7. Eva bought popcorn, candy and a drink at
the movies. The popcorn was three times as
expensive as the candy and the drink was
twice as expensive as the candy. Eva spent a
total of $10.50.
a. Write an equation to represent the situation.
Let c represent the cost of the candy.
b. Find the value of c.
c. How much did Eva's
drink cost?

Answer:  x=8

Step-by-step explanation:

3x - 5= 2.5x + 3 -(x-4)   apply the distributive property

3x -5 = 2.5x + 3 - x + 4     combine like terms  on the right side

3x - 5 = 1.5x + 7            Add 5 to both sides

    +5             +5

3x = 1.5x + 12      subtract 1.5x from both sides

-1.5x  -15.x

1.5x = 12       Now divide both sides by 1.5

x = 8

Add 2 x 2 + 5 x + 6 to − 4 x 2 − x + 7

Add the expressions.

13

Answer:

Step-by-step explanation:

Answer:

obtuse , 90 , 180 .

Step-by-step explanation:

Answer:

t = 32/5

Step-by-step explanation:

7 - (5t - 13) = -12

7 - (5t - (-13) = -12

7 - 5t + 13 = -12

-5t = -12 - 13 - 7

-5t = -32

t = -32 / -5

t = 32/5

Answer:

No solution (because the n's cancel out!)

Step-by-step explanation:

Let's solve your equation step-by-step.

8

2

=

6

n

+4

Multiply all terms by n and cancel:

8n

2

=6+4n

4n=4n+6(Simplify both sides of the equation)

4n−4n=4n+6−4n(Subtract 4n from both sides)

0=6

Answer:

No solutions.

Answer:

A

Step-by-step explanation:

So we have the piecewise function:

[tex]f(x)= \begin{cases}\sqrt{2x} & \text{if }x<3 \\2x+10 & \text{if }3\leq x<8\\42&\text{if } x\geq 8\end{cases}[/tex]

And we want to find f(8).

Since our input value is 8, choose the equation that fits our input.

The first equation demand x to be less than 3. 8 is not less than 3, so we won't use that.

The second equation demand x to e greater than or equal to 3 and less than 8. 8 is not less than 8. So, we won't use that.

The third equation demands x to be greater than or equal to 8. 8 is greater than or equal to 8, so we'll use the third equation.

So:

[tex]f(x)=42\text{ if }x\geq 8[/tex]

[tex]f(8)=42[/tex]

There're nothing more to do, we're done :)

The answer is A.

Edit: Improved Format

Answer:

(7, 3)

Step-by-step explanation:

(2+5, 6-3) = (7, 3)

Answer:

  C. 72 degrees

Step-by-step explanation:

Complementary angles total 90 degrees.

The second angle is ...

  90° - 18° = 72°

Answer: the distance is 9,

Step-by-step explanation: If you count the blocks you will see it's nine! Hope this helped you!

Answer:

384 inches per second.

Step-by-step explanation:

We are given that the acceleration of an object due to gravity is 32 feet per second.

And we want to find the acceleration in inches per second.

The acceleration can be represented as a ratio of 32 feet : second. This can be written as a fraction:

[tex]\displaystyle \frac{32\text{ feet}}{\text{second}}[/tex]

Use dimensional analysis. It is known that there is 12 inches in a feet. So, multiply by 12in/feet:

[tex]\displaystyle = \frac{32\text{ feet}}{\text{second}}\cdot\frac{12\text{ inches}}{\text{feet}}[/tex]

Cancel like units:

[tex]\displaystyle =\frac{32\cdot 12\text{ inches}}{\text{second}}[/tex]

Multiply:

[tex]\displaystyle =\frac{384\text{ inches}}{\text{second}}[/tex]

In conclusion, our answer is 384 inches per second.

