Question 7

let f(x) = x^2 + 3
let g(x) = (x + 6)^2 + 3

Which statement describes the graph of g(x) with respect to the graph of f(x)?

A: It is translated right 6 units.
B: It is translated left 6 units.
C: It is compressed horizontally by a factor of 6.
D: It is compressed vertically by a factor of 6.

Answer: 2.3716 <-------- This is the Code

Step-by-step explanation:

1.4 x 2.5 = 3.5

2.2 x 2.5 = 5.5

1.4 x 0.2 = 0.28

2.2 x 0.2 = 0.44

3.5 x 0.28 = 0.98

5.5 x 0.44 = 2.42

Then:

X         1.4           2.2

2.5      3.5          5.5

          - x -          - x -    

0.2      0.28        0.44

           - = -           - = -

        0.98  x    2.42 = 2.3716 <-------- This is the Code

Answer:

Option

Step-by-step explanation: The way tell what the answer is are the similar lines. The single yellow line helps indicate that it's a similar angle.

The dimensions that maximize the surface area are(r,h) = (5.42,10.84).

The surface area of a cylindrical can is S(r,h)= 2πr² +2πrh

The capacity or volume of the rectangular box is V(r,h) =πr²h

V(r,h) = πr²h-1000,S(r,h)= 2πr² +2πrh-2π

Find first-order partial derivatives of V and S:

\(V_{r}\) = 2πrh ,\(V_{h}\) =πr² ,\(S_{r}\) =4πr +2πrh,\(S_{h}\)=2πr.

Find the values of x,y, and z and λ such that simultaneously satisfy the equation:

▽S =λ▽V, and V(r,h) =0, that is

4πr +2πh =λ(2πrh)⇒ λ=(4πr +2πh) /2πrh= \(\frac{2r +h }{rh}\)

2πr = λ(πr²) ⇒λ=2πr/πr² = 2/r

πr²h-1000 =0

solving \(\frac{2}{r}\) = \(\frac{2r +h }{rh}\) ⇒2r²-2rh +hr =0⇒2r²-hr=0⇒r(2r-h)=0

⇒r=0,r=h/2.

Then,(r,h) =(h/2,h)

substitute this point in  πr²h-1000=0, and solving

π \((h/2)^{2}\)h -1000 = 0⇒ π×h³/4 =1000 ⇒1000×4×7×\(\frac{1}{22}\)

h≈ 10.84

Then, r =\(\frac{h}{2}\) = 5.42

The value of S(r,h) = S(5.42,10.84) =553.74

The dimensions that maximize the surface area are(r,h) = (5.42,10.84).

Quantity is defined as the distance occupied inside the barriers of an object in a three-dimensional area. it's also referred to as the capacity of the item. quantity is a degree of occupied 3-dimensional area.[1] it's far regularly quantified numerically through the use of SI-derived gadgets (which includes the cubic meter and liter) or through diverse imperial or US commonplace devices (consisting of the gallon, quart, and cubic inch). The definition of the period (cubed) is interrelated with the extent. The volume of a field is generally understood to be the capacity of the box; i.e., the amount of fluid (gas or liquid) that the box could hold, as opposed to the quantity of space the field itself displaces.

In ancient times, the extent is measured by the usage of similar-shaped natural packing containers and for a while, standardized packing containers. a few simple 3-dimensional shapes could have their quantity easily calculated with the usage of the arithmetic formulation. Volumes of greater complicated shapes can be calculated with essential calculus if a formula exists for the form's boundary.

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Answer:

No solution

Step-by-step explanation:

Multiply both sides by x - 3.

4x = 7(x-3) + 12

4x = 7x - 21 + 12

4x - 7x = -9

-3x = -9

(-3x)/-3 = -9/-3

x = 3

Plug in x = 3 to make sure it works.

x = 3 doesn’t work in the equation.

Answer:

\(\boxed{no \: \: \: solution}\)

Step-by-step explanation:

\( \frac{4x}{x - 3} = 7 + \frac{12}{x - 3} \\ \frac{4x}{x -3 } = \frac{7(x - 3)}{1(x - 3)} + \frac{12}{x - 3} \\ \frac{4x}{x - 3} = \frac{7x - 21 + 12}{x - 3} \\ \frac{4x}{x - 3} = \frac{7x - 9}{x - 3} \\\red{ use \: \: \: cross \: \: multipication} \\ 4x(x - 3) = (x - 3)(7x - 9) \\ 4 {x}^{2} - 12 = 7 {x}^{2} - 9x - 21x + 27 \\4 {x}^{2} - 12 = 7 {x}^{2} - 30x + 27\)

So the answer has to be no solution

To find the number of vinyl tiles needed to tile a kitchen measuring 24 ft. by 18 ft. with tiles measuring 8 in. each side, we need to convert all measurements to the same units.

