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ioda
2 years ago
15

Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two clas

ses, and he took a total of 90 minutes Which value of k would cause the system of linear equations 35 x + 14 y = 119 and 5 x + 2 y = k to have an infinite number of solutions?
3
7
17
21
Mathematics
1 answer:
Grace [21]2 years ago
5 0

A system of the equation to be Dependent Consistent System the system must have multiple solutions. The correct option is C.

<h3>What is a System of equation?</h3>

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the system of equations to have infinite number of solutions, the lines of the equations must coincide, therefore, the line must overlap on each other.

For the lines to overlap the equations must be in a ratio. Therefore, the ratio of the left sides of the equations must be equal to the right side,

\dfrac{35x+14y}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac{7(5x+2y)}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac71 = \dfrac{119}{k}\\\\k = 17

Hence, the value of k must be 17, therefore, the correct option is C.

Learn more about System of equation:

brainly.com/question/12895249

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A study analyzed the average yearly salt intake in the United States from 2012 thru 2017. The data is summarized in the table:
Ugo [173]

Answer:Is an estimate of the average grams of salt used in 2012

Step-by-step explanation: Let

x ---> the number of years since 2012

f(x) ---> is the total amount of salt ingested in grams

we have

This is a linear equation in slope intercept form

where

The slope is equal to

The y-intercept or initial value is equal to

The y-intercept is the value of the function f(x) when the value of x is equal to zero

In this context, the y-intercept is the average amount of grams of salt ingested  in the year 2012

The exact value of the average amount of grams of salt ingested  in the year 2012 is 3,554 grams (see the data in the table)

Compare the exact value with the y-intercept

therefore

3,548 grams Is an estimate of the average grams of salt used in 2012

7 0
3 years ago
9(5x + 1) ÷ 3y From the expression above, provide an example of each of the following: sum, term, product, factor, quotient, and
tatuchka [14]
5+1=6x9=54/3=18 use pemdas to solve it
8 0
3 years ago
A system of equations is graphed on the coordinate plane. y=−2x−3y=−2x+2 Graphs of the equations y equals negative two x plus tw
AleksandrR [38]
In y = mx + b form, the slope will be in the m position and the y int will be in the b position

y = -2x + 2....slope = -2 and y int = 2
y = -2x - 3.....slope = -2 and y int = -3

when u have 2 lines that both have the same slope but different y intercepts, u have parallel lines with no solution because ur lines never intersect.

so ur answer is : no solutions or 0 solutions


3 0
3 years ago
Read 2 more answers
Which costs more per gallon? 5 gallons for $12.50 or 11 gallons for $26.40
Effectus [21]

Answer: 5

Step-by-step explanation:

If;

5 gallons = $12.50 / 5 = $2.50/gallon

11 gallons = $26.40 / 11 = $2.40/gallon

In conclusion, 5 gallons cost more per gallon than 11.

6 0
3 years ago
Out of 600 seniors at a local high school, 60% went on the senior trip. At the hotel, one room was reserved for every 4 students
butalik [34]

Given:

Total number of senior students = 600

60% went on the senior trip.

One room was reserved for every 4 students.

To find:

The total number of reserved rooms.

Solution:

60% went on the senior trip from total 600 students. So, number of students who went on tripe is

600\times \dfrac{60}{100}=360

Now, one room was reserved for every 4 students. So,

\text{Required number of rooms}=\dfrac{\text{Number of students who went on tripe}}{\text{Number of students in room}}

\text{Required number of rooms}=\dfrac{360}{4}

\text{Required number of rooms}=90

Therefore, the required number of reserved rooms were 90.

4 0
3 years ago
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