Answer:

a = 2500mm

b = 5km

c = 2e+7

Step-by-step explanation:

Answer:

a)

1cm = 10mm

250cm = 250*10 = 2500mm

b)

1km = 1000m

5000m = 5000/1000 = 5km

c)

1km = 1000m

1m = 100cm

1km = 1000*100 = 100000cm

200km = 200*100000 = 20000000cm

Answer:

x=4

Step-by-step explanation:

2x+3=11

2x+3-3=11-3

2x=8

x=4

2x+3=11

2(4)+3=11

8+3=11

11=11

Answer:

x =4

Step-by-step explanation:

[tex]2x +3=11\\\\Collect \:like\:terms\\2x =11-3\\\\Subtract\\2x =8\\\\Divide\:both\:sides\:of\:the\:equation\:by\:2\\\frac{2x}{2} =\frac{8}{2} \\\\x = 4[/tex]

Answer:

-21

Step-by-step explanation: a negative times a positive will always be a negative

Answer:

13 5/8

Step-by-step explanation:

3 3/4+9 7/8

15/4+79/8

30/8+79/8

109/8

simplify

13 5/8

Answer:

Complementary

Step-by-step explanation:

Complementary Angles add up to 90°

Supplementary Angles add up to 180°

60 + 30 = 90

Answer:

Ok, the straightforward thing you can do, when you have a number line like in this situation, you can just "count" the number of units that are between A and B.

Now, a more correct way:

First, A is located at the value -3, then we can write:

A = -3.

And B is located at the value 5, then:

B = 5.

Now, the distance between A and B is equivalent to the difference between A and B:

D = B - A = 5 - (-3) = 8

The distance between A and B is 8 units.

Answer:

[tex]=3-4i[/tex]

Step-by-step explanation:

So we have:

[tex](2-i)-(-1+3i)[/tex]

First, distribute:

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

Combine like terms:

[tex]=-i-3i+2+1[/tex]

Add:

[tex]=-4i+3[/tex]

So, in the a+bi format, we will have:

[tex]=3-4i[/tex]

Answer:

3 -4i

Step-by-step explanation:

(2-i) - (-1+3i)

Distribute the minus sign

(2-i) + 1-3i

Combine like terms

3 -4i

Answer:

a. F=GMm/r^2; a. M =

[tex]M = \frac{Fr^{2} }{Gm}[/tex]

a.  F=GMm/r^2; b. r =

[tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]

b. M=kxa^3/p^2; a. P =

[tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]

b. M=kxa^3/p^2; b. a =

[tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]

Step-by-step explanation:

For a.  F=GMm/r^2; a. M =

To solve for M, we will rearrange the given equation F=GMm/r^2 such that M is the subject of the formula

From

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

First, Cross multiplication, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]Gm[/tex]

[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm} \\[/tex]

The equation becomes

[tex]\frac{Fr^{2} }{Gm} = M[/tex]

∴ [tex]M = \frac{Fr^{2} }{Gm}[/tex]

For a.  F=GMm/r^2; b. r =

Also, to solve for r, we will rearrange the given equation F=GMm/r^2 such that r is the subject of the formula

From

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

First, Cross multiplication, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]F[/tex], Such that we have

[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]

Then, [tex]r^{2} = \frac{GMm}{F} \\[/tex]

∴ [tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]

For b. M=kxa^3/p^2; a. P =

To solve for P, we will rearrange the given equation M=kxa^3/p^2 such that P becomes the subject of the formula

From

M=kxa^3/p^2

[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]

First, Cross multiply, we then get

[tex]Mp^{2} = kxa^{3}[/tex]

Divide both sides by [tex]M[/tex], such that the equation becomes

[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3}}{M}[/tex]

Then, [tex]p^{2} = \frac{kxa^{3}}{M}[/tex]

∴ [tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]

For b. M=kxa^3/p^2; b. a =

To solve for a, we will rearrange the given equation M=kxa^3/p^2 such that a becomes the subject of the formula

From

M=kxa^3/p^2

[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]

First, Cross multiply, we then get

[tex]Mp^{2} = kxa^{3}[/tex]

Now, Divide both sides by [tex]kx[/tex], such that the equation gives

[tex]\frac{Mp^{2}}{kx} = \frac{ kxa^{3}}{kx}[/tex]

Then, [tex]\frac{Mp^{2}}{kx} = a^{3}[/tex]

[tex]a^{3} = \frac{Mp^{2}}{kx}[/tex]

∴ [tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]

Answer:

a. Types of computer software used in a database management system. =Qualitative

b. Life-lengths of laser printers =Quantitative

c. Brands of calculators used by 100 engineering students on campus =Qualitative

d. Mileage attained by 12 automobiles powered by alcohol= Quantitative

Step-by-step explanation:

Data is described as quantitative when it deals with numeric values whereas qualitative data is categorical in nature. Quantitative data tells us how much, how many, or the frequency of occurrence of certain variables. Qualitative data provides answers to the what, why, which, and where questions.