First, we need to convert the kitchen measurements from feet to inches:

- 24 ft. = 24 x 12 = 288 in.
- 18 ft. = 18 x 12 = 216 in.

Next, we need to divide the length and width of the kitchen by the length of each tile to find the number of tiles needed in each direction:

- Length: 288 in. ÷ 8 in. = 36 tiles
- Width: 216 in. ÷ 8 in. = 27 tiles

Finally, we multiply the number of tiles needed in each direction to find the total number of tiles needed:

- Total tiles: 36 tiles x 27 tiles = 972 tiles



To tile a kitchen, it is important to accurately calculate the number of tiles needed to ensure that there is enough material to complete the job. In this case, we converted all measurements to the same units and then used division and multiplication to find the total number of tiles needed.



To tile a kitchen measuring 24 ft. by 18 ft. with vinyl tiles measuring 8 in. each side, we need a total of 972 tiles.

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0.80 = (x + 8)(0.05) is the equation used to find x.

Given,

Darryl has a solution of bleach with the concentration of 10%.

10% bleach solution means in 100 ml solution amount of bleach is 10 gm

Here,

Darryl wants to change the concentration of this solution to 5%, means he wants to add water so that amount of liquid will change but amount of bleach in grams will remain the same.

Amount of bleach in 8 gallons of 10% solution of bleach will be = (Volume)×(concentration) = 8(.10) gm

Let Darryl adds x gallons of water in 10% solution of bleach to make it 5% solution of bleach.

Amount of bleach in 5% solution of bleach = (x + 8)(0.05) gm

Now in both the concentrations of bleach solution amount of bleach will remain same.

So, 0.8 = (x + 8)(0.05) will be the equation from which he can find the value of x.

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Answer 10:

X = (5,0)

Answer 11:

AB = 11.18

Answer 12:

N/A

Step-by-step explanation:

If the area between the function and the -axis on the interval [a, b] is 10 and the function is continuous on and on, then the average value of the function on this interval is between m and M, where m and M are the lower and upper bounds for the function on the interval.

To find the average value of a continuous function on an interval, we need to use the following formula:
Average value = (1 / b-a) * ∫[a,b] f(x) dx
where a and b are the endpoints of the interval, and ∫[a,b] f(x) dx represents the definite integral of the function over the interval.
In this case, we are given that the area between the function and the -axis on the interval [a, b] is 10. This means that ∫[a,b] f(x) dx = 10.
We don't know the values of a and b, but we do know that the function is continuous on and on, which means that it is continuous on the entire interval [a, b]. Therefore, we can assume that the function is integrable on this interval.
To find the average value of the function, we need to know the length of the interval [a, b]. This is given by the difference between the endpoints: b-a.
We don't know the value of b-a, but we do know that the function is continuous on and on, which means that it is bounded on this interval. This means that there exist numbers M and m such that m ≤ f(x) ≤ M for all x in [a, b].
We can use this information to find an upper bound and a lower bound for the average value of the function:
Lower bound = (1 / (b-a)) * ∫[a,b] m dx = m
Upper bound = (1 / (b-a)) * ∫[a,b] M dx = M
Therefore, the average value of the function on the interval [a, b] is between m and M. We cannot determine the exact value of the average value without knowing more information about the function or the interval.
In summary, if the area between the function and the -axis on the interval [a, b] is 10 and the function is continuous on and on, then the average value of the function on this interval is between m and M, where m and M are the lower and upper bounds for the function on the interval. The length of the interval [a, b] and the exact value of the function would be needed to find the exact value of the average value.

