Please find the area of the trapezoids:

Line l passes through the point of intersection,A, of the lines 4x-3y+4=0 and x+2y=5. Without finding A,find the equation of lin

klemol [59]

Answer:

$\large\boxed{y=\dfrac{15}{14}x+1.5}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

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You must solve the system of equations:

$\left\{\begin{array}{ccc}4x-3y+4=0&(1)\\x+2y=5&(2)\\y=mx+1.5&(3)\end{array}\right\qquad\text{substitute (3) to (1) and (2)}\\\\\left\{\begin{array}{ccc}4x-3(mx+1.5)+4=0\\x+2(mx+1.5)=5\end{array}\right\qquad\text{use the distributive property}\\\left\{\begin{array}{ccc}4x-3mx-4.5+4=0\\x+2mx+3=5&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx-0.5=0&\text{add 0.5 to both sides}\\x+2mx=2\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx=0.5&\text{multiply both sides by 2}\\x+2mx=2&\text{multiply both sides by 3}\end{array}\righ$

$\underline{+\left\{\begin{array}{ccc}8x-6mx=1\\3x+6mx=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=7\qquad\text{divide both sides by 11}\\.\qquad x=\dfrac{7}{11}\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\\dfrac{7}{11}+2m\left(\dfrac{7}{11}\right)=2\qquad\text{multiply both sides by 11}\\\\7+2m(7)=22\qquad\text{subtract 7 from both sides}\\\\14m=15\qquad\text{divide both sides by 14}\\\\m=\dfrac{15}{14}$

8 0

3 years ago

Natalie bought 9 CDs to add to her collection.

GalinKa [24]

Answer:

36 i think

Step-by-step explanation:

she lost half and she has 18 so multiply 18 by 2 u will get 36

4 0

3 years ago

Determine the domain and range of the graph

madreJ [45]

Answer:

5 ≤ x ≤ 10 5 ≤ y ≥ -1

Step-by-step explanation:

3 0

3 years ago

Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown. After each

Dima020 [189]

Answer:

Five touchdowns were made in the game

Step-by-step explanation:

Here, we want to know the number of touchdowns made during the game.

We proceed as follows;

Let the number of touch downs be x

So the total points earned through touchdowns is 6 * x = 6x

The number of scores is 10 times

Let the number of extra kick be y which means that the number of conversions will be (y-1)

So the total number of score times will be ;

x + y + y-1 = 10

x + 2y = 11 •••••••••(i)

Now let’s work with points

Touch down points = 6 * x = 6x

Points from extra kick = 1 * y = y

Points from 2-point conversions = 2(y-1) = 2y - 2

So;

6x + y + 2y -2 = 37

6x + 3y = 37 + 2

6x + 3y = 39

divide through by 3

2x + y = 13 •••••••(ii)

So now solve simultaneously

From ii, y = 13 - 2x

Put this into i

x + 2(13-2x) = 11

x + 26 - 4x = 11

x -4x = 11-26

-3x = -15

x = -15/-3

x = 5

There are five touchdowns in the game

6 0

4 years ago

Jasmine thinks that the images are the same because they are both isosceles triangles. Do you agree with Jasmine why or why not?

lorasvet [3.4K]

Answer:

No, images are not same as their dimensions are different although two sides in each of the two triangles are equal.

Step-by-step explanation:

Given: images of two isosceles triangles.

To check: if images are the same

Solution:

A triangle is a polygon made up of three sides.

An isosceles triangle is a triangle in which two sides are equal. Also, in an isosceles triangle, angles opposite to equal sides are equal.

The given images of two isosceles triangles A and B are not the same as their dimensions are different although two sides in each of the two triangles are equal.

6 0

4 years ago