The volume of a cylinder is 980pi in3. The radius is 7 in. What is its height?

A) 10 in
B) 140 in
C) 70 in
D) 20 in

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers

Step-by-step explanation:

Final answer:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers have many interesting properties and applications in mathematics.

Explanation:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it is a number that is only divisible by 1 and itself.

For example, the numbers 2, 3, 5, and 7 are prime numbers because they have no divisors other than 1 and themselves. On the other hand, the number 4 is not prime because it is divisible by 1, 2, and 4.

Prime numbers have many interesting properties and applications in mathematics, including their role in number theory and cryptography.

#2

Step-by-step explanation:

it is opening downwards so the number multiplying the function must be negative (in this case it is -2)

Answer:

y = -2(x -­ 1)² + 2

Step-by-step explanation:

recall that the vertex form of a quadratic equation is :

y = a(x - h)² + k, where (h, k) is the coordinate of the vertex (i.e maxima point)

from the graph we can see that the vertex is at x = 1, y = 2

hence the answers that are valid would have h = 1 and k = 2

right away by observing the answers, we can see that the last 2 choices have h = (-1) and so these are NOT the answers.

To decide between the first 2 choices, we observe from the given graph, that when x=0, y=0.

The only choice which satisfies this is the 2nd option

Proof:

for y = -2(x -­ 1)² + 2, when x = 0,

y = -2(0 -­ 1)² + 2

y = -2(-­ 1)² + 2

y = -2(1) + 2 = -2 + 2 = 0 (Proven to be valid)

Sanity check: check the first choice

y = (x ­- 1)² + 2

when x = 0,

y = (0- 1)² + 2

y = 1 + 2 ≠ 0 (not the answer)

Answer:

[tex]x_1=x_2=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

For the quadratic equation [tex]ax^2+bx+c=0[/tex] the discriminant is defined as

[tex]D=b^2-4ac[/tex]

and the quadratic formula for the roots gives us two roots:

[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}[/tex]

and

[tex]x_2=\dfrac{-b+\sqrt{D}}{2a}[/tex]

For the equation [tex]9x^2 +12x+4=0[/tex] use quadratic formula to find roots:

[tex]D=12^2-4\cdot 9\cdot 4=144-144=0[/tex]

So,

[tex]x_1=x_2=\dfrac{-12\pm \sqrt{0}}{2\cdot 9}=-\dfrac{12}{18}=-\dfrac{2}{3}[/tex]

Answer:

constant of variation = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

The constant of variation is 1/2.

Step-by-step explanation:

y = kx where k is the constant of variation.

So k = y/x = 2/4 = 1/2.

Answer:

The 4th day so 21 miles the girls would have to run

Step-by-step explanation:

Answer:

Each girl would have ran a total of 21 miles and boys would have ran a total of 20 miles by the end of the fourth day before the couch order new javelins.

Step-by-step explanation:

Girls track team

First day of practice=3 miles

Days afterwards= 6 miles

Boys track team

Everyday= 5 miles

coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's.

First day

Each girl total mileage= 3 miles

Each boy total mileage= 5 miles

Second day

Each girl total mileage= 3miles+6miles=9 miles

Each boy total mileage=5 miles+5 miles= 10 miles

Third day

Each girl total mileage= 3+6+6=15 miles

Each boy total mileage=5+5+5=15 miles

Fourth day

Each girl today mileage= 3+6+6+6=21 miles

Each boy total mileage=5+5+5+5= 20 miles

Difference=girls-boys

=21-20= 1 mile

The fourth day is the day each girl's total mileage(21 miles) surpasses each boy's total mileage(20 miles) with a total of 1 mile

Answer:

[tex]\large\boxed{x^2-6x+9+x^2+2x-15=2x^2-4x-6}[/tex]

Step-by-step explanation:

[tex]x^2-6x+9+x^2+2x-15\qquad\text{combine like terms}\\\\=(x^2+x^2)+(-6x+2x)+(9-15)\\\\=2x^2-4x-6[/tex]

Answer:

O D. (2,5)