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To solve the trigonometric equation 2cos2x=cosx on the interval 0 to 2π, we can use some basic trigonometric identities and algebraic manipulations. The solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π are x = π/2, 3π/2, π/3, and 5π/3

First, we can simplify the equation by moving all the terms to one side:
2cos2x - cosx = 0
Next, we can use the double angle formula for cosine to express cos2x in terms of cosx:
2cos^2x - cosx = 0
Then, we can factor out the common factor of cosx:
cosx(2cosx - 1) = 0
This equation is satisfied when either cosx = 0 or 2cosx - 1 = 0. Solving for cosx in the second equation, we get:
2cosx - 1 = 0
2cosx = 1
cosx = 1/2

Therefore, the solutions to the original equation 2cos2x = cosx on the interval 0 to 2π are the values of x for which either cosx = 0 or cosx = 1/2. Using the unit circle or a calculator, we can find the values of x that satisfy these conditions:
cosx = 0 when x = π/2 and x = 3π/2
cosx = 1/2 when x = π/3 and x = 5π/3
Thus, the solutions to the equation 2cos2x = cosx on the interval 0 to 2π are x = π/2, π/3, 3π/2, and 5π/3.
Hi! I'd be happy to help you find the solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π.
Step 1: Rearrange the equation to create a quadratic equation.
Subtract cos(x) from both sides:
2cos^2(x) - cos(x) = 0
Step 2: Factor out cos(x).
cos(x)(2cos(x) - 1) = 0
Step 3: Solve for x.

Set each factor equal to zero:
a) cos(x) = 0
b) 2cos(x) - 1 = 0
Step 4: Find the solutions for each equation within the interval 0 to 2π.
a) cos(x) = 0
x = π/2, 3π/2
b) 2cos(x) - 1 = 0
cos(x) = 1/2
x = π/3, 5π/3
Step 5: Combine the solutions.
The solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π are x = π/2, 3π/2, π/3, and 5π/3.

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Answer:

"Side-Angle-Side" and "can be proven congruent"

Step-by-step explanation:

It is SAS because you are given that two of the sides and one angle are congruent, meaning that you can use SAS to prove that the two triangles are congruent.

The values of the trigonometric identities are;

1. tan X = 10/17

2.  tan X = 29/25

3. sin A = 24/25

4. tan C = 15/17

5. sin A = 8/17

6. cos A = 9/41

7. cos Z = 3/4

Note that fractions are the part of a whole number.

Also,

sin θ = opposite/hypotenuse

cosθ = adjacent /hypotenuse

tan θ = opposite/adjacent

1. tan X = opposite/ adjacent

tan X = 30/21 = 10/7

2. tan X = 29/25

3. sin A = opposite/hypotenuse

sin A = 24/25

4. tan C = opposite/adjacent

tan C = 30/34

tan C = 15/17

5. sin A = 16/34

sin A = 8/17

6. cos A = adjacent/hypotenuse

cos A = 9/41

7. sin A = 21/35

8. cos Z = 21/28

cos Z = 3/4

Hence, the fractions takes the function of the trigonometric identities.

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The given function f(x) = (1/2)(x-5)^2 - 6 is a transformation of the parent function f(x) = x^2. It has been horizontally shifted 5 units to the right, vertically stretched by a factor of 1/2, and vertically translated downward 6 units. There is no reflection.

The parent function in this case is the quadratic function f(x) = x^2.

The given function f(x) = (1/2)(x-5)^2 - 6 is a transformation of the parent function f(x) = x^2. Here are the transformations that were applied

Translation: The function has been shifted horizontally by 5 units to the right. This is because the term (x-5) appears inside the function.

Vertical stretch: The coefficient 1/2 indicates that the function has been vertically stretched by a factor of 1/2. This means that the graph of the function is narrower than the graph of the parent function.

Vertical translation: The term -6 indicates that the function has been shifted vertically downward by 6 units.

Reflection: There is no reflection in this case since there is no negative sign outside the function.

Overall, the given function is a horizontally shifted, vertically stretched, vertically translated version of the parent function f(x) = x^2.

