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madam [21]
1 year ago
13

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

#SPJ1

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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

8 0
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}
hence p(no. <= 6) = 6/6 =1
6 0
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
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}
1x^2-3x+1=0
a=1
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}
x=\frac{3+ \sqrt{5} }{2} or \frac{3- \sqrt{5} }{2}


aprox
x=2.61803 or 0.381966


7 0
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

5 0
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

#SPJ1

6 0
1 year ago
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