The area of a square is 289 ft2. What is the length of each side?​

1.

[tex]f(x)=-3x\qquad g(x)=5x-6\\\\g(f(x))=5(-3x)-6=\boxed{-15x-6}[/tex]

2.

[tex]f(x)=x-6\qquad g(x)=x^2+6x-2\\\\g(f(x))=(x-6)^2+6(x-6)-2=x^2-12x+36+6x-36-2=\\\\=\boxed{x^2-6x-2}[/tex]

3.

[tex]f(x)=4x+3\qquad g(x)=2x^2-x+1\\\\g(f(x))=2(4x+3)^2-(4x+3)+1=2(16x^2+24x+9)-4x-3+1=\\\\=32x^2+48x+18-4x-3+1=\boxed{32x^2+44x+16}[/tex]

4.

[tex]f(x)=2x^2\qquad g(x)=8x^2+3x\\\\g(f(x))=8(2x^2)^2+3(2x^2)=8\cdot4x^4+6x^2=\boxed{32x^4+6x^2}[/tex]

Answer:

d.)

C = 1200x + 765

Step-by-step explanation:

The substitution property of equality allows you to substitute an expression for a variable. Since y equals 40x + 25, you can substitute (40x + 25) for y in the C = 30y + 15 equation:

C = 30y+ 15

y = 40x + 25

C = 30y + 15

C = 30(40x + 25) + 15

C = 1200x + 750 + 15

C = 1200x + 765

The equivalent expression for C = 1200x+765.

C = 30y+15; y = 40x+25 Equivalent relation between C and x to determine.

Equations are defined as the mathematical expression intended meaning to something that contains an equal sign.

Here, C=30y+15
        y = 40x+25
Putting y in C = 30y+15
          C= 30(40x+25)+15
          C = 1200x + 750 +15
          C = 1200x +765

Thus, the equivalent expression for C = 1200x+765.  

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Answer:

75.408 ft

Step-by-step explanation:

In 20 minutes, the angle swept by a minute hand is calculated as

(20/60) x 360° = 120°

The length of the minute hand = 36 ft

To calculate the distance moved by the minute hand, we solve for the fraction of the circumference of a circle swept by the minute hand in going through this 20 min.

we use the expression

Distance moved by the tip of the minute hand d = (θ/360) x 2πR

where

θ is the angle swept in the 20 minutes = 120°

R is the length of the minute hand, which is the radius of the circle formed if the minute hand moves completely in a 360° motion round the clock.

R = 36 ft

substituting values, we have

d = (120/360) x (2 x 3.142 x 36) = 75.408 ft

The tip of the minute hand moves 0.21 ft in 20 minutes.

The minute hand sweeps an arc of length L given by

L = Ф/360° × 2πR where

So, substituting the values of the variables into the equation, we have

L = Ф/360° × 2πR

L = 1/3°/360° × 2π × 36 ft

L = 1/(3 × 360) × 2π × 36 ft

L = 1/(3 × 10) × 2π ft

L = 1/30 × 2π ft

L = 1/15 × π ft

L = 3.1416/15 ft

L = 0.2094 ft

L ≅ 0.21 ft

So, the tip of the minute hand moves 0.21 ft in 20 minutes.

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Answer:

Step-by-step explanation:

f(x) = x + 1, find f(x+3)

f(x+3) = x + 3 + 1 = x + 4

Answer: f(x+3)=x+4

Step-by-step explanation:

f(x)=x+1

f(x+3)=(x+3)+1 ⇔ substitute x

f(x+3)=x+3+1 ⇔ take of parentheses

f(x+3)=x+4 ⇔ simplify

Hope this helps!! :)

Please let me know if you have any question

Answer:

[tex]4p\geq 12[/tex]

Step-by-step explanation:

So, when there were 4 innings left, the score was 17 to 6 and Kim was losing.

Since the score was 17 to 6, in order for her to win, they must've scored at least another 12 points.

This is because we are told that the other team didn't score, so their final score is 17.

And for Kim to win, they must have more points, so their must've scored at least 12 points for their score to be 18.

And we also know that they scored the same per inning for the next four innings.

Thus, in an inequality, this is:

[tex]4p\geq 12[/tex]

The score per inning times 4 innings must be greater than or equal to 12:

Further notes:

To solve, divide both sides by 4:

[tex]p\geq 3[/tex]

In other words, Kim's team must've scored at least 3 points per inning.

Also note that this solution include only integers, since you can't score 3.5 points.

Answer:

yes

Step-by-step explanation:

because it sells the best price

Answer:

No

Step-by-step explanation:

Stores D dose not have the best deal when you compare the unit prices. The best deal isn't from having more loaves. The best deal from store B because the unit price is the lowest.

Answer:

three consecutive integers that add up to 675 are 224, 225, and 226.