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Answer:

58.55 inches

Step-by-step explanation:

Answer:

58.55 confirmed correct

Step-by-step explanation:

Answer:

The equation of the parallel line is x + 3y = 17

Step-by-step explanation:

Parallel lines have the same slopes and different y-intercept

The form of the equation y = m x + b, where

∵ The equation of the given line is x + 3y = 4

→ We must put it in the form above to find its slope

→ Subtract x from both sides to move x to the right side

∵ x - x + 3y = 4 - x

∴ 3y = 4 - x

→ Divide both sides by 3 to make the coefficient of y = 1

∴ \(\frac{3y}{3}=\frac{4}{3}-\frac{1}{3}x\)

∴ y = \(\frac{4}{3}\) -  \(\frac{1}{3}\) x

→ Compare it with the form of the equation above

∴ m = \(-\frac{1}{3}\)

∵ Parallel lines have the same slopes

∴ The slope of the parallel line is \(-\frac{1}{3}\)

→ Put it in the form of the equation

∴ y =  \(-\frac{1}{3}\) x + b

→ To find b substitute x and y in the equation by the coordinates

   of a point on the line

∵ The line passes through the point (2, 5)

∴ x = 2 and y = 5

→ Substitute them in the equation

∴ 5 =  \(-\frac{1}{3}\) (2) + b

∴ 5 =  \(-\frac{2}{3}\) + b

→ Add  \(\frac{2}{3}\)  to both sides

∴ \(\frac{17}{3}\) = b

→ Substitute it in the form of the equation above

∴ y = \(-\frac{1}{3}\) x + \(\frac{17}{3}\)

→ Multiply each term by 3

∴ 3y = - x + 17

→ Add x to both sides

∴ x + 3y = 17

∴ The equation of the parallel line is x + 3y = 17

Answer:

\(\displaystyle y-5=-\frac{1}{3}(x-2)\)

Step-by-step explanation:

Equation of a Line

Two lines are parallel if they have the same slope. We are given the equation of the line:

x+3y=4

To find the slope of this line, we must solve for y:

\(\displaystyle y=-\frac{1}{3}x+\frac{4}{3}\)

The slope of this line is:

\(\displaystyle -\frac{1}{3}\)

The equation of the new line has the same slope. To find its equation, we use the point-slope form of the line:

y-k=m(x-h)

Where (h,k)=(2,5). Thus:

\(\boxed{\displaystyle y-5=-\frac{1}{3}(x-2)}\)

The radius of the middle marble is 12.  To find the radius of the middle marble, we can use the concept of similar triangles and proportions.

Let's denote the radii of the marbles as follows:

r1 = radius of the smallest marble (8)

r2 = radius of the middle marble (unknown)

r3 = radius of the largest marble (18)

Since each marble is in contact with the adjacent marble(s) and with the funnel wall, we can consider the three marbles (smallest, middle, and largest) as forming a triangle within the funnel.

By observing the arrangement of the marbles, we can see that this triangle is similar to a triangle formed by connecting the centers of the marbles.

Now, let's focus on the ratio of the radii of the marbles in the two triangles:

r1 : r2 : r3

We know that r1 = 8 and r3 = 18. To find r2, we can set up the proportion:

r1 / r2 = r2 / r3

Substituting the known values:

8 / r2 = r2 / 18

Cross-multiplying:

(r2)^2 = 8 * 18

Simplifying:

(r2)^2 = 144

Taking the square root of both sides:

r2 = √144

r2 = 12

Therefore, the radius of the middle marble is 12.

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Answer:

The median of the scores in this stem-and-leaf plot is 78

Step-by-step explanation:

The total data set represented by Stem and leaf in order from the least to the greatest are as following:

58, 59, 64, 64 , 66, 68, 72, 74, 75, 76, 78, 79, 83, 84, 86, 87, 88, 91, 93, 93, 95

The number of data is 21

The median of the data at the place number 11

So, median = 78

9514 1404 393

Answer:

  m∠c = 52°

Step-by-step explanation:

Corresponding angles are congruent:

  13x +11° = 15x -7° . . . . . the corresponding angles have equal measures

  18° = 2x . . . . . . . . . . . . add 7° -13x to both sides

  9° = x . . . . . . . . . . divide by 2

Now, we can find c. It is supplementary to the corresponding angles.

  c = 180° -(15x -7°) = 180° -15(9°) +7° . . . . . substitute for x

  m∠c = 52°

The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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 x = 8 , -3 are the factor of x .

What is factor ?

The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.

                         Factors are the figures that can divide an amount precisely. There is therefore no residual after division.

x² - 5x - 24 = 0

x² - ( 8 - 3 )x - 24 = 0

x² - 8x + 3x - 24 = 0

x(x - 8 ) + 3 ( x - 8) = 0

( x + 3 ) ( x - 8 ) = 0

  x = 8 , -3

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The complete question is -

x² - 5x - 24 = 0  by factoring.

