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umka2103 [35]
3 years ago
12

One equation in a system of equations is given in the graph. Which equation below would have to be the second equation so that t

he system has no solutions?

Mathematics
1 answer:
Tems11 [23]3 years ago
6 0

Solution:

To classify the system of equations as no solutions, the lines must be parallel (Not intersect).

<u>First, let's identify the equation forming the line.</u>

  • Slope = Rise/Run = 2/-3 = -0.66
  • Y-intercept = 0
  • Equation formed: y = -2/3

We also know that the slope of the equation must be -1.5.

<u>A) 2x + 3y = 0</u>

  • 3y = 0 - 2x
  • => 3y = -2x
  • => (y = -2x/3) ∦ (y = -2x/3)

<u>B) 2x + 3y = 6</u>

  • => 3y = -2x + 6
  • => (y = -2x/3 + 2) ║ (y = -2x/3)

<u>C) 2x - 3y = 9</u>

  • => -3y = -2x + 9
  • => y = -2x/-3 + 9/-3
  • => (y = 2x/3 - 3) ∦ (y = -2x/3)

<u>D) y = 3x + 2</u>

  • (y = 3x + 2) ∦ (y = -2x/3)

Option B is correct.

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The first week of January,there are 49 dogs and 28 cats in an animal shelter. Throughout the month,the ratio of dogs to cats rem
Elina [12.6K]

Answer:

35 dogs

Step-by-step explanation:

x ---> the number of dogs

y ---> the number of cats

The last week of January we have 20 cats and the ratio is the same

so

\frac{x}{y}=\frac{49}{28} ----> equation A

y=20 ---> equation B

substitute equation B in equation A

\frac{x}{20}=\frac{49}{28}

solve for x

x=\frac{49}{28}(20)=35 dogs

7 0
4 years ago
88 + 10 = 98 × 30 + 100​
Nataly_w [17]

Answer:

<u><em>1520/49</em></u>

Step-by-step explanation:

  1. 88+10= 98
  • <u><em>next you have to solve the numbers on the right side using the order of operations.</em></u><u><em> </em></u><u><em>(PEMDAS)</em></u>
  1. 98 x 30= 2940
  2. 2940 + 100= 3040

  • <em>now you have solved the equations on both sides of the equal sign...</em>

<em>98=3040</em>

  • <em>the final step is to divide the numbers in order to get the solution...</em>

3040/ 98 = 31.02040816

<em>*if you need it in fraction form it is </em>1520/49

<em>Hope I helped answer the question!</em>

7 0
3 years ago
Alex is making puppets for a show. He bought all the string needed for $125. It costs $18 for the remaining materials to make ea
Alexus [3.1K]

Alex bought all the string needed for $125.

It costs $18 for the remaining materials to make each puppet.

So if we closely observe then we see that here $125 is the fixed cost because its not going to change with number of puppets.

And the variable cost is $18.

In this case we can model a Total cost function C(x) for for x number of puppets as below

C(x)=125+18x\\ \\ \text{Here x is the number of puppets}\\ \\ \text{Since in our case the number of puppets is 50 so replace x by 50 we get }\\ \\ C(50)=125+18*50\\ \\ C(50)=125+900\\ \\ C(50)=1025  \ dollar.

The total cost to make 50 puppets=$1025

3 0
3 years ago
Read 2 more answers
Given that is the angle bisector of A, determine the length of x. (SHOW YOUR WORK PLEASE!!!)
Sunny_sXe [5.5K]

The length of x will be 4 cm if is the angle bisector of A.

<h3>What is an angle bisector?</h3>

A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.

Given sides;

AB=12

AE=8

BD=6

DE=x

From the triangle angle bisector theorem;

\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4

Hence the length of x will be 4 cm.

To learn more about the angle bisector refer to:

brainly.com/question/12896755#SPJ5

#SPJ1

6 0
2 years ago
Write a recursive sequence that represents the sequence defined by the
n200080 [17]

Answer:

            a_1=1\\a_n=a_{n-1}-5

Step-by-step explanation:

a₁ = 1 - 5(1 - 1) = 1 - 5·0 = 1

a₂ = 1 - 5(2 - 1) = 1 - 5·1 = 1 - 5 = a₁ - 5

a₃ = 1 - 5(3 - 1) = 1 - 5·2 = 1 - 5 - 5 = a₂ - 5

a₄ = 1 - 5(4 - 1)  = 1 - 5·3 = 1 - 5 - 5 - 5 = a₃ - 5

and so on, therefore:

<h3>                               aₙ = aₙ₋₁ - 5</h3>
8 0
3 years ago
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