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3 years ago

Solve the system of linear equations by using substitutions

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

7 0

Start by placing the second equation in for Y so you have
2x+2(5+x)=10
Then distribute the 2
2x+10+2x=10
Then combine like terms
4x+10=10
Then subtract the 10 over
4x=0
Then divide the 4 and because 0 divided by 4 is 0
x=0
Then plug it back into one, Ill choose the second
y=5+0
Then add 5+0 and you get y=5
Your solution is (0,5)

Hope I Helped! :) <3

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A student sees a newspaper ad for an apartment that has 1330 square feet (ft2 ) of floor space. how many square meters of area a

kkurt [141]

We know 1 meter = 3.28084 feet

So 1 square meter = 3.28084 × 3.28084 square feet.

Now to convert from square feet to square meters, we need to divide by 3.28084 × 3.28084.

The area given in the news paper advertisement is 1330 square feet.

So to convert to square meters we divide by 3.28084 × 3.28084

We get

1330 square feet = $\frac{1330}{(3.28084)^{2} } =123.56$

Hence 1330 square feet of area is equal to 123.56 square meters.

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3 years ago

Questions are in the picture

gtnhenbr [62]

The closest point is (3.5, 1.9) and the distance is 1.96 units

<h3>How to determine the point and the distance?</h3>

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

Read more about distance at:

brainly.com/question/23848540

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1 year ago

Put these 3 problems in order from least to greatest: (WILL GIVE BRAINLIEST)

-BARSIC- [3]

1.) -15.9, -15.2, -3.6, 3.6
2.) second one is already correct
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2 years ago

Last week, the price of bananas at a grocery store was $0.80 per pound. This week, bananas at the same grocery store are on sale

monitta

Answer:

3.30

Step-by-step explanation:

You multiply the 5.5 pounds by the 80 cents then multiply the awnser of that by .25 and subtract that from the awnser of 5.5*.80

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3 years ago

Roberta has $10,540 to invest. She plans to invest her money in certificates of deposit (CDs) that have 2.1% interest, a stock p

ira [324]

Answer:

The amount invested in CDs is $1,340

The amount invested in the stock portafolio is $6,900

The amount invested in the saving accounts is $2,300

Step-by-step explanation:

Let

x ---->the amount invested in CDs at 2.1%

y ---> the amount invested in the stock portfolio at 2.5%

z ---> the amount invested in the savings account at 1.5%

$x+y+z=10,540$ ----> equation A

$z=\frac{1}{3}y$ ----> equation B

substitute equation B in equation A

$x+y+\frac{1}{3}y=10,540$

$x+\frac{4}{3}y=10,540$

$x=10,540-\frac{4}{3}y$ ----> equation C

we know that

The total interest earned by the three amount must be equal to $231.69

$0.021x+0.025y+0.015z=231.69$ ----> equation D

substitute equation B and equation C in equation D

$0.021(10,540-\frac{4}{3}y)+0.025y+0.015(\frac{1}{3}y)=231.69$

solve for y

$221.34-0.0315y+0.025y+0.005y=231.69$

$0.0015y=231.69-221.34$

$0.0015y=10.35$

$y=\$6,900$

<em>Find the value of x</em>

$x=10,540-\frac{4}{3}(6,900)$

$x=\$1,340$

<em>Find the value of z</em>

$z=\frac{1}{3}(6,900)$

$z=\$2,300$

7 0

3 years ago