What are the vertex and x-intercepts of the graph of y= x2 - 6x - 7?Select
one answer for the vertex and one for the x-intercepts.
A. x-intercepts: (1,0), (7,0)
B. Vertex: (3,-16)
C.Vertex: (-3,20)
D. Vertex: (3, 20)
E. x-intercepts: (-1,0). (7.0)
F. x-intercepts: (1.0), (-7,0)

Answers

Answer 1
The answer is B and E
Answer 2

The vertex and [tex]x-[/tex]intercepts of the graph of [tex]y= x^2 - 6x - 7[/tex] will be  [tex](3,-16)[/tex] and [tex](7,-1)[/tex], respectively.

What are vertex and  [tex]x-[/tex]intercepts of the graph?

A vertex in a quadratic equation is the minimum or maximum point of the equation and  an [tex]x-[/tex]intercept of a graph is the point at which the graph intersects the [tex]x-[/tex]axis.

Vertex form, [tex]y=a(x-h)^2+k[/tex]

We have,

[tex]y= x^2 - 6x - 7[/tex]

Now,

Find the [tex]x-[/tex]intercept  and to find [tex]x-[/tex]intercept put [tex]y=0[/tex] ;

i.e. [tex]y= x^2 - 6x - 7[/tex]

[tex]0= x^2 - 6x - 7[/tex]

[tex]x^2 - 6x - 7=0[/tex]

Now using Mid-term split method find value of [tex]x[/tex];

[tex]x^2 - 7x+1x - 7=0[/tex]

[tex]x(x - 7)+1(x - 7)=0[/tex]

[tex](x - 7)(x +1)=0[/tex]

[tex](x - 7)=0[/tex]⇒[tex]x=7[/tex]

[tex](x +1)=0[/tex]⇒[tex]x=-1[/tex]

So, these are the [tex]x-[/tex]intercept [tex](7,-1)[/tex] of the expression.

Now find the vertex using the above given formula;

[tex]y=a(x-h)^2+k[/tex]

Rewrite in vertex form

[tex]y= x^2 - 6x - 7[/tex]

Add and subtract [tex](-3)^2[/tex] in given expression;

[tex]y= x^2 - 6x + (-3)^2 -7 - (-3)^2[/tex]

[tex]y = x^2 - 6x + 9 -7 - 9[/tex]

[tex]y = x^2 - 6x + 9 -16[/tex]

Now convert quadratic part of equation in [tex](a-b)^2[/tex];

[tex]y = (x-3)^2-16[/tex]

Now compare it with [tex]y=a(x-h)^2+k[/tex]

We get,  [tex]h=3,\ k=-16[/tex]

So, these are the vertex [tex](3,-16)[/tex] of expression.

Hence, we can say that the vertex and [tex]x-[/tex]intercepts of the graph of [tex]y= x^2 - 6x - 7[/tex] will be  [tex](3,-16)[/tex] and [tex](7,-1)[/tex], respectively.

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Related Questions

60 POINTS!!!!!!!!!!!!!! yes really 60 POINTS Please Help

The number of wins for a high school football team is measured for the season. When the team plays at home, it is generally believed that they will win. Compa
the location of the game and the number of wins, a correlation coefficient of 0.891 is calculated. What would this imply about the football team winning at home
The scatter plot would closely resemble a straight line with a positive slope. The data has a strong, positive correlation, but causation cannot be
determined
The scatter plot would closely resemble a straight line with a positive slope. The data has a strong positive correlation, and a causal relationship exists
between the team playing at home and winning.
The scatter plot would not be represented by a line of best fit with a positive slope. There is a weak correlation between the football team playing at home
and winning
There is no causation and almost no correlation between the football team playing at home and winning

Answers

Answer:

The scatter plot would closely resemble a straight line with a positive slope. The data has a strong positive correlation, and a causal relationship exists

No the answer is:

There is no causation and almost no correlation between the football team playing at home and winning.

Which equation is not a linear function?

Answers

Answer:

the second answer Is the right one

solve the volume formula V = lwh for w

Answers

Answer:

v/lh = w

Step-by-step explanation:

Divide Both Sides by the length and height to isolate width.

David's monthly house payment is $468 21.
If his annual real estate tax is $1,231 and his annual insurance is $1,087, what is his total
payment to the lender each month?
Round each answer to the nearest dollar before adding

Answers

assuming his house payment is $468.21

you just add them all together

468.21+1231+1087= $2786.21

then rounded to the nearest dollar
$2786

Hence total payment for expenses is $46281

What is Total payment?

Payments refers to outstanding amount to be paid for the liable items. We can also say that banknotes and coins (cash), as well as deposits and credit on an account with a financial institution or a similar entity that can be run using payment instruments, are all examples of means of payment.

