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3 years ago

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Jason has to type 4 pages in 3 class periods. He says when he divides 4 by 3, he gets 1 R1. He is not sure what this means. Whic

h of the following represents how many pages he needs to complete each period?

1 answer:

Verizon [17]3 years ago

4 0

Answer: he needs to get 1 1/3 pages done each class period.

Step-by-step explanation:

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Can someone answer the 2 questions in the picture i really need help

Radda [10]

Hi.

The first question is a direct variation — specifically y = 1.8x

In the second one (if my calculations are correct), it's not a direction variation.

Hope this helps :)

Calculations:

y = 1.8(3) = 5.4

y does not equal x, 2x, or -2x.

7 0

3 years ago

2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

$f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0$

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1 10 35 50 24

<u>| 0 -1 -9 -26 -24</u>

<u> 1 9 26 24 0</u>

Hence quotient is $x^{3} +9x^{2} +26x+24$

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

$(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0$

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1 9 26 24

<u>| 0 -2 -14 -24</u>

<u> 1 7 12 0</u>

Hence quotient is $x^{2} +7x+12$

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

$(-3)^{2}+7(-3)+12=-9-21+12=0$

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1 7 12

<u>| 0 -3 -12</u>

<u> 1 4 0</u>

Hence quotient is x+4.

So, $f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)$

Please have a look at the graph attached.

4 0

3 years ago

8 is 1/6 of what number

charle [14.2K]

8 is 1/6 of 8/6 = 1 1/3

125 is 5/10 of 625/10 = 62 1/2

32 is 4/10 of 128/10 = 12 4/5

6 0

3 years ago

Read 2 more answers

The circumference of the bike tire above is 83.524 inches. What is the radius of the bike tire? (Use 3.14 for .) A. 262.27 in B.

Shtirlitz [24]

Answer:

Option <u>C. 13.3 in</u>.

Step-by-step explanation:

Here's the required formula to find the radius of the bike tire :

$\longrightarrow{\pmb{\sf{C_{(Circle)} = 2\pi r}}}$

C = circumference
π = 3.14
r = radius

Substituting all the given values in the formula to find the radius of the bike tire :

$\begin{gathered} \qquad{\longrightarrow{\sf{C_{(Circle)} = 2\pi r}}} \\ \\ \qquad{\longrightarrow{\sf{83.524 = 2 \times 3.14 \times r}}} \\ \\ \qquad{\longrightarrow{\sf{83.524 = 6.28 \times r}}} \\ \\ \qquad{\longrightarrow{\sf{83.524 = 6.28r}}} \\ \\ \qquad{\longrightarrow{\sf{r = \frac{83.524}{6.28}}}} \\ \\ \qquad{\longrightarrow{\sf{r = 13.3 \: in}}} \\ \\ \qquad \star{\underline{\boxed{\sf{\red{r = 13.3 \: in}}}}}\end{gathered}$

Hence, the radius of bike tire is 13.3 inches.

$\rule{300}{2.5}$

6 0

2 years ago

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Two numbers add up to 102 and the first is 8 bigger than the second. What are the two numbers?

lorasvet [3.4K]

The correct numbers are 55 and 47, because they have a difference of 8 and a sum of 102.

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3 years ago

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