Factor 1-3

1. X to the second power -14x+45

2.X to the second power -15x+36

3.X to the second power -7x-44

the answer can also be written as 1.3(3,1)

Final Answer:

The volume of the box that will hold nine 9.425 cm³ cylindrical containers, each measuring 3 centimeters long, is approximately 108 cm³.

Explanation:

First, we need to find the radius of each cylindrical container since we have its volume and the length. The volume V of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where r is the radius and h is the height (or length) of the cylinder. We are given:
[tex]\[ V = 9.425 \text{ cm}^3 \\\\\[ h = 3 \text{ cm} \][/tex]

We need to solve for r:

[tex]\[ 9.425 = \pi r^2 (3) \\\\\[ r^2 = \frac{9.425}{3\pi} \\\\\[ r^2 = \frac{9.425}{3 \times 3.14159} \\\\\[ r^2 = \frac{9.425}{9.42477} \\\\\[ r^2 \approx 1 \\\\\[ r \approx 1 \text{ cm} \][/tex]

Now we know the radius of one cylindrical container is approximately 1 cm. Although this rounding might lead to a slightly inaccurate result, we'll proceed with this approximation for simplicity's sake.

Since each container is a cylinder with a radius of 1 cm, the diameter of each container is [tex]\( 2 \times 1 = 2 \)[/tex] cm. If we wanted to pack these containers without any wasted space in one layer, we would arrange them in a 3 by 3 grid, given there are 9 containers. The length and the width of the box would then each be 3 times the diameter of one container.

Hence:
Length of box = Width of box = [tex]\( 3 \times 2 \)[/tex] cm = 6 cm.
The height of the box would be equal to the length of one of the containers, which is 3 cm.

Now we can find the volume of the box:
Volume of box [tex]\( V_{\text{box}} \) = Length \( \times \) Width \( \times \) Height[/tex]
[tex]\[ V_{\text{box}} = 6 \text{ cm} \times 6 \text{ cm} \times 3 \text{ cm} \\\\\[ V_{\text{box}} = 36 \text{ cm}^2 \times 3 \text{ cm} \\\\\[ V_{\text{box}} = 108 \text{ cm}^3 \][/tex]
Rounding to the nearest whole number, the volume of the box that will hold nine 9.425 cm³ cylindrical containers, each measuring 3 centimeters long, is approximately 108 cm³.

Answer:

Option B is correct.

Step-by-step explanation:

We are given units.

we have to find unit that represents the surface area of a solid.

We know that unit of area is square unit.

⇒ Unit for surface area is also square unit.

inches is a unit of a length.

square inches is unit of area

cubic inches is unit of volume

quadratic inches does not exist as unit.

Therefore, Option B is correct.

Answer:

THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE  TOTAL COST OF GASOLINE PURCHASED.

THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE TOTAL GALLONS OF GASOLINE PURCHASED

The complete problem is:

Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.

Annabella can express her average cost per gallon of gasoline as [tex]y = \frac{(2.25x + 2.15(x+5))}{2x+5}[/tex]

What is the meaning of the parts of this rational expression in the context of the situation?

THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE __________.

(select one)

1. total cost of the gasoline purchased

2. total number of gallons of gasoline purchased

3. cost per gallon of gasoline

THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE ________.

1. total cost of the gasoline purchased

2. total number of gallons of gasoline purchased

3. cost per gallon of gasoline

So, in this context and based on the given data, the numerator of the expression is referring to the total cost of gasoline purchased, and the denominator is expressing the total gallons of gasoline purchased.

You can deduct this because, the numerator contains the amounts of costs per gallon, being x gallons. On the other hand, you can see in the denominator that there's no costs multiplying the variable, it's just a quantity which refers to the amount of gasoline, not the cost.

I added more CORRECT answers for everybody. Your answer is in the last pic.

Answer:

B) 2 x-intercepts

Answer:

ya 2.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Final answer:

To find the equation of a line with a given slope and y-intercept in standard form, substitute the values of the slope and y-intercept into the equation y = mx + b.

Explanation:

To write the equation of a line given the slope m and y-intercept b in standard form y = mx + b, you can directly substitute the values of m = 1/2 and b = 3 into the equation.

Substitute m = 1/2 and b = 3 into y = mx + b: y = (1/2)x + 3

Therefore, the equation of the line in standard form is y = (1/2)x + 3.

