Please help me with my algebra.

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.

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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Answer:

a^2 + 15^2 = 17^2

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 + b^2 =c^2

where a and b are the legs and c is the hypotenuse

a^2 + 15^2 = 17^2

Answer:

Answer is A

Step-by-step explanation:

its what the guy above me is saying

Answer:

Option D.

The discriminat is equal to 24 which

Step-by-step explanation:

The quadratic equation is

-2x² + 3 = 0

Discriminat in quadratic equation tells us the number of solution a quadratic equation has.

For example, the quadratic equation

Ax² + bx + c = 0 will have a discriminat of b² - 4ac.

b² - 4ac is equal to the value of the discriminat and equal to the number of solutions the quadratic equation has.

In our question, we have -2x² + 3 = 0

A = -2

B = 0

C = 3

b² - 4ac = 0

Substitute the values into the above equation.

0² - 4(-2 ×3) = 0

0 + -4 × -6 = 0

24 = 0

The discriminat of the equation is 24

Answer

A.) 2

Step-by-step explanation:

Edge 2021

Answer:

60

Step-by-step explanation:

→Before you use the formula to find the area of the isosceles triangle, you must find the height, and to do this, you can use the Pythagorean Theorem:

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

→We are given the hypotenuse, "c," as 13, and the leg is 5 (we split the base of 10 in half).

[tex]5^2+b^2=13^2[/tex]

[tex]25+b^2=169[/tex]

→Subtract 25 from both sides:

[tex]b^2=144[/tex]

→To get "b," by itself, take the square root of both sides:

[tex]\sqrt{b^2} =\sqrt{144}[/tex]

[tex]b = 12[/tex]

→Formula for area:

A = [tex]\frac{bh}{2}[/tex]

A = [tex]\frac{(10)(12)}{2}[/tex]

A = 60

The area of the isosceles triangle is 60 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

The area is calculated by having the height of the triangle and the base of the triangle.

The height is calculated by using the Pythagorean theorem.

H² = P² + B²

13² = P² + 5²

P² = 169 - 25 = 144

P = √144 = 12 units

The perpendicular is the height of the triangle.

The area is calculated as:-

A = ( 1 / 2 ) x B x H

A = ( 1 / 2 ) x 10 x 12

A = 60 square units.

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Answer:

Step-by-step explanation:

Answer:

The answer is simple the slope is in the drop box

Step-by-step explanation:

Answer:

w: 56

b: 40

r: 64

Step-by-step explanation:

A pair of pom-poms need: 80 × 2 = 160 (strands)

To make a pair of pom-poms:

w: 160 × 35% = 56 (strands)

b:  160 × 25% = 40 (strands)

r:   160 × 40% = 64 (strands)

28 white, 20 blue and 32 red strands are needed to make a pair of pom-poms.

Percentage is defined as ratio expressed as a fraction of 100.

Given that, total Strands = 80

∵white strands = 35%

w =  35%×80 =

w= 35/100×80

w =  28

∵blue strands = 25%

b =  25%× 80

b =  25/100× 80

b = 20

∵red strands = 40%

r = 40%× 80

r = 40/100× 80

r = 32

Thus, 28 white, 20 blue and 32 red strands are needed to make a pair of pom-poms.

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Hope it helps

Good luck on your assignment

Stay safe

Answer:

7x^2-20x

Step-by-step explanation:

6x(x-3)-x(2-x)

6x^2 - 18x -2x + x^2

7x^2-20x

Answer:

correct choice is option d  [tex]v=2/9*s^3[/tex]

Step-by-step explanation:

volume of pyramid is given by 1/3(Area of base* height)

Given base of pyramid is square with length of each side s

area of square is given by [tex]side^2[/tex]

Thus, area of base of pyramid = [tex]s^2[/tex]

Height of pyramid = 2/3  of  side of base of pyramid = 2/3* s = 2s/3

Therefore volume of pyramid = 1/3(area of base of pyramid *Height of pyramid)

