May someone please help me on this one.

Answer:

Step-by-step explanation:

The absolute value (or modulus) | 5 - 3x | of a real number  5 - 3x is the non-negative value of 5 - 3x without regard to its sign.

| 5 - 3x| + 2 = 19

| 5 + 3x | = 19 - 2

| 5 + 3x | = 17

Ans: D

Answer:

5 line of symmetry

Step-by-step explanation:

If function \(f(x) = 7x - 8\)  and  \(g(x) =4\) then the answer is \((fog)(-1) = -36.\)

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behaviour of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

We need to find (fog)(-1) = f(g(-1)).

First, we find g(-1):

g(-1) = 4(-1) = -4

Then, we plug in g(-1) into f:

f(g(-1)) = f(-4) = 7(-4) - 8 = -36

Therefore, (fog)(-1) = -36.

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The exercise involves calculations with matrices A, B, and C. We need to determine if matrix products AB, BA, BC, and CB are defined. Additionally, we need to calculate the specific matrix products and determine if BC is equal to CB.

Let's perform the calculations step by step:

(a) To determine if AB is defined, we need to check if the number of columns in matrix A is equal to the number of rows in matrix B. If they are equal, the matrix product AB is defined. If not, the product is not defined.

Matrix A has 2 columns and matrix B has 2 rows, so the product AB is defined.

Calculating AB:

AB = [23 + 83 20 + 88]

[23 + 03 20 + 08]

= [30 64]

[6 0]

To calculate BA, we need to check if the number of columns in matrix B is equal to the number of rows in matrix A. In this case, matrix B has 2 columns and matrix A has 2 rows, so the product BA is also defined.

Calculating BA:

BA = [32 + 02 38 + 02]

[32 + 02 38 + 02]

= [6 24]

[6 24]

(b) To determine if BC is defined, we need to check if the number of columns in matrix B is equal to the number of rows in matrix C. In this case, both matrices have 2 columns and 2 rows, so the product BC is defined.

Calculating BC:

BC = [26 + 85 23 + 81]

[06 + 05 03 + 01]

= [52 22]

[0 0]

To calculate CB, we need to check if the number of columns in matrix C is equal to the number of rows in matrix B. In this case, matrix C has 2 columns and matrix B has 2 rows, so the product CB is also defined.

Calculating CB:

CB = [62 + 30 68 + 30]

[52 + 10 58 + 10]

= [12 48]

[10 40]

Is it true that BC = CB?

BC = [52 22]

[0 0]

CB = [12 48]

[10 40]

BC and CB are not equal. The matrix product is not commutative, so BC and CB may yield different results.

In summary:

(a) AB is defined and the result is:

AB = [30 64]

[6 0]

BA is also defined and the result is:

BA = [6 24]

[6 24]

(b) BC is defined and the result is:

BC = [52 22]

[0 0]

CB is also defined and the result is:

CB = [12 48]

[10 40]

BC and CB are not equal, indicating that matrix multiplication is not commutative.

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Answer:

f(g(5)) = 64

g(f(5)) = 28

Step-by-step explanation:

Given  that f(x) = x^2 and g(x) = x+3

f(g(x) = f(x+3)

f(x+3) = (x+3)^2

f(g(x)) = (x+3)^2

f(g(5)) = (5+3)^2

f(g(5)) = 8^2

f(g(5)) = 64

b) g(f(x)) = g(x^2)

g(f(x)) = x^2 + 3

g(f(5)) = 5^2 +3

g(f(5)) = 25 + 3

g(f(5)) = 28

Hence the value of g(f(5)) is 28

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

Answer:

D. Convergence hope it helps

x=-6

Explanation

to solve this, let´s complete the tables and then compare

Step 1

complete the table:

to do that we need to input the x value and evaluate to obtain f(x)

so

a) for

i)when x=-12

ii) when x= -9

iii) when x=-6

iv) when x= -3

hence

Step 2

Now , for equation(2) g(x)

a) when x=-12

b) when x=-9

c) when x=-6

d)when x=-3

so

Step 3

finally, compare and check wich input value produces the same out put

therefore, the answer is

x=-6

I hope this helps you

Answer:

x=-6

Step-by-step explanation:

exam

For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Answer:

Area of the plot of the land is 4840 square units.

Step-by-step explanation:

Let's draw the rectangle approximately on an x y plane. That would help us to find the length and width of the rectangle.

Answer: 4,480yd^2

Step-by-step explanation:

You have the x and y coordinates of the vertices (10, 10), (10,90), (70.5,90),  and (70.5, 10) you have the coordinates: x and y as the first two which are the ones in bold. From that you do 70.5-10= 60.5.

