What is the vertex of the parabola given by y = x2 − 10x + 17? A. (5, -8) B. (-5, 8) C. (5, 8) D. (-5, -8)

Answer:

-36

Step-by-step explanation:

You have to rearrange the quadratic into an equation where one side is zero.

This example works by subtracting 7x^2 from both sides leaving

-5 = 9x^2 - 7x^2 + 2x

-5 = 2x^2 + 2x

Now add 5 to both sides

-5 + 5 = 2x^2 + 2x + 5

0 = 2x^2 + 2x + 5

Now the equation you gave is in the form of a quadratic. The discriminate is found from

a = 2

b = 2

c = 5

b^2 - 4ac is the discriminate

2^2 - 4(2)(5)

4 - 40

Discrimate = 4 - 40 = - 36

Answer:

p+q

Step-by-step explanation:

[tex]\dfrac{p^2-q^2}{p+q}\div\dfrac{p-q}{p+q}= \\\\\\\dfrac{(p-q)(p+q)}{p+q}\times \dfrac{p+q}{p-q}= \\\\\\\dfrac{(p-q)(p+q)}{p-q}= \\\\\\p+q[/tex]

Hope this helps!

Answer:

p+q

Step-by-step explanation:

We can use difference of squares to make the fractions

[tex]\frac{(p+q)(p-q)}{(p+q)} *\frac{p+q}{p-q}[/tex]

Since dividing is the same as multiplying bt the reciprocal

The (p+q) and the (p-1) cancel out so we are left with (p+q)

Answer:

4,5, and 8

Step-by-step explanation:

corresponding angles

Answer:

Angle 4 coz vertical angle of angle 1

Angle 5 coz corresponding angle

Angle 8 coz vertical angle of angle 5

Answer: C. 

Both functions are decreasing, but function f is decreasing at a faster average rate on that interval.

Step-by-step explanation:

Let first work out g(x)

When x = 0

g(x) = 75

When x = 1

g(x) = 75( 1 - 50%)

g(x) = 75(0.5) = 37.5

Which is less than 43

With this, we can conclude that:

Both functions are decreasing, but function f is decreasing at a faster average rate on that interval.

Answer:

Step-by-step explanation:

The awnser is c because the person above me was right

Answer:

x-intercept:   x=24

DOMAIN: (0,24) where x∈Natural Numbers

RANGE: (0,12) where y∈Natural Numbers

Step-by-step explanation:

Remain money = y

Number of games = x

Given function:

[tex]y=12-0.5x\\[/tex]

x-intecept is the value of x where y becomes zero.

Substitute y=0 in the given equation:

[tex]0=12-0.5x\\0.5x=12\\x=\frac{12}{0.5}\\x=24[/tex]

Domain is a set of all possible values of x.

x= No. of games (So x cannot be negative)

y= Remain Amount (So y cannot be negative)

So the minimum value of x is 0 because x cannot be negative.

Maximum value of x is the value for which y doesn't become negative. For any value of x>24, y <0 which is not possible.

So maximum value of x is 24

DOMAIN: (0,24) where x∈Natural Numbers

Range:

Range is a set of all outcomes of y for all possible values of x.

For x=0 , y =12

for x=24 , y = 0

So

RANGE: (0,12) where y∈Natural Numbers

Answer:

4+2.4=6.4+1.44=7.84

The infinite geometric sum of 4+2.4+1.44+... will be 10.

At each point in the sequence, you multiply or divide by the common ratio. Divide two sets of phrases that follow one another to find it. Whichever pair of terms is picked, as long as they appear next to one another in the sequence, is irrelevant.

It is given that, the sequence is 4+2.4+1.44+...

The sequence is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is obtained that the common ratio is,

r=2.4/4

r=0.6

The Sum of an infinite geometric sequence is,

S = a / (1-r)

S=4 / (1-0.6)

S=10

Thus, the infinite geometric sum of 4+2.4+1.44+... will be 10.

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Answer:

(7, 9)

Step-by-step explanation:

Answer:

Your answer should be 7, 9

Answer:

yes of course it is correct good job

Answer:

yes your answer is correct

Answer: gradpoint “b”

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

x=12-7

x = 5

Answer:

x=5

Step-by-step explanation:

x+7=12

If you do the same thing to both sides of the equation, then the trueness of the equation does not change. Therefore, I can subtract 7 from both sides of the equation to isolate x.

x+7-7=12-7

x=5

Hope this helps!

