The Distributive Property Use the Distributive Property to rewrite each expression without parenthesis. 1. 6(x + 3) 2. 5( y - 4 ) 3. -7( m - 1 )

The equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation is given below.

4x + 5y = 15

5y = −4x + 15

y = −(4/5)x + 3

The slope of the equation is −4/5. Then the slope of the perpendicular line will be 5/4. Then the equation is given as,

y = (5/4)x + c

The equation that passes through (−10, 2) will be

2 = (5/4)(−10) + c

2 = −12.5 + c

c = 14.5

Then the equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.

More about the equation of a perpendicular line link is given below.

https://brainly.com/question/14200719

#SPJ1

[tex]m=\frac{y_{2-y_{1} } }{x_{2} -x_{1} } \\m=\frac{8-4}{3-2} \\m=\frac{4}{1} \\m=4[/tex]

I also provided the formula on how to calculate the slope between the points

the total price paid for a pair of shoes after tax is included is $37.1.

A sales tax is a tax paid to the government for sales of certain types of goods and services.

According to the question,

Cost of the shoes =  $35.             (given)

Total amount/price paid = cost + tax

As the tax percentage is not given in the question, we will assume it to be 6% for example. Then,

Tax amount = 6% of $35

= 6/100*35

= $2.1

Now, total price = cost + tax

= $35+$2.1

= $37.1

Therefore, we conclude that the total price paid for a pair of shoes after tax is included is $37.1.

To learn more about tax payment

visit; https://brainly.com/question/14178691  

#SPJ1

Variable x as the subject of the equation given is expressed as: x = p(m - n).

To make a variable the subject of a formula implies that we express the equation in terms of the variable. Thus, to make a variable the subject of the formula, we have to make the variable stand alone on one side of the equation.

Given the equation, m = n + x/p, make x the subject as explained below:

m = n + x/p [given]

Subtract n from both sides

m - n= n + x/p - n (subtraction property of equality)

m - n = x/p

Multiply both sides by p

p(m - n) = x/p(p) (multiplication property)

p(m - n) = x

x = p(m - n)

Learn more about subject of a formula on:

https://brainly.com/question/11000305

#SPJ1

They plant a total number of 480 seeds.

In the given question, Chrystal and her grandmother plant seeds in the garden. They plant a total of 4 types of seeds: Squash, Corn, Sunflower, and Tomato. They plant 6 rows of each type of seed. Also, each row has 20 seeds. We have to calculate the total number of seeds that they plant.

Given that,

=> Total number of types of seeds, T = 4

=> Number of rows, R = 6

=> Number of seeds in each row, S = 20

To calculate the Total Number of seeds planted we use the formula:

=> Total = T * R * S, Putting values we get:

=> Total = 4 * 6 * 20

=> Total = 480

Hence, the Total number of seeds planted is 480.

To know more about Product word problems, Click here:

https://brainly.com/question/8595169

#SPJ9

The force created by the object is 3.75 Newton.

Given

Mass of the object (m)  = 1250 grams

Convert 1250 grams to kilograms by dividing it by 1000.

Mass (m) = 1.25 kg

Acceleration of the body (a) = 3 [tex]m/s^{2}[/tex]

From Newton's second law we know [tex]F= m *a[/tex]

By Substituting in the above equation we get

Force = 1.25 x 3

Force = 3.75 [tex]kg/m /s^{2}[/tex]

It can also be written as force = 3.75 N

Hence Force created by the body is 3.75 Newton.

To know more about Force refer

https://brainly.com/question/13191643?referrer=searchResults

We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

So, the wood we need to make 120 pins:

Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

Know more about mathematical operations here:

brainly.com/question/20628271

#SPJ3

The approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.

As given in the question,

Area of the square game board is equal to 160in².

Let 'x' inches be the side length of the square game board.