The correct answer is:

B. TX and TL  

Explanation:

Opposite rays are rays that have the same endpoint and extend in opposite directions.  The ones in the diagram that fit this description are TX and TL.

9514 1404 393

Answer:

  x/4 +1

Step-by-step explanation:

The quotient of a number (x) and 4 is written ...

  x/4

One more than that is ...

  x/4 +1

Let 3x = the length of the first rope

       2x = the length of the second rope

This representation is based on the given that the ratio of the two ropes is 3:2.

3x + 2x = sq rt. 250

5x = sq rt. 250

x = sq rt. 250 / 5

x = sq rt. 25(10) / 5

x = 5 sq rt. 10 /5

The five would be cancelled resulting to:

x =sq rt. 10

Answer:

The cost of the desk is 124 dollars.

Step-by-step explanation:

irst, change this into an equation

tax=1/16x-.31

x equals the cost of the desk without tax:

x+tax=131.44

tax=131.44-x

Set the first equation equal to the second:

1/16x-.31=131.44-x

Solve for x:

17/16x=131.75

x=$124

Hope that helps

The equivalent percentage value for the decimal number 1.16 is 116% which is obtained by multiplying the decimal by 100. Before including the tax the price of the desk was $60.99.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

And to convert a fraction or a decimal into percentage, they are multiplied by 100.

Given that,

The amount paid by Rachel for a desk is $131.44.

Suppose the price of desk is before adding the tax is x.

Then, as per the problem the following expression can be written for the tax amount as,

1.16x - 0.31  

Now, the expression for the price of desk after tax is,

x + 1.16x - 0.31  = 131.44

⇒ 2.16x =  131.44 +  0.31

⇒ 2.16x = 131.75

⇒ x = 131.75 / 2.16

⇒ x = 60.99

Hence, the price for the desk before adding the tax is $60.99.

To know more about percentage click on,

brainly.com/question/29306119

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The cost of each apple will be 20 cents per apple. Then the correct option is C.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Conversion means to convert the same thing into different units.

If apples are on sale at 15 for $3.

We know that $1 = 100 cents

Then the number of the cents in 3 dollars will be

⇒ 3 x 100

⇒ 300 cents

Then the cost of each apple will be the ratio of the 300 cents and 15 apple.

⇒ 300 / 15

⇒ 20 cents per apple

Thus, the cost of each apple will be 20 cents per apple.

Then the correct option is C.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

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Answer:

D

Step-by-step explanation:

Answer:

Correct option is B.

Step-by-step explanation:

Given the radius of circle and the angle in sector we have to find the area of shaded region i.e minor sector.

[tex]Radius=r=16 in.[/tex]

[tex]Angle=\theta=110^{\circ}[/tex]

[tex]Area of sector=}\frac{\theta}{360}\times\pi r^2[/tex]

                      [tex]=\frac{110}{360}\times\frac{22}{7}\times(16)^2[/tex]

                      [tex]=\frac{11}{36}\times \frac{22}{7}\times 16\times 16=245.841=246(approx.)[/tex]

∴ Area of sector is [tex]246in^2[/tex]

Correct option is B.

Answer:B

Step-by-step explanation:

NICE

Here we want to write the quadratic function for the parabola shown in vertex form.

We will get the function: f(x) = 2*(x - 5)^2 + 3

So the general function of a parabola with vertex (h, k) and leading coefficient a is:

f(x) = a*(x - h)^2 + k

Here, we know the formula:

f(x) = a*(x - 5)^2 + 3

where:

So the vertex is the point (5, 3), and we only must find the value of a to completely determine the parabola's function

We also know that:

f(6) = 5

So we can solve:

5 = a*(6 - 5)^2 + 3

5 = a*(1)^2 + 3

5 = a + 3

5 - 3 = a = 2

So we just found the value of a, replacing this on the parabola's function we get:

f(x) = 2*(x - 5)^2 + 3

If you want to learn more about parabolas, you can read:

https://brainly.com/question/1480401

Final answer:

The properties of real numbers include closure, commutative, associative, identity, and inverse properties. These properties govern how real numbers behave in addition and multiplication operations.

Explanation:

The properties of real numbers refer to the characteristics and behavior of numbers that belong to the real number system. The real number system includes all rational and irrational numbers, such as whole numbers, integers, fractions, decimals, and square roots.

The properties of real numbers include:

These properties of real numbers are fundamental in algebraic operations and calculations. They provide a basis for solving equations, simplifying expressions, and working with mathematical concepts.