A movie collection has 6 mystery, 10 comedy, 4 adventure, 9 drama, and 12 science fiction discs. How many 5-disc combinations can be made from the collection? (Hint: Divide the total combinations by 5. )

Answer:

x = 14

Step-by-step explanation:

Vertical angles are congruent ( equal to each other )

If ∠A and ∠B are vertical angles

Then 5x + 2 = 6x - 12

                     ^ ( Note that we just created an equation that we can use to                                   solve for x )

The rest comes down to basic algebra

5x + 2 = 6x - 12

step 1 subtract 5x from each side

5x - 5x cancels out

6x - 5x = x

we now have 2 = x - 12

step 2 add 12 to each side

- 12 + 12 cancels out

2 + 12 = 14

we're left with x = 14

Given:

Consider the sides of the rectangle are (x+7) and (x+5) units.

To find:

The area of the entire rectangle in standard form.

Solution:

The area of the rectangle is:

[tex]A=l\times w[/tex]

Where, l is length and w is width of the rectangle.

So, the area of the given rectangle is:

[tex]A=(x+7)\times (x+5)[/tex]

[tex]A=(x)(x)+(x)(5)+(7)(x)+(7)(5)[/tex]

[tex]A=x^2+5x+7x+35[/tex]

[tex]A=x^2+12x+35[/tex]

Therefore, the area of the rectangle is [tex]A=x^2+12x+35[/tex].

Answer:

d. alternate interior angles are congruent

Answer:

(a) Neither

(a) Perpemdicular

Step-by-step explanation:

Required

Determine the relationship between given lines

(a)

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

and

[tex]y = \frac{2}{5}x + 7[/tex]

An equation written in form: [tex]y=mx + b[/tex] has the slope:

[tex]m \to slope[/tex]

So, in both equations:

[tex]m_1 = -\frac{2}{5}[/tex]

[tex]m_2 = \frac{2}{5}[/tex]

For both lines to be parallel

[tex]m_1 = m_2[/tex]

This is false in this case, because:

[tex]-\frac{2}{5} \ne \frac{2}{5}[/tex]

For both lines to be perpendicular

[tex]m_1 * m_2 = -1[/tex]

This is false in this case, because:

[tex]-\frac{2}{5} * \frac{2}{5} \ne -1[/tex]

(b)

[tex]5y + 2x = -10[/tex]

and

[tex]-5x + 2y = 4[/tex]

Write equations in form: [tex]y=mx + b[/tex]

[tex]5y + 2x = -10[/tex]

[tex]5y = -2x +10[/tex]

Divide by 5

[tex]y = -\frac{2}{5}x +2[/tex]

[tex]-5x + 2y = 4[/tex]

[tex]2y = 5x + 4[/tex]

Divide by 2

[tex]y = \frac{5}{2}x + 2[/tex]

In both equations:

[tex]m_1 = -\frac{2}{5}[/tex]

[tex]m_2 = \frac{5}{2}[/tex]

For both lines to be parallel

[tex]m_1 = m_2[/tex]

This is false in this case, because:

[tex]-\frac{2}{5} \ne \frac{5}{2}[/tex]

For both lines to be perpendicular

[tex]m_1 * m_2 = -1[/tex]

This is true in this case, because:

[tex]-\frac{2}{5} * \frac{5}{2} = -1[/tex]

Cancel out 2 and 5

[tex]-1 = -1[/tex]

Answer: 60

Step-by-step explanation:

If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60

Answer:

3.844 x 10 to the power of 5 is the answer i think

Step-by-step explanation:

Answer:

If the other person is correct then it should be 3.844 x 10^5 and 3.844E5 as well

Step-by-step explanation:

Answer:

85 units²

Step-by-step explanation:

Add up your given areas to find the missing area using the Pythagorean Theorem:

a²+b²=c²

35+50=c²

85=c²

Therefore, the area of the blue square is 85 units²

Answer:

85 units²

Step-by-step explanation:

Answer: 274 votes

Step-by-step explanation:

Since we are informed that in a a​ poll that 411 students voted and Nominee C received ⅔ of the votes.

Therefore, the number of votes that Nominee C ​received will be:

= ⅔ × 411

= 274

Therefore, Nominee C got 274 votes

Answer:

The answer is "Find the tallest stack of dots".

