The length of a rectangle is 7 cm more than 4 times the width. If the perimeter of the rectangle is 44 cm, what are its dimensions?

Answer:8

Step-by-step explanation:

Because Angle GJH is 90 degrees, Angle HJZ is also 90 degrees. (Because all right angles are 90 degrees)

Now, find Angle WJZ

90 - 18 = 72 degrees

By the Vertical Angles Theorem, Angle GJL is congruent to Angle ZJW

Now solve for x

72 = 9x

x = 8

The shape that CANNOT possibly describe the cross section is a rectangle.

1. The given three-dimensional object consists of two congruent parallel trapezoids.

2. A plane intersects the object perpendicularly to the trapezoids, resulting in a cross section.

3. To determine the shape that cannot possibly describe the cross section, we need to examine the possible outcomes.

4. When a plane intersects the object perpendicularly to the trapezoids, the resulting cross section can be various shapes, such as a parallelogram, triangle, trapezoid, or rectangle.

5. Let's consider each of these possibilities:

  a. Parallelogram: If the cross section is a parallelogram, it means the intersecting plane is parallel to the bases of the trapezoids.

  b. Triangle: If the cross section is a triangle, it means the intersecting plane passes through one of the vertices of the trapezoids.

  c. Trapezoid: If the cross section is a trapezoid, it means the intersecting plane is parallel to one base of the trapezoids and intersects the other base.

  d. Rectangle: If the cross section is a rectangle, it means the intersecting plane is perpendicular to both bases of the trapezoids.

6. Out of these possibilities, the shape that cannot possibly describe the cross section is a rectangle because a perpendicular plane would not intersect both bases of the trapezoids at right angles simultaneously.

7. Therefore, the shape that cannot possibly be the cross section is a rectangle.

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer:

Don't know....

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The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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Answer:

1.809

Step-by-step explanation:

Beacuse 4 is less than 5, the number round down.

I think the answer is 1.809 though im not sure

Answer:

Step-by-step explanation:

total number of nail polish = 15

number of pink nail polish= 7

number of purple nail polish = 2

so 7+2 = 9

15-9 = 6

so probability( of not getting pink or purple nail polish ) = favourable outcomes/ total outcomes

= 6/15

Check the picture below.

\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=x\\ h=6x-20\\ A=50 \end{cases}\implies 50=\cfrac{1}{2}(x)(6x-20) \\\\\\ 50=\cfrac{6x^2-20x}{2}\implies \boxed{50=3x^2-10x}\)

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Answer:

Step-by-step explanation:

Distributive property of multiplication:

Apply to the given expression:

Answer:

27x+6

Step-by-step explanation:

SOLUTION:

The x-intercepts are

The vertex is the point

The minimum occurs at x = 2, its value is - 18

The axis of symmetry is the line x = 2

The y-intercept is the point ( 0, -14)

The domain is;

The range is;

Answer:

\(\displaystyle \int {x^{-11}(1 + x^4)^\Big{- \frac{1}{2}}} \, dx = \boxed{ - \frac{\sqrt{x^4 + 1} (8x^8 - 4x^4 + 3)}{30x^{10}} + C }\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:
\(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Integration Methods: U-Substitution, U-Solve, Trigonometric Substitution

Step-by-step explanation:

*Note:

The problem is too big to fit all work. I will assume that you know how to do basic calculus.

Step 1: Define

Identify given.

\(\displaystyle \int {x^{-11}(1 + x^4)^\Big{- \frac{1}{2}}} \, dx\)

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for u-substitution/u-solve.

Step 4: Integrate Pt. 3

Start solving the integral using u-solve:

\(\displaystyle \begin{aligned}\int {x^{-11}(1 + x^4)^\Big{- \frac{1}{2}}} \, dx & = \int {\frac{1}{x^{11}\sqrt{x^4 + 1}}} \, dx \\& = \int {\frac{1}{2u^6 \sqrt{u^2 + 1}}} \, du \\& = \frac{1}{2} \int {\frac{1}{u^6 \sqrt{u^2 + 1}}} \, du \\\end{aligned}\)

Step 5: Integrate Pt. 4

Identify variables for trigonometric substitution.

Step 6: Integrate Pt. 5

Let's focus on just the integral itself. Apply the Trigonometric Substitution Integration Method and other basic integration techniques listed under "Calculus":

\(\displaystyle \begin{aligned}\int {\frac{1}{u^6 \sqrt{u^2 + 1} }} \, du & = \int {\frac{\sec^2 v}{\tan^6 v \sqrt{\tan^2 v + 1} }} \, dv \\& = \int {\frac{\sec v}{\tan^6 v}} \, dv \\& = \int {\cot v \csc v (\csc^2 v - 1)^2} \, dv \\\end{aligned}\)

Step 7: Integrate Pt. 6

Identify variables for u-substitution/u-solve again.

Use another variable besides u to avoid confusion with earlier substitutions:

Step 8: Integrate Pt. 7

Reduce the integral using the U-Solve Integration Method and other basic integration techniques listed under "Calculus":

\(\displaystyle \begin{aligned}\int {\frac{1}{u^6 \sqrt{u^2 + 1} }} \, du & = \int {\frac{\sec^2 v}{\tan^6 v \sqrt{\tan^2 v + 1} }} \, dv \\& = \int {\frac{\sec v}{\tan^6 v}} \, dv \\& = \int {\cot v \csc v (\csc^2 v - 1)^2} \, dv \\& = \int {-(w^2 - 1)^2} \, dw \\& = - \int {(w^2 - 1)^2} \, dw \\& = - \int {\bigg( w^4 - 2w^2 + 1 \bigg)} \, dw \\\end{aligned}\)

Step 9: Integrate Pt. 8

Solve the integral using basic integration techniques listed under "Calculus":

\(\displaystyle\begin{aligned}- \int {\bigg( w^4 - 2w^2 + 1 \bigg)} \, dw & = - \Bigg[ \int {w^4} \, dx - \int {2w^2} \, dx + \int {} \, dx \Bigg] \\& = - \Bigg[ \int {w^4} \, dx - 2 \int {w^2} \, dx + \int {} \, dx \Bigg] \\& = - \Bigg[ \frac{w^5}{5} - \frac{2w^3}{3} + w + C \Bigg] \\& = - \frac{w^5}{5} + \frac{2w^3}{3} - w + C \\& = - \frac{\csc^5 v}{5} + \frac{2\csc^3 v}{3} - \csc v + C \\\end{aligned}\)

\(\displaystyle\begin{aligned}- \int {\bigg( w^4 - 2w^2 + 1 \bigg)} \, dw & = - \frac{(u^2 + 1)^\Big{\frac{5}{2}}}{5u^5} + \frac{2(u^2 + 1)^\Big{\frac{3}{2}}}{3u^3} - \frac{\sqrt{u^2 + 1}}{u} + C \\\end{aligned}\)

Step 10: Integrate Pt. 9

Let's substitute our integral value into our integral from "Step 4":

\(\displaystyle\begin{aligned}\frac{1}{2} \int {\frac{1}{u^6 \sqrt{u^2 + 1}}} \, du & = - \frac{(u^2 + 1)^\Big{\frac{5}{2}}}{10u^5} + \frac{(u^2 + 1)^\Big{\frac{3}{2}}}{3u^3} - \frac{\sqrt{u^2 + 1}}{2u} + C \\& = - \frac{(x^4 + 1)^\Big{\frac{5}{2}}}{10x^{10}} + \frac{(x^4 + 1)^\Big{\frac{3}{2}}}{3x^6} - \frac{\sqrt{x^4 + 1}}{2x^2} + C \\& = \boxed{ - \frac{\sqrt{x^4 + 1}(8x^8 - 4x^4 + 3)}{30x^{10}} + C } \\\end{aligned}\)

∴ we have found the indefinite integral.

___

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Topic: Calculus

Answer:

no need to skip a line between the office equipment and common stock.

Step-by-step explanation:

The factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2

The polynomial is given as:

2x^3 - 3x^2 - 5x + 6

Next, we test the factors

Option A. x + 6

Set the factor to 0

x + 6 = 0

Solve for x

x = -6

So, we set up the division as follows:

-6  l   2    - 3     -5      6

Bring down the leading coefficient

-6  l   2    - 3     -5      6

        2

Multiply 2 and -6

-6  l   2    - 3     -5      6

                -12

        2

Add -3 and -12

-6  l   2    - 3     -5      6

                -12

        2      -15

Repeat this process

-6  l   2    - 3     -5      6

                -12    72    -402

        2      -15    67    -396

-396 is the remainder of the above division.

This means that x + 6 is not a factor of the polynomial

Option B. x - 2

Set the factor to 0

x - 2 = 0

Solve for x

x = 2

So, we set up the division as follows:

2  l   2    - 3     -5      6

Bring down the leading coefficient

2  l   2    - 3     -5      6

        2

Multiply 2 and 2

2  l   2    - 3     -5      6

                4

        2

Add -3 and -12

2  l   2    - 3     -5      6

                4

        2      1

Repeat this process

2  l   2    - 3     -5      6

                4      2      -6

        2      1       -3     0

0 is the remainder of the above division.

