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1 year ago

Solve the following system of equations by substitution 3 x + 0.5 y = 11 x + 2 y = 0

Mathematics

1 answer:

SVEN [57.7K]1 year ago

6 0

The solution to the system of equations using substitution is given by:

x = 4 and y = 2.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the equations are given by:

3x + 0.5y = 11.

x + 2y = 0.

From the second equation, we have that:

x = -2y.

Replacing in the first equation, we have that:

3(-2y) + 0.5y = 11

-5.5y = 11.

5.5y = -11

y = -11/5.5

y = -2.

Then the solution for x is:

x = -2y = -2(-2) = 4.

The solution to the system of equations using substitution is given by:

x = 4 and y = 2.

More can be learned about a system of equations at brainly.com/question/24342899

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Charles drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ( -2.3 and

mote1985 [20]

Answer:

The coordinates of the fourth vertex is ( 2.1 , -3.6)

Step-by-step explanation:

Given:

The vertices are ( -2.3 and −3.6), (−2.3, and 2.2), and (2.1, and 2.2).

To Find :

The fourth coordinate = ?

Solution:

Let (a,b) be the missing coordinates

Now let us use the the mid point formula and find the missing coordinate.

Let ( -2.3 ,−3.6) be the point A

Let (−2.3,2.2) be the point B

Let (2.1, 2.2) be the point C

The mid point of AC should be BD

Step 1: Finding The mid pint of AC

The mid pint of AC

$(\frac{(-2.3+2.1)}{2} , \frac{(-3.6+2.2)}{2})$

$(\frac{(-0.2)}{2} , \frac{(-1.4)}{2})$

$(-0.1, -0.7)$

Step 2: Lets Equate the midpoints'

The mid pint of BD

=> $(\frac{(a+(-2.3))}{2} , \frac{(b+2.2)}{2})$ = (-0.1, -0.7)

$\frac{(a+(-2.3))}{2} = -0.1$

$(a-2.3) = -0.1 \times 2$

$(a-2.3) = -0.2$

$a = -0.2 +2.3$

a = 2.1

$\frac{(b+2.2)}{2} = -0.7$

$(b+2.2)= -0.7 \times 2$

$(b+2.2)= -1.4$

$b= -1.4 -2.2$

b = -3.6

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3 years ago

what is the probability of rolling a number less or equal to a 6 when rolling a six-sided number cube

Murrr4er [49]

There are six numbers that can come up when the dice is rolled
the sample space is{ 1 2 3 4 5 6}
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3 years ago

Which is the solution to the following equation?<br> 4x^2-12x+9=5

Scilla [17]

We assume that
if xy=0
x and y=0

first make it equal to zero

minus 5 on both sides
4x^2-12x+4=0
undistribute 4 for ease
4(x^2-3x+1)=0
since 4 does not equal zero, and the only thing that will get it to zero is 0,
x^2-3x+1=0
use quadratic equation

if you hahve
ax^2+bx+c=0
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1x^2-3x+1=0
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b=-3
c=1

x= $\frac{-(-3)+/- \sqrt{(-3)^{2}-4(1)(1)} }{2(1)}$
x= $\frac{3+/- \sqrt{9-4} }{2}$
x= $\frac{3+/- \sqrt{5} }{2}$
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aprox
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3 years ago

joy has a square picture that is 4 inches on each side. the picture is framed with a length of ribbon. she wants to use the same

Umnica [9.8K]

Step 1

we know that

The perimeter of a square is equal to

P=4*b

where

b is the length side of a square

<u>Find the perimeter of the square picture</u>

b=4 in

P=4*4=16 in

Step 2

<u>Find the maximum radius of the circular frame</u>

we know that

the perimeter of a square frame is equal to the circumference of the circular frame

the circumference is equal to

$C=2\pi r$

$16=2\pi r$

$8=\pi r\\\\r=\frac{8}{\pi}$

r=2.5 in

therefore

<u>the answer is</u>

the maximum radius of the circular frame is 2.5 in

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3 years ago

A candle on pauline’s dresser is 10 inches tall and burns at a rate of 0.75 inches per hour. how many hours will it take for the

Natalija [7]

Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

0.25 = 10 - 0.75t

0.75t = 9.75

t = 9.75/0.75

t = 13 hours.

More can be learned about linear functions at brainly.com/question/24808124

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6 0

1 year ago