Use vertical multiplication to find the product of:
[tex]x ^{3} + 2x + 3 \times x ^{3} - x + 1[/tex]

​

Answer:

[tex]1024 {\pi} \: {unit}^{2} [/tex]

units

Answer:

1024 π units square

Step-by-step explanation:

The area of a circle is found by the formula:

Area of Circle = π × [tex]r^{2}[/tex] units square

where r is the radius of a circle

And π is a Greek letter it is a constant whose approximate value is equal to 3.14159 or 22÷7 is also used sometimes.

The area has a square unit this means if the radius is given in meter then Area has unit meter square.

The area can also be determined by diameter whose formula is given by,

Area of Circle = (π ÷ 4 )× (d)² units square

where d is the radius of a circle

Therefore here,

Area of Circle C = π × r × r

                          = π × 32 × 32 (unit)²

                          = 1024 π (unit)²

Thus, the last option is correct and first four given option is not correct.

Circumference of a circle is found by 2×π×r, where π and r are same as defined above. This is usually determined when we have to ask to find the length of a given boundary in a question.

and Area is found when

We can also derive the formula of a circle which is given by Archimedes, here we consider the circle as the limit of a sequence of regular polygons. And the Area of a regular polygon can be found by half of a perimeter of the circle (i.e. 2×π×r ) multiplied by the distance from its center to its sides i.e. 1÷2×(2×π×r)×r.

Answer:

A

Step-by-step explanation:

The general rule for the quadratic function is

[tex]y=ax^2+bx+c[/tex]

Use the data from the table:

[tex]y(0)=6\Rightarrow 6=a\cdot 0^2+b\cdot 0+c\\ \\y(1)=4\Rightarrow 4=a\cdot 1^2+b\cdot 1+c\\ \\y(-1)=10\Rightarrow 10=a\cdot (-1)^2+b\cdot (-1)+c[/tex]

We get the system of three equations:

[tex]\left\{\begin{array}{l}c=6\\ \\a+b+c=4\\ \\a-b+c=10\end{array}\right.[/tex]

From the first equation

[tex]c=6,[/tex] then

[tex]\left\{\begin{array}{l}a+b=-2\\ \\a-b=4\end{array}\right.[/tex]

Add these two equations:

[tex]a+b+a-b=-2+4\\ \\2a=2\\ \\a=1[/tex]

So,

[tex]b=-2-a=-2-1=-3[/tex]

The quadratic function is

[tex]y=1\cdot x^2-3x+6\\ \\y=x^2-3x+6[/tex]

[tex]\bf \begin{array}{llll} \stackrel{miles}{x}&\stackrel{cost}{y}\\ \cline{1-2} 0&2.75+1.50(0)&\leftarrow \textit{initial fee}\\ 1&2.75+1.50(1)\\ 2&2.75+1.50(2)\\ 3&2.75+1.50(3)\\ 4&2.75+1.50(4)\\ x&2.75+1.50(x)\\ \end{array}~\hspace{7em}\boxed{y=2.75+1.5x}[/tex]

Answer:

MW=CD

Step-by-step explanation:

Answer:

We have divided the bar into two parts. For example, x and y.

Step-by-step explanation:

So, we have

63cm=x+y    (1)

But one of those parts is 7 centimeters smaller than the other.We take y as the smallest part.Then:

y=x-7cm    (2)

we replace this information in the first equation

63cm=x+(x-7cm)

63cm=x+x-7cm

7 goes to add to the other side

63cm+7cm=2x

70cm=2x

2 goes to divide to the other side

35cm=x

from the second equation we have

y=x-7cm

y=35cm-7cm=28cm

Finally

x=35cm

y=28cm

x+y=35cm+28cm=63cm

Answer:

3 people

Step-by-step explanation:

We can write a proportion, putting lbs of beef over people

21 lbs            7 lbs

-----------   = ------------

9 people         x people

Using cross products

21x = 7*9

21x = 63

Divide each side by 21

21x/21 = 63/21

x =3

You can have 3 people

For the equation cross multiplication is key. i do recommend you take in the fact it takes 2.3333etc. to make each persons portion

but none the less the quation should look like 7x9=63 then 63/21 which gives you 3.

