Which of the following is equivalent to the expression x² - 64?
A) (x-8)²
B) (x-64)²
C)(x-8)(x-8)
D) (x+8) (x-8)

Answer:

8640in²

Step-by-step explanation:

A = I * W * H

A= 27*16*20

A=8640in²

Answer: A= 2, B= −2, C= −2

Step-by-step explanation:

A = −1^2 −3 (−1) −2

= 1 + 3 -2 = 2

A = 2

B = 0^2 −3 (0) −2

= 0 − 0 − 2 = −2

B = −2

C = 3^2 −3 (3) −2

= 9 − 9 − 2

C = −2

Answer:

A = 2

B = -2

C = 16

Step-by-step explanation:

Plug in the numbers into the equation.

y = x^2 - 3x - 2

y = -1(-1) - 3 (-1) - 2

y = 1 + 3 - 2

y =2

y = 0^2 - 3(0) - 2

y = 0 - 0 - 2

y = -2

y = 3^2 - 3(3) - 2

y = 9 - 9 - 2

y = -2

Answer:

see below

Step-by-step explanation:

The interior angle of the triangle on the right is   180 - ( 9x+12)

  this plus the other two sum to 180 degrees

180 - (9x+12)     +     4x-3      +       6x + 3 = 180

  x   = 12

then the angles are        6(12)  + 3 = 75      4(12) -3 = 45    and    60°      

Answer:

E would be 6 spaces or the middle of points C and D.

Step-by-step explanation:

Please see picture.

Answer:

750 students are boys, 250 are girls.

Step-by-step explanation:

1/4 of 1000 is 250.

250 + 250 + 250 = 750 boys.

if 3/4 are boys, then 1/4 (the rest of the school population) are girls.

150 students are girls.

Given:

[tex]\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}[/tex]

Express 16 as [tex]4^{2}[/tex]: [tex]x^2+y^2=16[/tex]

[tex]x^2+y^2=4^2\\x^2+y^2=4^2 \times 1[/tex]

Trignometry,

[tex]\cos ^2(t)+\sin ^2(t)=1[/tex]

Now, substitute [tex]\cos ^2(t)+\sin ^2(t)[/tex] for 1:

[tex]\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)[/tex]

Law of indicates:
[tex]\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2[/tex]

Taking positive square roots as follows:

[tex]x=4 \cos (t), y=4 \sin (t)[/tex]

Recall that, z = xy.

Now, we have:

[tex]\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}[/tex]

Now, substitute the values:
[tex]r(t)=x_t i+y_t j+z_t k[/tex]

So, the vector r(t) is: [tex]r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i[/tex]

Therefore, the vector function r(t) is written as: [tex]r(t)=x_t i+y_t j+z_t k[/tex]

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We get that the solution to this scenario will be 50 t-shirts and 59 yearbooks.

Selling price of t shirts = $ 20

Selling price of year books = $ 24.

Let the number of t shirts sold be x and the number of yearbooks sold be y.

Goal to sell at least = $ 2400 in merchandise.

So, we get the equation as:

20 x + 24 y ≥ 2400

5 x + 6 y ≥ 600

Now, we are given some options:

50 t-shirts and 59 yearbooks

Substituting it, we get that:

5 ( 50) + 6 ( 59) ≥ 600

250 + 354 ≥ 600

604 ≥ 600

which is true.

51 t-shirts and 57 yearbooks

Substituting it, we get that:

5 ( 51) + 6 ( 57) ≥ 600

255 + 342 ≥ 600

597 ≥ 600

which is not true

60 t-shirts and 48 yearbooks

Substituting it, we get that:

5 ( 60) + 6 ( 48) ≥ 600

300 + 288 ≥ 600

588 ≥ 600

which is not true

62 t-shirts and 48 yearbooks

Substituting it, we get that:

5 ( 62) + 6 ( 48) ≥ 600

310 + 288 ≥ 600

598 ≥ 600

which is not true.

Therefore, we get that the solution to this scenario will be 50 t-shirts and 59 yearbooks.

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Answer:

50 tshirts and 59 yearbooks is the correct answer.

Step-by-step explanation:

Answer:

x = -2

TU = 4

UB = 2

Step-by-step explanation:

you can add x^2 with 4x+10 and equate it to 6:

x^2 + 4x + 10 = 6

x^2 + 4x + 4

then u can use the roots formula : x = (-b ± √ (b2 - 4ac) )/2a

so it'll be   x = {-4±[√16 - 4(4)]}/2

x= -2

then u can substitute it and find TU and UB

TU= (-2)^2 = 4

UB= 4(-2)+10 = 2

The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.

