Why is the product of a rational number and an irrational number irrational?
A) because the product is always a non-terminating, non-repeating decimal
B) because the product is always a fraction
C) because the product is always a negative number
D) because the product is always a repeating or a terminating decimal

Answer:

128 cm²

Step-by-step explanation:

Given linear scale factor of 2 similar shapes = a : b , then

ratio of areas = a² : b²

Here linear scale factor = 3 : 4 , then

ratio of areas = 3² : 4² = 9 : 16

let x be the area of the larger shape then by proportion

[tex]\frac{9}{72}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )

9x = 1152 ( divide both sides by 9 )

x = 128

That is area of larger shape is 128 cm²

Answer:

7.5 = OM

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite side / hypotenuse

sin 30 = OM / UN

sin 30 = OM / 15

15 sin 30 = OM

7.5 = OM

Here, if you use the law of sines, you cannot find the measure of the required angle. But if you use the law of cosines, you will get the desired result.

The measure of the angle C of the given triangle is 43.61°

According to the law of cosine, the square of any one side of a triangle is equal to the difference between the squares of the other two sides and double the product of the other sides and cosine angle added together between them. If AB, BC, and CA are lengths of the three sides of a triangle, then using the law of cosine, we can write

AB² = BC² + CA² - 2(BC)(CA)cos C.

Here, AB = 16, BC = 22, and AC = 21.

Now, 16² = 22² + 21² - 2 * 22 * 21 * cos C

i.e. 256 = 484 + 441 - 924 * cos C

i.e. 256 - 925 = - 924 * cos C

i.e. - 669 = - 924 * cos C

i.e. cos C = 669/924 = 0.724

i.e. C = cos⁻¹(0.724) = 43.61

Therefore the measure of the angle C of the given triangle is 43.61°

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Answer:

18.84 feet.

Step-by-step explanation:

The formula for the circumference of a circle is:

2Pi*radius

The radius would be half the diameter so 3.

2*3.14*3

Answer:

[tex] \frac{1}{ {6}^{8} } [/tex]

Step-by-step explanation:

when the is a base raised to a negative power.....put it under 1 and the negative power now becomes a positive power

Example: 5^-2 = 1/5^2

Answer:

1000

Step-by-step explanation:

the math

Answer:

$205.60

160(1.135)+ 160(.15)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

If 15% of quizzes don't have to be A's, that means that its 9 quizes that can be lower than an A. She already lost 5 which means she has four left.

Answer:

D; 4

Step-by-step explanation:

Step 1:

Let us figure out exactly how many As Liya has to earn for the year. We must find 85% of 60:

[tex]85 \%\ of\ 60=\\\frac{85}{100}*\frac{60}{1}=\\\frac{85}{5} *\frac{3}{1} =\\17*3=\\51[/tex]

Liya must earn 51 As this year to reach her goal. This also means that she can earn 9 grades lower than an A to still reach her goal ([tex]60-51=9[/tex]).

Step 2:

So far, Liya has earned 35 As out of 40 tests in total. This means that so far, Liya has earned 5 test grade lower than an A:

[tex]40-35=5[/tex]

In total, Liya can only have 9 grades lower than an A. Therefore:

[tex]9-5=\fbox{4}[/tex]

Liya can only earn [tex]\fbox{4}[/tex] grades lower than an A in the remaining quizzes.

I hope this helps! Let me know if you have any questions :)

Answer:

That's a parabola

explanation:

Answer: there are 2 terms

Step-by-step explanation: A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. ... Examples of single terms: 3x is a single term.

2 terms

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. The number in front of a term is called a coefficient.

Answer:

11.8 ft

Step-by-step explanation:

Since the length of one side, l = 5.3 ft, the longer base b = 12.7 ft and the one brace, d form a triangle with angle between the longer base and side being the angle facing the brace is θ = 68.4°, we use the cosine rule to find the length of thee brace.

So d² = l² + b² -2lbcosθ

So, substituting the values of the variables into the equation, we have

d² = (5.3 ft)² + (12.7 ft)² -2(5.3)(12.7)cos68.4°

d² = 28.09 ft² + 161.29 ft² - 134.62(0.3681)

d² = 189.38 ft² - 49.56 ft²

d² = 139.82 ft²

taking square-root of both sides, we have

d = √139.82 ft²

d = 11.82 ft

d ≅ 11.8 ft to the nearest tenth of a foot.

Answer:

less than is the correct answer

Answer:

-3x+30

Step-by-step explanation:

[tex]4\left(x+7\right)-7x+2[/tex]

Expand [tex]4(x+7)= 4x+28[/tex]

[tex]4x+28-7x+2[/tex]

Simplify [tex]4x+28-7x+2[/tex]

[tex]-3x+30[/tex]

Answer:

56851200

Step-by-step explanation:

The expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12

A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56 etc. are the numbers.