you could also do 12/9=2.3, then 7/2.3= 3.04 for a more accurate answer

Answer:

4

Step-by-step explanation:

Pounds of salt : gallons of water

(2 : 9) x 2

4 : 18

- 4 pounds

Answer:

1/4

Step-by-step explanation:

3/5 x 1/4 = 3/20

3/20 + 2/5 = 3/4

1 - 3/4 = 1/4

so the answer is A

Answer:

The area of triangle ACD is 4 centimeters squared.

Step-by-step explanation:

The formula to find the area of a triangle is 1/2 * base * height. The base of this triangle is 2 cm and the height is 4 cm, so you can multiply that and then the answer by half.

Area = 1/2 * 4 * 2

= 1/2 * 8

= 4

Answer: 4 cm squared.

Hope this helped :)

Check the picture below.

For this case we must write as a percentage the following expression:

[tex]\frac {21} {25}[/tex]

Dividing we have to:

[tex]\frac {21} {25} = 0.84[/tex]

Now we multiply by 100%. So:

[tex]0.84 * 100 =[/tex]

We run the decimal two spaces to the right, finally we have:

84%

Answer:

84%

[tex]\text{Hey there!}[/tex]

[tex]\text{Percentages usually run out of 100}[/tex]

[tex]\dfrac{21}{25}\ = \ 21\div25\ = \ 0.84[/tex]

[tex]\huge\text{Decimal form: 0.84}[/tex]

[tex]\text{Remember what I said, percentages run out 100. ( e.g. x * 100)}[/tex]

[tex]\text{0.84\% }\times\text{ 100 = 84\%}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: 84\%}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:b

Step-by-step explanation:

The factors of the trinomial is option (D) (x+15)(x-2) is the correct answer.

Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

For the given situation,

The trinomial is x^2 + 13x - 30.

The trinomial can be factored as

⇒ [tex]x^2 + 13x - 30=0[/tex]

⇒ [tex]x^2 + 15x-2x - 30=0[/tex]

⇒ [tex]x(x+15)-2(x+15)=0[/tex]

⇒ [tex](x+15)(x-2)=0[/tex]

Hence we can conclude that the factors of the trinomial is option (D) (x+15)(x-2) is the correct answer.

Learn more about factorization here

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Answer:

No

Step-by-step explanation:

In order to be the lengths of sides of a triangle:

Sum of any two side lengths must always be greater than the third side.

Here,

[tex]1 + 2 = 3 \ngtr 5 \\ [/tex]

Hence, 1, 2, 5 can't be lengths of triangle.

The measure of angle C in triangle ABC, given that the measure of angle a is 24 degrees and angle b is 130 degrees, is 26 degrees.

To find the measure of angle C in triangle ABC, we use the fact that the sum of the angles in a triangle is 180 degrees. Given the measure of angle a is 24 degrees and angle b is 130 degrees, we can add these two measures and subtract from 180 degrees to find the measure of angle C.

Therefore, the measure of angle C in triangle ABC is 26 degrees.

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Answer:

67 boards

Step-by-step explanation:

Given :

Total board length = 814 ft

Each board must be exactly 12 feet

Number of 12 ft boards which can be cut from 814 feet,

= 814 ÷ 12

= 67.83 boards

But because the question requires boards which are exactly 12 feet long, so we have to round down to the nearest whole number

hence 67.83 boards rounded down to the nearest whole board becomes 67 boards.

Answer:

Step-by-step explanation:

Find the x-value that makes the denominator zero.  This x = a is the equation of the vertical asymptote.  Next, determine the behavior of the function as x increases without bound in either direction.  If there is a limiting value, then this y = d is the horizontal asymptote.

Consider the rational function

     [tex]f(x)=\frac{P(x)}{Q(x)}[/tex]

We will find the Domain of Rational function first, means those value of  rational function for which f(x) is defined, To do this we will evaluate those  point first for which, Q(x)=0.