Step-by-step explanation:

Answer:

S infinity= -51/4

Step-by-step explanation:

First term

ar= -9

Fifth term

ar⁴= 1/3

Solving for the value of the r and a

ar= -9

ar⁴= 1/3

Dividing each other

r³=1/3 * -1/9

r³=-1/27

r= 3√-1/27

r= -1/3

Solving for a

ar= -9

a(-1/3)= 9

a= 9*-3

a= -27

Sum of a go to infinity is given by the formula

S infinity= a/(1-r)

S infinity= -27/(1-(-1/3))

S infinity= -27/(1+1/3)

S infinity= -27 * 3/4

S infinity= -51/4

Answer:

13 cm

Step-by-step explanation:

We can use the Pythagorean Theorem to find the length of the hypotenuse. The Pythagorean Theorem is used to find a missing side to a right triangle.

The theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are the legs, and c is the hypotenuse.

The legs of this triangle are already states - 5 and 12, so we can plug it's values into the formula.

[tex]5^2 + 12^2 = c^2\\\\25 + 144 = c^2\\\\169 = c^2\\\\c = \sqrt{169}\\\\c=13[/tex]

So the hypotenuse of this triangle is 13 cm.

Hope this helped!

Answer:

(0,3) and (1,-1)

Answer:

C on edge 2020

Step-by-step explanation:

For the equation below, x is the input and y is the output. Choose the ordered pair that makes a true statement for the equation.

y = -4x + 3

A-(-1, 1)

B-(0, -3)

C-(1, -1)

D-(2, 11)

Answer:

Carla has been running 7 miles each day for 13 days.

Step-by-step explanation:

Carla ran 3 miles on her first day, 5 miles on her second day and then 7 miles each day onward.

Let the number of days she ran 7 miles each day = x

Total distance run by Carla = 3 + 5 + 7(x)

                                             = 8 + 7x

If her log book shows that she has run total distance = 99 miles

Equation representing her total run will be,

8 + 7x = 99

7x = 99 - 8

7x = 91

x = [tex]\frac{91}{7}[/tex]

x = 13 days

Therefore, Carla has been running 7 miles each day for 13 days.

Answer:

A.

Step-by-step explanation:

Answer:

$ 2250

Step-by-step explanation:

3375 = s³

s = ∛3375

s = 15 ft.

floor area = s² = (15 * 15)

floor area = 225 ft²

the contractor charges $10 per ft².

therefore,  

the hardwood cost = 225  x  $10 = $2250

Answer:

$2,250.

Step-by-step explanation:

So first, we need to find the area of the floor (the side shaded green). To do so, we first need to find the length of the one side of the room.

Since we know that the room is a cube, all side lengths are equivalent. And since we are given that the volume of the room is 3375, we can find the length of the side.

The volume of a cube is given by the formula:

[tex]V=s^3[/tex]

Substitute 3375 for V:

[tex]s^3=3375[/tex]

Take the cube root of both sides:

[tex]s=\sqrt[3]{3375}=15[/tex]

So, the side length of the room is 15.

This means that the area of the floor is:

[tex]A=(15)^2\\A=225\text{ in}^2[/tex]

They charge $10 per square foot. There are 225 square feet. Thus, the total cost will be:

[tex]10(225)=$2250[/tex]

$2,250.

Answer: C, y^5 + 13x + 12

Step-by-step explanation:

A trinomial is a polynomial that consists of three terms. y^5 is one term, 13x is the second, and 12 is the third term. Each term is separated by an operator (ie +,-,*, etc). Constant terms are terms that do not change. In this case, your constant term is 12.

Answer:

C

Step-by-step explanation: A trinomial has 3 terms and a constant term is just a number.

Answer:

Step-by-step explanation:

Please, share any answer choices that were given to you.

                                       -1                 -1                 -1

-1/64 is equivalent to   -------- and ---------- and ---------

                                      4^3              2^6             8^2

Answer:

  70

Step-by-step explanation:

Here, you're expected to round the numbers to the nearest 10, then do the subtraction:

  92.1 -18.56 ≈ 90 -20 ≈ 70 . . . estimated answer

Answer:

The answer is z=-35.

5=z/-4-3.=-35.

And if the question is the other way around that the -3 is for the whole question and not with the -4 like if they are not together then the answer is -32.

Answer:

Answer: approximately -1.63 and -7.37

Step-by-step explanation:

First of all, let's expand the parenthesis by multiplying x into both of its terms.

