Solve for X. pls help asap

If AC is parallel to DE, find X

UNO [17]

Answer: x = 50

Concept:

Here, we need to know the idea of alternative interior angles and the angle sum theorem.

Alternative interior angles are angles that are formed inside the two parallel lines, and the values are equal.

The angle sum theorem implies that the sum of interior angles of a triangle is 180°

If you are still confused, please refer to the attachment below or let me know.

Step-by-step explanation:

Given information:

AC ║ DE

∠ABC = 85°

∠A = 135°

Find the value of ∠BAC

∠A + ∠BAC = 180° (Supplementary angle)

(135°) + ∠BAC = 180°

∠BAC = 45°

Find the value of ∠BCA

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)

(85°) + (45°) + ∠BCA = 180°

∠BCA = 50°

Find the value of x (∠EBC)

∠EBC ≅ ∠BCA (Alternative interior angles)

Since, ∠BCA = 50°

Therefore, ∠EBC = 50°

$\Large\boxed{x=50}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

1 year ago

Your friend has $100 when he goes to the fair He spends $10 to enter the fair and $20 on food. Rides at the fair cost $2 per nde

mihalych1998 [28]

Answer:

f(x) = -2x + 70

6 0

3 years ago

142 students are going on a field trip. There will be six drivers, and two different types of vehicles. A bus can hold 51 people

otez555 [7]

Answer: 2 buses and 4 vans would be needed

Step-by-step explanation:

Let x represent the number of buses that would be needed.

Let y represent the number of vans that would be needed.

There will be six drivers, and two different types of vehicles. This means that

x + y = 6

142 students are going on a field trip. A bus can hold 51 people while a van can hold 10. This means that

51x + 10y = 142 - - - - - - - - - - - 1

Substituting x = 6 - y into equation 1, it becomes

51(6 - y) + 10y = 142

306 - 51y + 10y = 142

- 51y + 10y = 142 - 306

- 41y = - 164

y = - 164/ - 41

y = 4

x = 6 - y = 6 - 4

x = 2

8 0

3 years ago

how many pounds of rock will you need to fill an area 25 ft by 35 ft to a depth of 2 in. If the rock weighs 1050 lb cubic yard?

Eduardwww [97]

The volume of the area is Length x width x height:

25 x 35 x 2/12 = 145.83 cubic feet.

1 cubic foot = 0.037 cubic yards:

145.83 x 0.037 = 5.40 cubic yards.

5.4 cubic yards x 1050 lbs/ cubic yard = 5,665.6 pounds.

Note:

Rounding and conversion may change the answer slightly, but I believe I rounded everything as it should be.

6 0

3 years ago

A simple linear regression analysis was conducted to predict the Exam 3 score of students in STA 2023 based on their Exam 1 scor

Katena32 [7]

Answer:

Option A) As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points.

Step-by-step explanation:

We are given the following in the equation:

A simple linear regression analysis was conducted to predict the Exam 3 score of students in STA 2023 based on their Exam 1 score.

Thus, Exam 3 score becomes the dependent variable and exam 1 score is the independent variable.

The regression equation is given by:

$\hat{y} = 50.57+0.4845x$

Comparing the equation to a linear equation:

$y = mx + c$

m = 0.4845

c = 50.57

Where m is the slope and tells the rate of change and c is the y intercept that is the value of y when x is 0.

When, there is a increase in x, we can write:

$\hat{y}(x) = 50.57+0.4845x\\\hat{y}(x+1) = 50.57+0.4845(x+1)\\\hat{y}(x+1) - \hat{y}(x) = 50.57+0.4845(x+1)-(50.57+0.4845x)\\\hat{y}(x+1) - \hat{y}(x) = 0.4845$

Thus, the slope of equation can be interpreted as:

Option A) As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points.

5 0

3 years ago