===================================================
Explanation:
A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.
The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where
a = 1
b = 8
c = -2
Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.
h = -b/(2a)
h = -8/(2*1)
h = -4
The x coordinate of the vertex is x = -4. Plug this into the original equation to get
f(x) = x^2+8x-2
f(-4) = (-4)^2 + 8(-4) - 2
f(-4) = -18
Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)
------------
Alternatively, you can complete the square as shown below
y = x^2 + 8x - 2
y = (x^2 + 8x) - 2
y = (x^2 + 8x + 0) - 2
y = (x^2 + 8x + 16 - 16) - 2
y = (x^2 + 8x + 16) - 16 - 2
y = (x+4)^2 - 18
y = 1(x+4)^2 - 18
y = 1(x-(-4))^2 - 18
The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.
A car dealer just took delivery on forty new cars. He plans to put four of these cars on display at the front of the lot. In how many ways can the dealer combine four of the forty cars if order is not important? A.1,096,680 B.45,695 C.91,390 D.2,193,360
Answer:
B
Step-by-step explanation:
Please Answer ASAP!!!
-343x , x = -2
g(x) { (x-1)(x+2) , x = -1
x^3 - x^2 + 1 , x is not equal to -2, -1
What is g(1) ???
Answer: g(1) is 1.
Step-by-step explanation:
If we are solving for g of 1 then the first equation can't be used to solve for g of 1 because it only works in x is equal to -2.
The same way the second function will not work because x has to equal to -1.
But in the last function which is written as a polynomial it will work for this situation because x is not equal to -2 or -1 so apart from those numbers every number will work the same way 1 will work.
So plot 1 into the function and solve for it .
g(1) = 1^3 - 1^2 + 1
g(1)= 1 - 1 + 1
g(1)= 1
Liam tried to define a translation. - Point A maps to point A' - Every point P maps to point P' such that PP' is parallel to AA' and points in the same direction as AA' Which counterexample shows that Liam's definition does not fully define a translation?
Answer:
B
Step-by-step explanation:
This is the correct answer.
From The diagrams shown here, the option that does not fully define a translation is B.
What is a translation in mathematics?
In mathematics, this is another word for a transformation. What the translation does is that it helps to move a shape in different ways without altering the appearance of the shape.
The translation in this question is option B given the definition that we have above.
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Triangle ABC is dilated to form new triangle DEF. If angle A is congruent to angle D, what other information will prove that the two triangles are similar by the AA similarity postulate?
Angle B is congruent to angle E.
Side AB is congruent to side DE.
Angle C is congruent to angle D.
Side BC is congruent to side EF.
Answer:
Step-by-step explanation:
option A , angle B is congruent to angle E { SINCE IT IS AA POSTULATE
Answer:
B=E (b)
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLY!!!!!!!!!!!!!!!!!!!!!Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)?
f(x) = −6(x + 1)(x + 5)
f(x) = −6(x − 1)(x − 5)
f(x) = −5(x + 1)(x + 5)
f(x) = −5(x − 1)(x − 5)
Answer:
f(x) = −6(x + 1)(x + 5)
Step-by-step explanation:
f(x) = −6(x + 1)(x + 5) & f(x) = −5(x + 1)(x + 5) are the only ones on the correct side of the y-axis, and f(x) = −6(x + 1)(x + 5) has a y-intercept of -30.
(5.3.4 journal: describing distributions) Looking at the box plots, do you agree or disagree with each team's conjecture? Explain your reasoning(3 points: 1 point for each row of the chart)
Factor this expression.
3x2 - 6x
Answer:
3x(x - 2)
Step-by-step explanation:
Both terms have a GCF (greatest common factor) of 3x so factoring that out, we get 3x(x - 2).
Answer:
3x ( x - 2 )
Step-by-step explanation:
First we hv to find wat is common in both of them.....
As we can see " 3x " is common in both of them
so....
If we take 3x from both the terms.... It will become....
3x square = 3x ( x )
-6x - 3x ( -2 )
Therefore the expression will become....
3 x square - 6x
= 3x ( x - 2 )
Hope this helps...
HAVE A GOOD DAY !!! ( no the biscuit ) (lol)
Pls mark my ans as brainliest If u mark my ans as brainliest u will get 3 extra points1% social security tax is charged up to the annual income of Rs 3,50,000 to an unmarried individual. If the monthly salary of an individual is Rs 16,400, how much social security tax should he pay in a year?