Area of the square game board = (side length)²

⇒ 160 = ( x )²

Take square root both the sides we get,

    x = √160

⇒ x = 12.649 inches

⇒ x = 12.6 inches( approximately)

Therefore, the approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.

Learn more about area here

brainly.com/question/27683633

#SPJ1

Answer:

206

Step-by-step explanation:

Let x=4.

[tex]f(4)=-3.334(4)^4+35.607(3)^3-97.645(4)^2+41.268(4)+177.537 \approx 206[/tex]

Answer:

The pattern the sequence follows is a perfect square, minus 2

Step-by-step explanation:

esentially use ( n^2 - 2 ) to find the nth number in the sequence.

the 5th number ( n = 5 ), would look like ( 5^2 - 2 ), simplfiying to ( 25 - 2 ), then being 23.

The same applies to all numbers listed in the sequence.

Answer:

53 sets

Step-by-step explanation:

730 - 204 = 526

526 / 10 = 52 r 6

therefore he'd have to buy 53 sets to have enough knives.

There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The restaurant needs at least 730 knives.

There are currently 204 knives.

And, each set on sale contains 10 knives.

Now,

By the given condition, we formulate;

⇒ 730 ≤ 204 + 10x

Solve for x as;

⇒ 730 ≤ 204 + 10x

⇒ 730 - 204 ≤ 204 + 10x - 204

⇒ 529 ≤  10x

Divide by 10 as;

⇒ 52.9 ≤ x

After rounding, we get;

⇒ 53 ≤ x

Thus, There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.

Learn more about the inequality visit:

https://brainly.com/question/25275758

#SPJ2

The product of 1.0×[tex]10^{2}[/tex] and 1.8×[tex]10^{3}[/tex] expressed in scientific notation is 1.8×[tex]10^{5}[/tex]

Scientific notation is the notation that used to express a very large  number or very smaller number is the simplest form. In scientific notation there will be number between 1 to 10 times multiplied by the power of 10.

The first number = 1.0×[tex]10^{2}[/tex]

The second number = 1.8×[tex]10^{3}[/tex]

Multiply the first number by second number, then the result will be

( 1.0×[tex]10^{2}[/tex] )×(1.8×[tex]10^{3}[/tex] )= 100×1800

= 180000

Convert the result to the scientific notation

180000 = 1.8×[tex]10^{5}[/tex]

Hence, the product of 1.0×[tex]10^{2}[/tex] and 1.8×[tex]10^{3}[/tex] expressed in scientific notation is 1.8×[tex]10^{5}[/tex]

Learn more about scientific notation here

brainly.com/question/18073768

#SPJ1

Answer: -0.875

Step-by-step explanation:

Answer: -1 1/8

Step-by-step explanation:

6 - 4 3/4 = 1 1/4

1 1/4 - 2 1/8 = -1 1/8

The correct option c: Subjective Probability, defined by teacher estimated that 95% of the Senior class would attend the prom.

For the given question,

As the probability estimated by the teacher that 95% of the Senior class would attend the prom, is the personal opinion.

Thus, the given case is of Subjective Probability.

To know more about the Subjective Probability, here

https://brainly.com/question/16101256

#SPJ13

Answer: B) 90º counterclockwise

Step-by-step explanation:

           First, let us look at clockwise vs counterclockwise. Clockwise is in the direction of a clock, spinning around to the right. Counterclockwise is the opposite, spinning to the left.

     A) 90º clockwise

➜ This is 90 degrees to the right.

     B) 90º counterclockwise

➜ This is 90 degrees to the left

     C) 180º

➜ This is directly flipped.

     D) 270º clockwise

➜ This is 270 degrees to the right.

     E) 270º counterclockwise

➜ This is 270 degrees to the left.

           We will look at the answer options and decide which makes the most sense. This looks to be option B, 90º counterclockwise as shown in the image attached.