Step-by-step explanation:

In this question, we assume that the prices of the plot area on the X (horizontal), and the Y (Vertical) axis are on the cell phone. This price is 90 dollars. Whenever the price is X1, she sets a dot there. When brand X2 is that price also, it places a coordinate point ($90, X2) well above point on either brand at the same price. Therefore, the bigger pile of teams overall that the rates are more mobile phones.

Answer:

y = -3/2 or -1.5

Step-by-step explanation:

-2/3 + y = -2 1/6

-2 1/6 = -13/6

So, our equation is

-2/3 + y = -13/6

Add 2/3 to both sides

y = -3/2

So, the answer is

y = -3/2 or -1.5

Answer:
Y= -3/2
in decimal form it is -1.5
in mixed number form it is -1 1/2

Step-by-step explanation:

Answer:

$8173

Step-by-step explanation:

For this problem you will use the formula P(t)=Pe^r(t). P=5800 r=4.9%=0.049

t=7 years. With using this formula you should get your answer. I hope this helps!

The effective annual rate of interest if you do not make any payments for a year is 35%.

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.

We can write -

A = 500(1 + 0.3/12)¹²⁽¹⁾

A = 500(1 + 0.025)¹²

A = 500 x (1.025)¹²

A = 675

Effective annual interest rate for a year is as follows -

A = 500(1 + r/1)⁽¹⁾⁽¹⁾

675 = 500(1 + r)

1 + r = 675/500

1 + r = 1.35

r = 0.35

r = 35%

Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.

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Answer:

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

The width of the space for computer stations is:

Each computer station has a space of:

Answer:

166 square units

Step-by-step explanation:

Let’s find the area of the shapes that in the net.

First, we can see two of the triangles have a base of 2 and a height of 13. The formula for surface area of a triangle is bh÷2. (13x2)÷2=13. Since there are two triangles, we multiply 13 by 2 and get 26.

Second, we can see two of the triangles have a base of 10 and a height of 12. (10x12)÷2=60. Since there are two triangles, we multiply 60 by 2 and get 120.

Third, we can see a rectangle has a base of 10 and a height of 2. The formula for surface area of a rectangle is bh. 10x2=20.

Last, we add up all the areas:

20+120+26=166.

Answer: O x<12

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+25<85

Step 2: Subtract 25 from both sides.

5x+25−25<85−25

5x<60

Step 3: Divide both sides by 5.

5x/5 < 60/5

x<12

The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.

From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.

An expression have at least two terms which have to be related by through an operator.

Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:

2 - (25% × h)

= 2 - 0.25h

h = number of hours.

The expression is 2 - 0.25h.

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Complete question

Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression

Answer:

5/8

Step-by-step explanation:

15/3=5 and 24/3=8

Answer:

5/8

Step-by-step explanation:

divide both by 3

Step-by-step explanation:

The way that you would multiply polynomials is pretty easy. Say we had a binomial and a trinomial and we wanted to multiply them. As an example, we will use (2x + 4) (x^2 + x + 4).

You have to multiply each number with each other number. For example, we would multiply 2x by x^2, 2x by x, and 2x by 4 to get the first part of the bigger equation. These come out to being 2x^3 + 2x^2 + 8x when multiplied and added.

Then, you have to do the same thing for the 4 in the binomial. Multiply 4 by x^2, 4 by x, and 4 by 4 to get the second part of the bigger equation. These come out as 4x^2 + 4x + 16 when added and multiplied.

After both of those are done, simply add the two parts together and simplify.

2x^3 + 2x^2 + 8x + 4x^2 + 4x + 16

2x^3 + 6x^2 + 12x + 16

That is your example answer, and that is how you multiply polynomials.

Answer:

Step-by-step explanation:

he small ones cost $2 and the bigger ones cost $3. So to get the answer you will need to multiply the number of flowers with the cost. In this case 2 times x and 3 times y. x represents the small flowers and y represents the big flowers.

Answer:

2x + 3y = 40

Step-by-step explanation:

Blank space 1: 3

Blank space 2: 4.242

Blank space 3: 6

Blank space 4: 6

Blank space 5: 3

This can be solved using triangle theorem.

Given that,

Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal.