Then you subtract the x and y coordinates again, which are underlined. From that do 90-10=80

Last you do 60.5x80=4,840 yards squared

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Hope this Helps!!!

Answer:

Step-by-step explanation:

51 feet / 1.5 = 34 bags needed minimum

But trini needs more than 51 bags so:

X>34 is the answer

2x-3=7

The answer would be 5.

Answer:

x=5

Step-by-step explanation:

2x−3=7

Add 3 to both sides.

2x=7+3

Add 7 and 3 to get 10.

2x=10

Divide both sides by 2.

x=10/2

Divide 10 by 2 to get 5.

x=5

Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer: 145

Step-by-step explanation: I say this because it has 14. 4 then

The probability of being assigned all hardback books is approximately 0.33 or 33%.

This can be done by combination formula C(n,r) = n!/(r!(n-r)!)

The total number of ways to choose three books from a list of 14 books is given by the combination formula,

C(14,3) =14!/(3!(14-3)!) =  (141312) / (321) = 364.

To find the probability of selecting all hardback books, we need to determine the number of ways to select 3 books from the 10 hardback books. This is given by the combination formula,

C(10,3) = 10!/(3!(10-3)!) = 1098 / (321) = 120.

Therefore, the probability of selecting all hardback books is:

P(all hardback) = C(10,3) / C(14,3) = 120/364 = 0.3297

So, the probability of being assigned all hardback books is approximately 0.33 or 33%. This means that out of all possible combinations of 3 books, about 33% will consist of only hardback books.

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Answer:

Step-by-step explanation:

54-16=38

38 divided by 1/2 is 19

so your answer is 19

hope that helps

At the end of ten years, Jeri has saved $660.00.

To calculate the total amount Jeri has saved at the end of ten years, we can sum up the savings for each month over the ten-year period.

In the first year, she saves $1.00 per month for 12 months, so her total savings for the first year is:

Year 1 savings = $1.00/month * 12 months = $12.00

In the second year, she saves $2.00 per month for 12 months, so her total savings for the second year is:

Year 2 savings = $2.00/month * 12 months = $24.00

Similarly, in the third year, she saves $3.00 per month for 12 months, and so on, until the tenth year where she saves $10.00 per month.

We can calculate the total savings for each year and then sum them up to find the total savings over ten years:

Total savings = Year 1 savings + Year 2 savings + ... + Year 10 savings

Total savings = $12.00 + $24.00 + $36.00 + ... + $120.00

To simplify the calculation, we notice that the savings for each year form an arithmetic progression with a common difference of $12.00:

Year 1 savings = $12.00

Year 2 savings = $12.00 + $12.00 = $24.00

Year 3 savings = $12.00 + $12.00 + $12.00 = $36.00

The last term of the progression is $120.00 (savings in the tenth year).

We can use the formula for the sum of an arithmetic series to calculate the total savings:

Total savings = (n/2) * (first term + last term)

where n is the number of terms (in this case, 10 years).

Total savings = (10/2) * ($12.00 + $120.00)

Total savings = 5 * $132.00

Total savings = $660.00

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Answer:

13x = 13

Step-by-step explanation: 2(5x-3)= 10x -6  3x + 10x = 13x-6=7

6+7=13=  13x =13

Answer:

 = 1

Step-by-step explanation:

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

3x + 10x - 6 = 7

your gonna combine 3x + 10x - 6 = 7

13x -6 = 7

(sorry if wrong)

Answer:

-7/3

Step-by-step explanation:

The first step is to combine like numbers. Although there are several different ways to go about doing this, I started by adding 2y to both sides which left me with -8-6y=6. I then added 8 to both sides and got 6y=14. Now divide 6 on both sides to get "y" by itself which left me with y = -14/6. When you simplify the answer you get -7/3.

Answer:

5.19

Step-by-step explanation:

Answer: The answer is A.addition property of equality

Hope I helped

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To find the side lengths of a triangle using angles, you can employ trigonometric ratios like sine, cosine, and tangent

To find the side lengths of a triangle using angles, you can follow these steps:

Identify the given information: Determine which angles are known and which angles are unknown. Let's assume you have the measures of angles A, B, and C.

Apply the angle sum property: In a triangle, the sum of the interior angles is always 180 degrees. So, if you have the measures of two angles, you can find the measure of the third angle by subtracting the sum of the known angles from 180 degrees.

Determine the relationship between angles and side lengths: In a triangle, the lengths of the sides are related to the angles through the trigonometric ratios. The most common ratios are sine (sin), cosine (cos), and tangent (tan).