How to  solve?

annual real estate tax = $1,231

annual insurance         = $1,087

David' monthly house payments=$46821

To calculate total payments we will now add all the payments.

Hence total payments=$49,139

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Jose is mailing a package shaped like the rectangular prism shown in the figure. Use a net to find the surface area of the package ​

Answers

Answer:

222cm

Step-by-step explanation:

8*7.5*2=120

3.4*7.5*4=102

222cm

3 times the sum of k and d
A 3(k + d)
B 3 + k +d
C 3k + d
D 3kd​

Answers

It’s c zzzzzjzjdjdjdbbebbebbebsbsbbsbshhsh
The answer is C. Hope it helps

ignore the circled one and actually try please​

Answers

Answer:

A

Step-by-step explanation:

= 2x5−8x4 /(6x3+30x2)

=  2x3−8x2 /(6x+30 )

= x3−4x2 /(3x+15)

Answer:

a.[tex] \frac{x^3-4x^2}{3x+15}[/tex]

Step-by-step explanation:

[tex]\huge{ \frac{2x^4}{x+5} \div \frac{6x^2}{x-4} }\\\\\huge{= \frac{2x^4}{x+5} \times \frac{x-4}{6x^2}}\\\\\huge{ =\frac{x^2}{x+5} \times \frac{x-4}{3}}\\\\\huge {=\frac{x^2(x-4)}{3(x+5)}}\\\\\huge{=\frac{x^3-4x^2}{3x+15}}[/tex]

10(x+6)=40 need answer

Answers

Answer:

x = -2

Step-by-step explanation:

10(x+6)=40

Divide each side by 10

10/10 (x+6)=40/10

x+6 = 4

Subtract 6 from each side

x+6-6 = 4-6

x = -2

Help me please I keep getting it wrong.

Answers

Answer:

Whats the problem?

Step-by-step explanation:

The graph shows the midday temperature in Cambridge over the summer.
a)What is the range of the temperatures?
b)is the trend downward or upward?

Answers

Answer:

a) 6°C

b) upward

Step-by-step explanation:

a) The range of temperatures is the difference between the maximum and the minimum temperatures. From the graph we can see that:

maximum temperature: 18 °C

minimum temperature: 12 °C

Then:

range of temperatures: 18-12 = 6°C

b) The trend is upward because, given any temperature, the next one is higher.

Answer:

Step-by-step explanation:

a) range is 6.

b) trend is upward.

Does anyone have the answers for this please help

Answers

Answer is 7,20 and 104 for the first question

Answer:

1. 7, 20, and 104

2. 42, 16, and 1

3. 64, 180 and 10

4. 12, 4.5, and 0

5. 26, 56, 2, and 6.5

6. 19, 31, 75, and 52.6

7. 18, 28, 15, and 30

8. 26, 50, 145, and 401

Step-by-step explanation:

hope this helps


Question 1
Here is the base of a prism.


a. If the height of the prism is 5 cm, what is its surface area? What is its volume?



b. If the height of the prism is 10 cm, what is its surface area? What is its volume?


c. When the height doubled, what was the percent increase for the surface area? For the volume?


Answers

Answer:

a ) Surface Area ⇒ 222 cm^2, Volume ⇒ 180 cm^3

b ) Surface Area ⇒ 372 cm^2, Volume ⇒ 360 cm^3

c ) Surface Area Increase ⇒ ( About ) 67.56 %, Volume Increase ⇒ 100 %

Step-by-step explanation:

a ) Consider dividing the figure into parts, first solving for the area of the base, using the attachment below for guidance;

As you can see, in the picture I have made it so that the base is nested in a rectangle with dimensions 8 by 5. Calculating the area of this rectangle, subtracting the area of a square with dimensions 2 by 2 cm, we can derive the area of the base in a much quicker manner;

[tex]Area of Base - ( 8 cm * 5 cm ) - ( 2 cm* 2 cm ) = 40 square cm - 4 square cm = \\Solution; Base = 36 square cm[/tex]

Now let us imagine adding the another dimensions to this two dimensional base. That would make a 3 - d prism, with surface area equivalent to mini rectangles and squares with a common dimension being the length of the height; 5 cm

