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3 years ago

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The sum of 5 times one number, x, and 4 times a second number, y, is 75. If the sum of the two numbers is 18, find the two numbe

rs.
Enter a system of equations to represent the situation, then solve the system.

1 answer:

satela [25.4K]3 years ago

4 0

Answer: $x=3$ and $y=15$

Step-by-step explanation:

First, we are told "sum of 5 times one number, x, and 4 times a second number, y, is 75":

$5x+4y=75$ (1)

Then, we are told "he sum of the two numbers is 18":

$x+y=18$ (2)

At this point we have our system of equations and now we are able to find the values of $x$ and $y$ .

So, let's begin by isolating $x$ from (2):

$x=18-y$ (3)

Substituting (3) in (1):

$5(18-y)+4y=75$ (4)

Finding $y$ :

$90-5y+4y=75$

$y=15$ (5) This is the value of $y$

Substituting (5) in (1):

$5x+4(15)=75$ (6)

Finding $y$ :

$5x+60=75$ (7)

$x=3$ (8) This is the value of $x$

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Step-by-step explanation:

<em>The question is incomplete because the area of the parallelogram is missing. However, the following will guide you in answering the question</em>

Given

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Required

Determine the Height

Area of a Parallelogram is:

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$Height = \frac{Area}{Base}$

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This implies that you divide the value of area by 16 to get the height of the parallelogram.

Take for instance;

$Area = 64ft\²$

The height would be

$Height = \frac{64}{16}$

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Step-by-step explanation:

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2 years ago

I need some help with this

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The angle of elevation from the hiker to the park ranger is the same as the angle of depression from the ranger to the hiker, 29°.

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3 years ago

Jana and Tim both sell cleaning products to local housecleaning services. When Jana orders from the manufacturer of the products

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Answer: Jana and Tim will only spend the same amount on purchase orders to their manufacturers when they each order products with a total purchase value of $100.

Step-by-step explanation:

Jana and Tim would only be incurring same amount when both total purchase is to a value of $100. This is so because by purchasing a goods worth same amount, they both end up incurring $15 dollar additional cost. Jana would spend $15 on shipping her goods, while Tim would pay $4 Handling fees and $11 dollar shipping fee which would also amount to $15. What this means is total spent for both Jana and Tim would amount to $115 each.

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2 years ago

The function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year.

AlexFokin [52]

The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.

<h3>How to graph a function?</h3>

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

Consider certain values of x
Substitute x values in the given function to obtain y values
Plot the x and y values in the graph
Join the points to know the variation.

<h3>Calculation:</h3>

It is given that,

f(x) = 200 × $(1.098)^x$

Village's population growing rate = 9.8%

Creating a table for x and f(x) values:

x: 0 2 4 6 8 10

f(x = 0) = f(0) = 200 × $(1.098)^0$ = 200

f(x = 2) = f(2) = 200 × $(1.098)^2$ = 241

f(x = 4) = f(4) = 200 × $(1.098)^4$ = 291

f(x = 6) = f(6) = 200 × $(1.098)^6$ = 350

f(x = 8) = f(8) = 200 × $(1.098)^8$ = 423

f(x = 10) = f(10) = 200 × $(1.098)^1^0$ = 509

So,

(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)

Plotting these points in the graph and joining the points, the graph is shown below.

Finding the time for the village to dig a new well:

It is given that the population doubled from its current size, the village will need to dig new water well.

The current size of the village = 200

If it doubles for a certain time 't' = 400

So,

400 = 200 × $(1.098)^t$

⇒ $(1.098)^t$ = 2

⇒ log $(1.098)^t$ = log 2

⇒ t log(1.098) = 0.301

⇒ t × 0.04 = 0.301

∴ t = 7.525 years

Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.

Learn more about the function and its graph here:

brainly.com/question/4025726

#SPJ1

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1 year ago