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Ahat [919]
3 years ago
14

To solve y and x, I am adding a picture

Mathematics
1 answer:
Viktor [21]3 years ago
4 0

Answer:

x =\sqrt 5

y = \sqrt{5

Step-by-step explanation:

Given

The attached triangle

Required

Solve for x

Considering angle 45 degrees, we have:

\cos(45) = \frac{y}{\sqrt{10}} --- cosine formula i.e. adj/hyp

Solve for y

y = \sqrt{10} * \cos(45)

In radical form, we have:

y = \sqrt{10} * \frac{1}{\sqrt 2}

y = \sqrt{10/2}

y = \sqrt{5

To solve for x, we make use of Pythagoras theorem

x^2 + y^2 = (\sqrt{10})^2

x^2 + y^2 =10

Substitute for y

x^2 + (\sqrt 5)^2 =10

x^2 + 5 =10

Collect like terms

x^2  =10-5

x^2=   5

Solve for x

x =\sqrt 5

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1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)
Sveta_85 [38]

Answer:

1. -5x+3y+44=0

2. 2x+y-2=0

3. 2x+y-4=0

Step-by-step explanation:

Standard form of a line is Ax+By+C=0.

If a line passing through two points then the equation of line is

y-y_1=m(x-x_1)

where, m is slope, i.e.,m=\dfrac{y_2-y_1}{x_2-x_1}.

1.

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)

y+3=\dfrac{-5}{-3}(x-7)

y+3=\dfrac{5}{3}(x-7)

3(y+3)=5(x-7)

3y+9=5x-35

-5x+3y+9+35=0

-5x+3y+44=0

Therefore, the required equation is -5x+3y+44=0.

2.

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2 x + y =-5.

Slope of the line : m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

y-2=-2(x-0)

y-2=-2x

2x+y-2=0

Therefore, the required equation is 2x+y-2=0.

3.

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y =-5.

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

y-0=-2(x-2)

y=-2x+4

2x+y-4=0

Therefore, the required equation is 2x+y-4=0.

5 0
3 years ago
Can someone help please??????
denis23 [38]

Answer:

Please refer to the attachment

8 0
3 years ago
Write an equation of a line parallel to the line y=2x+7 and passing through the point (4,2)
trasher [3.6K]
Y=mx+b
lines are parallels so m=2

y=2x+b
 line passing through the point (4,2), so x=4 y=2
put these value in equation
2=2*4+b
2=8+b
b=2-8
b=-6
y=2x-6
Answer: y=2x-6

(verification on the picture)

4 0
3 years ago
Read 2 more answers
 14
tatyana61 [14]
We can display the information given as an equation:
2000 * r^{19} = 4000; r = increase per annum
Now, we rearrange and solve for r:
r^{19} = 2
r = \sqrt[19]{2} = 1.037.....
We can now work out the increase for 5 years like so:
2000 * r^{5} = 2400.205..... ⇒ $2400
4 0
3 years ago
Whats the answer of p-6=19;p=13
mash [69]
P-6=19; p=13

so you just plug the value of P into the problems P and solve the equation

(13) - 6 = 19

7=19

so...that's incorrect because 7 can't equal 19 making the problem No solution. if that's wrong then idk what they're teaching in math any more...
7 0
3 years ago
Read 2 more answers
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