[tex]Area of 1 Square = 5 cm * 5 cm = 25 square cm,\\Area of 2 Square = 25 square cm,\\Area of 1 Rectangle = 3 cm * 5 cm = 15 square cm,\\Area of 2 Rectangle = 15 square cm,\\Area of 3 Rectangle = 2 cm * 5 cm = 10 square cm,\\Area of 4 Rectangle = 10 square cm,\\Area of 5 Rectangle = 10 square cm,\\Area of 6 Rectangle = 8 cm * 5 cm = 40 square cm\\Area of Base 2 = 36 square cm,\\\\Surface Area of Figure = 25 + 25 + 15 + 15 + 10 + 10 + 10 + 40 + 36 + 36 = 222 square cm\\Volume = 36 square cm * 5 cm = 180cubiccm[/tex]

b ) We have calculated the area of the base before, now let us solve for all the " mini shapes " given a new height of 10 cm;

[tex]Area of Rectangle 1 = 5 cm * 10 cm = 50 cm^2,\\Area of Rectangle 2 = 50 cm^2,\\Area of Rectangle 3 = 3 cm* 10 cm = 30 cm^2,\\Area of Rectangle 4 = 30 cm^2,\\Area of Rectangle 5 = 2 cm * 10 cm = 20 cm^2,\\Area of Rectangle 6 = 20 cm^2,\\Area of Rectangle 7 = 20 cm^2,\\Area of Rectangle 8 = 8 cm * 10 cm = 80 cm^2,\\\\Surface Area of Figure = 50 + 50 + 30 + 30 + 20 + 20 + 20 + 80 + 36 + 36 = 372 cm^2\\Volume of Figure = 36 cm^2 * 10 cm = 360 cubic cm[/tex]

c ) Solution; Increase of Surface Area ⇒ ( About ) 67.56 %, Increase of Volume ⇒ 100 %

Can somebody help me with this problem please.

Answers

The answer Is Description

WILL GIVE BRAINLIST AND THANKS IF CORRECT

Solve this equation:

3(x+2)+2x=21

Answers

Answer:

x=3

Step-by-step explanation:

First distribute the 3!

3x+6+2x=21

Then, combine like terms.

5x+6=21

Move the 6 to the other side

5x=15

Divide each side by 5

x=3

The answer is 3.
Check the steps
⬇️

HELP PLEASE!! ASAP!!

Answers

Answer:

The estimated distance is 8.1cm.

The actual distance is 8.106cm.

Step-by-step explanation:

Given that the Pythogorean Theorem, c² = a² + b². Then substitute the following values into the formula :

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

Let a = 5.1cm,

Let b = 6.3cm,

[tex] {c}^{2} = {5.1}^{2} + {6.3}^{2} [/tex]

[tex] {c}^{2} = 26.01 + 39.69[/tex]

[tex] {c}^{2} = 65.7[/tex]

[tex]c = \sqrt{65.7} [/tex]

[tex]c = 8.106cm \: (3d.p)[/tex]

help !!!!!!!!!! i need somebody to answer this

Answers

Answer:

B

Step-by-step explanation:

because it says between 4 and 8 and doesn't have a negative so its positive

B it is constant

This is because the graph during that part has no fluctuations.

What are the potential solutions of In(x? - 25) - 0?
O x-+ 13
X-V28
O x-=10

Answers

Answer:

V 8 on 8 D

Step-by-step explanation

On Orbitz, you found a flight for $345.00 to Miami. Whoooo! As you are about to check it out, Orbitz offers you a promotion. “ Get 20% off“ What is the discount that you will be saving, if tickets are needed for you, one of your parents, and two friends?

Answers

Answer:

276$ off

Step-by-step explanation:

345*4 = 1380

ans*.2 = 276

Find the measure of the arc.
А)
146°E
B
MACB = [? ]°

Answers

Answer:

214°

Step-by-step explanation:

The measure of an arc that sees the center angle of the circle is equal to the very same angle that it sees

Since the measure of circle is 360° and arc AB is given as 146° the measure of arc ACB should be 360 - 146 = 214°

The measure of arc ACB from the given circle is 214 degree.

What is the relationship between a central angle and its arc?

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Given that, ∠AOB=146° (Minor sector)

So,  ∠AOB=360°-146°=204°

The measure of an arc that sees the center angle of the circle is equal to the very same angle that it sees

Since the measure of circle is 360° and arc AB is given as 146° the measure of arc ACB is 214°.

Therefore, the measure of arc ACB from the given circle is 214 degree.

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please help as soon as possible
I WILL MARK YOU AS BRAINLIEST ​

Answers

Answer:

Both coordinates are negative

Answer:

The x-coordinate is negative, and the  y-coordinate is negative.

Step-by-step explanation:

It's a bite hard to explain it without a xy-plane. I don't want to upload it, so I will try to draw it:

            [tex]\left[\begin{array}{ccc}a&|&b\\-&-&>\\c&|&d\end{array}\right][/tex]

We have point [tex]a[/tex] in the coordinates [tex](-x, y)[/tex]

We have point [tex]b[/tex] in the coordinates [tex](x, y)[/tex]    

We have point [tex]c[/tex] in the coordinates [tex](-x, -y)[/tex]        

We have point [tex]d[/tex] in the coordinates [tex](x, -y)[/tex]

A point with a positive x-coordinate and a negative y-coordinate is reflected over the y-axis.