                                            = [tex]1/3(s^2*2s/3)[/tex]

                                             = [tex]2/9*s^3[/tex]

Thus, correct choice is option d [tex]v=2/9*s^3[/tex]

Answer:

Option D

Step-by-step explanation:

[tex]v=\frac{2}{9} s^{3}[/tex]

Answer:

4. No

5. No

6. No

7. No

8. No

9a. 2 : 3 = 8 : 12 Extremes: 2, 12. Means: 3, 8

9b. 90 : 36 = 135 : 54 Extremes: 90, 54. Means: 36, 135

Step-by-step explanation:

4. 12 : 25 and 6 : 13 are NOT equal. NO.

5. 64 : 120 = 8 : 15 and 60 : 100 = 3 : 5. NOT equal. NO

6. 37 : 115 and 296 : 966 =  148 : 483. NOT equal. NO

7. 300 : 200 = 3 : 2 and 6 : 5 are NOT equal. NO.

8. 8 : 10 = 4 : 5 and 11 : 14 are NOT equal. NO.

9a. 2 : 3 = 8 : 12 Extremes: 2, 12. Means: 3, 8

9b. 90 : 36 = 135 : 54 Extremes: 90, 54. Means: 36, 1135

Answer:

The range of the Morning box plot is the same as the range of the Afternoon box plot.

Step-by-step explanation:

Data provided in the question

Number line = 0 to 16

Morning whiskers range = 3 to 15

Box range = 5 to 12

Line divided = 8

Afternoon whiskers range = 4 to 16

Box range = 8 to 15

Line divided = 14

Based on the above information,

The morning whiskers range difference is

= 12 - 5

= 7

And, the afternoon whiskers range difference is

= 15 - 8

= 7

Therefore the first option is correct

Answer: A. The range of the Morning box plot is the same as the range of the Afternoon box plot.

Answer:

B

Step-by-step explanation:

Answer:

pi pi pi pi

Step-by-step explanation:

The arc length covered by the central angle equal to 72° is 12.56°

Arc length is the distance between two points along a section of a curve.

Given that, a circle with radius 10 units and a central angle equals 72°, we need to find the arc length covered by the central angle = 72°

We know that,

Arc length = 2π × radius × (θ / 360°), where θ is the central angle

Arc length = 2 × 3.14 × 10 × 72°/360°

= 12.56°

Hence, the arc length covered by the central angle equal 72° is 12.56°

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The complete question is attached

Answer:

a^9b^5x^2

I think that is right

Question:

[tex]a^{4}*b^{3}*(a^{5}*b^{2}[/tex][tex])[/tex]

Answer:

[tex]a^{9}b^{5}[/tex]

Step-by-step explanation:

remove brackets:

[tex]a^{4}b^{3}a^{5}b^{2}[/tex]

Simplify:

[tex]a^{9}b^{5}[/tex]

Answer:

 y = 4

Step-by-step explanation:

The two given points both have the same y-value, so the line through them is a horizontal line. None of the answer choices is correct for the points given here.

Answer:

D

Step-by-step explanation:

2^2 + x^2 = 4^2

4 + x^2 = 16

16-4=12

Area of rectangle ABCD is, 32 units²

And, Perimeter of rectangle is, 24 units

We have to given that,

A rectangle ABCD is shown in image.

And, Coordinates are,

A = (- 5, 5)

B = (- 1, 5)

C = (- 5, - 3)

D = (- 1, - 3)

Now, We can use the distance formula for finding the length and width of rectangle.

Lenght (AC) = √(- 5 + 5)² + (5 + 3)²

AC = √8²

AC = 8

Width (AB) = √(- 5 + 1)² + (5 - 5)²

AB = √16

AB = 4

Therefore, Area of rectangle ABCD is,

Area = Length × Width

Area = 8 × 4 = 32 units²

Perimeter of rectangle is,

P = 2 (Length + Width)

P = 2 (8 + 4)

P = 2 × 12

P = 24 Units

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Answer:

Step-by-step explanation:

Let the sequence as :

[tex]T_1, T_2, T_3, 17, T_5, T_6,......T_{13}[/tex]

I put 17 there as [tex]T_4[/tex] because I want 3 consecutive elements. Let A is the sum of them.

