deviation = 13.9 kg
To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]
Where, [tex]\sigma[/tex]=standard deviation
n= number of reindeer
substitute the values in the formula,
[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]
Now,
[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]
from z-score table,
=0.1492
Thus, the probability the their mean weight is less than 100 kg is 0.1492.
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Your question is incomplete, here is the complete question.
The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg
if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?
what is the point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents? if required, round your answer to two decimal places.
The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.
The point estimate of P, is defined as the proportion of successes in the sample.
P' = X/N ; where X = number of successes; N = total trials.
Here, N = 1000
According to the Child outlook file, number of "yes" = 240.
Hence, P' = 240/1000
P' = 0.24
Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.
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The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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Sadie is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Sadie will earn $40 every time one of her songs is played in a commercial and she will earn $120 every time one of her songs is played in a movie. Sadie's songs were played on 3 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $440. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Sadie's songs were played. Define the variables that you use to write the system.
The number of commercials and movies on which the songs were played are 5 and 2.respectively
How to determine the number of commercials and movies on which the songs were played.From the question, we have the following parameters that can be used in our computation:
Earnings from songs played in commercial = $40Earnings from songs played in movie = $120Total earnings = $440The number of commercials is x, and the number of movies is y
The above parameters when represented as an equation is as follows
40x + 120y = 440
x = y + 3
Substitute x = y + 3 in 40x + 120y = 440
40(y + 3) + 120y = 440
Expand
40y + 120 + 120y = 440
Evaluate the like terms
160y = 320
Divide by 160
y = 2
Recall that
x = y + 3
So, we have
x = 2 + 3
x = 5
Hence, the number of commercials is 5 times
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suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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32. What is the area of the rhombus in simplest radical form? The figure is not drawn to scale.
(1 point)
The area of the rhombus is 49√6. Option B
How to determine the area of the rhombusThe formula for calculating the area of a rhombus is expressed as;
Area = pq/2
Where;
p and q are the diagonals of the rhombus
From the diagram shown, let's determine the value of p
Using the trigonometric identity;
Tan θ = opposite/adjacent
Opposite side = pAdjacent side = 7Substitute the values into the formula, we have;
tan 60 = p/7
Find the value of tan 60 and then substitute
√3 = p/7
cross multiply
p = 7√3
But;
Area = 7√3 × 7√3/2
Area = 49√6
Hence, the value is 49√6
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plsss help i’ll give brainlist to right answer
Answer:All I know is that it’s not < or > but It might be ≤
Step-by-step explanation: Bye the way, you can only give brainliest when there is two questions.
[tex]\leq[/tex]
Step-by-step explanation:
Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
a company makes wax candles in the shape of a cylinder. each candle has a diameter of 4 inches and a height 8 of inches. if the company used of wax, how many candles did it make? use for , and do not round your answer.
If the company has made 6732.16 in³ wax , Total number of candles made is 67
According to the question,
It is given that a wax candle is in cylindrical shape
Diameter of candle = 4 in
Radius will be = 4 / 2
=> 2 in
Height of each candles = 8 in
Company has used 6732.16 in³ of wax
We have to calculate number of candles company has made
Volume of cylinder = πr²h
Where r is radius and h is height
Substituting all the values,
Volume of candle = π (2)² (8)
=> V = 3.14 × 4 × 8 (putting π = 3.14)
=> V = 100.48
Therefore , Number of candles made = Total volume /volume of one candles
=> 6732.16 / 100.48
=> 67 candles are made by company
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The Population of New York State can be modeled by
Answer: 19.71 Million.
The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, …
Let n represent the term number and f(n) the term in the sequence. The function ____ represents the sequence
A: f(n)=-3n+23
B: f(n)=-3n +61
C: f(n)= 20-3n
D: f(n) =20n-3
Click or tap the graph to plot a point.
Function representing the sequence will be f(n) = (23 - 3n
The first five terms of an arithmetic sequence are as 20, 17, 14, 11, 8....
Let n represents the number of term and f(n) the the term in the sequence.
Then we have to find the function that represents the sequence.
As we know explicit formula of an arithmetic sequence is given by
Or the function representing the sequence will be
f(n) = a + (n-1)d
where a represents first term of the sequence a = 20
and common difference d = 17-20 = (-3).
Now the function which represents this sequence will be
f(n) = 20 + (n-1)(-3) = 20 - 3n + 3 = 23 - 3n
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Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
6x-7=1-3x[tex]6x-7=1-3x[/tex]
Answer:
x=8/9
Step-by-step explanation:
step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.
3x+-3x cancels itself out and 3x+6x=9x.
now, the equation looks like: 9x-7=1
step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.
7+-7 cancels itself out and 7+1=8.
now, the equation looks like 9x=8
step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".
9x/9= x, 8/9
so the answer is x=8/9
hope this helped!!
read the picture plsss
Answer:
Step-by-step explanation:
how is (-7.5)-21.04 and (-7.5)+21.04 the same value?
The values (-7.5)-21.04 and (-7.5)+21.04 are not the same
What is a decimal?A decimal can be defined as a number consisting of a whole number and also a fractional part.
These numbers are separated by a dot known as the decimal point
The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.
It is important to note the following operations;
+ × + = ++ × - = -- × + = -- × - = +From the information given, we have;
(-7.5)-21.04
Multiply the operation
+ 157. 8
Then,
(-7.5)+21.04
Multiply the operation
- 157. 8
Hence, the values are either negative or positive.
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If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
7x+14y=21,-7x+7y=7 using elimation
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
Solve for c.
4(c + 17) = 16
C =
Please help
21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
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64 divided by blank equals 8
Answer: 8
Step-by-step explanation:
8 times 8 is 64
for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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Provide the missing statements and reasons for the following proof:
The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:
S1: Line m is parallel to line n.
S2: ∠1 = ∠2
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
What are Supplementary Angles?
Supplementary angles, when added together will give us a sum of 180°.
Linear pair angles and corresponding angles are supplementary.
Thus, to prove that ∠1 is supplementary to ∠3:
We are given that lines m and n are parallel.
∠1 and ∠3 are corresponding angles.
So therefore, ∠1 = ∠3 by the corresponding angles postulate.
∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.
Based on the substitution property, we have the following:
m∠2 + m∠3 = m∠1 + m∠3
m∠1+m∠3=180°
Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.
The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:
S1: Line m is parallel to line n.
S2: ∠1 = ∠2
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
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