The length of the shortest side of a 30-60-90 triangle is 2 cm. Which of the following is the length of the hypotenuse?

2cm
√3cm
4cm
2 √3cm

Answer:

a) 29%   b) 22%

Step-by-step explanation:

The quantities must be expressed in the same units.

a) compare 35 minutes to 2 hours.  2 hours is 2 x 60 = 120 minutes.

35/120 = .291667 = 29%

b) compare 650 grams to 3 kilograms.  3 kg = 3 x 1000 = 3000 g.

650/3000 = .21667 = 22%

Answer:

see explanation

Step-by-step explanation:

To express as a percentage, first express as a fraction and multiply by 100%

The quantities must be expressed in the same units.

(a)

2 hours = 2 × 60 = 120 minutes, thus

[tex]\frac{35}{120}[/tex] × 100% ≈ 29.2% ( to 1 dec. place )

(b)

3 Kg = 3 × 1000 = 3000 g, thus

[tex]\frac{650}{3000}[/tex] × 100% ≈ 21.7% ( to 1 dec. place )

Answer x=-14.

Step-by-step explanation:

4+x/7

4+ -14/7

4+-2

2

Answer:

[tex]4 +\frac{x}{7}=2[/tex]

[tex]\frac{28 + x}{7} = 2[/tex]

28 +x = 14

x =14 - 28

x = -14

Hope this helped.

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

Interior angle + exterior angle = 180

Because they form a linear pair.

Exterior angle = 180 - interior angle

= 180 - 150

= 30°

The measure of each exterior angle is 30°.

Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. These angles are always equal.

Given that the measure of each Interior angle is 150°

We have to determine the measure of each exterior

Since an interior angle and an adjacent exterior angle of a polygon form a linear pair.

Therefore, the sum of the Interior angle and exterior angle adds up to 180°.

So Exterior angle = 180 - interior angle

⇒ Exterior angle = 180 - 150

⇒  Exterior angle = 30°

Hence, the measure of each exterior angle is 30°.

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Answer:

4.65 x 10^-5

Step-by-step explanation:

.00465

[tex]4.65 x 10^{-5}[/tex]

Answer:

d

Step-by-step explanation:

Answer:

-7 3=-4

-5 1=-4

-3 -1=-4

-7 and 3 make -4. -5 and 1 make -4. -3 and -1 make -4.

The three pairs with the same total are as follow:

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes:

Given:

Number on cards -7 -5 -3 3 1 -1

Now, we have to make the pair according it gives the same total

-7 + (3) = -4

-5 + 1 = -4

-3 -1 = -4

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Answer:

b

Step-by-step explanation:

Answer:

foreshadowing

Step-by-step explanation:

Is that what you're looking for?

If it is:

Foreshadowing includes the clues the author throws into a story to hint at what may happen in the future, or further in the book. For instance, Character A says to Character B that "I've never broken a bone before! I've never even been hospitalized" but does so near the climax of the story.

Answer:

number d im (pretty sure)

Step-by-step explanation:

The value of the expression is  [tex]\frac{m^4}{n^2}[/tex].

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex](m^{2/3}n^{-1/3})^6[/tex]

This can be simplified as,

[tex]m^{2/3 \times6}[/tex] x [tex]n^{-1/3 \times 6}[/tex]

=[tex]m^{2\times2}[/tex] x [tex]n^{-1 \times2}[/tex]

= [tex]m^4[/tex][tex]n^{-2}[/tex]

= [tex]\frac{m^4}{n^2}[/tex]

Thus,

The value is  [tex]\frac{m^4}{n^2}[/tex].

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To rewrite an expression using only positive integer exponents, apply the rules of exponentiation and simplify the expression.

To rewrite an expression using only positive integer exponents, you can apply the rules of exponentiation. For example, if you have an expression like [tex]a^{-2}[/tex], you can rewrite it as [tex]\frac{1}{a^{2} }[/tex]

. Similarly, if you have a term with a negative exponent in the denominator, you can move it to the numerator and change the sign of the exponent to make it positive.

Here's a step-by-step example:

By following these steps, you can rewrite expressions using positive integer exponents.

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The height of the tree is 5.4 m

Step-by-step explanation:

Let the height of the tree be 'h'

Angle of elevation= 34°

distance from the rock on the ground

to the base of the tree = 8 m

we can use the tan function of trigonometry to find the height of the tree,

tan 34° = h/8

tan 34° = 0.67

tan 34° = h/8

0.67 = h/8

h = 8 x 0.67

h = 5.4m

The height of the tree is 5.4 m

The height of the tree to the nearest tenth of a meter is approximately 5.6 meters.

To calculate the height of the tree, we can use trigonometry, specifically the tangent function since we have the angle of elevation and the distance from the observer to the base of the tree.

Let's denote:

According to trigonometry,

[tex]\[ \tan(\text{angle of elevation}) = \frac{\text{height of the tree}}{\text{distance to the tree}} \][/tex]

Substituting the given values:

[tex]\[ \tan(34^\circ) = \frac{h}{8} \][/tex]

Now, let's solve for h:

h = 8 × tan(34°)

Using a calculator, we find:

h ≈ 8 × 0.6947

≈ 5.5576

Therefore, the height of the tree to the nearest tenth of a meter is approximately 5.6 meters.