So, The first Step is "Finding Domain of the rational function" as well as the point where function is not defined.

⇒Consider the function

    [tex]f(x)=\frac{x-3}{x-2}[/tex]

→Domain of the function is

x-2=0

x=2

=All Real Numbers , except at x=2.

=R- {2}

Answer:

4

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

So for the given shape, we can observe that the shape has four same type of sides. The shape in rotation will be like original shape 4 times in a complete rotation. So the order of symmetry is 4 ..

Answer:

The camera should low by 12 meters

Step-by-step explanation:

* Lets explain how to solve the problem

- From the figure:

# The length of the camera is represented by FE

∴ EF = 20 meters

# The ground distance covered by the camera represented by AC

∴ AC = 125 meters

# The camera will be flown at an altitude represented by DB

∴ DB = 75 meters

# The altitude should the camera hanged below the blimp

   represented by GD

∴ Find the length of GD

* Lets solve the problem

- In the two triangles ADC and EDF

∵ EF // AC

∴ m∠A = m∠E ⇒ alternate angles

∴ m∠C = m∠F ⇒ alternate angles

∵ m∠ADC = m∠EDF ⇒ vertical angles

∴ Δ ADC ≈ Δ EDF ⇒ AAA similarity

∴ Their corresponding sides are proportions

∴ AC/EF = AD/ED = CD/FD = constant ratio

∵ AC = 125 and EF = 20

∴ The constant ratio is 125/20 = 25/4

∵ Their Altitudes have the same ratio of their corresponding sides

∵ BD is the altitude of Δ ADC and GD is the altitude of Δ EDF

∴ BD/GD = 25/4

∵ BD = 75

∴ 75/GD = 25/4

- Use cross multiplication to find GD

∴ 25 GD = (75)(4)

∴ 25 GD = 300

- Divide both sides by 25

∴ GD = 12

∴ The camera should low by 12 meters

The camera should low by 12 meters

Answer:

A: second one or middle choice

B: (5x + 8)(3x - 2)

Step-by-step explanation:

First question (A)

It is a trinomial. You can't use the difference of squares on it. The difference of squares have two terms as an answer.

It is not a perfect square. 15 is not a perfect square and c would have to be positive not minus to even think about using a perfect square.

So the A answer is the second one. You need two different binomials to factor this.

Second Question

You could try all the possible pairings and solve them by brute force.

The are five choices the go with the first one (3x + 4). Eventually you would get the answer, you would have to try 5 + 4 + 3 + 2 + 1 = 15 attempts.

There must be a shorter way.

14 means that the expressions are fairly far apart. This was just luck on my part. There is no logic. 8 and 2 for 16 are fairly far apart.

(5x + 8)(3x - 2)

The middle term is 8*3x - 2*5x = 14x and that looks like the answer.

Final answer:

By setting up an equation based on the proportions of players who bike, walk, and are driven to practice, and solving for the total number of players, it is determined that there are 36 players on the soccer team.

Explanation:

To determine the total number of players in the soccer team, we can use the information given about the fractions of players commuting by different modes of transportation and the number of players who are driven by their parents.

We know that 1/3 of the players ride a bike, 25% (which is equivalent to 1/4) walk, and the remaining 15 players are driven by their parents.

Let's denote the total number of players as T. The parts of the team that ride a bike and walk can be represented as T/3 and T/4, respectively. The remaining players are represented by the number 15.

Since these components add up to the whole team, we can write the equation:

T/3 + T/4 + 15 = T

To solve for T, we first need to find a common denominator, which is 12 in this case. The equation becomes:

4T/12 + 3T/12 + 15 = T

Combining the T terms gives us:

7T/12 + 15 = T

This simplifies to:

7T/12 = T - 15

Multiplying both sides of the equation by 12 to eliminate the fraction gives us:

7T = 12T - 180

Subtracting 7T from both sides results in:

5T = 180

Dividing both sides by 5, we finally get:

T = 36

Therefore, there are 36 players in the soccer team.