Answer: 100

Step-by-step explanation:

525/84 x 100= 625 total students

625 - 525 = 100

Answer:

k = 4

Step-by-step explanation:

Polynomials:

 p(x) = 2x³ - 3x² - kx - 17

  x - 3 = 0

       x = 3

It is given that when p(x) is divided by (x - 3), it leaves the remainder -2

                ⇒  p(3) = -2

 2(3)³ - 3(3)² - k *3 - 17 = -2

       2*27 -3*9 - 3k -17 = -2

           54 - 27 - 3k -17 = -2

                       -3k + 10 = -2

                             -3k  = -2 - 10

                             -3k = -12

                                 k = (-12) ÷ (-3)

                                  [tex]\sf \boxed{k = 4}[/tex]

Answer:

The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway

Step-by-step explanation:

if a car uses 3 1/8 gollon per one hour

Multiply the gallon usage of the car by the hours the car will travel on the road

3 1/8(gallons) x 3(hours on the road)

9 3/8 or if you change it to simple form it will be equal to 9.375

Answer:

14137167 liters approximately

Step-by-step explanation:

Total Volume of a cylinder

V = π R² H

where R - base radius

H = height

Given diameter of base = 30m, base radius R = 30/2 = 15

H  = 20m

Volume = π x 15² x 20 = 4500π m³ = 14,137.16694 m³

Since 1 m³ = 1000 liters

this works out to  14137.16694 x 1000 ≈ 14137167 liters

In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.

An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.

Both Ang and Julia have savings balances of x and y dollars, respectively.

Ang = x dollars

Julia = y dollars

Ang offers Julia a third of his savings, which she then transfers to her own savings account.

Amount in Julia's account = (1/3)x + y

Julia then spends a quarter of the total into her savings account.

Amount of money Julia spent = 1/4 × [(1/3)x + y]

                                                 = (1/12)x + (1/4)y

                                                 = y/4 + x/12

Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.

Learn more about representation of algebraic expressions here:

https://brainly.com/question/28036476

#SPJ13

Answer:

I believe it should be 5/6

Step-by-step explanation:

Here's why, the probability of getting a B, or an even number is 3/6 since there are 3 even numbers on a dice. The probability of getting a multiple of 3 is 2/6 since the only multiples of 3 are 1 and 3. Add the 2 together to get 5/6. Hope this helps.

Answer:

[tex]\text{P}(B \text{ or }C)=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Mutually Exclusive Events

For two events, A and B, where A and B are mutually exclusive:

[tex]\boxed{\text{P}(A \text{ or }B)=\text{P}(A)+\text{P}(B)}[/tex]

Probability distribution table:

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6 \\\cline{1-7} \text{P}(X=x)\phantom{\dfrac11}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}\\\cline{1-7}\end{array}[/tex]

where X is the score on a fair, six-sided dice.

P(B or C) means "the probability of rolling an even number or a multiple of 3".

As an even number of a fair, six-sided dice can never be a multiple of 3, the two events B and C are mutually exclusive.

Calculate the probabilities for events B and C.

Event B

Rolling an even number.

[tex]\begin{aligned}\implies \text{P}(X \text{ is even})&=\text{P}(2 \text{ or }4\text{ or }6)\\\\&=\text{P}(X=2)+\text{P}(X=4)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{3}{6}\end{aligned}[/tex]

Event C

Rolling a multiple of 3.

[tex]\begin{aligned}\implies \text{P}(X \text{ is multiple of 3})&=\text{P}(3 \text{ or }6)\\\\&=\text{P}(X=3)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{2}{6}\end{aligned}[/tex]

Solution

[tex]\begin{aligned}\implies \text{P}(B \text{ or }C)&=\text{P}(B)+\text{P}(C)\\\\& = \dfrac{3}{6}+\dfrac{2}{6}\\\\& = \dfrac{5}{6}\end{aligned}[/tex]

Answer: x=3

Step-by-step explanation:

40-25=15

15 divided by the 5 movies is 3

so $3 per movie

please mark brainliest if this helps :)

Answer:

[tex]-5x^2 + 3x+9[/tex]

Step-by-step explanation:

Let the polynomial be p(x).