In this problem we find a resulting expression, that is, the function g(x) = - |x|   + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.

After a quick inspection, we find that two rigid transformations were used in the following order:

Now we proceed prove this procedure:

f(x) = |x|

Step 1

f'(x) = - |x|

Step 2

g(x) = - |x| + 2

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Answer:

14

Step-by-step explanation:

g(3)=(3)+3

g(3)=6

f(3)=-(3)-5

f(3)=-8

6-(-8)=14

========================================================

Explanation:

The parabola has its lowest point when either x = -8 or x = 8

Plug either value into the function

f(x) = -x^2 + 4

f(-8) = -(-8)^2 + 4

f(-8) = -60

You should find that f(8) = -60 as well

This is the lowest output possible. Confirmation of such can be done using a graph. Look for the lowest point and only focus on the interval [tex]-8 \le \text{x} \le 8[/tex]

The highest point is at the vertex (0, 4), so the largest output is y = 4

------------

We have the lowest output y = -60 and the highest output y = 4

The possible set of outputs is the interval [tex]-60 \le \text{y} \le 4[/tex] which turns into the interval notation [-60, 4]

Check out the graph below.

The function that models the given situation is; f(x) = 109(0.935)^(t) + 72

We are given that;

Temperature of hot tea = 181°F

Room temperature = 72°F

Rate of the hot tea cooling on a desk in the room = 6.5% every minute

We know that an exponential function is of the form of;

y = A(r)^(x)

where;

A is the initial value.

r is the rate of increase/decrease in decimals.

Thus, our initial value is;

A = 181 - 72 = 109

The rate of increase/decrease in decimals = 1 - (6.5%) = 0.935

Since the room temperature is 72 degrees Fahrenheit, then the function is;

f(x) = 109(0.935)^(t) + 72

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Answer:

15

Step-by-step explanation:

225/15

All the data points are plotted on the number line and mentioned clearly as an image with the solution.

What is a number line?

For easy plotting on the number lines and for comparison of points, we will be converting all the fractions into decimals.

Kloee : [tex]3\frac{1}{4} = \frac{13}{4} =3.25[/tex]

High School :1.0

Middle School : 1.5

Football field : 5.7

KB: [tex]-4\frac{1}{8} = \frac{-33}{8} =-4.125[/tex]

Ben : -2.65

All the data points are plotted on the number line and mentioned clearly as an image with the solution.

(a) Distance between Ben and Kloee - 5.9

Plotted on the number line and mentioned clearly as an image with the solution.

(b) Distance of middle school from football field- 4.2

Plotted on the number line and mentioned clearly as an image with the solution.

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The rounded form of the number 9.19 which represents $9 and 19 cents to the nearest 25 cents is; 9.25

It follows from the task content that the number is required to be rounded off to the nearest 25 cents.

On this note, it follows that only 25 cent intervals are considered.

Hence, the number in discuss can either be rounded up to 9.25 or 9.00.

However, since the fractional 19 cents is closer to 25 more than it is to 0 on the number line, the rounded form of the number is;

= 9.25.

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Scale factor for the drawing from actual park = 1/20

Area of the actual park = 1200 cm²

Area of a Rectangle. A = l × b. The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension

Length of the rectangular city park = 5 cm

Width of the rectangular park = 6 cm

Using scale factor 1 cm = 20 meters

Scale factor = Length of the park in drawing/ actual length of park

⇒1/20.

5/actual length of park = 1/ 20

Actual length = 5 × 20 = 100 meters

Actual width = 6 × 20 = 120 meters

Area of the rectangular park = length × width

square meters

Therefore, Scale factor from actual length to the length in drawing = 1 : 20

Area of the rectangular park = 1200 square feet

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The polynomial equation is (x³ - 7x² + 20x - 24) = 0 and the Error that made by Andrew is incorrect factors of the roots.

Polynomial Equation:

The equations formed with variables, exponents and coefficients are called as polynomial equations.

Roots of the Polynomial:

Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.

Given,

Roots of the polynomial are: 3, 2 + 2i, 2 - 2i.

Here we need to find the error he made and the correct form of the equation.

According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is  a factor of P(x).

According to this definition:

=> (x - 3) , (x - (2 + 2i)) , (x - (2 - 2i))

are factors of the required polynomial.

Simplifying the brackets, we get:

=> (x - 3), (x - 2 - 2i), (x - 2 + 2i)

are factors of the required polynomial.