The bigger square = 36 sq. in.

Then the side of the bigger square = √36 inch = 6 inch

Next, The side of the bigger square = Diagonal of the smaller square

Let the side of the smaller square = a (let)

Diagonal (smaller square): a√2 = 6 inch

so, a = 3√2 inch

Thus,  a = 3 x 1.414 = 4.242

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The complete question is as follows:

The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

It means one of four parts and two of five parts.

We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!

The carnations of a set of flowers is 7/10. It is 4200 carnations.

The carnations part is 7 and the whole part of flowers is 10.

Using fraction, the whole flowers would be

= 10/7 × 4200

= 6.000 flowers

Hence, the number of flowers needed to be on the float is 6.000 flowers.

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Therefore , the solution of the given problem of equation comes out to bem² + p² =z².

The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.

Here,

Given : a triangle of m,p,z of length of right triangle :

By using Pythagoras theorem :

The relationship comes out to be :

=> m² + p² =z²

Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.

Therefore , the solution of the given problem of equation comes out to be m² + p² =z².

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Answer:

d. Atlantic Ocean

Answer:

Atlantic Ocean

Answer: The length of each side of the triangle is; 

Equal sides, x = 21.02 = PQ = PR

QR = 28.03

Step-by-step explanation: The trusses made by the manufacturer have the shape of an isoscellestriangle and as such two congruent sides PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.

The perimeter of each truss is 70ft.

Let the length of each congruent side be x ft.

Therefore,

Perimeter = x + x + (4/3)x

Perimeter, p = 70 = 3.33x

x = 70/3.33

x = 21.02

Therefore, Length of QR is; QR = (4/3) x

QR = (4/3) × 21.02

QR = 28.03

Answer:

The area of the shaded region is, [tex]24mm^{2}[/tex]

Step-by-step explanation:

First we have to calculate the area of ΔABC and ΔXYZ.

Area of ΔABC = [tex]\frac{1}2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔABC = [tex]\frac{1}{2}[/tex]×[tex]5mm[/tex]×[tex]12mm[/tex]

Area of ΔABC =[tex]30mm^{2}[/tex]

and,

Area of ΔXYZ = [tex]\frac{1}{2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔXYZ = [tex]\frac{1}{2} X3mmX4mm[/tex]

Area of ΔXYZ = [tex]6mm^{2}[/tex]

Now we have to calculate the area of the shaded region.

Area of the shaded region = Area of ΔABC - Area of ΔXYZ

Area of the shaded region = [tex]30mm^{2} - 6mm^{2}[/tex]

Area of the shaded region = [tex]24mm^{2}[/tex]

Therefore, the area of the shaded region is, [tex]24mm^{2}[/tex]

Answer:

o, we should add 16 on both sides in order to make it a complete square

Step-by-step explanation:

For making a perfect square we will add 16 on both sides of the given equation.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Given equation is:-

x² - 8x = 5

x² - 8x + 16  = 5 + 16

x² - 4x -4x + 16  = 5 + 16

x ( x - 4 ) -4 (x - 4 ) = 21

( x - 4 )²  =  21

Therefore to make a perfect square we will add 16 on both sides of the given equation.

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Answer:

Trina is 45 years old.

Her grandfather is 50 years old.

Step-by-step explanation:

Trina is 5 years younger than grandfather, therefore:

45+50 = 95

The == operator determines if two operands are equivalent in terms of value. The === operator determines if two operands are equivalent in terms of value and datatype.

The assignment operator = is straightforward. The left side operand receives values from the right side operands.

On the other hand, == determines whether or not the values of two operands are equal.

The Python is operator determines if two variables point to the same memory item as opposed to the == operator, which compares the value or equality of two objects. This implies that you should almost always employ the equality operators == and != Difference between == and = in Python.

A single equal sign is used to assign a value to a variable in Python and many other programming languages, whereas two successive equal signs are used to determine if two expressions provide the same result.

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Answer:

A.   2w² + 8w

Step-by-step explanation:

rectangle:  A = w(w+4) = w² + 4w

triangle:  A = 1/2(2(w+4)(w)) = 1/2(2w+8)(w) = 1/2(2w²+8w) = w² + 4w

Total Area = w² + 4w + w² + 4w = 2w² + 8w