The solutions are x =

The various types of studies here are:

John is a psychologist. He wants to understand the correlation between exercise and severe depression. For five consecutive years, he decides to keep track of adults who exercise at least 30 minutes per day, five times a week, and adults who do not exercise at all. All studies yield the same results. This can be described as an observational study.

Mendy spins a spinner and rolls a die to find the probability that the next spin and roll will have a sum of 8 to 10. The spinner has seven sections labeled 1 to 7, and the die has six sides labeled 1 to 6. This can be described as an experimental study.

An auto insurance company wants to compare the number of auto accidents in Seattle caused by adult drivers to the number caused by teen drivers. For seven consecutive months, the company decides to record the number of auto accidents caused by teen drivers and the number of auto accidents caused by adult drivers. This can be described as an observational study.

Ryan randomly asks a group of 200 students at his school which sport among soccer, rugby, and lacrosse should be added as an intramural sport for students to play after school. Based on their answers, he concluded that lacrosse should be added as an intramural sport. This can be described as a survey or questionnaire study.

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Answer:

Yes, it is

Step-by-step explanation:

It is biased because all of the employees have over a decade of experienc, what about the newly hired ones?

Answer:

15minutes / 2miles = 7.5 minutes to run a single mile.

7.5minutes * 5miles = 37.5minutes

37.5minutes to run 5 miles

Step-by-step explanation:

Answer:

A. 12

Step-by-step explanation:

I hope this helps!

Answer:

1 11/24

Step-by-step explanation:

30/48+40/48=70/48=1 11/24

Answer:

15/24 + 20/24 = 35/24 = 1 11/24

Step-by-step explanation:

because 6 and 8 lcm = 24 soooo

5x4 + 5x3 = 20 + 15 = 20/24 + 15/24

which is 35/24 which equals 1 11/24

hope it helps :>

Answer:

Jamal's age = 2×x+12= 2x+12

sum og ages = 45

2x+12+x= 45

=3x+12=45

=45-12= 3x

= 32=3x

x= 32/3= 10.67

2x+13 =21.34+12= 33.34

hope.ot helps

plz mark as brainliest

Jebb is 6 feet 4.5 inches tall.

What is height?

The distance between the bottom and top of an object or person is a measurement of its height.

Height, altitude, and elevation all refer to the vertical distance, either between the top and bottom of something or between its base and something above it. Height is a term for something that can be high or low and is measured vertically.

Given: Jebb is the tallest player on the basketball team.

He is 1 1 /2 times as tall as the shortest girl in the sixth grade, who is 4 1 /4 feet tall.

Here

1 1/2 times 4 1/4

change to improper fractions

\(1\frac{1}{2} = \frac{(2)(1)+1}{2}= \frac{3}{2}\)

\(4\frac{1}{4}= \frac{(4)(4)+1}{4} = \frac{17}{4}\)

⇒  1 1/2 times 4 1/4  is (3/2)*(17/4)

\(\frac{3}{2}(\frac{17}{4})=\frac{51}{8}\)

Convert 51/8 into improper fraction.

\(\frac{51}{8} = 6\frac{3}{8}\)  feet tall.

3/8 of 12 inches is,

\(\frac{3}{8}(12) = \frac{36}{8}\)

Convert 36/8 into improper fraction

\(\frac{36}{8} = 4\frac{4}{8}\)  inches

Here 4/8 = 0.5

⇒ \(4\frac{4}{8} = 4.5\)

Hence, Jebb is 6 feet 4.5 inches tall.

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The probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.

To analyze the given scenario and calculate the probabilities for all six possible scenarios, let's create a decision tree and timeline to visualize the information provided.

Timeline:

Year 1: Initial investment of $12 million in new technology.

Year 2: Results evaluated by shareholders.

Year 3: Final decision made by shareholders.

Decision Tree:

```                 ┌─── Continue (95%)

                │

       15% ─────┼─── Continue (75%)

                │

$12 million ─────┼─── Continue (40%)

investment       │

                │

       10% ─────┼─── Abandon ($5 million cost)

                │

                │

        5% ─────┼─── Abandon ($5 million cost)

                │

                └─── Abandon ($5 million cost)

```

Now, let's calculate the probabilities for each scenario:

1. New equipment reduces expenses by 15% (40% probability):

  Probability = 40% * 95% = 0.4 * 0.95 = 0.38 (38%)

  Outcome: The shareholders vote to continue for another 3 years.

