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Hello!

[tex]\bf y = ( x + 3 )^{2} - 5 [/tex]

- Separate the function into parts to determine the domain of each part.

[tex]\bf ( x + 3 )^{2} \\ x + 3 \\ 5 [/tex]

- The domain of a polynomial function is the set of all real numbers.

[tex]\bf x ∈ ℝ [/tex]

Domain: ( -∞; ∞ )

[tex]\bf y = ( x + 3 )^{2} - 5 [/tex]

- Write the second degree function in standard form.

[tex]\bf y = x^{2} + 6x + 4 [/tex]

- Identifies the coefficients a and b of the second degree function.

[tex]\bf a = 1, b = 6 [/tex]

- Find the x coordinate of the vertex by substituting a = 1 and b = 6 in x = -b / 2a.

[tex]\bf x = -\frac{6}{2×1} [/tex]

[tex]\bf x = -\frac{6}{2} [/tex]

[tex]\bf x = -3 [/tex]

- Calculates the value of the function for x = -3.

[tex]\bf y = ( x + 3 )^{2} - 5 [/tex]

[tex]\bf y = -5 [/tex]

Range: ( -3; -5 )

Answer: No answer

Good luck! :)

Answer:

the left side of the histogram is the mirror image of the right side.

Answer:

x = 1

Step-by-step explanation:

2(76x - 1) = 150

76x - 1 = 75

76x = 76

x = 1

Answer:

The number of sedans before any vehicle was sold is 168

Step-by-step explanation:

Let's define the variables:

x = number of sedans

y = number of SUVs

We know that:

"If 36 sedans are sold and 36  SUVs are added, there will be an equal number  of sedans and SUVs"

If 36 sedans are sold, the new number of sedans is:

x - 36

if 36 SUVs are added, the new number of SUVs is

y + 36

And these numbers are equal, then:

x - 36 = y + 36

We also know that:

" If 8 SUVs are sold and 8  sedans are added, there will be twice as many

sedans as SUVs. "

If 8 SUVs are sold, the new number of SUVs will be:

y - 8

If 8 sedans are added, the new number of sedans wil be:

x + 8

From this we can write the equation:

(x + 8) = 2*(y - 8)

x + 8 = 2*y - 16

Then we have two equations:

x - 36 = y + 36

x + 8 = 2*y - 16

We want to find the number of sedans, x, then we need to isolate the other variable in one of the equations, let's isolate y in the first one:

Let's isolate x in the first one:

x - 36 - 36 = y

x - 72 = y

Now we can replace it in the other equation:

x + 8 = 2*y - 16

x + 8 = 2*(x - 72) - 16

Now we can solve this for x.

x + 8 = 2*x - 144 - 16

8 + 144 + 16 = 2x - x

168  = x

The number of sedans before any vehicle was sold is 168

Answer:

Hello,

k=-3 and h=-2

Step-by-step explanation:

[tex]5\ is\ a \ root \of \ x^2+(k-1)*x-5=0\\\\5^2+(k-1)*5-5=0\\\\5*(k-1)+20=0\\\\k-1=\dfrac{-20}{5} \\\\k=-4+1\\\\\boxed{k=-3}\\[/tex]

h+1 is thus a root of x²+(-3-1)*x-5=0

x²-4x-5=0

x²+x-5x-5=0

x(x+1)-5(x+1)=0

(x+1)(x-5)=0

h+1=-1

h=-2

Answer:

[tex]\sqrt{84^{2} } -37^{2} /47[/tex]=257 9/47

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

x = 7

1 / x^-2

= x^2

= 7^2

= 49

Answer: 49

Step-by-step explanation: yeet

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{d^2 = 41}}[/tex]

[tex]\huge\boxed{\text{TAKE the SQUARE ROOT}}[/tex]

[tex]\huge\boxed{\mathsf{d = \pm \sqrt{41}}}[/tex]

[tex]\huge\boxed{\textsf{SIMPLIFY it}}[/tex]