This point is [tex]d[/tex]. Once it is reflected over the y-axis, it turns to be point [tex]c[/tex].

What is the area of the two triangles and the quadrilateral

Answers

Answer:

Hope this is correct

Using the image below, solve for . Make sure to double check your work at the end.

Answers

Step-by-step explanation:

They are Alternate angles so they need to be equal to each other meaning you can right them like this;

[tex]4x + 2 = 86[/tex]

So to work out x you just have to separate x;

[tex]4x = 86 - 2 \\ 4x = 84 \\ x = \frac{84}{4} [/tex]

So

[tex]x = 21[/tex]

Alisha wants to buy some Ripples (XRP). One Ripple is worth 0.331 American dollars. How many Ripples can she buy with $20.00? Enter your answer as a whole number, such as 23.

Answers

Answer:

Your answer would be 60 Ripples.

Step-by-step explanation:

$20.00 / 0.331 = 60.42296072507553.

                            Hope this helped! Have a great day!

Answer:

60

Step-by-step explanation:

20/0.331

=20×1000/o.331×1000

=20000/331

=60.422

Select the three correct ways to describe an angle with a measure of 13°

Answers

Answer:

its not the top right one

Step-by-step explanation:

the other three are right

The three correct ways to describe an angle with a measure of 13° are  it turns through 13 one degree angles. It turns through 13/360  of a circle and It is the same size as 13 one degree angles.

What is Angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

We have been given an angle with a measure of 13°

Acute: An angle with a measure less than 90° is considered acute. 13° is an acute angle.

Straight: An angle with a measure of exactly 180° is considered straight. 13° is not a straight angle.

Obtuse: An angle with a measure greater than 90° and less than 180° is considered obtuse. 13° is not an obtuse angle.

13° measure means it turns through 13 one degree angles.

It turns through 13/360  of a circle

It is the same size as 13 one degree angles.

Hence, the three correct ways to describe an angle with a measure of 13° are  it turns through 13 one degree angles. It turns through 13/360  of a circle and It is the same size as 13 one degree angles.

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Jake can read 45 pages of a book in 9 minutes. Kayleigh can read 60 pages of a book in 10 minutes. Which person reads at a faster rate per minute? A. Jake because he read at a rate of 5 pages per minute. B. Kayleigh because she read at a rate of 6 pages per minute. C. Jake because he read at a rate of 15 page per minute. D. Kayleigh because she read at a rate of 16 page per minute

Answers

Answer:

B. Kayleigh because she reads at a rate of 6 pages per minute.

Step-by-step explanation:

To find the amount of pages both people read in a minute, we can simply divide:

Jake- 45/9 = 5 pages a minute

Kayleigh- 60/10 = 6 pages a minute

Therefore, Kayleigh reads more pages a minute because 6 > 5.

jane earns £1800 every month. She pays 40% of the £1800 in the rent and 1/3 of the £1800 on food

Work out how much of the £1800 jane has left.

Answers

Answer:

£480

Step-by-step explanation:

40 percent of 1800 is 720, and 1/3 of 1800 is 600, 720+600=1320, 1800-1320=480.

Roughly £480 hope that helps

Find the equation of the line below. If necessary, use a slash (/) to indicate a
division bar.

Answers

Y=7X is the linear equation. There’s no y intercept and the slope is 7/1 which equals 7.

\frac{(2_1-4_{2}) ^{4} } {2}
Quick I need help

Answers

Answer:

what is /frac part supposed to be??

Step-by-step explanation:

which expression is equivalent to -28x^2+35x ? F. 7x(4x+5) G.-7x(4x-5) H.7x(4x-5) J.-7x(4x+5) please explain w the steps

Answers

Hey!!

Solution,

-28x^2+35x

take the common,

-7x(4x-5)

The answer is -7x(4x-5)

Here,

If we solve,

-7x(4x-5)

Then, the answer would be:

= -7x*4x+7x*5

= -28x^2+35x

Hope it helps

Good luck on your assignment

Answer:

G

Step-by-step explanation:

-28x² + 35x = -7 * 4 * x² + (-7)*(-5)*x

                  = -7x(4x - 5)

Answer for 100 points! If you answer as a joke or dont even answer at all, I will report your answer, your points will be removed, and you wont have brainliest. Remember moderators are ALWAYS around.

Answers

Answer:

Edited: heads and tails

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

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