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3 years ago

Find the value of x in each case:

Mathematics

1 answer:

Vlada [557]3 years ago

6 0

Answer:

$x = 18$

Step-by-step explanation:

Given:

Angle ABC = 2x

Angle CDE = 8x

Required:

Value of x

SOLUTION:

Line AB is parallel to line CD, therefore, angle ABC and angle BCD are alternate interior angles. Alternate interior angles are equal. Thus:

Angle ABC = Angle BCD = 2x

Since, line BC is parallel to line DE, angle BCD and angle CDE are consecutive interior angles.

Consecutive interior angles are supplementary, therefore:

Angle BCD + Angle CDE = 180°

$2x + 8x = 180$

Use this equation to solve for x

$10x = 180$

Divide both sides by 10

$\frac{10x}{10} = \frac{180}{10}$

$x = 18$

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It takes 3 1/2 spoons of chocolate syrup to make 3 2/5 gallons of chocolate milk. How many spoons would it take to make 4 gallon

vladimir2022 [97]

Answer:

4 2/17

Step-by-step explanation:

It takes 3 1/2 spoons of chocolate syrup to make 3 2/5 gallons of chocolate milk

3 1/2= 3 2/5

7/2= 17/5

1 gallon = 7/2÷17/5

= 7/2 × 5/17

= 35/34

Therefore the number of spoons required to make 4 gallons

= 4 × 35/34

= 140/34

= 70/17

= 4 2/17

7 0

3 years ago

I need help deriving : (7x)/(3+x^2), I keep on deriving it wrong and I am not sure as to why

denis-greek [22]

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\cfrac{dy}{dx}=\cfrac{21+7x^2-14x^2}{(3+x^2)^2}\implies \cfrac{dy}{dx}=\cfrac{21-7x^2}{(3+x^2)^2}\implies \cfrac{dy}{dx}=\cfrac{7(3-x^2)}{(3+x^2)^2}$

4 0

3 years ago

HELP ME WITH THE EXERCISES PLEAASE

Zinaida [17]

1.

1=87 corresponding angle.
2=180-87=93

2.

1=78 corresponding angles
2=78 verticle angles

3.

Set it up as (6x - 11) = 37
37 + 11 =48

6x = 48

x = 8

4.

Take 142 and see that it is supplementary to angle 2 so 180-142 = 38

38 is corresponding to the equation 2(x + 9)

So 2(x + 9) =38
Distributive property

2x + 18 = 38
38-18=20

2x =20

x = 10

Angle 2 is equal to 38 from supplementary to 142

I’m pretty positive about 1-3 but 4 maybe not be correct. But most likely these are correct

6 0

3 years ago

What was done to the previous equation?

zubka84 [21]

The “2” outside the brackets was multiplied onto everything that is inside the brackets.

4 0

3 years ago

The area of a ferris wheel is about 154 square meters. Which of the following is closest to the length of one of the spokes? [As

babunello [35]

Answer:

The length of one of the spoke is 7 m

Option C is correct answer.

Step-by-step explanation:

Area of Ferris Wheel = 154 square meters.

We need to find the length of one of the spokes.

We are given: Assume the spokes go from the centre to the edge of the Ferris wheel.

So, We are given area of circle and we need to find radius of circle.

The formula used is: $Area\:of\:circle=\pi \:r^2$

Putting values and finding radius

$Area\:of\:circle=\pi \:r^2\\154=3.14\:r^2\\r^2=\frac{154}{3.14}\\r^2=49\\Taking\:square\;root\\\sqrt{r^2}=\sqrt{49}\\r=7\:m$

So, Radius of circle = 7 m

The length of one of the spoke is 7 m

Option C is correct answer.

4 0

3 years ago