Use the trigonometric ratios: Depending on the given information, you can use the appropriate trigonometric ratio to find the side lengths. For example:

If you know an angle and the length of the side opposite to that angle, you can use the sine ratio: sin(A) = opposite/hypotenuse.

If you know an angle and the length of the adjacent side, you can use the cosine ratio: cos(A) = adjacent/hypotenuse.

If you know an angle and the lengths of the two sides that form that angle, you can use the tangent ratio: tan(A) = opposite/adjacent.

Solve for the unknown side lengths: Once you have the trigonometric equation involving an angle and side lengths, you can solve for the unknown side length using algebraic manipulations or a calculator.

Repeat these steps for the other angles to find the lengths of the remaining sides. Remember to consider the units of measurement (degrees or radians) and apply the appropriate trigonometric functions based on the given information.

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The sled is moving at approximately 9.38 m/s when you reach the other side of the pond.

To solve this problem, we can use the concept of work and energy. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. In this case, the work done is equal to the change in kinetic energy of the sled.

Let's break down the problem into two parts: when you're pulling with a constant force of 200 N and when you're pulling with a force increasing linearly from 200 N to 500 N.

First, let's calculate the work done during the first part of the motion, where the force is constant. The work done is given by:

Work = Force × Distance

Work = 200 N × (24 m/2)

Work = 200 N × 12 m

Work = 2400 N·m

The work done during this part is 2400 N·m. This work contributes to the sled's change in kinetic energy.

Next, let's calculate the work done during the second part of the motion, where the force is increasing linearly. The average force during this part is (200 N + 500 N) / 2 = 350 N. The distance covered during this part is 24 m/2 = 12 m. The work done is given by:

Work = Average Force × Distance

Work = 350 N × 12 m

Work = 4200 N·m

The total work done on the sled is the sum of the work done in both parts:

Total Work = Work (constant force) + Work (linearly increasing force)

Total Work = 2400 N·m + 4200 N·m

Total Work = 6600 N·m

Now, we can equate the work done to the change in kinetic energy:

Total Work = Change in Kinetic Energy

6600 N·m = (1/2) × mass × (final velocity)^2

Here, the mass of the sled is 150 kg. We need to solve for the final velocity.

Rearranging the equation:

(final velocity)^2 = (2 × Total Work) / mass

(final velocity)^2 = (2 × 6600 N·m) / 150 kg

(final velocity)^2 = 88 N·m/kg

final velocity = √(88 N·m/kg)

final velocity ≈ 9.3808 m/s

Therefore, the sled is moving at approximately 9.38 m/s when you reach the other side of the pond.

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Answer:

36

Step-by-step explanation:

consider the multiples of each denominator

9 : 9, 18, 27, 36, 45, .....

12 : 12, 24, 36, 48, 60, ......

the lowest multiple gives the lowest common denominator , that is 36

==========================================================

Explanation:

Focus on triangle HKL. This is a right triangle with the horizontal leg KL = 2. The vertical leg is the unknown side HK. The hypotenuse is HL shown by the single tickmark.

Triangle HKJ is also a right triangle. It shares the leg HK and the hypotenuse JH is congruent to HL as indicated by the single tickmark.

By the hypotenuse leg theorem, we can show that triangle HKL is congruent to triangle HKJ

From there, the corresponding pieces JK and KL must be the same length. So we can say JK = 2 because KL = 2.

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

Now use the segment addition postulate

GK = GJ + JK

GK = 7 + 2

GK = 9

Focus now on triangle GKH and triangle MKH. We can prove these are congruent triangles using the hypotenuse leg theorem. Here HK = HK as mentioned before; also, GH = HM due to the double tickmarks.

As you can probably guess by now, the hypotenuse leg theorem only applies to right triangles.

Since  triangle GKH is congruent to triangle MKH, we know that

GK = KM

Since GK = 9, this makes KM = 9.

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

Therefore,

GM = GK + KM

GM = 9 + 9

GM = 18

The differential equation describing the relationship between the balance B of Rachel's car loan and time t is given by dB/dt = 0.045B - 375.

The equation represents the change in the balance of Rachel's car loan over time. The term dB/dt represents the rate of change of the balance with respect to time. The right-hand side of the equation consists of two terms. The first term, 0.045B, represents the increase in the balance by 4.5% per month. This term accounts for the growth of the loan balance due to accrued interest.

The second term, -375, represents the decrease in the balance by $375.00 each month, which could be the monthly payment towards the loan principal. By subtracting this payment from the growth, the equation captures the net change in the balance. The equation allows us to model and analyze the behavior of the loan balance as time progresses.

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