2. New equipment reduces expenses by 10% (30% probability):

  Probability = 30% * 75% = 0.3 * 0.75 = 0.225 (22.5%)

  Outcome: The shareholders vote to continue for another 3 years.

3. New equipment reduces expenses by 5% (30% probability):

  Probability = 30% * 40% = 0.3 * 0.4 = 0.12 (12%)

  Outcome: The shareholders vote to continue for another 3 years.

4. New equipment does not reduce expenses (10% probability):

  Probability = 10%

  Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.

5. New equipment reduces expenses by 15%, but shareholders vote to abandon (5% probability):

  Probability = 15% * (1 - 95%) = 0.15 * 0.05 = 0.0075 (0.75%)

  Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.

6. New equipment reduces expenses by 10%, but shareholders vote to abandon (5% probability):

  Probability = 10% * (1 - 75%) = 0.1 * 0.25 = 0.025 (2.5%)

  Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.

To summarize, we have calculated the probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.

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Answer:

66

Step-by-step explanation:

Replace t with 9 in the equation.

\(28(1.1)^9\)

Simplify.

\(28(2.358)\)

\(66.023\)

Rounded, it equals 66

Answer:

The base and height of three parallelograms with the same area as the 12 square inches rectangle are

1) First parallelogram;

Base length of parallelogram = 4 units

Height of parallelogram, = 3 units

2) Second parallelogram

Base length of parallelogram = 6 units

Height of parallelogram, = 2 units

3) Third parallelogram

Base length of parallelogram = 5 units

Height of parallelogram, = 2.4 units

Step-by-step explanation:

The vertices of the rectangle are; (0, 0), (4, 0), (4, 3), and (0, 3)

Let ABCD represent the vertices of the rectangle such that we have;

A(0, 0), B(4, 0), C(4, 3), and D(0, 3)

The area of the rectangle, A = The length of AB × The length of CB

The length of AB = √((4 - 0)² + (0 - 0)²) = 4

The length of CB = √((4 - 4)² + (3 - 0)²) = 3

∴ The area of the rectangle, A = 4 × 3 = 12 square units

The area of a parallelogram = Base length × Height

The base and height of three parallelograms with the same area as the 12 square inches rectangle are;

1) Base length of parallelogram = 4 units

Height of parallelogram, = 3 units

The area of the parallelogram, A = Base × Height;

∴ A = 4 units × 3 units = 12 units²

2) Base length of parallelogram = 6 units

Height of parallelogram, = 2 units

The area of the parallelogram, A = Base × Height;

∴ A = 6 units × 2 units = 12 units²

3) Base length of parallelogram = 5 units

Height of parallelogram, = 2.4 units

The area of the parallelogram, A = Base × Height;

∴ A = 5 units × 2.5 units = 12 units².

Answer:

First son receives $15000

Second son receives $8000

Third son receives $7000.

Step-by-step explanation:

Let first son receive $x and deposit it at 7%

Second son receive $y and deposit in 8%

Third son receive $z and deposit in 6%

Now, let's set up equation using the given information.

The second son share is 1000 more than the third son.

So, we can set up equation as

y= 1000+z

First son share is equal the second son and the third son put together.

So, x=y+z

And we can set up equation for total 30000 as

x+y+z=30000

Plug in y as 1000+z and x as y+z

We get third equation as

y+z+1000+z+z=30000

Plug in again y as 1000+z

It gives,

1000+z+z+1000+z+z=30000

Combine like terms,

2000+4z=30000

Subtract both sides 2000

4z=28000

Divide both sides by 4

z=7000

Now, plug in z as 7000 into y=1000+z to get y =8000

Now, x =y+z plug in the y and z values

x= 8000+7000=15000

Let's check with interest,

15000(7%)+8000(8%)+7000(6%)=2110

1050+640+420= 2110

2110=2110.

Yes! The calculations are correct!

The solution is, B) yes; -2/3, i.e. a proportional relationship exists & -2/3  is the constant ratio of y/x .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

if it is proportional

then.,

y = kx

so, we get,

-2 = 3 k ⇒ k= (-2/3)

-4 = 6 k ⇒ k= (-2/3)

-8 = 12k ⇒ k= (-2/3)

Hence, The solution is, B) yes; -2/3, i.e. a proportional relationship exists & -2/3  is the constant ratio of y/x .

To learn more on ratio click:

brainly.com/question/13419413

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