[tex]p(x)+(5x^2 -3x-9)=0 \\ \\ p(x)=-(5x^2 -3x-9) \\ \\ =-5x^2 + 3x+9[/tex]

The value of a is 9 and b is 4.5

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that can be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

[tex]sin(60)=\frac{opposite}{hypotenuse} \\\frac{\sqrt{3} }{2}=\frac{\frac{9\sqrt{3} }{2} }{a}\\ a =9\\ tan(60)=\frac{opposite}{adjacent}\\ \sqrt{3}=\frac{\frac{9\sqrt{3} }{2} }{b} \\b=4.5[/tex]

The value of a is 9 and b is 4.5

To learn more about trigonometric function visit :

brainly.com/question/14746686

#SPJ9

Answer: 36

Step-by-step explanation:

The answer is 36 because if you multiply:

6 * 2 = 12

12 * 3 = 36

And so that equals 36 sq cm

OR:

6 * 2 * 3 = 36 sq cm

I hope this helped!

The quadratic equation will be; 3x² + 6x + 9

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.

The factors are; (x + 3) and (x + 1)

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

As, a = 3.

Then we get;

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

= 3(x² + 2x + 3)

= 3x² + 6x + 9

The quadratic equation will be; 3x² + 6x + 9

Learn more about quadratic equation here:

brainly.com/question/15262743

#SPJ1

Answer:

105

Step-by-step explanation:

5 minutes=75 pages

1 minute=15 pages

7 minutes=15*7

7 minutes=105pages

Answer: 105

Step-by-step explanation:

75pg —-> 5mins

X ——> 7 mins

•

•

x= (75 x 7)/5 = 105pages

Answer: 7/12 =x

Step-by-step explanation:

The expression in term numerator and denomerator of P the write answer would be

25.

Sol-

we have a deal an arrangement where, at the end of 5 years, the value of the car is going to be a fifth, the original price. So that's what i have written here after 5 years, the value of the car will be the price, the original price divided by 5 point. What we also know is that at 0 years, our initial value, the output here- should be the price of the car. So what we're going to do is when we use these 2 values to find the slope of this line, so we're going to do y 2, minus 1 y 1 over x, 2 minus x 1. It doesn't matter which 1 is y 2 and which 1 is y 1 as long as you're consistent here, i'm going to do p minus p over 5, and since i started here in the numerator, i need to start there in the denominator.

So we know here that x equals 4 we're doing that in the problem. So i'm goin t go ahead and replace this right here. We'Re gonna have y equals 16 p over negative 25 plus p, and if we get a common denominator here to add this, we have y equals 16 p plus 25 over 25. With this p right here, because it's gonna be 25 p over 25 here and then i recognize that are y value here, that was that was v or value here. All right and, let's see 25 p minus 16 p is going to give us 9 p. All right, so 9 p over 25 is going to be the value of the car, giving the original price p after 4 years.

To know more about numenator and denominator click-

https://brainly.com/question/20712359

#SPJ9

The output value of f( -4 ) in the function f(x) = -x² - 4x + 42 is 42

A function is simply a relationship that maps one input to one output. Every x-value can only have one y-value to qualify as a function.

Given the data in the question;

To find the output value of f( -4 ), replace all the occurrence of x with -4 in the function and simplify.

f( x ) = -x² - 4x + 42

f( -4 ) = -(-4)² - 4(-4) + 42

f( -4 ) = -( 16 ) + 16 + 42

f( -4 ) = -16 + 16 + 42

f( -4 ) =  42

Therefore, the output value of f( -4 ) is 42, this forms an ordered pair of (-4, 42).

Lear more about functions here: brainly.com/question/2541698

#SPJ1