Review: Key Concepts
.
The equation of a linear function in slope-intercept form is written as
y = mx + b, where mand b are real numbers, m is the
and b is the
y-intercept of the line
.
Changing the value of b moves the graph
or
Changing the value of m affects the
and whether the line
slopes up or down from left to right.

Answer:

24 quarts

Step-by-step explanation:

1 qrt = 75/2 = 37.5

900 / 37.5 = 24

Answer:

6

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

9b⁶c⁵

Step 2 Identify

Our largest degree is the variable raised to the highest exponent.

b⁶ > c⁵

Therefore our degree is 6.

Answer:

More students have hazel eyes than blue.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

30 boxes of tea

Step-by-step explanation:

27 (overall tea boxes) - 12 (boxes sold) = 15

15 (leftover boxes) x 18 (kg of each box) = 270

270 (overall kg of the boxes) divided by 9 (kg of the bags) = 30, so all the tea boxes can be placed into the bags

Answer:

-18z3+(-15z3)

-18z3-15z3

-33z6

Answer:

f(x)= 3x^2+5x

Step-by-step explanation:

f(x)= x(x+1)(x-4)(x+8)

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

f(x) 3x^2 + 5x

Answer:

[tex](f-g)(x)=2x-3[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=3x-1\text{ and } g(x)=x+2[/tex]

And we want to find:

[tex](f-g)(x)[/tex]

This is equivalent to:

[tex]=f(x)-g(x)[/tex]

By substitution:

[tex]=(3x-1)-(x+2)[/tex]

Simplify. Distribute:

[tex]=(3x-1)+(-x-2)[/tex]

Rearrange:

[tex]=(3x-x)+(-1-2)[/tex]

Therefore:

[tex](f-g)(x)=2x-3[/tex]

Answer:

$50

Step-by-step explanation:

Make the equation where x is the original price:

x - 0.2x = 40

Combine like terms

0.8x = 40

Divide both sides by 0.8

40/0.8 = 50

Answer:

8.5

Step-by-step explanation:

Answer:

$2 more.

Step-by-step explanation:

In this question, we have to find how much more money Victoria is saving.

We know that Jacob saved $174 in 3 months.

We also know that Victoria saved $360 in 6 months.

Lets find how much money they save per month:

Jacob:

174 ÷ 3 = 58

Victoria:

360 ÷ 6 = 60

Jacob is saving $58 per month and Victoria is saving $60 per month.

This means that Victoria is saving $2 more than Jacob per month.

Answer:

2

Step-by-step explanation:

multiply by 2 and then divide by 6

Answer: x = 4

Step-by-step explanation:

3(x+2)=2(x+5)

3x + 6 = 2x + 10

x + 6 = 10

x = 4

Answer:

1) 2x-3 = x -3 + x

2) 2x - 6 = -6 + 2x

3) [tex]\frac{3}{5}-\frac{13}{5}=-6.9+4.9[/tex]

4) 3x+0 = 3x

5)  [tex]\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x[/tex]

Step-by-step explanation:

We need to match each expression on the left with an equivalent expression on the right

The expressions are equivalent if the have the same results.

1) 2x - 3

Looking at the options the best match is:

x -3 + x

When solve we get:

2x-3

So, 2x-3 = x -3 + x

2) 2x - 6

Looking at the options the best match is:

-6 + 2x

Because according to commutative property: a+b = b+a

So, 2x - 6 = -6 + 2x

3) [tex]\frac{3}{5}-\frac{13}{5}[/tex]

First simplifying the given expression:

[tex]\frac{3}{5}-\frac{13}{5}\\=\frac{3-13}{5}\\=\frac{-10}{5}\\=-2[/tex]

Looking at the options, -6.9+4.9 = -2

So, [tex]\frac{3}{5}-\frac{13}{5}=-6.9+4.9[/tex]

4) 3x + 0

Looking at the options the best match is:

3x

Because, adding 0 in 3x will result in 3x

So, 3x+0 = 3x

5) [tex]\frac{5}{3}-x+\frac{1}{3}[/tex]

First simplifying:

[tex]\frac{5}{3}-x+\frac{1}{3}\\=\frac{5-3x+1}{3}\\=\frac{6-3x}{3}\\= \frac{3(2-x)}{3}\\=2-x[/tex]

Now, solving the option: [tex]-\frac{3}{2}x+2+\frac{1}{2}x[/tex]

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

So, [tex]\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x[/tex]

Answer: A) 6 in^2

First, you need to find the length of the base.

a = 3, b = ?, c= 5

Using Pythagorean Theorem*: a^2 + b^2 = c^2

b^2 = c^2 - a^2

b^2 = 5^2 - 3^2

b^2 = 25 - 9

b^2 = 16 (square root both sides)

b = 4

Now, you have to find the area using the area of a triangle formula: A = (bh)/2

A = (bh)/2

A = (4·3)/2

A = 12/2

A = 6 in^2

Pythagorean Theorem is used for this question since it's a right triangle.