[tex]\huge\boxed{\mathsf{d = \pm \sqrt{41}\ or \sqrt{-41}}}}[/tex][tex]\huge\boxed{\mathsf{Answer: d = \bf \sqrt{41} \ or \ \sqrt{-41}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge{\boxed{\frak{Amphitrite1040:)}}}[/tex]

Answer:

2048

Step-by-step explanation:

Formula for volume of a sphere is given:

V = 4/3πr^3

Where r = radius

The sphere shown has a given radius of 8

All we have to do to find the volume of the sphere is simply plug in the given value of the radius (8) into the volume of a sphere formula

(Note it says use 3 for π )

V = 4/3(3)r^3

Substitute 8 for r

V = 4/3(3)(8)^3

Plug this into a calculator and you get that the volume is 2048

Answer:

2,048in³

Step-by-step explanation:

The formula to find the volume of the sphere is already given to you in the problem. All we need to do is substitute and solve.

V = 4/3π(8)³

V = 4/3π(512)

V ≈ 682.67(3)

V ≈ 2,048

Best of Luck!

9514 1404 393

Answer:

  1/12

Step-by-step explanation:

The probability of any given outcome is the ratio of the number of ways that outcome can happen to the total number of outcomes.

  P(4) = 1/6 . . . . . roll = 4 is one of 6 possible outcomes

  P(odd) = 3/6 = 1/2 . . . . . of the 6 possible outcomes, 3 are odd

__

The two rolls of the die are presumed to be independent, so the probability of the two outcomes is the product of their individual probabilities.

  P(4 & odd) = (1/6)(1/2) = 1/12

Answer:

A = 93.31 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height and b₁, b₂ the parallel bases

Here h = 6.2, b₁ = 7.8, b₂ = 14.7 + 7.6 = 22.3 , then

A = [tex]\frac{1}{2}[/tex] × 6.2 × (7.8 + 22.3) = 3.1 × 30.1 = 93.31 ft²

Answer:

they are congruent.

Step-by-step explanation:

just move A down to -1 and and you can see they are the same.

Answer:

they are congruent.

Step-by-step explanation:

just move the A shape down to -1 and and you can see that they are the same.

Given:

The polynomial is:

[tex]3n^2(n^2+4n-5)-(2n^2-14n+3)[/tex]

To find:

The difference of the polynomials and classify it in terms of degree and number of terms.

Solution:

Consider the polynomial,

[tex]P(x)=3n^2(n^2+4n-5)-(2n^2-14n+3)[/tex]

On simplification, we get

[tex]P(x)=3n^4+12n^3-15n^2-2n^2+14n-3[/tex]

[tex]P(x)=3n^4+12n^3-17n^2+14n-3[/tex]

The degree of this polynomial is 4 and the number of terms is 5.

Therefore, the correct option is D.

Answer:

answer for  n^4 equation (see attached)

Step-by-step explanation:

Answer:

The total number of girls is 47.

Step-by-step explanation:

Below are the following values:

Total number of students = girls + boys

Total number of students = 47 + 324

Total number of students = 371

We are required to find the number of girls in the school.

Since a total number of boys is 324 and thus total number of girls is 47.

Answer:

D. undefined

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

A horizontal line has a slope of 0.

A vertical line has a undefined slope.

Any other line will have a slope of some number.

Answer:

D

Step-by-step explanation:

The slope of a line represents  the number of units a line rises or falls vertically for each unit of horizontal change from left to right.

1) A line with positive slope (m > 0) rises from left to right.

2) A line with negative slope (m < 0) falls from left to right.

3) A line with zero slope is horizontal (parallel to x-axis).

4) A line with undefined slope is vertical (parallel to y-axis).

Ans: The line is parallel to y-axis. So, the slope is undefined

5.

1m = 0.001 km

So, 1m² = 10^-6

Area = 5027 m² = 5027 × 10 ^-6 km²

6.

1mm = 0.1 cm

1mm² = 10^-2

Area = 210× 297 mm² =62370 mm² = 62370 ×10^-2 cm²

Answer:

line LM

Step-by-step explanation:

When it is perpendicular, the slope will be 6/5.

