Simplify -2 (x+8) +1 (3x+16)

Answer:

The original tax credit was $2500, so 15% of that is:

0.15 x $2500 = $375

Therefore, buyers would receive a $375 tax credit if they purchased the vehicle one year after the sales reached the 60,000 unit threshold.

Answer:

654 ft

Step-by-step explanation:

in this case you have a SOH-CAH-TOA problem.

we need Adjacent and opposite so we use tan

tan (17) = O/A

tan (17) = 200ft / x

x = 654.17 ft

to the nearest foot = 654 ft

Leave a like and mark brainliest if this helped

Leave a like and mark brainliest if this helped

The distance that represent the ship from the base of the cliff should be considered as the 654 ft.

Since

A ship’s captain sights the top of a 200 foot cliff at a 17° angle of elevation.

So the following formula should be applied

\(tan (17) = O/A\\\\tan (17) = 200ft / x\)

x = 654.17 ft

= 654 ft

hence, The distance that represent the ship from the base of the cliff should be considered as the 654 ft.

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The answer is 31

Step-by-step explanation:

A = 1/2 bh

279= 1/2b x 18

558 = 18b we divided both side by 18

b=31

By the Pythagorean theorem,

\(\sin^2 t +\cos^2 t = 1 \\ \\ \sin^2 t +(-3/4)^2 = 1 \\ \\ \sin^2 t =7/16 \\ \\ \sin t=-\frac{\sqrt{7}}{4}\)

(I took the negative case because of the range of values of t)

Using the cosine double angle formula,

\(\cos 2t=2\cos^2 t -1 =2(-3/4)^2 - 1 =1/8\)

Using the sine double angle formula,

\(\sin 2t=2\left(-\frac{3}{4} \right)\left(-\frac{\sqrt{7}}{4} \right)=\frac{3\sqrt{7}}{8}\)

Using the cosine half-angle formula,

\(\cos \frac{t}{2}= -\frac{\sqrt{1+\cos A}}{2}=-\frac{\sqrt{1+\frac{3\sqrt{7}}{8}}}{2}\)

(I took the negative case because of the range of values of t)

Using the sine half-angle formula,

\(\sin \frac{t}{2}=\frac{\sqrt{1-\cos A}}{2}=\frac{\sqrt{1-\frac{3\sqrt{7}}{8}}}{2}\)

(I took the positive case because of the range of values of t)

Answer:

t ^3

Step-by-step explanation:

t^2.t

= t × t^2+1

= t^3

Step-by-step explanation:

Make f(x) = 0

\( {x}^{2} + 6x + 11 = 0\)

\( {x}^{2} + 6x = - 11\)

\(( \frac{6}{2} ) ^{2} = 3 ^{2} = 9\)

\( {x}^{2} + 6x + 9 = - 11 + 9\)

(x+3)²= -2

(x+3)²+2= 0

f(x)= (x+3)²+2

Which is the f(x) in graphing form.

Answer:

13.3 miles

Step-by-step explanation:

Total distance needed to travel= 16 miles

Distance travelled= 2.7 miles

Total distance - distance travelled

16-2.7= 13.3

Therefore, Isabel needs to drive 13.3 miles more to work.

Question ) - Which recursive formula can be used to represent the sequence 2, 4, 6, 8, 10, ... ?

Answer ) - an+1 = an+2

Answer:

3

Step-by-step explanation:

A cube will have six sides, therefore the numbers would run from 1 to 6 on a cube. There are only 3 numbers after 3 up until 6. So it is 3.

The total number of possible outcomes for the probability is P = 24 outcomes

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Rolling a cube: A standard six-sided cube has numbers 1 through 6. However, we are only interested in outcomes where the number on the cube is greater than 3.

So there are only 3 possible outcomes: 4, 5, or 6.

Spinning a spinner: The number of possible outcomes on a spinner depends on the specific spinner being used. Now , the spinner has 4 equally likely outcomes: A, B, C, and D.

Flipping a coin: A standard coin has 2 sides: heads (H) and tails (T). So there are 2 possible outcomes.

Multiplying the number of outcomes for each event, we get:

Number of outcomes for rolling a cube: 3

Number of outcomes for spinning a spinner: 4

Number of outcomes for flipping a coin: 2

Total number of possible outcomes: 3 x 4 x 2 = 16

Hence , there are 24 unique outcomes possible where the number on the cube is greater than 3

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The complete question is attached below :

Tina will roll the cube, spin the spinner, and flip the coin one time each to form an outcome.

How many unique outcomes are possible where the number on the cube is greater than 3?

Answer:

157 Minutes

Step-by-step explanation:

20.27 - 30 = 17.27

17.27 / .11 = 157

Since both of the factors are binomials, FOIL Method may be used.

Product of the First terms: (x)(2x)= 2x²

Product of the Outer terms: (x)(3)= 3x

Product of the Inner terms: (-2)(2x)= -4x

Product of the Last terms: (-2)(3)= -6

Since the product of the outer and the inner terms are like terms, we may add the two products.

Thus, combining all terms in one expression would be as follows.

The situation can be represented by expression 3x + 5y = 900

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of cookies and y represent the number of cake slice.

The class wants to raise $900.Hence:

3x + 5y = 900

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The value of the house was increased by $75420 and the current value of the house is $494420.