It is given that:

The word expression:

"five thousand six hundred eighty-five and twelve hundredths"

The number would be:

= 5685.12

In the expanded form the number can be written as:

The expanding form can be used to indicate the value of each digit in a number in arithmetic.

Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.

Expanded Form:

5685.12 = 5000 + 600+ 80 + 5 + 0.1 + 0.02

Thus, the expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12

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Answer:

QSR = 68º

Step-by-step explanation:

TSQ + QSR = TSR

15x + (10x - 2) = 173

Combine like terms

25x = 175

Divide both sides by 25

x = 7

QSR = 10x - 2

QSR = 10(7) - 2

QSR = 68º

Answer:

an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle (since the sign is "left than")

Step-by-step explanation:

Given the inequalities

17+4x < 9

Subtract 17 from both sides

17+4x -19 < 9 - 17

4x < -8

Divide both sides by 4

4x/4 < -8/4

x < -2

To represent the solution on a number line, an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle.

Answer:

4th term = 29

to generate the terms, substitute n = 2, 3, 4 into the rule

noting that b(1) = - 7

b(2) = b(2 - 1) + 12 = b(1) + 12 = -7 + 12 = 5

b(3) = b(3 - 1) + 12 = b(2) + 12 = 5 + 12 = 17

b(4) = b(4 - 1) + 12 = b(3) + 12 = 17 + 12 = 29

Answer:

Step-by-step explanation:

i dont know this I am sorry :(

Answer:

Tree C

Step-by-step explanation:

each of the charts/tables/paragraphs are talking about a different tree.

Tree A started with 5 inches, as it says.

Tree B started with 3 inches, as you can see under the 0 months.

Tree C, at the month 0 mark, has a height of 10 inches, so it started with 10.

10>5 and 10>4, so Tree C is the biggest

Answer:

C

Step-by-step explanation:

(S=D/T)S=216KM, T=8HOURS : 216/8=27KM/HOUR

The average speed of the train is 27 km/hour if It takes a train 8 hours to travel a distance of 216 km.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

It takes a train 8 hours to travel a distance of 216 km.

As we know,

Average speed = distance/time

Average speed = 216/8 = 27 km/hour

Thus, the average speed of the train is 27 km/hour if It takes a train 8 hours to travel a distance of 216 km.

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Answer:

675 sq feet

Step-by-step explanation:

Radius =15ft

Area = 3(15)^2

= 3(15)(15)

= 3(225)

=675 sq ft

Answer:

675

Step-by-step explanation:

We square r first, so 15 ^ 2 = 225.

Then multiply by pi, which is 3 for this problem. 225 x 3 = 675.

Therefore, the answer is 675.

Answer:

50

Step-by-step explanation:

trust me bro

The height of the kite is 47.5 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 95

h = 47.5 feet

Therefore the height of the kite is 47.5 feet.

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Answer:

A

Step-by-step explanation:

If lines are parallel and intersected by another line then there are 2 alternating angles between them.

Answer:

Step-by-step explanation:

That exterior angle is equal to the sum of the remote interiors, specifically:

2x + 3 = 45 + x + 8 and

x = 50

So the angles inside the triangle...we already know one of them is 45. If x = 50, then x + 8 is 50 + 8 = 58. That means that the third angle is 180 - 45 - 58 which is 77.

Answer:

they intersect at 0,-2

Answer:

The tenths place.

Step-by-step explanation:

If you want to buy 2 1/2 lb of cheese, you want to buy 2.5lbs. The tenths place is the first place after the decimal, and the place the scale needs to show to show you 2.5lbs.

Answer:

tenths place

Step-by-step explanation:

Answer:

The distance is 12 miles

Step-by-step explanation:

Given

See attachment for grid

Required

The distance

From the attached:

[tex]B = (-8,6)[/tex] --- Bank

[tex]H = (4,6)[/tex] --- Hiroto's house

Using distance formula, we have:

[tex]d = \sqrt{(x_1- x_2)^2 + (y_1 - y_2)^2}[/tex]

This gives:

[tex]d = \sqrt{(-8- 4)^2 + (6 - 6)^2}[/tex]

[tex]d = \sqrt{(-12)^2}[/tex]

[tex]d = \sqrt{144}[/tex]

[tex]d = 12[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {c) \:1}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] = \frac{1}{9} \times 9\\[/tex]

[tex] = \frac{9}{9} \\[/tex]

[tex] = \frac{1}{1} \\[/tex]

[tex] = 1\\[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]