Answer:

The solution of the equation is [tex]x=2.169..[/tex]  

Step-by-step explanation:

Given : Equation [tex]2^{3x}=91[/tex]

To find : What is the solution to the equation below?

Solution :

Equation [tex]2^{3x}=91[/tex]

Taking log both side,

[tex]\log(2^{3x})=\log(91)[/tex]

Apply logarithmic property, [tex]\log a^x=x\log a[/tex]

[tex]3x\log(2)=\log(91)[/tex]

[tex]3x=\frac{\log(91)}{\log(2)}[/tex]

[tex]x=\frac{\log(91)}{3\log(2)}[/tex]

[tex]x=2.169..[/tex]

Therefore, The solution of the equation is [tex]x=2.169..[/tex]

By the Pythagorean theorem [tex]a^2+b^2=c^2[/tex], the length of BC [tex]=\sqrt{22^2+120^2}=122[/tex]

Answer:    D. 122

Step-by-step explanation:  The given polygon is a right triangle, and to calculate any length of any side in a triangle we use Pythagorean Theorem. According to Pythagorean Theorem, the right triangle consists of one hypotenuse that is opposite to the right angle and two other sides that lie at an right angle. From this comes the relationship that always applies to the right triangles, that the area of the square located on the hypotenuse is equal to the sum of the areas of the squares that are located on the other two sides.

Pythagorean Theorem can also be expressed using the equation:

a² + b² = c²

where c is the hypotenuse and a and b are the other two sides of the right triangle.

According to the given triangle, the length of the BC side is the length of the hypotenuse we are looking for, while the lengths of the sides a and b are given, a = 22 and b = 120.

Using Pythagorean Theorem, hypotenuse BC is equal to

c² = a² + b² = 22² + 120² ⇒ c = √(22² + 120²) = √(484 + 14400) =  √14884

c = 122

Answer:

Segment GD is half the length of segment HC​ ⇒ answer D

Step-by-step explanation:

* Look to the attached file

Answer: D) Segment GD is half the length of segment HC​

Answer:

[tex]\sum_{n=5}^{\infty}n^2[/tex]

Step-by-step explanation:

The pattern given is:

25+36+49+64+...+n^2+...

The pattern can be written as

(5)^2+(6)^2+(7)^2+(8)^2+.....+n^2+....

The series is started with 5 and it continues up to infinity.

The summation notation for the given series is:

[tex]\sum_{n=5}^{\infty} n^2[/tex]

n= 1 and goes up to infinity and the series is made up of taking square of n,

The sum using summation notation, assuming the suggested pattern continues is :

     [tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]      

We are given a series of numbers as

          25 + 36 + 49 + 64 + ... + n^2 + ...

To write the sum using summation notation means we need to express this series in terms of a general n such that there is a whole summation expressing this series.

Here we see that each of the numbers could be expressed as follows:

[tex]25=5^2\\\\36=6^2\\\\49=7^2\\\\64=8^2[/tex]

and so on.

i.e. the series starts by taking the square of 5 then of 6 then 7 and so on.

and the series goes to infinity.

Hence, the summation notation will be given by:

[tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]

Answer:

4/5

Step-by-step explanation:

you need to find the common denominator first, being 15.

then you can do 4/15, 6/15, 8/15, 10/15 making the next one 12/15 or simplified 4/5

Answer:

[tex]\large\boxed{\dfrac{4}{5}}[/tex]

Step-by-step explanation:

Find LCD:

LCM of 15, 5 and 3 is 15

15 = (15)(1)

15 = (5)(3)

15 = (3)(5)

[tex]\dfrac{2}{5}=\dfrac{2\cdot3}{5\cdot3}=\dfrac{6}{15}\\\\\dfrac{2}{3}=\dfrac{2\cdot5}{3\cdot5}=\dfrac{10}{15}[/tex]

Therefore we have:

[tex]\dfrac{4}{15},\ \dfrac{2}{5},\ \dfrac{8}{15},\ \dfrac{2}{3}\to\dfrac{4}{15},\ \dfrac{6}{15},\ \dfrac{8}{15},\ \dfrac{10}{15}[/tex]

Look at the numerators. The next numerator is created from the previous one by adding the number 2.