Answer:

13

Step-by-step explanation:

To get the hypotenuse (the longest side) you would use the Pythagorean Theorem ([tex]a^{2} + b^{2} = c^{2}[/tex])

Replace a and b with the two given sides and solve for c

[tex]5^{2} + 12^{2} = c^{2}[/tex]

25 + 144 = [tex]c^{2}[/tex]

169 = [tex]c^{2}[/tex]

Find the square root of both sides

[tex]\sqrt{169} = \sqrt{c^{2}}[/tex]

13 = c

Answer:

516

Step-by-step explanation:

First

34% small and 40% large means that 100 - (34 + 40) = 26% medium

26% of 600 = 0.26 × 600 = 156

----------------------------------------------------

Second

[tex]\frac{3}{10}[/tex] are small and [tex]\frac{1}{10}[/tex] are large, which means [tex]\frac{6}{10}[/tex] are medium

[tex]\frac{6}{10}[/tex] × 400 = 0.6 × 400 = 240

-----------------------------------------------------

Third

sum the parts of the ratio, 3 + 4 = 7

Divide 210 by 7 to find the value of one part of the ratio

210 ÷ 7 = 30 ← value of 1 part of ratio

Thus medium = 4 × 30 = 120

Total number of medium packets = 156 + 240 + 120 = 516

|7m + 4| = 1

It can equal either 1 or -1, so:

7m + 4 = 1

7m = -3

m = -3/7

7m + 4 = -1

7m = -5

m = -5/7

Answer:

36 leaves

Step-by-step explanation:

1 clover has 4 leaves

so if you have 9 clovers multiply the leaves by clovers by 4

1:4

9:36

Answer:

95°

Step-by-step explanation:

Since, quadrilateral DUCK is inscribed in circle O

sum of the opposite angles of the quadrilateral is 180°

m<K +m<U= 180°

m<K= 180°- 85°= 95°

Answer:

95 degrees

Step-by-step explanation:

Quadrilaterals that are inscribed in circles are often called "cylic". Cyclic quadrilaterals have many unique properties. One of these is that opposite angles add up to 180 degrees.

Here, DUCK is a cyclic quadrilateral. "Opposite angles" are < U and < K, as well as < D and < C. So, since < U and < K are opposite angles in this inscribed quadrilateral, they add up to 180 degrees:

< U + < K = 180

We already know that < U = 85, so:

85 + < K = 180

< K = 95

Thus, < K is 95 degrees.

Hope this helps!

Answer:

3x+12 is the sum

9x-2 is differences

Step-by-step explanation: Combine like terms

Answer: the answer is 190

Step-by-step explanation: I multiplied 95 by two

Answer:

C) 190

Step-by-step explanation:

Answer:

253,440

Step-by-step explanation:

12inches make a foot

So, in 1 miles, total inches equal

5280 × 12 = 63360 inches in one mile

In 4 miles then, total inches would be

63360 × 4 = 253440 inches

Answer:

  9.89 billion

Step-by-step explanation:

At that rate of growth, the population is multiplied by 1.023 each year. After 22 years, the population would be ...

  6·1.023^22 ≈ 9.89 . . . billion

Answer:

Let the equation for the population (P) growth be given by

P = P0ert, where P0 is the initial population in billioins at time t,

                           t is the number of years since 1987,

                           r is the rate of growth of population/year

In this case P0 = 5 billion and r = 0.02.  Putting these values into the equaation:

P = 5e0.02t

Year 1995 is 8 years after 1987, then the population would be

P = 5e0.02*8 = 5e0.16 ≈ 5.87 billion people

Step-by-step explanation:

Answer:

m=7

Step-by-step explanation:

m +2+5=14

m+7=14

-7       -7

m=7

Answer:

The radius is 7 inches

Step-by-step explanation: The radius is half of the diameter and the unit of measure is inches. Unit of measurement includes inches, centimetres, meters, kilometres, etc.

Answer:

-5

Step-by-step explanation:

H is the value that is being added or subtracted from x in the equation

f(x)=a(x-h)^2 +k

Answer:

she can put it in a bank to gain interest

she can invest in the stock market

she can loan out money

Step-by-step explanation:

Depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:

- Continuous compounding: approximately $18,843.48

- Daily compounding: approximately $19,212.03

- Monthly compounding: approximately $18,867.02

Leah's inheritance presents her with a golden opportunity to grow her wealth through strategic investment. With $12,000 at her disposal, she can explore various avenues to maximize the value of her funds. One option she's considering is investing in an account that offers a 4.5% annual interest rate.

To evaluate the potential returns from this investment, she needs to understand how different compounding frequencies affect the growth of her investment over time.

Let's start by defining the equations for the amount A(t) in the account after t years, using continuous compounding, daily compounding, and monthly compounding.