Answer:
Rs. 1968
Step-by-step explanation:
Tax rate = 1%
Monthly income of the person = rs. 16400
Now,
Yearly income of individual = rs. 16400×12=rs196800
Tax = tax rate × yearly income
= 1% × rs. 196800
= Rs.1968
Was the question this simple
Or I misunderstood the question :-(
Plot the function
y = (x + 1)(x - 3) by following these steps:
4
Step 1: Plot the x-intercepts of the function.
Answer:
Zoom it to see well
Step-by-step explanation:
The equation of the parabola is y = (x - 1)² - 4. Then the vertex of the parabola is at (1, -4) and the parabola passes through (0, -1) and (0, 3).
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The equation is given below.
y = (x + 1)(x - 3)
We know that the equation is a parabolic equation.
And the value of y at -1 and 3 is zero.
The equation can be written as
y = x² - 2x -3
y = (x - 1)² - 4
And the vertex of the parabola is at (1, -4).
The graph is shown below.
More about the parabola link is given below.
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In the following diagram CDFG ~ HJLK. use this information to find the value x.
Answer:
x=2.25
Step-by-step explanation:
4x=3 x 3
Me need big brain to answer this question c:
Answer:
[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]
Step-by-step explanation:
Let x be the amount of dough required for small pizza, y be the amount of dough required for medium pizza and z be the amount of dough required for large pizza.
As per the question , we have
[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]
Hence, the equation for the question with the variable representing the amount of dough needed for small pizza.
[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]
What is the volume of the following rectangular prism?
===================================================
Explanation:
Convert the mixed number 3 & 2/3 to an improper fraction
3 & 2/3 = 3 + 2/3
3 & 2/3 = 9/3 + 2/3
3 & 2/3 = (9+2)/3
3 & 2/3 = 11/3
The prism has a base area of 9 square units and a height of 11/3 units.
Multiply the base area by the height to get the volume
volume = (base area)*(height)
volume = (9)*(11/3)
volume = 99/3
volume = 33 cubic units
------------
You could choose to not convert to an improper fraction, and your steps may look like this
volume = (base area)*(height)
volume = (9)*(3 + 2/3)
volume = 9*3 + 9*(2/3) .... distribute
volume = 27 + 18/3
volume = 27 + 6
volume = 33 cubic units
Either way we get the same volume.
If $a+b = 8$, $b+c = -3$, and $a+c = -5$, what is the value of the product $abc$?
Answer:
a=3
b=5
c=-8
3+5+-8=0
Step-by-step explanation:
3+5=8
5+-8=-3
3+-8=-5
i think thia is correct you can double check
f(x) = [tex]\sqrt{x+7} -\sqrt{x^2+2x-15}[/tex] find the domain
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = [tex]\sqrt{x+7}-\sqrt{x^2+2x-15}[/tex] .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
Write a equation representing the area Bruce covered, y, in terms of the number of tiles he used,x.
A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation
According to the question
The area Bruce covered shows by y axis
The number of tiles he used is x axis .
The tiles Bruce used is 1/4 of a square foot in area .
Therefore,
Area of tiles in square foot = 4 number of titles
= 4x
now,
Equation will be :
y = 4x
Hence, A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x
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kristen and melissa spent 35% of their $32 on movie tickets. how much money did they spend
Answer:
11.2$
Step-by-step explanation:
Kristina and Melissa had 32$ at total
● 32$ => 100%
They have spent 35%
Let x be that amount
● x => 35%
●32 => 100
● x => 35
● x = (35×32)/100 = 11.2$
They have spent 11.2$
Answer:
They spent $20.80
Step-by-step explanation:
Since they had $32 and spent 35% of it you would do 32 * 35%
then you would get 11.2
now that is not the answer because that is just what 35% of 32 is
to get the answer you would then subtract 11.2 from 32 to get 20.8
and since this is a matter of money you would write 20.8 as $20.80.
WILL GIVE BRAINLY!!!!PLEASE HELP!!!!
What are the domain and range of f(x) = 4x – 8?
domain: {x | x is a real number}; range: {y | y > –8}
domain: {x | x is a real number}; range: {y | y > 8}
domain: {x | x > 4}; range: {y | y > –8}
domain: {x | x > –4}; range: {y | y > 8}
Answer:
None of the above
Step-by-step explanation:
A graph of the function f(x) = 4x- 8 is straight line passing through (0,-8) on y axis and (2,0) on x axis.
Thus, we observe that both Domain and Range belongs R (real no.), but none of above options states that.
Given: m || n and p is a transversal
Prove: mAngle2 = mAngle7
Horizontal and parallel lines m and n are cut by transversal p. On line m where it intersects line p, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line n where it intersects line p, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.
What is the missing reason in the proof?