[tex]x(x+9)+12 = 0\\x^2+9x+12=0[/tex]

We get the equation:

[tex]x^2+9x+12=0[/tex]

The quadratic formula looks like this

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

where the equation is of the form

[tex]ax^{2}+bx+c=0[/tex]

Comparing this to our equation above,

[tex]x^2+9x+12=0[/tex]

we can see that

[tex]a = 1\\b= 9\\c= 12[/tex]

Let's put these values into the quadratic formula.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-9\pm\sqrt{9^2-4*1*12}}{2*1}\\x=\frac{-9\pm\sqrt{9^2-48}}{2}\\x=\frac{-9\pm\sqrt{81-48}}{2}\\x=\frac{-9\pm\sqrt{33}}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x_{1}=\frac{-9+5.744...}{2}=\frac{-3.255...}{2}=-1.62771867\\x_{2}=\frac{-9-5.744...}{2}=\frac{-14.744...}{2}=-7.3722813\\[/tex]

Answer: approximately -1.63 and -7.37

You can also choose not to approximate the square root of 33, and you'd receive the answers:

[tex]x_{1}=\frac{-9+\sqrt{33}}{2}\\x_{2}=\frac{-9-\sqrt{33}}{2}[/tex]

Answer:

|x - 89| ≤ 5  

Step-by-step explanation:

Here the range is 84 to 94 ft, with the midpoint being 89 and the greatest variation from the midpoint being ±5.  

We adapt |x| ≤ a as follows:  replace x with 'x - 89' and a with 5:

|x - 89| ≤ 5  

It is customary to regard '89' as the 'center' of the solution interval and 5 as the 'maximum difference' or 'radius' separating x from this center.

Answer:

HOPE THIS WILL BE HELPFUL FOR YOU

Answer:

a line starting at -6 going to the left of this number, and with an open circle around the -6.

Step-by-step explanation:

To solve for this inequality, we need to isolate "x" on one side of the inequality symbol (<):

4 x + 8 < -16

subtract 8 from both sides:

4 x < -16 - 8

4 x < - 24

now divide both sides by 4 to get rid of the 4 that appears multiplying "x":

x < - 24/4

x < - 6

To graph this inequality one needs to highlight all the real numbers of the number line to the left of the value -6, making sure that one draws an open circle around the -6 because we don't want this number to be included (notice that x < -6 implies x-values strictly smaller than -6)

Then one would draw a line starting at -6 going to the left of this number, and with an open circle around the -6.

In edg:

A & B

A: StartFraction x over 2 EndFraction less than 1 or StartFraction 4 x minus 2 over 2 EndFraction greater than or equal to 13.< 1 or ≥ 13

B: 3x – 3 < 3 or 2x + 8 ≥ 22

Answer:

Hey there!

11 is greater than 14.

Positive numbers are greater than negative numbers.

Hope this helps :)

Answer:

(6.3*10³) ÷ (1.8*10⁵)

6.3*10³ = 0.063*10⁵

then:

(6,3*10³) ÷ (1.8*10⁵) = (0.063*10⁵) ÷ (1.8*10⁵)

= 0.063/1.8

= 0.035

0.035 = 3.5 *10⁻² = 35*10⁻³

Answer:

1.) 10 is R, Q, Z, W, N

2.) 5/6 is R,Q,

3.) sqrt 24 is I

4.) 0 is R, Q, Z, W

5.) none, neagative sqrt are imaginary.

Answer:

Quantity of ice cream  = 50 litre

Quantity of ice cream contained in one ice cream tub = 750 ml

1 litre = 1000 mL

Quantity of one ice cream tub in litres = 0.75 litres

we need to calculate the number of ice cream tubs filled by using 50 litres of ice cream

Number of ice cream tubs filled = 66 tubs 500 ml

hope it helps :)

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Answer:

1/4

Step-by-step explanation:

Since the denominatior is the same, we can look at only the numerator. So 7/8 - 5/8 is basically 7 - 5 which is 2.

The denominator doesn't change so it's 2/8. We can further simplify this into 1/4.

Answer:

16:12

Step-by-step explanation:

if there is 12 boys, that leaves the other 16 to be girls

Answer:

4:3

Step-by-step explanation:

If there are 12 boys then 28-12=16

So there are 16 girls

The girls to boys ratio is 16:12 and you simplify

Now it's 4:3

Answer:

The simple interest was found to be $9.6 after 1 year at 3%

Step-by-step explanation:

Given that

principal p= $350

rate r= 3%= 3/100= 0.03

time t= 1 year

The expression for the simple interest is given as

SI= p*r*t

SI= 320*0.03*1

SI= $9.6

After 1 year at 3% the simple interest is $9.6

Simply put the extra money earned after an investment is called the simple interest

Answer:

Tom's pay for the week should be over 500 dollars. Sorry if this isn't very helpful. :(

Step-by-step explanation:

Answer: is D

Answer is D

Using the simple method of quadratic expression:

we find two  numbers(the first and last word) that when we multiply is the same as when we add them together.

a²+9a+20

a²+4a+5a+20

The answer is D

a(a+4)+5(a+4)

(a+4)(a+5)