1. Continuous Compounding:

The formula for continuous compounding is given by:

[tex]\[ A(t) = P \times e^{rt} \][/tex]

where:

- A(t) is the amount of money in the account after t years,

- P is the principal amount (initial investment),

- r  is the annual interest rate (expressed as a decimal),

- t is the time in years, and

- e is the base of the natural logarithm, approximately equal to 2.71828.

Using Leah's values:

P = $12,000

r = 0.045 (4.5% expressed as a decimal)

Substituting these values into the formula, we get:

[tex]\[ A(t) = 12000 \times e^{0.045t} \][/tex]

To find the amount after 10 years, we can plug t = 10  into the equation and calculate the result.

[tex]\[ A(10) = 12000 \times e^{0.045 \times 10} \][/tex]

[tex]\[ A(10) \approx 12000 \times e^{0.45} \][/tex]

[tex]\[ A(10) \approx 12000 \times 1.57029 \][/tex]

[tex]\[ A(10) \approx \$18,843.48 \][/tex]

So, after 10 years of continuous compounding, Leah's investment would be approximately $18,843.48.

Next, let's consider daily compounding. In this case, interest is compounded 365 times per year, so the formula becomes:

[tex]\[ A(t) = P \times \left(1 + \frac{r}{365}\right)^{365t} \][/tex]

Using the same values as before, we can calculate:

[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{365}\right)^{365 \times 10} \][/tex]

[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{365}\right)^{3650} \][/tex]

[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00012328767123\right)^{3650} \][/tex]

[tex]\[ A(10) \approx 12000 \times (1.00012328767123)^{3650} \][/tex]

[tex]\[ A(10) \approx 12000 \times (1.60100220887) \][/tex]

[tex]\[ A(10) \approx \$19,212.03 \][/tex]

After 10 years of daily compounding, Leah's investment would be approximately $19,212.03.

Finally, let's explore monthly compounding. With monthly compounding, interest is compounded 12 times per year, so the formula becomes:

[tex]\[ A(t) = P \times \left(1 + \frac{r}{12}\right)^{12t} \][/tex]

Using the same values as before, we can calculate:

[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{12}\right)^{12 \times 10} \][/tex]

[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{12}\right)^{120} \][/tex]

[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00375\right)^{120} \][/tex]

[tex]\[ A(10) \approx 12000 \times (1.00375)^{120} \][/tex]

[tex]\[ A(10) \approx 12000 \times (1.5722520173) \][/tex]

[tex]\[ A(10) \approx \$18,867.02 \][/tex]

After 10 years of monthly compounding, Leah's investment would be approximately $18,867.02.

In summary, depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:

- Continuous compounding: approximately $18,843.48

- Daily compounding: approximately $19,212.03

- Monthly compounding: approximately $18,867.02

These calculations illustrate how different compounding frequencies can affect the growth of an investment over time. Daily compounding typically results in slightly higher returns compared to monthly compounding, while continuous compounding offers the highest potential returns due to its continuous nature.

By understanding these dynamics, Leah can make an informed decision about how to maximize the growth of her inheritance based on her investment preferences and goals.

The complete question is:

Leah has just inherited $12,000. She wants to invest the money so that she can increase the value of her inheritance. What are some of the ways she can do this?

1. Leah wants to invest the $12,000 in an account that pays 4.5% annual interest.

a. Write equations for the amount A(t) that will be in the account after t years, if the interest is

compounded continuously, daily, and monthly. Then, find the amount after 10 years, rounded

to the nearest cent, for each method of compounding.

Answer: 6 and 4

Step-by-step explanation:

Fill in the numbers with the correct variable and you get your answer. 6-0=6 6-2=4

Answer: H

Step-by-step explanation:Question 1(Multiple Choice Worth 5 points) (06.07A MC) What is the length of the third side of the window frame below? (Figure is not drawn to scale.) A picture of a right triangular window frame is shown. The longest side has length labeled as 87 inches. The height of the frame is labeled as 63 inches. 48 inches 60 inches 70 inches 75 inchesanswer - 60Question 2(Multiple Choice Worth 5 points) (06.07A MC) The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 9 miles. The length BC of the triangle is labeled as 6 miles. This length BC is also the length of an irregular gray shaded shape. Which of the following options is closest to the distance (in miles) between points A and B? 6.71 miles 7.35 miles 8.66 miles 10.82 miles answer - 6.71Question 3(Multiple Choice Worth 5 points) (06.07A LC) The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. 8.54 units 9.54 units 11.00 units 24.00 units answer - 8.54Question 4(Multiple Choice Worth 5 points) (06.07A LC) Jessica calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it? Four triangles E, F, G, H are shown from left to right. Triangle E has one side labeled as 2 and the other as 3, and the included acute angle is shown. Triangle F has both sides labeled as 3, and the included acute angle is shown. Triangle G has one side labeled as 4 and the other as 2, and the included right angle is shown. Triangle H has one side labeled as 6 and the other as 7, and the included obtuse angle is shown. answer h

Answer:

15 hope it helps:)

Step-by-step explanation:

because it divides 5 in each side

Answer:

0.00045 (A)

Step-by-step explanation:

Answer:

A)  0.00045

Step-by-step explanation: