Calculate the area of each figure.

\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

According to given question, Angle z and 124° forms linear pair,

so,

\(\qquad \sf  \dashrightarrow \: 124 \degree + z = 180 \degree\)

\(\qquad \sf  \dashrightarrow z = \: 180 \degree - 124\degree\)

\(\qquad \sf  \dashrightarrow z = \: 56 \degree \)

Answer:

the answer is $292 :)

have a nice day

Answer: 30k-24m

Step-by-step explanation:

so 9(2k-3m), there is an invisible multipulaction sign between the 9 and the parenthesis which means you have to multiply everything in there. 18k-27m.

Then -9m+12m+12k. Its a plus because two minuses make a positive.

18k-27m-9m+12m+12k. Now you put like terms together.

18+12k=30k, -27m-9m+12m= -24m

30k-24m

Answer:

5,004,300

Step-by-step explanation:

Answer:

$107.52

Step-by-step explanation:

a percentage is always over hundred therefore divide 28% by hundred then multiply by $384.

Answer:

$300

Step-by-step explanation:

Let x = starting investment

1.28x = 384

Divide 384 by 1.28

1.28x/1.28 = 384/1.28

x = 300

From the given information, the measure of DEF is 81°

From the question, we are to determine the measure of DEF

From the given information,

DEF and RST are complementary angles. This means they sum up to 90°

Thus,

(3(-5 + 2x)) + (x - 7) = 90

(3(-5 + 2x)) + (x - 7) = 90

(-15 + 6x) + (x - 7 ) = 90

-15 + 6x + x - 7 = 90

6x + x = 90 + 15 + 7

7x = 112

x = 112/7

x = 16

Then, substitute the value of x to determine the measure of DEF

(3(-5 + 2x))

= (3(-5 + 2(16)))

= (3(-5 + 32))

= (3(27))

= 81°

Hence, the measure of DEF is 81°

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Answer:

Step-by-step explanation:

90 degrees is the answer because there is no movement

Answer:

d = 14

43.96/3.14 = 14

The proportion equivalent with Two-thirds would be 6/9.

Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the  proportion with Two-thirds

If you actually divide it’ll make since , so first  we want to divide the 2 , then you want to multiply the third of the two

2/3 x 3/3

6/9

thus, the answer will be 6/9.

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The quantity of popcorn each friend of the students receive is 5/36 gallons.

Quantity of popcorn each friend receive = Number of gallons of popcorn the student has / Number of the student's friends

= 5/9 ÷ 4

= 5/9 × 1/4

= (5 × 1) / (9 × 4)

= 5/36

Therefore, the quantity of popcorn each friend of the students receive is 5/36 gallons

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Answer:

Step-by-step explanation: to find the slope rise over run

Acute triangle from one point to the other

Answer 4/11

x+y=180 a+b=y

180−(a+b)=y

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

-660

Step-by-step explanation:

Answer:

3.60m

Step-by-step explanation:

In backwaters of Kerala, a boatman was throwing a boat with a long pole which has a length of 4.80m

The boatman put the pole into the water vertically, the part of the pole that was seen above the water level is 0.25m

The first step is to calculate the length of the pole that is seen above the water level

= 4.80 × 0.25

= 1.20m

Therefore the depth of the water at that point can be calculated as follows

=4.80m - 1.20m

= 3.60m

Hence the depth of the water at that point is 3.60m

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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The result of dividing the polynomial (m² + 10m + 18) by (m + 5) using long division is a quotient of m + 5 and a remainder of -7.

To divide the polynomial (m² + 10m + 18) by (m + 5) using long division, we follow these steps:

Step 1: Arrange the polynomial in descending order of powers of m. So, we have:

m² + 10m + 18

Step 2: Divide the first term of the dividend (m²) by the first term of the divisor (m). The result is m.

Step 3: Multiply the entire divisor (m + 5) by the result obtained in Step 2 (m), and write the result below the dividend, aligning like terms:

m² + 5m

__________________

m + 5 | m² + 10m + 18

Step 4: Subtract the result obtained in Step 3 from the dividend:

m² + 10m + 18

- (m² + 5m)

__________________

5m + 18

Step 5: Bring down the next term from the dividend, which is 18.

Step 6: Divide the new polynomial (5m + 18) by the divisor (m + 5). The result is 5.

Step 7: Multiply the entire divisor (m + 5) by the result obtained in Step 6 (5), and write the result below the previous subtraction:

m² + 5m

__________________

m + 5 | m² + 10m + 18

m² + 5m

______________

5m + 18

- (5m + 25)

______________

-7

Step 8: Since we have no more terms to bring down, the remainder is -7.

