The area of a rectangle is x² + 3x – 28 and the width is x + 7. What is the length of the
rectangle?

Answer:

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.

Step-by-step explanation:

He appies the empirical 68-95-99.7 rule, where 68% of the data is expected to be within ne standard deviation from the mean, to the right and to the left.

Half of this (68%/2=34%) will be between the mean and one deviation standard to the right. This is between 10 hours and 10+2=12 hours.

The right answer is:

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.

Answer:

8/9

Step-by-step explanation:

5/6 x 2/3 = 10/18 (5/9 reduced)

5/9 x 8/5 = 40/45 ( 8/9 reduced)

The length of the apothem of the pentagon is approximately 11 meters.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here, we have,

To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)

 = 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

Learn more about polygon here:

brainly.com/question/24464711

#SPJ1

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

The prism has a greater surface area is the rectangular prism

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

The rectangular prism and the triangular prism

To determine the prism that has a greater surface area, we calculate the surface area of each

So, we have

Rectangular prism = 2 * (8 * 12 + 8 * 6 + 6 * 12)

Rectangular prism = 432

Triangular prism = 6 * 8 + 10 * 12 + 8 * 12

Triangular prism = 264

By comparison

432 is greater than 264

Hence, the prism has a greater surface area is the rectangular prism

Read more about surface area at

https://brainly.com/question/26403859

#SPJ1

Answer:

2/18 = 1/9

Step-by-step explanation:

2/3 x 1/3 = 2/9

2/9 x 1/2 = 1/9

The interest rate she should ask for is 8. 4%

The formula for calculating simple interest is expressed as;

I = PRT/100

Where;

Now, substitute the values into the formula, we have;

$929.73 =  $3,689.21 × R × 3/ 100

Multiply the numerator

$929.73 = $11, 067R/100

cross multiply, we have;

$11, 067R = $92,973

Divide both sides by the coefficient of R

R = $92,973/$11, 067

R = 8. 4%

Hence, the value is  8. 4%

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

Learn more about circles at:

https://brainly.com/question/1559324

#SPJ1

Given: A graph of the function F(x) and G(x) and

Required: To find the equation of the function F(x).

Explanation: The graph of F(x) is translated 4 units down. To shift a function down we subtract from the function. The given function is shifted 4 units down. Hence the function F(x) is-

Hence the function is

Final Answer: Option B is correct.

Answer:

12 dozen eggs is 12x12 which is 144 eggs there are 12 eggs in 1 dozen so 12+12+12+12+12+12+12+12+12+12+12+12=144 hope that helped

144

1dozen =12 eggs

12×12=144

Transforming the ODE yields

\(L\left\{y'' - y'\right\} = L\left\{e^{-3t}\right\}\)

\((s^2 Y(s) - sy(0) - y'(0)) - (s Y(s) - y(0)) = \dfrac1{s+3}\)

\((s^2 - s) Y(s) = \dfrac1{s+3}\)

\(Y(s) = \dfrac1{(s^2 - s)(s+3)} = \dfrac1{s(s-1)(s+3)}\)

Partial fractions:

\(Y(s) = \dfrac as + \dfrac b{s-1} + \dfrac c{s+3}\)

\(\implies 1 = a(s-1)(s+3) + b s(s+3) + c s(s - 1)\)

\(\implies 1 = -3 a + (2 a + 3 b - c) s + (a + b + c) s^2\)

\(\implies \begin{cases}-3a=1 \\ 2a+3b-c=0 \\ a+b+c=0\end{cases} \implies a=-\dfrac13, b=\dfrac14, c=\dfrac1{12}\)

\(\implies Y(s) = -\dfrac13 \times \dfrac1s + \dfrac14 \times \dfrac1{s-1} + \dfrac1{12} \times \dfrac1{s+3}\)

Take the inverse transform:

\(\boxed{y(t) = -\dfrac13 + \dfrac{e^t}4 + \dfrac{e^{-3t}}{12}}\)

Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

For more such questions on Geometry visit:

https://brainly.com/question/24375372

#SPJ8

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 2 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular} \) = - \(\frac{1}{m} \) = - \(\frac{1}{3} \) , then

y = - \(\frac{1}{3} \) x + c ← is the partial equation

To find c substitute (- 6, - 3 ) into the partial equation

- 3 = 2 + c ⇒ c = - 3 - 2 = - 5

y = - \(\frac{1}{3} \) x - 5 ← equation of perpendicular line

Answer:

102 in.²

Step-by-step explanation:

the given figure is made up of a triangle and a rectangle. we can find out the areas of two of them separately and then add it up for the area of the whole figure as

area of rectangle:-

= length* breadth

= 15 * 5 in.²

= 75 in.²

area of triangle :-

= 1/2 *base*height

= 1/2*9*6in.²

= 27in.²

Total area

= 75 + 27 = 102in.² { required answer }

Answer:

D)  102 in²

Step-by-step explanation:

The given composite figure is made up of a triangle and a rectangle.

