What are the values of x in the equation x2 – 6x + 9 = 25? a. x = –2 or x = 8b. x = –1 or x = –11c. x = 1 or x = 11 d. x = 2 or x = –8

The total cost of metal that made up the cylinder tank is 4220.16 dollars.

The cylinder has a diameter of 8 ft and a height of 2 ft. The cylinder tank is made up of metals. The metal cost 28 dollars for each foot .

Therefore, the cost of the whole metal for the cylinder tank can be found as follows:

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 8 / 2 = 4 ft

h = 2 ft

surface area of a cylinder = 2 × 3.14 × 4(4 + 2)

surface area of a cylinder = 25.12(6)

surface area of a cylinder = 150.72 ft²

Therefore,

1 ft² = 28 dollars

150.72 ft² = ?

cross multiply

cost of the whole metal of the cylinder = 150.76 × 28

cost of the whole metal of the cylinder = 4220.16 dollars

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The true statement regarding the hypothesis will be:

The correct option is D II and III only.

A two-sample t-test of the hypotheses Hoμ1-2 = 0 versus H 41-μ2> 0 produces a p-value of 0.03.

In this case, a 95 percent confidence interval for the difference in means will contain the value 0.

Also, a 99 percent confidence interval for the difference in means will contain the value 0.

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The amount of cookie each sister receives is A = 1/12

Given data ,

Let the amount of cookie each sister receives be A

Now , the equation is

If Jessica ate a part of the cookie and had 1/4 remaining, then she ate 3/4 of the original cookie

Since she wants to give the remaining 1/4 of the cookie to her three sisters to share equally, each sister will receive 1/3 of that 1/4

To find the fraction of the original cookie that each sister will receive, we need to multiply the fraction received by the fraction of the cookie that is left

(1/3) x (1/4) = 1/12

Hence , each sister will receive 1/12 of the original cookie to eat

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Answer:

C

Step-by-step explanation:

Recall the point-slope form of a linear equation:

[tex]y-y_{1}=m(x-x_{1} )[/tex]

Where y1 and x1 are points from the ordered pair (x1, y1),

and m represents the slope of the line.

We are given that the point (-5, 7) belongs to the graph. Here, the x-coordinate is -5, and the y-coordinate is 7.

Let's plug in these values, were x1=-5, and y1=7:

[tex]y-y_{1}=m(x-x_{1} )=\\y-7=m(x-(-5))=\\y-7=m(x+5)[/tex]

We are also given that the slope is -4/3.

In other words, m=-4/3. Let's plug this value in:

[tex]y-7=m(x+5)=\\y-7=-\frac{4}{3}(x+5)[/tex]

Thus, the answer is C.

Answer:

C

Step-by-step explanation:

The point-slope form of the equation of a line passing through the point (x1, y1)with a slope of m is given by:

y - y1 = m(x - x1)

To find the equation of the line passing through the point (-5, 7)with a slope of -4/3, we substitute m = -4/3, x1 = -5, and y1 = 7 into the point-slope form equation:

y - 7 = (-4/3)(x - (-5))

Simplifying this equation, we get the final result in slope-intercept form:

y = (-4/3)x + (17/3)

Therefore, the equation of the line in a point-slope form that passes through (-5,7) and has a slope of -4/3 is y + 7 = -4/3 (x + 5)

The amount it will cost to recarpet the the whole room is $891.12

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

For example, the area of a circle is given as: A = πr², where r is the radius and π is constant.

The room takes the shape of a rectangle, therefore,

Area of the room = l× w, where l is the length and w is the width.

Area = 3×8 = 24 m²

The cost of 1m² = $33.38

therefore the cost for 24m²

= 24× 33.8

= $801.12

therefore the cost to recarpet the room is $801.12

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The simplified ratio is 3 light bulbs for every 1 chandelier.

It should be noted that to find equivalent ratios, we need to multiply or divide both the numerator and denominator of the ratio by the same number.

In this case, the ratio is 9 light bulbs for every 3 chandeliers, which can be simplified by dividing both the numerator and denominator by 3:

9 light bulbs ÷ 3 = 3 light bulbs

3 chandeliers ÷ 3 = 1 chandelier

So the simplified ratio is 3 light bulbs for every 1 chandelier.

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Stacia needs 9 light bulbs for every 3 chandeliers she makes Complete the table using equivalent ratios.

The solution to the linear equation is determined as 5.

The equation to solve is:

3x - 8 = 7

To solve for x, you can follow these steps:

Step 1: Add 8 to both sides of the equation to isolate the term with x on one side:

3x - 8 + 8 = 7 + 8 (combine constants here)

This simplifies to:

3x = 15

Step 2: Divide both sides of the equation by 3 to solve for x:

3x/3 = 15/3

This simplifies to:

x = 5

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The area of the parallelogram shown in the figure is 30 in². Option D is correct.

The area of the parallelogram is given by the following formula,
Area = base * height,

From the figure we have base = 10 in and height  = 3 in

So area can be given as,
Area = 10 * 3

Area = 30 in²

Thus, the area of the parallelogram shown in the figure is 30 in².

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The solution for the value of x is 55.

Since the segments of the secant segment and the tangent segment share an endpoint outside of the circle.

According to Tangent-Secant Theorem, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. That is:

x² = 5 * (5 + 6)

x = 5 * 11

x = 55

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The total area of the triangle tablecloths for one table is 4 ft².

The height of the parallelogram is 6 mm.

Yes, he has enough paint because the total area of the wall space is less than the gallon of paint that Charles bought.

The length of each diagonal is 12 ft.

The height of the trapezoid is 4/3 km.

In Mathematics and Geometry, the area of a triangle can be calculated by using this formula:

Area of triangle = 1/2 × base area × height

Area of triangle tablecloths = 1/2 × 2 × 4

Area of triangle tablecloths = 4 ft².

In Mathematics and Geometry, the area of a parallelogram can be calculated by using this formula:

Area of a parallelogram = base area × height

78 = 13 × height

Height = 78/13 = 6 mm.

Total area of wall space = 2 × [8(10) + 9(15)]

Total area of wall space = 2 × [80 + 135]

Total area of wall space = 2(215) = 430 ft².

For the length of each diagonal, we have;

Area of rhombus with diagonals, A = (1/2) × (diagonal 1)( diagonal 2)

xy = 144

12 × 12 = 144

In Mathematics, the area of a trapezoid can be calculated by using this mathematical expression:

Area of trapezoid, A = ½ × (a + b) × h

32 = ½ × (16 + 32) × h

64 = 48h

h = 64/48

Height, h = 4/3 km.

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Answer:

Have a Nice Best Day : )

Answer:

The solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).

Step-by-step explanation:

To solve the equation x^2 = 4x + 41, we can first rearrange it as x^2 - 4x - 41 = 0.

Next, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -4, and c = -41.

Substituting these values into the formula, we get:

x = (4 ± sqrt((-4)^2 - 4(1)(-41))) / 2(1)

Simplifying:

x = (4 ± sqrt(176)) / 2

x = (4 ± 4sqrt(11)) / 2

x = 2 ± 2sqrt(11)

Therefore, the solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).

Given statement "3-6 You can determine the slope of a roof using a flat board, a bubble level and a ruler,or a sight card can be used." is true. Because flat board, a bubble level and a ruler,or a sight card methods are commonly used to determine the slope of a roof, and both are effective.

Determining the slope of a roof is an important task for many construction and roofing projects.

One method to determine the slope of a roof is to use a flat board, a bubble level, and a ruler.

First, place the flat board horizontally on the roof surface, and use the bubble level to make sure it is level.

Then, measure the distance between the bottom of the board and the roof surface at the point where the board intersects with the roof using the ruler. This distance is the rise.

Next, measure the distance from the point where the board intersects with the roof to the end of the board using the ruler. This distance is the run. Finally, divide the rise by the run to get the slope.

Another method to determine the slope of a roof is to use a sight card. A sight card is a specially designed tool that can help to measure the angle of a slope or pitch. The sight card is held at the bottom of the roof and lined up with a known vertical or horizontal line, such as the edge of a building.

Statement is true.

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The probability of winning a giveaway with 73 entries and 2 winners is the fraction 2/73.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 73

the event of winning = 2

probability of winning the giveaway = 2/73

This means that each winner has a 2/73 chance of winning the giveaway.

Therefore, the probability of winning a giveaway with 73 entries and 2 winners is the fraction 2/73.

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Answer:

67 [tex]ft^{2}[/tex]

Step-by-step explanation:

Divide the shape into more recognizable shapes.
5*7 = 35
7*4 = 28
35+28
67

Answer:

B. It is not a function.

This graph is a circle.

The slope of the function f(x) = -3x^2 +11 at any value of x is given by 6x.

The definition of derivative is given by the limit as h approaches 0 of [f(a+h) - f(a)] / h,

where f(x) is a function and a is a fixed value of x.

To find the slope of the function[tex]f(x) = -3x^2 +11[/tex]  at any value of x, we need to use this definition of derivative.
So, let's plug in f(x) = -3x^2 +11 and a = x into the formula.

This gives us:
lim as h approaches 0 of [tex][-3(x+h)^2 + 11 - (-3x^2 + 11)] / h[/tex]
Simplifying this expression, we get:
lim as h approaches 0 of [tex][-3x^2 - 6hx - 3h^2 + 11 + 3x^2 - 11] / h[/tex]
Combining like terms, we get:
lim as h approaches 0 of [tex][-6hx - 3h^2] / h][/tex]
Factoring out an h from the numerator, we get:
lim as h approaches 0 of [-h(6x + 3h)] / h
Canceling out the h in the numerator and denominator, we get:
lim as h approaches 0 of 6x + 3h
Now, we can plug in h = 0 to find the slope of the function at any value of x:
6x + 3(0) = 6x.

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Taking the quotient between the total volume and the flow rate, we can see that the correct option is D.

We know that water flows at a rate of 1.5*10^4 gallons per second. We know that 6.525*10^6 gallons flowed while Jeremy was watching, then the time that he has been watching is the quotient between these values, we will get:

time = ( 6.525*10^6)/(1.510^4) seconds =  (652.5/1.5) second = 435 seconds

We know that 60 secons = 1 minute, then:

435/60  = 7 + 15/60

So he has been watching for 7 minutes and 15 seconds, the correct option is D.

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Step-by-step explanation:

Perimeter =  2 m + 2 * 7m

Perimeter = 2 ( m + 7m)

Perimeter = 2m + 14m

Perimeter = 16 m                          Pick any of them

The requreid volume of the right cone is 1,411.2 cubic units.

We need to use the formula for the volume of a cone:
[tex]V = (1/3)\pi r^2h[/tex],

where r is the radius of the base of the cone and h is the height of the cone.We are given that the height of the cone is 21 and the radius of the base is 8.

V = (1/3)π(8²)(21)
V = 1,411.2 cubic units (rounded to the nearest tenth).

Therefore, the volume of the right cone is approximately 1,411.2 cubic units.

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Answer:

[tex]0.42[/tex]÷[tex]7[/tex]

Step-by-step explanation:

First, let's count the number of colored squares in the hundredth-grid.

There are a total of 42 hundredth-squares.

Since this is measured in hundredths, the number it represents is 0.42.

Each of the different colors represents a separate group that 0.42 is being divided into. There are 7 separate groups.

Since 0.42 is being divided into 7 groups, the equation that is being represented is:

[tex]0.42[/tex]÷[tex]7[/tex]

The volume of the other solid (Solid B) is 3456 cubic feet.

Solid A has edges of 4 feet, and its volume is given as 16 cubic feet. Solid B has edges of 24 feet.

Since the solids are similar, they have the same shape, and their corresponding lengths are proportional. To find the ratio of their corresponding lengths, we can divide the length of an edge of Solid B by the length of an edge of Solid A:

Ratio = (length of edge of Solid B) / (length of edge of Solid A)

Ratio = 24 feet / 4 feet

Ratio = 6

Now that we have the ratio of their corresponding lengths, we can find the ratio of their volumes. The ratio of the volumes of similar solids is the cube of the ratio of their corresponding lengths:

Volume ratio = (length ratio)³

Volume ratio = 6³

Volume ratio = 216

Now we can use the volume ratio to find the volume of Solid B:

Volume of Solid B = (Volume of Solid A) × (Volume ratio)

Volume of Solid B = 16 ft³ × 216

Volume of Solid B = 3456 ft³

So, the volume of the other solid (Solid B) is 3456 cubic feet.

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Therefore, expression 3x5/6 simplifies to 3 5/6.

In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables. Expressions can be evaluated, simplified, and manipulated using mathematical rules and operations to obtain new expressions or values.

Here,

To simplify 3x5/6, we can rewrite it as (3/1) × (5/6). Multiplying the numerators and denominators, we get:

(3/1) × (5/6) = 15/6

= 2 3/6

Since 3/6 can be simplified to 1/2, we have:

2 3/6 = 2 1/2

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The quotient of the expression 5x^2/7÷10x^3/21 is 3/(2x)

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

5x^2/7÷10x^3/21

Assume that no denominator has a value of 0, we have

5x^2/7÷10x^3/21 = 5x^2/7 ÷ 10x^3/(7 * 3)

Express as products

So, we have the following representation

5x^2/7÷10x^3/21 = 5x^2/7 * (7 * 3)/10x^3

When the factors are evaluated, we have

5x^2/7÷10x^3/21 = 5 * 3/10x

So, we have

5x^2/7÷10x^3/21 = 15/10x

This gives

5x^2/7÷10x^3/21 = 3/(2x)

Hence, the solution is 3/(2x)

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Answer:

Step-by-step explanation:

539.22 dollars

Answer:

There are 2 answers:

Step-by-step explanation:

110 = c²

√110 = √c²

±10.5 = c

Solve for c:

[tex]110=c^2[/tex]

Take the square root of 110

[tex]10.48\thickapprox10.5[/tex]

[tex]\longrightarrow \boxed{\bold{c=10.5}}[/tex]

[tex]\text{so} \ \boxed{110=\bold{10.5^2}}[/tex]

Answer:

(C) and (D) are correct.

The exponential function f(x) = 2^x is given by the blue graph on the given graph.

The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function in this problem is defined as follows:

y = 2^x.

Two relevant numeric values are given as follows:

Hence the function is represented by the blue graph.

The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.

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The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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