Therefore, the result of dividing (m² + 10m + 18) by (m + 5) using long division is:

Quotient: m + 5

Remainder: -7

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If the graph of \(f(x) = 4e^{0.1x}\) is blue, then the graph of \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is: C. red.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

For the rate of change of the blue exponential function \(f(x) = 4e^{0.1x}\), we have the following:

b = \(e^{0.1}\)

b = 1.11

For the rate of change of this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\), we have the following:

b = 1 + 0.1/0.5

b = 1.2

Therefore, this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is represented by the red line on the graph.

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer: D

Step-by-step explanation:

The stem-and-leaf plot of the given data is attached.

A stem-and-leaf plot refers to a device used to present quantitative data in a graphical format to help in visualizing the shape of a distribution. It is a table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

From the given options, the statements that describe the percentages distributed, distribution skewness and whether there are any gaps are:

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Answer:

( 2, 60 )

Step-by-step explanation:

→ Read along the x - axis and then the y axis

A pair of corresponding angles, alternate interior angles, and alternate exterior angles include the following:

Corresponding angles: ∠1 ≅ ∠5.

Alternate interior angles: ∠4 ≅ ∠6.

Alternate exterior angles: ∠2 ≅ ∠8

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines:

∠1 ≅ ∠5

By applying the alternate interior angles theorem to parallel lines m and n, we have the following congruent angles:

∠4 ≅ ∠6

By applying the alternate exterior angles theorem to parallel lines m and n, we have the following congruent angles:

∠2 ≅ ∠8

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The number that has a 4 in the hundred places.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A 4 with a value ten times less than the 4 in the number 123,469.

First, the value of the 4 in the number 123,469 can be found by separating each digit as:

123,469 = 100,000 + 20,000 + 3,000 + 400 + 60 + 9

Then the value of the 4 is 400.

Now we want a number that has a 4 with a value then times less than 400. Then we have

400/10 = 40

Then we want a number that has a 4 in the hundred places.

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The sequence \(b_n = \frac{{2^n \cdot 3^n}}{{n!}}\) is strictly increasing for all values of n. It is bounded above by 6 and bounded below by 0. Thus, it is both a bounded and monotonic sequence.

To determine where the sequence is increasing or decreasing, we need to analyze the behavior of consecutive terms.

Let's analyze the sequence:

\(b_n = \frac{{2^n \cdot 3^n}}{{n!}}\)

To check if the sequence is increasing or decreasing, we can compare the ratio of consecutive terms:

\(\frac{{b_{n+1}}}{{b_n}} = \frac{{2^{n+1} \cdot 3^{n+1}}}{{(n+1)!}} \cdot \frac{{n!}}{{2^n \cdot 3^n}}\)

Simplifying this expression, we have:

\(\frac{{b_{n+1}}}{{b_n}} = \frac{{2 \cdot 3}}{{n+1}}\)

Since the numerator is a constant value (6), the ratio bₙ₊₁ / bₙ will always be greater than 1. Therefore, the sequence is strictly increasing for all values of n.

Next, let's determine if the sequence is bounded. To do this, we need to find both an upper bound and a lower bound.

Let's consider the value of bₙ when n approaches infinity:

\(\lim_{{n \to \infty}} b_n = \lim_{{n \to \infty}} \left[ \frac{{2^n \cdot 3^n}}{{n!}} \right]\)

By applying the ratio test, we can simplify this limit:

\(\lim_{{n \to \infty}} b_n = \lim_{{n \to \infty}} \left[\frac{{2 \cdot 3 \cdot 2 \cdot 3 \cdot \ldots \cdot 2 \cdot 3}}{{n \cdot (n-1) \cdot \ldots \cdot 2 \cdot 1}}\right]\)

Since the numerator remains constant while the denominator grows factorially, the limit of bₙ as n approaches infinity is 0.

Therefore, the sequence is bounded above by a constant value (6) and bounded below by 0.

To summarize:

- The sequence is strictly increasing for all values of n.

- The sequence is bounded above by 6 and bounded below by 0.

- The sequence is both monotonic and bounded.

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Answer:

5

Step-by-step explanation:

First,let find the area of AMY. It is given that

Am=5

MY=7

AY=3

We can add up those numbers to find the perimeter.

5+7+3=15.

2. Since AMY and MEG are similar shapes, there side lengths are proportional, and their perimeter is also proportional.

The only transformation that can accomplish that is a dilation.

MEG is a dilation of AMY by 1/3. so that means MEG is 3 times smaller than AMY.

We would just divide 3 by the perimeter of AMY to find MEG.

\( \frac{15}{3} = 5\)

Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles