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Anettt [7]
3 years ago
8

The graph below shows the relationship between two variables.

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
4 0

The graph adequately represents the following case

"The number of employees at a store increased at a constant rate for 5 years. There was a decrease in the number of employees for 2 years. Then the number of employees increased at a greater constant rate for the next few years."

Step-by-step explanation:

To solve the above-mentioned problems we need to filter the results through analysing the options given-

We have to keep in mind that-

  1. For an increase in value/quantity- the graph would be on an upswing
  2. For decrease in value/quantity- The graph would be in declining mode
  3. For constant value- horizontal graph line parallel to the x-axis

Now going through the options-

option 1:-

David drove at a constant speed initially- throughout the graph no horizontal line is present, hence this condition does not represent the graph.

option 2:-

test scores increased and then decline- In this condition only two phases are mentioned, whereas in the graph three different phases are present. Hence this condition too does not represent the graph.

option 3:-

After the period of slow.- The graph starts with an upswing. hence this condition too does not represent the graph.

option 4:-

Employees increased and then declined and then again increased. All the above condition corroborates to the above-mentioned graph. hence this condition is represented in the graph

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Please help me with this question
BartSMP [9]

Answer:

3x-28=2x+25\\x=53

Step-by-step explanation:

Parallel lines cut by a transversal are two lines which do not cross intersected by a third line. Because lines such as m and n are parallel, we have angles which are equal to each other.

  • Corresponding Angles - angles located in the same position in each intersection. Can be shown by translating or sliding the angle down/up.
  • Alternate Interior Angles - angles located inside the parallel lines across the transversal. Can be shown by reflecting and translating or rotation.
  • Alternate Exterior Angles - angles located outside the parallel lines across the transversal. Can be shown by reflecting and translating or rotation.
  • Vertical angles - angles across a vertex from one another. Can be shown by reflection.

The angles shown here are located outside the parallel lines and across the transversal from each other. Therefore we have Alternate Exteroir angles and can set them equal to each other to solve for x.

3x-28=2x+25\\3x-2x-28=2x-2x+25\\x-28=25\\x-28+28=25+28\\x=53

We check our work and should get equal angles:

3(53)-28=2(53)+25\\159-28=106+25\\131=131

4 0
4 years ago
Ian picked 5 times as many berries as Michelle. Joe take seven times as many theories as Michelle. Together they picked 208 berr
malfutka [58]
x-\ number \ of\ Michelle's\ berries\\
y-\ number\ of \ Joe's\ berries\\
z-number\ of \ Ian's\ berries\\\\
z=5x\\
y=7x\\
x+y+z=208\\\\
x+5x+7x=208\\\\
13x=208\ \ \ \ | divide\ by\ 13\\\\x=16\\\\
y=16*7=112\\\\
Joe\ picked\ 12\ berries.
4 0
3 years ago
Read 2 more answers
-6 1/2 by -1 1/4 I need to know the answer to this question
alexgriva [62]

Answer:

8 1/8

Step-by-step explanation:

~~~~~~~~~~~~~~~~~

8 0
3 years ago
What is <br> (2x - 5)(x + 4)
Lubov Fominskaja [6]

Answer:

2 · x² - 20

Step-by-step explanation:

2x - 5 · x + 4

2x · x - 20

2x² - 20

2 · x² - 20

3 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
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