Statement Reason
1. m || n and p is a transversal 1. given
2. ∠2 ≅ ∠3 2. ver. ∠s theorem
3. m∠2 = m∠3 3. def. of congruent
4. ∠3 ≅ ∠7 4. corr. ∠s theorem
5. m∠3 = m∠7 5. def. of congruent
6. m∠2 = m∠7 6. ?
corresponding angles theorem
alternate interior angles theorem
transitive property
subtraction property
Answer:
∠2 ≅ ∠6
Step-by-step explanation:
Select the correct answer. The edges of a cube are 5 centimeters each and the diagonal of a face is approximately 7 centimeters. What is the approximate area of the cross section passing through the diagonals of opposite faces of this cube? A. 12 square centimeters B. 25 square centimeters C. 35 square centimeters D. 49 square centimeters Reset Next
C : 35
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Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15
Answer:
-6723cw
Step by Step:
(-3c * 3w * 5) * 3 - 9c * 6w* 8 - 9c * 9w * 15 - 27c * 6w * 8 - 27c * 9w * 15
DONT ANSWER!! am i right? 20 points!
Answer:
yes
Step-by-step explanation:
Step-by-step explanation:
Hi, there!!!
It's so simple,
so, let's simply work with it;
Here, the given equation is;
4d-4 = 5d-8
so, let's take "4d" to right side and -8 to left side. we get,
-4+8 = 5d-4d
or, 4 = d
Therefore, the value of d is 4.
{here, we simply simplified to get answer}
YOU ARE ABSOLUTELY RIGHT...
Hope it helps....
Write an algebraic expression for the pair of numbers such that one is 33% more than the other one
Answer:
x = 1.33y
Step-by-step explanation:
33% is equal to 0.33. If a number x is 33% more than a number y, then x is 133% of y. 133% = 1.33
hello can plzz help me with this question wil mark u brainlest and its for 18 points the file is down below thank u :)
Answer:
a rectangular prism
Step-by-step explanation:
consists of 6 faces which are rectangles
A rectangular prism has a volume of 285.6. cubic feet. The prism is 12 feet long and 3.4 feet wide. What is the height of the prism? A. 7 ft B. 15 ft C. 19 ft D. 22 ft Please include all work!!
Answer:
A. 7 ft
Step-by-step explanation:
Volume is Length * Width * Height
12 * 3.4 * Height = 285.6
285.6 / 12 = 23.8
23.8 / 3.4 = 7
PLEASE HELP ME WITHT HIS QUESTION I NEED IT FOR HOMEWORK!!!!!
Answer: the answers are both A and B
Step-by-step explanation:
square root of 64 is 8 and the square root is 225 is 15. It can be both positive and negative
The function f is defined by f(x) = (x + 3)(x + 1).
The graph of f in the xy-plane is a parabola. Which
of the following intervals contains the x-coordinate
of the vertex of the graph of f?
Answer:
Below in bold.
Step-by-step explanation:
The zeroes ( = x-intercepts) are x = -3 and x = -1.
So the x -coordinate of the vertex is between x = -3 and x = -1.
The actual x-coordinate is halfway between these value: at x = -2.
Answer:
x = -3 or x = -1
Step-by-step explanation:
f(x) = (x + 3)(x + 1)
⇒ x = -3 or x = -1
Can someone solve -5x +2y=10
Answer:
[tex]x=\frac{2}{5}y-2[/tex]
Step-by-step explanation:
[tex]-5x+2y=10\\-5x+2y-2y=10-2y\\-5x=2y-10\\\frac{-5x}{-5}=\frac{2y-10}{5}\\ x=\frac{2}{5}y-2[/tex]
Solve the equation using the multiplication property of equality and the reciprocal of
1
4
.
1
4
( r −
5
2
) =
1
8
A farmer is packing eggs. Each box holds six eggs. The farmer has 860 eggs to pack. I. How many boxes can the farmer fill? 2. How many eggs will be leftover?
Answer:
1. boxes filled= 860/ 6
=143.3
= 143 boxes will be filled.
2. leftover eggs = 2
Step-by-step explanation:
Answer:
1. 143 2. 3
Step-by-step explanation:
860 divided by 6 is 143.3, so the .3 will be 3 leftover eggs
Name five fractions whose values are between 1/8 and 1/5
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The fraction numbers are given below.
1/8 and 1/5
Convert the fraction number into decimal numbers. Then we have
0.125 and 0.20
The five fractions whose values are between 1/8 and 1/5 will be given as,
0.13, 0.14, 0.15, 0.16, 0.18
13/100, 14/100, 15/100, 16/100, 18/100
13/100, 7/50, 3/20, 4/25, 9/50
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
More about the number line link is given below.
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