This is the step where Andrew made the error.

The factors will always be of the form (x - a) , not (x + a).

Andrew wrote the complex factors in form of (x + a)  which resulted in the wrong answer.

So, the polynomial would be:

=> (x - 3)(x - 2 - 2i)(x - 2 + 2i) = 0

=> (x - 3) (x² - 2x + 2xi - 2x + 4 - 4i - 2xi - 4i - 4i²) = 0

When we simplify it, then we get,

=> (x - 3)(x² - 4x + 4 + 4) = 0

=> (x - 3)(x² - 4x + 8) = 0

=> (x³ - 4x² + 8x - 3x² + 12x - 24) =0

=> (x³ - 7x² + 20x - 24) = 0.

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There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Answer:

25n

Step-by-step explanation:

product of n and 25

Product means multiply

25n

The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

According to the given question.

The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).

Also, it is given that the perimeter of the quadrilateral is 110 inches.

⇒ x + x+1 + x + 2 + x + 3 = 110

⇒ 4x + 6= 110

⇒ 4x = 110 -6

⇒ 4x = 104

⇒ x = 104/4

⇒ x = 26 inches

Thereofore, the length of the sides of the quadrilaterals is given by

x = 26 inches

x + 1 = 26 + 1 = 27 inches

x + 2 = 26 + 2 = 28 inches

x + 3 = 26 + 3 = 29 inches

Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

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The float type of data stores real numbers (numbers with decimal values) such as 3.2, 5.67 and 48.42.

A data type, in programming, is a classification that specifies which type of value a variable has and what type of mathematical, relational or logical operations can be applied to it without causing an error.

All number types that allow for the possibility of a fractional component, such as 42.7 or pi, are known as floating point types.

The precision of various floating point data types varies depending on how many bits are utilized to represent the digits, which is directly proportional to the total number of bits in the number. In the IEEE standard, for instance:

Hence, the type of data is floating point.

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Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

Length of the house = 35 feet

width of the house = 28 feet

Height of the house = 6 feet

Total surface area = 2 l b + 2 b h + 2 h l

A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)

A = 1960 + 336 + 420

A = 2716 feet²

If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²

Gallon of paint required = 5432 / 225 = 24.14 gallons.

Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

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Beginning with the graph of f(x) = x2, The transformations that are needed to form  [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is

The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units

This is further explained below.

Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.

The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.

In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.

[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]

The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.

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Answer:

The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

I got it right.

hmmm from the table, let's just pick one point since we know "y" is inversely proportional, so hmmm let's say hmm the point when x = 4 and y = 9/16

a)

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" inversely proportional to }x^2}{ {\LARGE \begin{array}{llll} y = \cfrac{k}{x^2} \end{array}}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=\frac{9}{16} \end{cases} \\\\\\ \cfrac{9}{16}=\cfrac{k}{(4)^2}\implies \cfrac{9}{16}=\cfrac{k}{(16)}\implies \cfrac{9(16)}{16}=k\implies 9=k~\hfill \boxed{y=\cfrac{9}{x^2}}[/tex]

b)

when y = 16, what's "x"?  

[tex]16=\cfrac{9}{x^2}\implies x^2=\cfrac{9}{16}\implies x=\pm\sqrt{\cfrac{9}{16}}\implies x=\pm \cfrac{\sqrt{9}}{\sqrt{16}}\implies \stackrel{positive~value}{x=+\cfrac{3}{4}}[/tex]

Answer:

see below

Step-by-step explanation:

1/11=0.0909....

3/11=0.090909...*3 or 0.27272727...

∠AOM ≅ ∠BOM  because they are both congruent to the same angle, not because they are vertical angles.

From the image of the angles attached, we are given that;

∠AOM ≅ ∠DON

Now, from the vertical angle theorem, we can say that;

∠AOM ≅ ∠CON

Similarly, by vertical angles theorem, we can also say that;

∠BOM ≅ ∠DON

From transitive property of congruence, we can equally say that since ∠AOM and ∠BOM are equal to the same angle, then;

∠AOM ≅ ∠BOM

From transitive property of congruence, we can equally say that since ∠CON and ∠BOM are equal to the same angle, then;

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Answer: ∠AOM≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.

Step-by-step explanation:

cause I did the mastery test

Answer:

BC = 12

Step-by-step explanation:

from the diagram

AB + BC = AC , that is

18 + BC = 30 ( subtract 18 from both sides )

BC = 12