Rectangle

\(\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=15 \times 5\\&=75\; \sf in^2\end{aligned}\)

Triangle

\(\begin{aligned}\textsf{Area of a triangle}&=\sf \dfrac{1}{2} \times base \times height\\\\&=\dfrac{1}{2} \times (15-3-3) \times (11-5)\\\\&=\dfrac{1}{2} \times 9 \times 6\\\\&=\dfrac{9}{2} \times 6\\\\&=\dfrac{54}{2} \\\\&=27\; \sf in^2\end{aligned}\)

Therefore, the area of the given composite figure is:

\(\begin{aligned}\textsf{Area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of triangle}\\&=75+27\\&=102\; \sf in^2\end{aligned}\)

Step 1

Given;

Required; To find the value of x,y,z.

Step 2

Find the value of x from equation 1 and substitute it into equations (2) and 3

Step 3

Find the value of y

Hence

Step 4

Find the value of z

Step 5

Find the value of x

Hence

x= -6

y=-9

z=8

Answer:

1 C

2 D

3 C

4 B

5 A

6 C

Step-by-step explanation:

Answer: 1 C

2 D

3 C

4 B

5 A

6 C

Step-by-step explanation:

The magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree 5.4<cos335°<, sin335°

What is direction ?

Direction is characterized as the course that anything follows, the route that must be taken to go to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

The basis of the x, y, and z directions of a line or unit vector is identified by the number triplet known as the direction number. They are easily identified as a percentage of a unit vector.

u = 7cos300°i + 7sin300j

v = 4cos70i + 4sin70 j

u = 7*0.5i + 7*(-√3/2)j

  = 3.5i - 6.062j

v = 1.368i + 3.758j

u + v =(3.5+1.368)i +(-6.062+3.758)j

        = 4.868i +(-2.304)j

Magnitude of (u+v) = √(4.868)² +(2.304)²

                               = 5.385 ≈ 5.4

For direction

tanФ = y/x

        = -2.304/4.868

    Ф = -25.327

∴(u+v) is in 4th Quandrant

∴ Ф = 360 - 25.327

     = 334.672

    ≈ 335°

To learn more about direction from the given link  

https://brainly.com/question/17305372

#SPJ1

Step-by-step explanation:

\( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \error \\ \madeindonesia\)

Answer:

The area is 54.6

Step-by-step explanation:

Hopefully this helps!

Answer:

(3,-3)

Step-by-step explanation:

First, plot the ordered pair (-2,-4). Since you're reflecting the ordered pair across the x-axis, change the -4 to a positive 4. Your new ordered pair should be (-2,4). The order pair when reflected across the x-axis is changing the positive or negative of the y value but keeping the x value the same(simple definition). Afterward, move/translate that reflected ordered pair across 5 units to the right which is (3,4). The last step is to translate that order pair 7 units down which will then give you your answer of (3, -3). I hope this helps you, I tried explaining it the best I could!

The coordinates of the image of the point (-2, -4) will be (3, -3).

Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.

Given is a point (-2, -4) which is reflected along the x - axis.

Now, when a point is reflected across the x - axis, then its final coordinates will change according to the rule -

(x, y)  ↔  (x, -y)

The given coordinates are (-2, -4) which on being reflected across the x - axis will  become (-2, 4).

Now, it is given that after reflection, it is translated five units right and seven units down. We can define it by the rule -

(x, y) ↔ (x + 5, y - 7)

So the new coordinates of the image will be -

(-2, 4) ↔ (-2 + 5, 4 - 7) or (3, -3)

Therefore, the coordinates of the image of the point (-2, -4) will be (3, -3).

To solve more questions on graph translation, visit the link below-

https://brainly.com/question/11805053?referrer=searchResults

#SPJ5

Answer:

6.320, 6.000, 6.215

Step-by-step explanation:

Three decimal points is the max number of decimal places between the three numbers (6.215). So, we need to convert the other numbers to have three decimal points as well.

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

Answer:

41.93 degrees

Step-by-step explanation:

It would take about 57 hours for the number of spores to be less than 500 spores.

An exponential function is in the form:

y = abˣ

Where y,x are variables, a is the initial value of y and b is the multiplication factor.

Let y is the number of pores after x hours.

a = 6200, b = 100% - 20% = 0.8, hence to be less than 500 spores:

\(6200(0.8)^\frac{x}{5} < 500\)

(x/5) * ln(0.8) < ln(0.08)

x > 56.4 hours

It would take about 57 hours for the number of spores to be less than 500 spores.

Find out more on Exponential Function at: https://brainly.com/question/12940982

The surface area of the rectangular prism is 396 square inches

He will need 504 tlles

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

The number of tiles is 7 * 12 * 6 = 504

Read more about surface area at

brainly.com/question/26403859

#SPJ1

Question

wants to tile the surface of a rectangular storage case that is 7 inches​ long, 12 inches​ wide, and 6 inches tall. If he uses all green​ tiles, how many tiles will he​ need?

Answer:

B

Step-by-step explanation:

(x-coordinate, y-coordinate) and the horizontal axis refers to the x-axis and the vertical axis refers to the y-axis.