Answer: A) 6in^2

Step-by-step explanation:

base = 4 in

height = 3 in (pythagorean theorem)

A = (bxh)/2 = (4x3)/2 = 12/2 = 6 in^2

Answer:

The answer is below

Step-by-step explanation:

Acceleration is the time rate of change in velocity. Acceleration is given by:

Acceleration = change in velocity / time taken

Acceleration = (final velocity - initial velocity) / time

1) The Ferrari is from rest, hence initial velocity = 0. The final velocity = 100 km/h = [tex]\frac{100\ km*1000\ \frac{m}{km} }{1\ hr*\frac{3600\ s}{1\ hr} } =27.78\ m/s[/tex], time = 5 s

Acceleration = (0 - 27.78) / 5 = 5.56 m/s²

2) The car has initial velocity = 10 m/s. The final velocity = 10 m/s since velocity is constant. time = 20 s

Acceleration = (10 - 10) / 20 = 0 m/s²

3) The ball has initial velocity = 12 m/s. The final velocity = 0 m/s since it stops. time = 36 s

Acceleration = (0 - 12) / 36 = -0.33 m/s²

Answer:

There are two numbers {1,2} which is less than 3. so, required probability P(E) = 2/6 = 1/3.

Step-by-step explanation:

hope this helps

Answer:

Jamarcus is the better shooter

Step-by-step explanation:

Jamarcus is better because he needs 10 more shots to reach 25 while tyrell needs 18 More shots to make 50

Answer:

Tyrell

Step-by-step explanation

Well this is simple you take Jamarcus shots made and divide it into the total shots which is 15/25=0.6 or 60%. So Jamarcus made 60% of the shots attempted. Tyrell made 32 out of 50 shots so that will be 32/50=0.64 or 64%. Since 64%>60% Tyrell is the better shooter

Answer:

Yes.

Step-by-step explanation:

3.5 + 5.5 > 7.8

Answer:

8.7 cm

Step-by-step explanation:

Since all sides of the given shape are equal, so it is a cube.

So length of the diagonal of cube is give as:

[tex]l(diagonal) = l \sqrt{3} \\ \\ = 5 \times 1.732 \\ \\ = 8.66 \\ \\ l(diagonal) \approx8.7 \: cm[/tex]

Answer:

14 more meters

Step-by-step explanation:

6 times square (4) = 24

24-10 = 14

Answer:

j=13

Step-by-step explanation:

The equation for this problem is 7j=91.

I would divide 7 on both sides, which would be j=13.

Answer: all i can do hope this helps a bit 2. 130 degrees

5. 13 units

Answer:

y+3 = -2(x-4)

Step-by-step explanation:

The point slope form of a line is

(y-y1) = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y- -3 = -2 (x-4)

y+3 = -2(x-4)

Step-by-step explanation:

The area of a circle is given by :

A = πr²

r is the radius of the circle

(4) Diameter = 22 cm

Since, radius = diameter/2

r = 11 cm

Now, area of the circle,

[tex]A=\pi \times (11)^2\\\\A=380.13\ cm^2[/tex]

(5) Diameter = 30 cm

Since, radius = diameter/2

r = 15 cm

Now, area of the circle,

[tex]A=\pi \times (15)^2\\\\A=706.85\ cm^2[/tex]

(6) Diameter = 4cm

Since, radius = diameter/2

r = 2 cm

Now, area of the circle,

[tex]A=\pi \times (2)^2\\\\A=12.56\ cm^2[/tex]

So, the area of circles 4,5 and 6 are 380.13², 706.85² and 12.56² respectively.

9514 1404 393

Answer:

  10

Step-by-step explanation:

Let L and T represent the initial amounts that Leo and Theo had. Let n represent the number of bills exchanged in the first exchange. Then we have ...

  L -20n +50n = T -50n +20n . . . . after the first exchange, each has the same

After the second exchange, amounts trade places:

  (L +30n) +6(50) = T

Substituting this into the first equation, we get ...

  L +30n = ((L +30n) +300) -30n

  30n = 300

  n = 10

Leo gave Theo ten $20 bills.

_____

Comment on the amounts

Theo started with $600 more than Leo, including exactly 16 $50 bills. Leo had at least 10 $20 bills, so he could make the initial exchange. Whatever initial amount Leo had in excess of that $200 was matched in Theo's initial amount, but Theo must have had that excess in $20 bills only. For example, Leo may have started with $300 as 10×$20 +2×$50, but Theo's initial $900 would need to be 5×$20 +16×$50.

Answer:

Maximum amount of toppings is 14 inequality is t <=14

Step-by-step explanation:

let t be the amount of toppings on the pizza

0.75t + 2 <= 12.50

0.75t <= 10.50

t <= 14

Answer:

3x - 5y = 17

3(9) - 5(2) = 17

27 - 10 = 17

x = 9

y = 2

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

9x - 15y = -4

I believe this equation has no proper solution. Every "solution" I have found ends with repeating decimals & fractions.

Answer:

7

Step-by-step explanation:

Answer:

Monkey: -5/2

Step-by-step explanation:

monkey = x

3x + 4 = -x - 6

3x + x = -6 - 4

4x = -10

4x/4 = -10/4

x = -5/2

Check:

3x + 4 = -x - 6

3(-5/2) + 4 = -(-5/2) - 6

-15/2 + 4 = 5/2 - 6

-15/2 + 8/2 = -3.5

-7/2 = -3.5

-3.5 = -3.5

Answer:

-2.5

Step-by-step explanation: 3x+4=-1x-6

                                            +1x       +1x

                                        4x+4=-6

                                             -4  -4

                                         4x=-10

       divide                           _     _

                                           4     4      = -2.5