Answer: smaller number is 4, bigger number is 20

Step-by-step explanation:

24 - 4 = 20

4 * 4 = 16

20 - 16 = 4

Answer:

4 and 20.

Step-by-step explanation:

Answer:

9x over x+9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Brother= 9*2=18

Me= 9

B+M= 18+9= 27

Answer:

C. $18

Step-by-step explanation:

The ratio between brother and her is 2:1. Therefore, there are 3 parts. $27/3 = $9. Thus, her brother gets 2*$9 = $18 and she gets 1*$9 = $9

Answer:

1000

Step-by-step explanation:

each number is 10 times more intense than the previous

Answer:1 23/28

Step-by-step explanation:

17/3/3 1/9

17/3/28/9

51/28

1 23/28

Hope this helps! : )

Answer:

B, 210

Step-by-step explanation:

there is 10 options for the first one, 9 option for the second, 8 options for the third and 7 for the last. 10*9*8*7=5040, which is d

First number can be 1 out of 10

Second number can be 1 out of 9

Third number can be 1 out of 8

Fourth number can be 1 out of 7

Total combinations = 10 x 9 x 8 x 7 = 5,040

The answer is D. 5,040

Answer:

36 °

Step-by-step explanation:

In this case a rectangular triangle is formed so we can use the trigonometric functions to calculate the angle, they give us the value of the two legs, therefore we can apply the tangent function.

Tan A ° = opposite / adjacent

replacing:

Tan A ° = 50/68

Tan A ° = 0.735

A ° = arc tan (0.735)

A ° = 36.32

Which means that the angle of inclination is 36°

Answer:

1/4

Step-by-step explanation:

printed part = 210

total pages = 280

probability to open printed page 210/280 =3/4

probability to not open printed page = 1 - probability to open printed page = 1 - 3/4 = 1/4

Answer:

1/4

Step-by-step explanation:

280-210=70

P=70/280=1/4

Answer:

C) 108°

Step-by-step explanation:

72°+k°=180° (straight line)

Subtract 72° from both sides

k°=108°

Our answer is C)108°.

Value of k = 108°

The correct option is C.

Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it. The measure of an exterior angle is equal to the sum of the two internal opposite angles.

Given,

In a triangle,

Interior angles are

A = 72°,

B = 83° and

C = 25°

exterior angle A = k°

Exterior angle A = Interior angle B + Interior angle C

k = 83° + 25°

k = 108°

Hence, 108° is the value of k.

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Answer:

A

Step-by-step explanation

the square in the corner

The shape of the given triangle is right angle.

The square in the corner

We have given that,

A. Right

B. Isosceles

C. Equilateral

D. Scalene

We have to determine the shape of the given triangle.

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.

The shape of the given triangle is right angle.

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Step-by-step explanation:

it's on the -0.8 number...

Answer:-0.8

Step-by-step explanation:count from -1 up to where B is

Answer: \frac{x+3}{x+4}

Step-by-step explanation:

\frac{x^2-9}{x^2+x-12}

\frac{(x+3)(x-3)}{(x+4)(x-3)} =\frac{x+3}{x+4}

Answer: x⁴+x³-12x²-9/x²

Answer:

Options C and D.

Step-by-step explanation:

The given functions are

[tex]f(x)=2^{x-6}+3[/tex]

[tex]g(x)=2^{x-3}+2[/tex]

We need to find the transformation from f(x) to g(x).

Now, write the function g(x) in the form of f(x).

[tex]g(x)=2^{x+3-3-3}+2+1-1[/tex]

[tex]g(x)=[2^{(x+3)-6}+3]-1[/tex]

[tex]g(x)=f(x+3)-1[/tex]     ...(1)

The translation is defined as

[tex]g(x)=f(x+a)+b[/tex]                .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2), we get

[tex]a=3>0[/tex], so graph shifts 3 units left.

[tex]b=-1<0[/tex], so graph shifts 1 unit down.

Therefore, the correct options are C and D.