[tex]T_1+T_2+T_3 = A[/tex]

   17

[tex]T_5+T_6+T_7 = A[/tex]

[tex]T_8+T_9+T_{10} = A[/tex]

[tex]T_{11}+T_{12}+T_{13}=A[/tex]

[tex]\sum T_i + 17 = 217 = 4A + 17[/tex]

Hence A = 50

Then, back to the condition

[tex]T_4+ T_5 + T_6 = A = 50[/tex]

[tex]T_5+T_6+T_7 = A = 50[/tex]

Subtract them, we get

[tex]T_4 - T_7 = 0[/tex]

That gives you

[tex]T_4 = T_7 = 17[/tex]

Do the same with other groups.

Answer:

For the second shape the answer is x=6 degrees

Step-by-step explanation:

180 degrees is the total supplementary angle. 180-148=12. Then you divide 12 by 2 to get 6 because there is to sides of the angles.

Answer:

Step-by-step explanation:

all i know is how to get the original answer not the verified sorry

Answer:

#6- you can verify this way by plugging the value you got for x or y back into the equation. If it works, then the equation will be true.

By graphing- The solution on the graph is where the 2 lines will intersect. Find the coordinates of the intersection point and see if your answer has the same x and y values, if so, it is correct.

Answer:

  On a coordinate plane, points (1, negative 2) and (2, negative 4) are plotted

Step-by-step explanation:

In the choice shown above, y/x has the same ratio for both points. That is the hallmark of a proportional relationship.

Answer:

A

Step-by-step explanation:

Answer

x= 60

Step-by-step explanation:

100/25= 4

25*4 =100

15*4 = x

x= 60

Answer:

60

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Good luck on your assignment

Answer:

  A 90 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the left

Step-by-step explanation:

The transformation of coordinates for figure ABCD ⇒ A'B'C'D' is ...

   (x, y) ⇒ (-y-1, x)

__

We know the transformation ...

  (x, y) ⇒ (-y, x)

represents a CCW rotation by 90°. And the transformation ...

  (x, y) ⇒ (x-1, y)

represents a translation 1 unit left.

Combined, the rotation and translation produce the transformation described above. This figure has undergone ...

   a 90° CCW rotation about the origin, followed by a translation 1 unit left.

Answer:

ratio

Step-by-step explanation:

Sign " : " is called Colon it represents the ratio, which is an ordered pair of a & b (b =! 0) which is a/b, represent as a:b.

The ratio is comparison of two quantities, usually by dividing them. By comparing one data point (A) to another data point (B), the formula would be A/B. This means you are dividing information A by information B.

Ratio data is a form of numeric data. It measures variables on a continuous scale, with an equal distance between adjacent values.

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Answer:

13, 14

Step-by-step explanation:

Solve the inequality, that is

Given

x + 2x + 6 < 50, that is

3x + 6 < 50 ( subtract 6 from both sides )

3x < 44 ( divide both sides by 3 )

x < 14 [tex]\frac{2}{3}[/tex]

The values in the set that are less than this value are 13 and 14

Answer:

Minimum number of voters for the democratic candidate would be 3120 voters.

Step-by-step explanation:

Total number of people turning out to vote = 12,000

Percentage of votes a democratic would get = 30%

Which means that it is expected that a democratic candidate will get: 30/100 · 12,000 = 3600 votes

However, the polling may have an error of +4% to -4%

Which means that the votes a democratic candidate will get will range from 30%+4% = 34% to 30%-4%= 26% of the total people who turn out to vote

Minimum number of voters can be determined by taking 26% of the total people who turn out to vote:

Minimum number of votes = 26/100 · 12,000 = 3120

Answer:

$68.00 (Ignoring tax)

Step-by-step explanation:

80 x 0.15 = 12

80-12=68