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dsp73
3 years ago
7

X + y = 4 3x + 4y= 14

Mathematics
2 answers:
Vaselesa [24]3 years ago
7 0
Y = 4 - x
3x + 4(4-x) = 14
3x + 16 -4x = 14
-x = -2
x = 2
y = 2
kupik [55]3 years ago
5 0

Answer:

x = 2

y = 2

Step-by-step explanation:

x + y = 4  \:  \:   \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \: ...1\\ 3x + 4y= 14  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: ...2\\  \\

from equation 1 we get

x = 4 - y

put x = 4 - y in equation 2

3(4 - y) + 4y= 14 \\ 12 - 3y + 4y = 14 \\ y = 14 - 12 \\ y = 2

again, put y = 2 in equation 1

x + 2 = 4 \\ x = 4 - 2 \\ x = 2

thus, x = 2 and y = 2

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How to find third coordinate when given midpoint and a point?
IgorLugansk [536]
Example : 
u have an endpoint at (6,5)......ad the midpoint is (4,2)....find the other endpoint.

midpoint formula : (x1 + x2) / 2, (y1 + y2) / 2
one endpoint (6,5)....x1 = 6 and y1 = 5
other endpoint (x,y)...x2 = x and y2 = y
sub into the formula
m = (6 + x) / 2, (5 + y) / 2

okay, so the midpoint is (4,2)....so ur x value will equal 4
(6 + x) / 2 = 4...multiply both sides by 2
6 + x = 4 * 2
6 + x = 8
x = 8 - 6
x = 2 <==

midpoint is (4,2)....so the y value will equal 2
(5 + y) / 2 = 2 ...multiply both sides by 2
5 + y = 2 * 2
5 + y = 4
y = 4 - 5
y = -1 <==

so ur other endpoints are (2,-1)
8 0
3 years ago
Help! will appreciate
Lera25 [3.4K]
Sorry I've got on idea
4 0
3 years ago
Plz help will mark brainless if right answer ;)
Pavel [41]

Answer:

A

Step-by-step explanation:

Since each triangle is an equilateral triangle all side are the same length. Thus, one side is 15/3=5 inches. The perimeter of the entire figure would then be 3x6=18 since there are 6 sides.

7 0
3 years ago
Read 2 more answers
If H is in the interior of ∠EFG, m∠EFH = 75°, and m∠HFG = (10x)°, and m∠EFG = (20x − 5)°, then x = ? and m∠HFG = ?
Diano4ka-milaya [45]

Answer:

x=8

\m\angle HFG= 80^\circ

Step-by-step explanation:

Given that:

Point H is interior of \angle EFG.

m\angle EFH = 75^\circ\\m\angle HFG = (10x)^\circ\\m\angle EFG = (20x-5)^\circ

To find:

x = ?\\m\angle HFG = ?

Solution:

First of all, let us represent the given values in the form of a diagram.

Kindly refer to the attached image for the given points and values of angles.

We can clearly see that:

m\angle EFG = m\angle EFH + m\angle HFG

Putting all the values given in above equation, we get:

(20x-5)^\circ = 75^\circ + 10x^\circ\\\Rightarrow 20x-10x=75+5\\\Rightarrow 10x =80\\\Rightarrow \bold{x =8}

m\angle HFG =10x^\circ\\\Rightarrow m\angle HFG =10\times 8^\circ\\\Rightarrow m\angle HFG = \bold{80^\circ}

8 0
3 years ago
Please help The dilation DO,2.5 is applied to triangle ABC below. Use the dilation of triangle ABC and its image to prove that t
viva [34]
A dilation D_{O,\,k} is a dilation with a scale factor, k centered at the origin.

A scale factor, k means that the distance of the image from the the center of dilation is k times the distance of the pre-image from the center of dilation and the size of the image is k times the size of the pre-image.

Given triangle ABC with vertices A(-2, 2), B(1, 2) and C(1, -1), a dilation D_{O,\,k} will result in the image with vertices A'2.5(-2, 2) = A'(-5, 5), B'2.5(1, 2) = B'(2.5, 5) and C'2.5(1, -1) = C'(2.5, -2.5)

Now, consider line AC, the equation of the line is given by

\frac{y-2}{x-(-2)} = \frac{-1-2}{1-(-2)} \\ \\ \Rightarrow \frac{y-2}{x+2} = \frac{-3}{1+2} = \frac{-3}{3} =-1 \\ \\ \Rightarrow y-2=-(x+2)=-x-2 \\ \\ \Rightarrow y=-x

Notice that line y = -x is a line passing through the origin which is the center of dilation.

Consider line A'C', the equation of the line is given by

\frac{y-5}{x-(-5)} = \frac{-2.5-5}{2.5-(-5)} \\ \\ \frac{y-5}{x+5} = \frac{-7.5}{2.5+5} = \frac{-7.5}{7.5} =-1 \\ \\ \Rightarrow y-5=-(x+5)=-x-5 \\ \\ \Rightarrow y=-x

As an be seen the line AC and the line A'C' is the same line.
4 0
3 years ago
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