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3 years ago

Adante begins to evaluate the expression 3 1/3 x 5 1/4 using the steps below

Mathematics

1 answer:

il63 [147K]3 years ago

4 0

Answer:

$\frac{35}{2}$

Step-by-step explanation:

To solve this problem we need to write the mixed fraction as a fractional number, as follows:

$3 1/3 = 3 + \frac{1}{3} = \frac{9+1}{3} = \frac{10}{3}$

$5 1/4 = 5 + \frac{1}{4} = \frac{20+1}{4} = \frac{21}{4}$

Then, evaluating the expression:

$\frac{10}{3}$ × $\frac{21}{4}$ = $\frac{210}{12}$ = $\frac{35}{2}$

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The size of the largest angle in a triangle is 3 times the size of the smallest angle.

tamaranim1 [39]

The sizes of the angles are 34° , 44° , 102°

Step-by-step explanation:

The given is:

The size of the largest angle in a triangle is 3 times the size of the smallest angle
The third angle is 10° more than the smallest angle
The size of the third angle is x

We need to find the size of each angle in the triangle

∵ The size of the smallest angle = x°

∵ The size of the largest angle is 3 times the size of the smallest angle

∴ The size of the largest angle = x × 3 = (3x)°

∵ The third angle is 10° more than the smallest angle

∴ The size of the third angle = (x + 10)°

Add the size of the three angles and equate the sum by 180°

∵ The sum of the sizes of the interior angles of a Δ is 180°

∴ x + (3x) + (x + 10) = 180

∴ x + 3x + x + 10 = 180

- Add like terms

∴ 5x + 10 = 180

- Subtract 10 from both sides

∴ 5x = 170

- Divide both sides by 5

∴ x = 34

∵ x is the size of the smallest angle

∴ The size of the smallest angle is 34°

∵ 3x is the size of the largest angle

∴ The size of the largest angle = 3(34) = 102°

∵ x + 10 is the size of the third angle

∴ The size of the third angle = 34 + 10 = 44°

The sizes of the angles are 34° , 44° , 102°

Learn more:

You can learn more about the triangles in brainly.com/question/1479138

#LearnwithBrainly

6 0

3 years ago

35% of what number is 35? Please solve all steps using a=p•w

son4ous [18]

35% * X = 35
first you would change 35% to .35
then the equation would be .35 * X = 35
next you would divide .35 from both sides making the equation-
x = 100

then to check plug it in
.35 * 100 = ?
.35 * 100 = 35
want me to message you how to i did it?

4 0

3 years ago

A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T

Westkost [7]

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly,

Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

Surface area of pre-image = 35 m²
Surface area of dilated image = 315 m²
Height of pre-image = 5.8 m
Height of dilated image.

Let the scale fator of dilation be k.

Then:

So area of pre-image = k² × area of dilated image

Thus, we get:

$35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3$

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

$5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m$

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

brainly.com/question/3266920

4 0

2 years ago

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The cost to visit a famous tourist attraction in Russia is 442.25 Rubles. What is the cost in USD if the exchange rate is 3 USD

Lubov Fominskaja [6]

Answer:

$14.5

Step-by-step explanation:

Given data

Cost for the visit=442.25 Rubles

exchange rate

3 USD= 91.5 Rubles

but 1 USD= 91.5/3

= 30.5

Therefore if 1 USD is 30.5 Rubles

Then xUSD is 442.25 Rubles

cross multiply

30.5x= 442.25

divide both sides by 30.5

x= 442.25/30.5

x=14.5USD

The cost of the attraction is $14.5

6 0

3 years ago

Figure ABCD is a parallelogram. Parallelogram A B C D is shown. Angle B is (2 n + 32) degrees and angle D is (4 n minus 2) degre

Kobotan [32]

Answer:

n=17

Step-by-step explanation:

you have to set the two equations equal to each other because its angles are the same. once you do this, its just simple algebra, trying to solve for n. Hope this helps :)

8 0

3 years ago

Read 2 more answers