Which image below is an equilateral triangle?

Triangle A has three sides each measuring 7 units. Triangle B has two sides that are equal in length, and the base is longer than the two sides. Triangle C has no sides of equal length. Triangle D has sides of length seven, three, and six.

Triangle A
Triangle B
Triangle C
Triangle D

Answer:

$886.47

Step-by-step explanation:

Given:

Total earning = $70

He spends \(\dfrac{1}{5}\) of the total amount on movies.

He then spends \(\dfrac{1}{2}\) of the remaining money on school clothes.

To find:

The remaining money.

Solution:

We have,

Total earning = $70

He spends \(\dfrac{1}{5}\) of the total amount on movies.

Money spent on movie is

\(\$70\dfrac{1}{5}=\$14\)

Remining money after movie is

\(\$70-\$14=\$56\)

He then spends \(\dfrac{1}{2}\) of the remaining money on school clothes.

Money spent on school clothes is

\(\$56\times \dfrac{1}{2}=\$28\)

Remining money after movie and school clothes is

\(\$56-\$28=\$28\)

Therefore, the remaining money is $28.

The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

Answer:

x = 11/7

Step-by-step explanation:

\(7x+6-2x=12x-7+2\\\\5x+6=12x-5\\\\5x+6-5x=12x-5-5x\\\\6=7x-5\\\\6+5=7x-5+5\\\\11=7x\\\\\frac{11}{7}=\frac{7x}{7}\\\\\frac{11}{7}=x\)

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer:

Number of tablet needed = 1 tablet

Step-by-step explanation:

Given:

Amount of calcium per day needed = 3 gram

Amount of calcium in a tablet = 300 mg

Find:

Number of tablet needed

Computation:

Number of tablet needed = Amount of calcium per day needed / Amount of calcium in a tablet

Number of tablet needed = 3gram / 300 milligram

Number of tablet needed = 300 milligram / 300 milligram

Number of tablet needed = 1 tablet

The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

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Answer: 23

Step-by-step explanation:

x = 90 - 67

x = 23

Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

Answer:

Combination with repetition

Step-by-step explanation:

This is a combination since the order in which Jackson purchases the fruit does not matter. Repetition is allowed (he’s at the store so he can buy as many as he wants).

The number of different collections of fruit can he choose should be considered when there is Combination with repetition

Since he can buy any 3 fruit (the store sells apples, oranges, pears, bananas, strawberries,blueberries, and kiwis)

So here it is the combination because the order where Jackson buy the fruit should not matter. Also, the repetition should be allowed that means he buy as he needs.

Therefore, the first option is correct.

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If Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021. The journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

Journal entry is used by companies to record their day to day business transaction.

July 1 2021

Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000

December 31 2021

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

December 31 2021

Debit Available-for-sale securities $300,000

Unrealized Gain - Other comprehensive income $300,000

($2,000,000 - $2,300,000)

June 30 2022

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

The entry necessary upon sale of the Jackson bonds on July 1, 2022 is:

July 1 2022

Debit Available-for-sale securities  $2,300,000

Unrealized Gain-Other comprehensive income account $300,000

Credit Cash $1,800,000

Credit Realized Loss on the sale of Available-for-sale securities $200,000  

[$1,800,000 - $2,000,000= $200,000 (Realized Loss)]

2. Table to show the effect of the Jackson bonds on Colah’s net income,

                             2021                   2022                       Total

Net Income       $60 ,000        ($140,000)              ($80,000)

( 60,000 - $200,000= -$140,000)

OCI                       $300,000                                         $300,000

Comprehensive Income $360,000 ($140,000) $220,000

Therefore the  journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

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Answer:

1) exponent

2) base

3) power

4) order of operations

5) algebraic expression

6) evaluating

7) like terms

8) variable

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Answer:

the answer is three

Step-by-step explanation:

48 divided by 16 is 3

The "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.

The inflation-adjusted pay rate is the rate after adjusting for inflation.