A percent is a measurement in hundredths. By dividing the percentage value by 100, percentages can be transformed into decimals and fractions.

Given, A house on the market was valued at 419,000.

Then after several years, the value increased by 18%.

Therefore, The increase in value is,

= (18/100)×41900.

= $75420.

Hence, The current value of the house is,

= $(419000 + 75420).

= $494,420

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To support her discussion, it would be best for Alex to use Graph A for her presentation. Alex should use this graph for her presentation because the number of faulty products appears to decrease less on this graph.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In order to determine an equation with a declining line, we would have to determine the slope of each line graphically and then taking note of the line with a negative rate of change (slope) because it indicates a decreasing function.

In this context, we can reasonably infer and logically deduce that Graph A is more suited for Alex's presentation because the number of faulty products appears to decrease less on it.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The second length of the piece because 141 times 2 which is two times the amount of the second piece is 282.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 47.

The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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Answer:

y = -1/9

Explanation:

Given the equation:

First, we bring all terms containing y to the left-hand side of the equation.

Next, subtract 4 from both sides.

Finally, we divide both sides by 9.

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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The total surface area of the triangular prism using the net is 96 square units

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

The net of a triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 2 * 3 * 7 + 6 * 7+ 2 * 1/2 * 2 * 6

Evaluate

Area = 96

Hence, the surface area is 96 square units

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The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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Answer:

the action of moving back and forth quickly and steadily

Explanation:

hopes this helps :D

Vibration is best defined as the action of moving back and forth quickly and steadily.

Vibration is a demonstation of simple harmonic motion. Simple harmonic motion is a regular and repeating motion.

The correct definition of vibration is that it is the action of moving back and forth quickly and steadily.

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Step-by-step explanation:

Write the following numbers in expanded form and exponential form a. 4081673 b.561827 c.892 d.3848 e. 777320916  

We need to write in expanded form and exponential form. So

1. 4081673 = 4000000 + 0 + 80000 + 1000 + 600 + 70 + 3

          = 4 x 10^6 + 0 + 8 x 10^4 + 1 x 10^3 + 6 x 10^2 + 7 x 10^1 + 3 x 10^0

2. 561872 = 500000 + 60000 + 1000 + 800 + 70 + 2

           = 5 x 10^5 + 6 x 10^4 + 1 x 10^3 + 8 x 10^2 + 7 x 10^1 + 2 x 10^0

3. 892 = 800 + 90 + 2

            = 8 x 10^2 + 9 x 10^1 + 2 x 10^0

4.    3848 = 3000 + 800 + 40 + 8

                = 3 x 10^3 + 8 x 10^2 + 4 x 10^1 + 8 x 10^0

5.    777320916 = 700000000 + 70000000 + 7000000 + 300000 +   20000 + 0 + 900 + 10 + 6

           = 7 x 10^8 + 7 x 10^7 + 7 x 10^6 + 3 x 10^5 + 2 x 10^4 + 0 + 9 x 10^2 + 1 x 10^1 + 6 x 10^0

\(~~\lim \limits_{x \to 0} \left(\dfrac{1- \cos mx }{1- \cos nx}} \right)\\\\\\=\lim \limits_{x \to 0} \left[\dfrac{2\sin^2 \left(\dfrac{mx}{2} \right)}{2 \sin^2 \left(\dfrac{nx}{2}\right)} \right]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[1-\cos 2x =2 \sin^2 x\right]\\\\\\\)

\(=\lim \limits_{x \to 0} \left[ \dfrac{\sin^2 \left(\dfrac{mx}2 \right)}{\left(\dfrac{mx}2 \right)^2 } } \times \left(\dfrac{mx}{2} \right)^2\times \dfrac{\left(\dfrac{nx}2 \right)^2} {\sin^2 \left(\dfrac{nx}2 \right)} \times \left(\dfrac{2}{nx} \right)^2\right]\\\\\\=\lim \limits_{x \to 0}\left[ \left( \dfrac{mx}2 \right)^2 \left( \dfrac{2}{nx} \right)^2\right]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\lim \limits_{x \to 0} \dfrac{\sin x}{x} = \lim \limits_{x \to 0} \dfrac{x}{ \sin x} = 1\right] \\\\\\\)

\(=\lim \limits_{x \to 0} \left( \dfrac{m^2 x^2}{4} \cdot \dfrac{4}{n^2 x^2 } \right)\\\\\\=\lim \limits_{x \to 0} \left( \dfrac{m^2}{n^2}\right)\\ \\\\=\dfrac{m^2}{n^2}\)

Answer:

12√3

Explanation:

First, we know that JL = 24.

Then, the triangle JKL is equilateral. It means that all the sides are equal, so JK is also equal to 24.

Finally, N is the midpoint of segment JK, so it divides the segment JK into two equal parts. Therefore, JN = 12.

Now, we have a right triangle JLN, where JL = 24 and JN = 12.

Then, we can use the Pythagorean theorem to find the third side of the triangle, so NL is equal to:

Because JL is the hypotenuse of the triangle and JN and NL are the legs.

So, solving for NL, we get:

Therefore, the length of NL is 12√3

Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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Answer:

3x - 8

please help me with a brainiest 5star

Step-by-step explanation:

You need to substitute x-1 wherever x is appearing in the equation

f(x) = 3x-5

so;

f(x-1) = 3(x-1) - 5

= 3x - 3 - 5

= 3x - 8