Answer:

x=100

Step-by-step explanation:

Since m is parallel to n and p is parallel to q

Answer:

C

Step-by-step explanation:

The correct answer is C

The domain of the points that are illustrated in the graph is C. (7, 3, 7).

A domain simply means the set of values that can be plugged into a function.

In this case, in the graph, the domain of the points that are illustrated include (7, 3, 7). These are the set of inputs that are accepted by the function.

Learn more about domain on:

https://brainly.com/question/2264373

Answer:

n=8

Step-by-step explanation:

57=8n-7

add 7 on both sides

64=8n

divide 8

n=8

Answer:

8

Step-by-step explanation:

57=8n-7

add 7 to both sides

64=8n

divide by 8 on both sides

n=8

Answer:

[tex]choice \: c. \: - 77 < f(x) < - 2[/tex]

Step-by-step explanation:

[tex]f( - 4) = - 5 ({ - 4}^{2}) + 3 = - 77[/tex]

[tex]f( - 1) = - 5( { - 1}^{2}) + 3 = - 2[/tex]

Thus finding the range of F(x).

The range of the given function is - 77 < f(x) < - 2.

"The range of a function is a set of all the images of elements in the domain."

The given function is:

f(x) = - 5x² + 3

It is defined over the domain - 4 < x < - 1.

For x = - 4, f(x) = - 5(- 4)² + 3 = - 80 + 3 = - 77

For x = - 1, f(x) = - 5(- 1)² + 3 = - 5 + 3 = - 2

Therefore, the range of the given function f(x) is:

- 77 < f(x) < - 2.

Learn more about the range of a function here: https://brainly.com/question/8841915

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Answer:

10 T Shirts to have 105 dollars

Step-by-step explanation:

[tex]10.5x = 7.5x + 30[/tex]

[tex]3x = 30[/tex]

[tex]x = 10[/tex]

Answer:

For the question below, you will need to find the GCF of 45 and 60. In this instance it is 5, so it will be outside the box. The GCF answers will be inside the parenthesis, which is 7 and 12.

45x + 60 = 5(7x + 12)

In this question you have to multiply 2 with every number inside the parenthesis. So 2 × 10x and 2 × 4.

2(10x+4) = 20x + 8

Hope this helped.

Answer:

On a number line, graph a number that is twice as far from 5 as it is from 8.

Step-by-step explanation:

11 is twice as far from 5 as it is from 8

Answer:

For x there is no distance since they are both for. For y, they are -6 apart.

Step-by-step explanation:

Answer:

Fox x Diya is no distance since they are both for they are six apart

Step-by-step explanation:

(4-10)

and= just opposite size (10- 4) .

10 -4 = 6 answer 6

and (4-4)

answer is

0

the answer is six apart

understand

Answer:

x = 7

Step-by-step explanation:

The triangles are similar

12/8 = (x+3+5)/(x+3) cross multiply expressions

12x + 36 = 8x + 64

12x - 8x = 64 - 36

4x = 28 divide both sides by 4

x = 7

Answer:

N = N0 e^-x t   is the general form for Half-Life decay of atoms

B would be the correct choice

The type of model is exponential if the situation is every day half a bacterial population dies option (B) is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×

where a is a constant and a>1

We have a situation:

Every day half a bacterial population dies

As we know from the exponential function, the function that rapidly increases or decreases.

The standard form of the exponential function is:

y = a×

As the everyday half of bacterial population dies

Let the starting population is a

After one day: = a/2

After second day: = a/4

After third day: = a/8

After nth day: = (a/2)(1/2)ⁿ⁻¹

The above expression represents an exponential function.

Thus, the type of model is exponential if the situation is every day half a bacterial population dies option (B) is correct.

Learn more about the exponential function here:

brainly.com/question/11487261

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60, because 6 times 10 is just that

Answer:

60

Step-by-step explanation:

6x10 is 60

Answer:

19.3

Step-by-step explanation:

The base of the top triangle is 24.158 (approximately) found from the bottom triangle using the sine rule

from that,

sin(53) = r/24.158

or, r = 24.158×sin(53)

or, r = 19.3 (rounded to the nearest tenth)