The number of fast-food restaurants = 16

The number of workers per restaurant = 55

Average weekly hours per worker = 20 hours

The number of weeks per year = 52

The current federal minimum wage per hour = $7.25

The total hours worked by the workers = 915,200 hours (16 x 55 x 20 x 52)

Total current wages = $6,635,200 (915,200 x $7.25)

Inflation rate = 7.5%

Inflation-adjusted wage rate = $7.79 ($7.25 x 1.075)

Total wages for next year = $7,129,408 ($7.79 x 915,200)

Additional wages next year = $494,208 ($7,129,408 - $6,635,200)

Thus, the "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.

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Answer:

You didnt give us a question to answer, just a statement.

Step-by-step explanation:

Answer:

it is 0.94 miles

Step-by-step explanation:

that is because to make a mile you need 63,360 but since you have 60,000 it is not technically a mile

Due to modulus there can be two answers, one with greater than equal to and one with less than equal to. So the answer is 11 and -7.

Solve the inequality |x−2|≥9

Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa.

a) |x−2|≥9 = x-2≥ 9

=> x≥ 9+2

=> x≥ 11

b)  |x−2|≥9 = x-2≥ -9 (when sign the negative the greater than equal to sign changes to less than equal to sign)

= x ≤ -9+2 ≤-7

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Answer:

The answer is 2

Step-by-step explanation:

2 x ? x 3 x 2 x 2 = 48

6 x 4 x ? = 48

24 x ? = 48

24 ÷ 24 x ? = 48 ÷ 24

? = 2

Answer:

No idea

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

please mark brainliest

Answer:

15

Step-by-step explanation:

20% of 75 is 15

For your question you can try option #3

The marginal cost of producing the next unit of output always affects the average total cost, so the marginal cost curve always intersects the average total cost curve at its lowest point.

The difference in overall production costs caused by creating or producing one more unit is known as the marginal cost.

By producing at the point where marginal cost (MC) equals marginal revenue, a business can optimize its earnings (MR).

Because fixed costs are fixed regardless of output levels, larger production spreads the total fixed cost over more units, resulting in a lower fixed cost per unit.

Production levels affect variable costs, so increasing the number of units will increase those costs.

Companies need to be aware of the situations when expanding production entails step costs as a result of shifting relevant ranges.

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Answer:

A:y= 2x+4 B:y= -1/3x +12

Step-by-step explanation:

Answer:

Under the first one

Step-by-step explanation:

The expression ⁵√p¹¹ is equivalent to the given expression. The correct answer would be an option (C).

Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied.

The exponential expression is given in the question, as follows:

\(p^\frac{11}{5}\)

We have to determine the equivalent expression to the given expression.

As per option (C), we have

⇒ ⁵√p¹¹

The above expression also can be written as:

⇒ \((p^{11})^\frac{1}{5}\)

⇒ \((p^{11})^{\times}{(\frac{1}{5})}\)

⇒ \(p^\frac{11}{5}\)

Hence, we can conclude that the expression ⁵√p¹¹ is equivalent to the given expression.

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The domain of f(x) is x >= -1, which means that the range of f(x) is y >= 0 (since the square root of a positive number is always non-negative).

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain or range) with the property that each input is related to exactly one output. In other words, a function is a rule or a mapping that assigns a unique output value to each input value. Functions can be represented in various ways, such as equations, tables, graphs, or diagrams. They are used to describe and model a wide range of phenomena in mathematics and other fields, such as physics, engineering, economics, and social sciences. Functions are often denoted by symbols such as "f(x)", "g(x)", or "h(t)" and can be composed or combined to form new functions. They can also be classified according to various properties, such as whether they are continuous, differentiable, invertible, or periodic.

In summary, in mathematics, a function is a relation between a set of inputs and a set of possible outputs that assigns a unique output value to each input value.

Here,

To determine the values in the range of f(x) that are not in the range of g(x), we first need to find the ranges of both functions.

The function g(x) is not given, so we cannot determine its range.

However, we can find the range of f(x) as follows:

Let y = f(x) = √(x+1) - 1

Adding 1 to both sides and squaring, we get:

y + 1 = √(x+1)

y² + 2y + 1 = x+1

x = y²  + 2y

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Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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