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3 years ago

Find the smallest value of k such that 3240k is a perfect cube

Mathematics

2 answers:

Zarrin [17]3 years ago

3 0

Answer:

225

Step-by-step explanation:

3240k = 2×2×2×3×3×3×3×5×k

Every factor should be in groups of 3

(3×5)² = k

k = 225

kodGreya [7K]3 years ago

3 0

Answer:

Step-by-step explanation:

Prime factorize 3240

3240 = 2*2*2*3*3*3*3*5

To be a perfect cube we have to multiply it by 5*5*3*3 = 25*9=225

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Is triangle ABC similar to triangle DEF? why or why not.

Lana71 [14]

Answer:

Step-by-step explanation:

Two triangles are congruent if they have the same three sides in proportion and they have exactly the same angles.

If the angles are different, the triangles are not similar.

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3 years ago

Hisako sells dolls at her doll store. If she sells a doll for $35, and there is 6% sales tax, what is the tax amount a customer

Sloan [31]

Given:

The price of a doll = $35

Sales tax = 6%

To find:

The tax amount that a customer will pay on one doll.

Solution:

The price of doll is $35 and the sales tax is 6%, so the tax amount on a doll is 6% of 35.

$\text{Tax amount}=35\times \dfrac{6}{100}$

$\text{Tax amount}=\dfrac{210}{100}$

$\text{Tax amount}=\dfrac{21}{10}$

$\text{Tax amount}=2.1$

Therefore, the tax amount that a customer will pay on one doll is $2.1.

7 0

2 years ago

Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.