This means that x - 2 is a factor of the polynomial

There is no need to check for the remaining options

Hence, the factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2

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Answer:

about 7 times

Step-by-step explanation:

First do 80 times 3 and get 240 then do 240 divided by 34 and get 7.058823529 which can be rounded to 7.

Answer:

12

Step-by-step explanation:

Answer:

3 = 12

Step-by-step explanation:

9 * (9+1) = 9 * 10 = 90

8 * (8+1) = 8 * 9 = 72

7 * (7+1) = 7 * 8 = 56

6 * (6+1) = 6 * 7 = 42

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

Optional Steps (for bigger numbers):

Hence, the formula is

a = b(b+1)

= b² + b

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

Hence,

3 * 4 = 12

Hence,

3 = 12

Hope this helps and be sure to have a wonderful time ahead! :D

Answer:

99

Step-by-step explanation:

99 + 19 = 118

Answer:

lj= lk din 30 give lj= 4✓2

and ml=x= lj cos 45

on solving x= 4✓2 cos45=4

According to the given information the Minimize equation is

Z = 110X11 + 120X12 + 120X21 + 130X22.

What is Statistics ?

Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It provides methods and techniques to make sense of complex data sets, to draw conclusions and make decisions based on the data. Statistics can be applied to a wide range of fields, including business, economics, social sciences, medicine, and many others. Some key topics in statistics include probability theory, hypothesis testing, regression analysis, and data visualization.

Minimize:

Z = 110X11 + 120X12 + 120X21 + 130X22

Subject to:

X11 + X12 ≤ 1500 (capacity constraint for Amarillo)

X21 + X22 ≤ 3300 (capacity constraint for Charlotte)

X11 + X21 ≥ 2100 (demand constraint for Detroit)

X12 + X22 ≥ 1000 (demand constraint for Atlanta)

where:

X11 = number of components produced in Amarillo and supplied to Detroit

X12 = number of components produced in Amarillo and supplied to Atlanta

X21 = number of components produced in Charlotte and supplied to Detroit

X22 = number of components produced in Charlotte and supplied to Atlanta

Therefore, according to the given information the Minimize equation is

Z = 110X11 + 120X12 + 120X21 + 130X22

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Force required to produce the acceleration 7.85 x 10^-3kgm/s^2

What is Force ?

According to physics, a force is an effect that has the power to change an object's motion. A force can cause a massed object to accelerate or change its velocity. A push or a pull is a straightforward way to explain force. Since a force has both magnitude and direction, it is a vector quantity.

Given that

Mass of the airplane = 1.57kg

Initial velocity (u)= 0.45 m/s

Final velocity (v)= 1.12 m/s

Since we know,

Force = mass x acceleration

So, to find out the force we need to find out the acceleration of the object first

Since,

Acceleration(a) = v - u / t

where,

v = final velocity

u = initial velocity

t = time

Putting the values we get

a = 1.12 - 0.45 / 2 x 60

a = 0.67 / 120

a = 0.005m/s^2

Now, that we know the Acceleration we can find force

mass = 1.57 kg

acceleration = 0.005 m/s^2 or 5 x 10^-3

F = m x a

F = 1.57 x 5 x 10^-3

F = 7.85 x 10^-3kgm/s^2

Hence, 7.85 x 10^-3kgm/s^2 Force is required to produce the acceleration

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I think it's 4 4/15.

Answer:

Step-by-step explanation:

Suppose that f(2) = −4, g(2) = 3, f '(2) = −5, and g'(2) = 1.

Find h'(2).

(a)    h(x) = 4f(x) − 5g(x)

Use the constant multiple and difference rules:

h'(x) = 4f '(x) − 5g'(x)

h'(2) = 4*f'(2) − 5*g'(2), now substitute values and solve

h'(2) = 4*(−5) − 5*1 = −20 − 5 = −25

Answer:700≥7c+464

Step-by-step explanation:

:)

The LSRL is the Least Squares Regression Line of the new engine design performance

This is the equation of the Least Squares Regression Line.

From the calculation summary, we have the following parameters:

So, the LSRL is:

y = 11.6559 + 3.47812x

Where y represents the predicted volume and x represents the weight.

In (a), we have:

y = 11.6559 + 3.47812x

Substitute 100 for x

y = 11.6559 + 3.47812 * 100

Evaluate

y = 359.4679

Hence, the predicted top speed when the weight is 100 tons is 359.4679

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The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

What is a quadratic equation?

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

x = [-b± (√b²-4ac )] / 2a

The quadratic equation:

x²+6x+9=20

x²+6x -11 = 0

a = 1, b = 6, c = -11

x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)

x = -3 + 2√5 , x = -3 - 2√5

Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

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