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3 years ago

Translate the given phrase into an algebraic expression and simplify if possible: the product of -13 and the difference of c

Mathematics

1 answer:

Musya8 [376]3 years ago

7 0

Answer: $-13c+13d$

Step-by-step explanation:

For this exercise it is important to remember the following:

1. By definition, the "Product" is the result of a multiplication.

2. The "Difference" is defined as the result of a subtraction.

3. The Distributive property states that:

$a(b+c)=ab+ac\\\\a(b-c)=ab-ac$

Keeping the above on mind, you know that:

"The difference of $c$ and $d$ " can be represented with the following expression:

$c-d$

Therefore, "The product of -13 and the difference of $c$ and $d$ " can be represented with this expression:

$-13(c-d)$

Finally, you must apply the Distributive property in order to simplify the expression. You get:

$=-13c+13d$

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A. The solution is (−2,−3)

Cerrena [4.2K]

9514 1404 393

Answer:

D. (-3, -2)

Step-by-step explanation:

The equations have different coefficients for x and y, so will have one solution. The solutions offered are easily tested in either equation.

Using (x, y) = (-2, -3):

x = y -1 ⇒ -2 = -3 -1 . . . . False

Using (x, y) = (-3, -2):

x = y -1 ⇒ -3 = -2 -1 . . . .True

2x = 3y ⇒ 2(-3) = 3(-2) . . . . True

The solution is (-3, -2).

If you'd like to solve the set of equations, substitution for x works nicely.

2(y -1) = 3y

2y -2 = 3y . . eliminate parentheses

-2 = y . . . . . . subtract 2y

x = -2 -1 = -3

The solution is (x, y) = (-3, -2).

5 0

2 years ago

Geometry Pythagorean theorem

lara31 [8.8K]

Answer:

Below!

Step-by-step explanation:

Using Pythagoras theorem, I will solve all of the problems.

<u>Question 9:</u>

10² = 6² + x²
=> 100 = 36 + x²
=> 100 - 36 = x²
=> 64 = x²
=> x = 8

<u>Question 10:</u>

26² = 24² + x²
=> 676 = 576 + x²
=> 676 - 576 = x²
=> 100 = x²
=> x = 10

<u>Question 11:</u>

15² = 12² + x²
=> 225 = 144 + x²
=> 225 - 144 = x²
=> 81 = x²
=> x = 9

<u>Question 12:</u>

x² = 8² + 12²
=> x² = 64 + 144
=> x² = 208
=> x = √208
=> x = 14.2 (Rounded)

<u>Question 13:</u>

7² = 2² + x²
=> 49 = 4 + x²
=> 49 - 4 = x²
=> 45 = x²
=> x = √45
=> x = 6.7 (Rounded)

<u>Question 14</u>

First, let's solve for the variable x using Pythagoras theorem.

=> 5² = 3² + x²
=> 25 = 9 + x²
=> 16 = x²
=> x = 4 units

Now, let's solve for the variable y using Pythagoras theorem.

(3 + 6)² = 5² + y²
=> (9)² = 25 + y²
=> 81 = 25 + y²
=> y² = 56
=> y = √56
=> y = 7.5 (Rounded) units

Answers (Nearest tenth):

x = 4 units
y = 7.5 units

<u>Question 15:</u>

First, let's find the value of the variable y using Pythagoras theorem.

8² = 6² + y²
=> 64 = 36 + y²
=> 28 = y²
=> y = √28
=> y = 5.3 (Rounded) units

Now, let's find the value of the variable x using multiplication.

x = 2y
=> x = 2(5.3)
=> x = 10.6 units

Answer (Nearest tenth)

x = 10.6 units
y = 5.3 units

5 0

2 years ago

Problem #2: A piece of wood that is 15 feet long is out in half. Each half is then cut into twelve

garri49 [273]

Answer: Each peice of wood is equal to 0.625

Step-by-step explanation:

15/2 = 7.5

7.5/12 = 0.625

4 0

3 years ago

What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?

kompoz [17]

Answer:

K(-4,8) is the ortho center.

Step-by-step explanation:

In a right angled triangle, The vertex of the right angle is the ortho center.

Here we are given

J(-4,-1), K(-4,8) & L(2,8)

Using distance formula we get

$JK^{2}= (-4+4)^{2}+ (8+1)^{2}=0+81=81$

$KL^{2}= (-4-2)^{2}+ (8+-8)^{2}=36+0=36$

$JL^{2}= (-4-2)^{2}+ (8+1)^{2}=36+81=117$

So we can say that

$JK^2 + KL^2=JL^2$

By converse of pythagorean theorem we get

Hence the Vertex of the right angle is K(-4,8)

K(-4,8) is the ortho center.

7 0

3 years ago

The Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week, he sold $4,500 worth of stocks. How m

AlexFokin [52]

Answer: last week he made $630

Step-by-step explanation:

14% of 4500 is 630

8 0

2 years ago