All categories

2 years ago

Use the Distributive Property to rewrite the algebraic expression. 5(2x + 7)

Mathematics

1 answer:

IceJOKER [234]2 years ago

6 0

Answer:

10x + 35

Step-by-step explanation:

In distributive property, you have to distribute that 5 to both the 2x and the 7, so then it would look like this:

5(2x) + 7(5)

Then we just further simplify and get:

10x + 35.

Hope this helped, let me know if you have any questions

You might be interested in

3x+10+70=180 I'm supposed to find the value of x

liubo4ka [24]

To find the value of x let's make the situation a bit easier

3x+10+70=180
3x+80=180
3x=180-80
3x=100
x = about 33.33

7 0

4 years ago

Read 2 more answers

A student raises her average grade from a 75 to a 90. What is the percent of the increase in the students average grade

tensa zangetsu [6.8K]

Since grades are out of 100, you can just subtract 75 from 90 which is 15. the percent of increase in the student's grade is 15%

5 0

3 years ago

A heated piece of metal cools according to the function c(x) = (.5)x − 9, where x is measured in hours. A device is added that a

konstantin123 [22]

In both cases, we have cooling. We can add together the 2 functions describing this cooling: z(x) = 0.5x - 9 - [-x-2] = 0.5x - 9 + x + 2, or

z(x) = 1.5x - 7

Provided that this is correct, all we have to do now is to subst. 5 for x:

z(5) = 1.5(5) - 7 = 7.5 - 7 = 0.5 (answer)

6 0

3 years ago

Read 2 more answers

Flying against the wind, a jet travels 8730mi in 9 hours. Flying with the wind, the same jet travels 7260mi in 6 hours. What is

Alex787 [66]

recall your d = rt, distance = rate * time.

j = jet's rate

w = wind's rate

so with the wind the actual speed of the Jet is really j + w, because the wind is adding speed to it, and against it is j - w, since the wind is eroding speed from it.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&8730&j-w&9\\ \textit{with the wind}&7260&j+w&6 \end{array}~\hfill \begin{cases} 8730=(j-w)(9)\\ 7260=(j+w)(6) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{\cfrac{8730}{9}=j-w\implies }970=j-w\implies 970+w=j \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{using the 2nd equation}}{\cfrac{7260}{6}=j+w}\implies 1210=j+w\implies \stackrel{\textit{doing some substitution on \underline{j}}}{1210=(970+w)+w} \\\\\\ 1210=970+2w\implies 240=2w\implies \cfrac{240}{2}=w\implies \boxed{120=w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{970+w=j}\implies 970+120=j\implies \boxed{1090=j}$

4 0

3 years ago

The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What

inn [45]

x2-16x+48=0 Two solutions were found : x = 12 x = 4

Step by step solution :Step 1 :Trying to factor by splitting the middle term

1.1 Factoring x2-16x+48

The first term is, x2 its coefficient is 1 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is +48 

Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48

Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -16 .

-48 + -1 = -49 -24 + -2 = -26 -16 + -3 = -19 -12 + -4 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -4
 x2 - 12x - 4x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :
 x • (x-12)
 Add up the last 2 terms, pulling out common factors :
 4 • (x-12)
Step-5 : Add up the four terms of step 4 :
 (x-4) • (x-12)
 Which is the desired factorization

Equation at the end of step 1 : (x - 4) • (x - 12) = 0 Step 2 :Theory - Roots of a product :

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve : x-4 = 0

Add 4 to both sides of the equation :
 x = 4

Solving a Single Variable Equation :

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :
 x = 12

Supplement : Solving Quadratic Equation DirectlySolving x2-16x+48 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex :

3.1 Find the Vertex of y = x2-16x+48

5 0

3 years ago

Read 2 more answers