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3 years ago

Given parallelogram abcd, find the value of y.

Mathematics

1 answer:

nekit [7.7K]3 years ago

4 0

Answer:

c) 82

Step-by-step explanation:

<ABE and <BEC are supplementary because they form a line.

<ABE + <BEC = 180

116+ x = 180

Subtract 116 from each side.

116-116+x = 180 -116

x = 64

The angles in triangle ECB add to 180 because it is a triangle

<BEC + <ECB + <CBE = 180

x + 34+y = 180

64 + 34+ y = 180

98 + y = 180

Subtract 98 from each side.

98-98+y = 180-98

y = 82

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What's a type of expression that contains a variable or variables

Crazy boy [7]

An expression is just a mathematical phrase. A numericalexpression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables!

Hope this helped :)

4 0

3 years ago

This robotic arm is made up of two cylinders with equal volume and two triangular prism hands. The volume of each hand is

BaLLatris [955]

Answer:

$\frac{r}{3\pi h+r}$

Step-by-step explanation:

Since the height isn't given, we assume it to be "h" (of cylinders). And the answer will be in terms of "r" and "h".

The area of 1 arm is given, so the area of 2 arms would be:

$A_{arm}=2*(\frac{1}{2}r*\frac{1}{3}r*2r)=\frac{2r^3}{3}$

Now, area of 2 cylinders would be the formula:

$A_{cyl}=2*(\pi r^2 h)=2\pi r^2 h$

So, total area is A_arm PLUS A_cyl. The fractional area the arms are would be gotten by taking expression A_arm divided by A_total.

Shown below:

$\frac{A_{arm}}{A_{total}}=\frac{\frac{2r^3}{3}}{2\pi r^2 h + \frac{2r^3}{3}}$

We simplify further:

$\frac{\frac{2r^3}{3}}{2\pi r^2 h + \frac{2r^3}{3}}\\=\frac{\frac{2r^3}{3}}{2r^2(\pi h + \frac{r}{3})}\\=\frac{r}{3(\pi h + \frac{r}{3})}\\=\frac{r}{3\pi h+r}$

THis is the answer.

6 0

3 years ago

Read 2 more answers

A rectangular prism has dimensions of 3x, 5x, and 6x. Write an expression for the total volume of the prism.

Evgesh-ka [11]

90because u multiple 3x in 5x equal to 15 then multiple 6x in 15x together equal to 90 prism

3 0

3 years ago

Read 2 more answers

1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o

tester [92]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

A) If the length of a rectangle was tripled, but the width did not change?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

B) If the length was tripled and the width was decreased by a factor of 1/4?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

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3 years ago

WORTH 20 POINTS PLS HELP!

scZoUnD [109]

Answer:80ft

Step-by-step explanation:

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3 years ago