1. Types of computer software are not numeric variables as they answer the 'what' question.

2. Length deals with numbers, so the life-lengths of laser printers is a quantitative variable.

3. Brands of calculators are categorical data and are thus qualitative.

4. Mileage is a numerical variable and is thus quantitative.

Answer:

Let's see it by an example!

The numbers are given:

5 , 77 , 23 ,45 & 0

Let's arrange this from least to greatest :

0<5<23<45<77

Note : This sign(<) means greater than.

Hope you understand!✔

You can also practice this by greatest to least!

You can use this sign(>) [ it means less than ]

SMALL Example is given :

55>2

Answer:

Hey there!

8(2)+8(6)

16+48=64

The total price is 64 dollars.

Let me know if this helps :)

Answer:

50 square units

Step-by-step explanation:

Using the formula provided, [tex]a = \frac{1}{2}h(b_1+b_2)[/tex], substituting the height (5), b1 (8) and b2 (12), we can solve for the formula.

[tex]a = \frac{1}{2}\cdot5(8+12)\\\\a = \frac{1}{2}\cdot5(20)\\\\a = \frac{1}{2}100\\\\a = 50[/tex]

Hope this helped!

Answer:

50 units²

Step-by-step explanation:

The area of a trapezoid can be found using the following formula.

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

The height of the trapezoid is 5 units. The bases are 8 units and 12 units.

[tex]h= 5 \\b_{1} = 8\\b_{2} = 12[/tex]

Substitute the values into the formula.

[tex]A=\frac{1}{2}*5(8+12)[/tex]

Solve inside the parentheses. Add 8 and 12.

8+12=20

[tex]A=\frac{1}{2}*5(20)[/tex]

Multiply 5 and 20.

5*20= 100

[tex]A=\frac{1}{2}*100[/tex]

Multiply 1/2 and 100 or divide 100 by 2.

100 * 1/2= 50     or      100/2= 50

[tex]A= 50[/tex]

Add appropriate units. For this problem, the units are units².

[tex]A= 50 units^2[/tex]

The area of the trapezoid is 50 square units.

Don't quite understand the question so I'm gonna provide 2 answers

The simplest one being 3

If you're making combinations then 7

hand-tossed(1), thin(2), pan(3), hand-tossed and thin(4), hand-tossed and pan(5), thin and pan(6), all 3(7)

Answer:

y = 4(x + 11)² - 484

Step-by-step explanation:

y = 4x² + 88x

factor the expression

y = 4(x² + 22x)

complete the square

y + ? = 4(x² + 22x + ?)

y + ? = 4(x² + 22x + 121)

add 4 • 121 to the left side

y + 4 • 121 = 4(x² + 22x + 121)

multiply

y + 484 = 4(x² + 22x + 121)

y + 484 = 4(x + 11)²

subtract both sides by 484

y = 4(x + 11)² - 484

Answer:

y = 4(x + 11)² - 484

Step-by-step explanation:

Answer:

8 cubic units

Step-by-step explanation:

Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D =  (0,6,3)

The edges of the parallelepiped are

AB = (6,3,8)  - (4,2,4) = (2,1,4)

AC = (6,1,10) - (4,2,4) = (2,-1,6)

AD = (0,6,3) - (4,2,4) = (-4,4,-1)

Therefore the volume of the parallelopiped is = |[AB,AC,AD]|

=  [tex]$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$[/tex]

= |2(1-24)+1(-2+24)+4(8-4)|

= |2(-23) + 1(22) + 4(4)|

= |8|

=8 cubic units

Answer:

-11

Step-by-step explanation:

start with PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)

so you would first start with 14 + (-12) so the + and - become a negative so it becomes 14 - 12 which is 2

so then do -8-5 which is -13

so then you combine them and get 2-13 which is -11

Answer:

  sin(x) = tan(x) = 0

  cos(x) = sec(x) = -1

  cot(x) = csc(x) = UNDEFINED

Step-by-step explanation:

An angle of -7π is co-terminal with an angle of π (or 180°). Its trig ratios are ...

  sin(x) = tan(x) = 0

  cos(x) = sec(x) = -1

  cot(x) = csc(x) = UNDEFINED