Therefore the next fraction is equal to

[tex]\dfrac{10+2}{15}=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}[/tex]

[tex]\huge{\boxed{54-x}}[/tex]

The difference is the result of a subtraction problem.

We are given two values that are being subtracted: 54 and a number, represented by [tex]x[/tex]

So, represent this mathematically with [tex]\boxed{54-x}[/tex].

54-x is the correct answer, the difference between number is x-54 or 54-x and the number of algebraic expressions subtracted or number symbol like x.

Answer:

The distance is [tex]3\sqrt{2}\ units[/tex]

Step-by-step explanation:

step 1

Find the slope of the give line

we have

y=x+2

so

the slope m is equal to

m=1

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other

so

we have

m=1 -----> slope of the given line

therefore

The slope of the perpendicular line is equal to

m=-1

step 3

With m=-1 and the point (8,4) find the equation of the line

y-y1=m(x-x1)

substitute

y-4=-(x-8)

y=-x+8+4

y=-x+12

step 4

Find the intersection point lines y=x+2 and y=-x+12

y=x+2 -----> equation A

y=-x+12 ----> equation B

Adds equation A and equation B

y+y=2+12

2y=14

y=7

Find the value of x

y=x+2 -----> 7=x+2 -----> x=5

The intersection point is (5,7)

step 5

Find the distance between the point (8,4) and (5,7)

we know that

The distance from the point (8,4) to the line y=x+2 is equal to the distance from the point (8,4) to the point (5,7)

Find the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute

[tex]d=\sqrt{(7-4)^{2}+(5-8)^{2}}[/tex]

[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]

[tex]d=\sqrt{18}[/tex]

[tex]d=3\sqrt{2}\ units[/tex]

see the attached figure to better understand the problem

Answer:

c and a

because 3k has to add up the an even number so k by it self can not be an even number, and k/2 would still be an odd number because an off number divided by a even number still makes it odd

If 3k is an even integer then k is an even integer, and k and k - 1 are also integers. However, k/2 cannot be assured to be an integer unless k is a multiple of 4, making it the correct answer for what cannot be an integer.

If 3k is an even number, then k must also be an even number because an even number divided by 3 still leaves k as an integer. So, we can infer that k is an integer.

The option k - 1 must also be an integer because if k is an integer, subtracting 1 from it will result in another integer. The option 3k is given as an even integer, to begin with. However, the option k/2 cannot be an integer unless k is not only even but also a multiple of 4, because when you divide an even number that is not a multiple of 4 by 2, the result is not an integer.

Given the information provided in the question, we can conclude that k/2 is the option that cannot definitely be an integer without additional information specifying that k is indeed a multiple of 4.

The volume of a sphere that has a radius of 9 inches is 3053.63in³.

V≈3053.63in³

V=4

3πr3=4

3·π·93≈3053.62806in³

Answer:

Therefore, C ) [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Step-by-step explanation:

Given :  A sphere that has a radius of 9 inches.

To find : Which equation can be used to find the volume of a sphere.

Solution: We have given

radius of sphere =  9 inches.

Volume of sphere = [tex]\frac{4*pi}{3} (radius)^{3}[/tex].

Plug the valu radius = 9 inches .

Volume of sphere = [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Then equation c is correct answere.

Therefore, C ) [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Answer:

10

Step-by-step explanation:

Setup a proportional for similar triangles when finding lengths.

We have FG~MN and GH~N0.

Corresponding sides of similar triangles are proportional.

[tex]\frac{FG}{MN}=\frac{GH}{NO}[/tex]

[tex]\frac{6}{x}=\frac{9}{15}[/tex]

Cross-multiply:

[tex]9x=6(15)[/tex]

Simplify right hand side:

[tex]9x=90[/tex]

Divide both sides by 9:

[tex]x=\frac{90}{9}[/tex]

Simplify right hand side:

[tex]x=10[/tex]