Step-by-step explanation:

y > 2x - 3

Substitute the points into the inequality and see if it is true

(3,2)

2 > 2(3) - 3

2> 6-3

2>3  False

(9,12)

12 > 2(9) - 3

12> 18-3

12>15  False

(4,4)

4 > 2(4) - 3

4> 8-3

4>5  False

(2,5)

5 > 2(2) - 3

5> 4-3

5>1  True

Answer:D

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================[/tex]

[tex]\text{We have}\ y=\dfrac{1}{5}x+10\to m_1=\dfrac{1}{5}\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{5}}=-5.\\\\\text{Put the value of a slope and the coordinates of the point (-3, 5)}\\\text{to the equation}\ y=mx+b:\\\\5=-5(-3)+b\\5=15+b\qquad\text{subtract 15 from both sides}\\-10=b\to b=-10\\\\\text{Finally:}\\\\y=-5x-10[/tex]

Answer:

Option D) cos52 = x/24

Step-by-step explanation:

In this problem angle of 38 degrees and angle of 52 degrees are complementary angles

so

38°+52°=90°

therefore

cos(38°)=sin(52°)

we know that

see the attached figure with letters to better understand the problem

In the triangle ABD

cos(38°)=24/x ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse

Remember that

cos(38°)=sin(52°)

so

sin(52°)=24/x

In the right triangle ABC

cos(38°)=x/34 ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse

In the right triangle ABD

Applying the Pythagoras Theorem

[tex]BD=\sqrt{x^{2}-576}\ units[/tex]

[tex]cos(52\°)=(\sqrt{x^{2}-576})/x[/tex]----> The cosine of angle of 52 degrees is equal to divide the adjacent side to angle of 52 degrees by the hypotenuse

Answer:

4/.5 = 8

Step-by-step explanation:

You can solve this by adding up .5 8 times to equal 4. Another way to look at it is that you have 4 individual pieces that are a foot long and you decide to split all of them in half. Let me know if you have any other questions.

Answer:

The equation that shows that is the division between 4 and 0.5 as:

[tex]\frac{4}{0.5}[/tex]

Step-by-step explanation:

First, it is necessary to know that one half foot is equivalent to 0.5 foot.

We can solve this using a rule of three in which we know that 1 piece has one half foot long, then 4 foot long how many pieces have. This is:

1 board -----------  0.5 foot

 X        ------------  4 foot

Where X is the number of pieces that he can get from a four foot long board.

Solving for X, we get:

[tex]X  = \frac{4*1}{0.5} = \frac{4}{0.5}[/tex]

So, the equation that shows how many one half foot pieces he can get from a four foot long board is:

[tex]X=\frac{4}{0.5}[/tex]

Answer:

Im pretty sure its C

Step-by-step explanation:

because when u line up the the right angles u see the hypotenuse and leg of another triangle is the same

The given triangles are not congruent since the hypotenuse of one triangle is equal to the length of leg of another triangle.

So the corresponding sides of the triangles are not equal.

So the triangles are not congruent.

So, option C is correct.

Find more about "Congruency" here:  brainly.com/question/2938476

#SPJ2

Answer:

P(S or T)= 3/4

Step-by-step explanation:

Given:

S and T are mutually exclusive events

find P(S or T)

P(S or T)= P(S) + P(T)

             = 1/3 +5/12

             =4+5/12

              =9/12

               =3/4 !

Answer:

The value of P(S or T) is 3/4.

Step-by-step explanation:

It is given that S and T are mutually exclusive events. It means intersection of S and T is 0.

[tex]S\cap T=0[/tex]

[tex]P(S\cap T)=0[/tex]

We need to find the value of  P(S or T). It means we have to find the probability of union of S and T.

[tex]P(S\cup T)=P(S)+P(T)-P(S\cap T)[/tex]

Substitute the given values in the above formula.

[tex]P(S\cup T)=\frac{1}{3}+\frac{5}{12}-(0)[/tex]

[tex]P(S\cup T)=\frac{4+5}{12}[/tex]

[tex]P(S\cup T)=\frac{9}{12}[/tex]

[tex]P(S\cup T)=\frac{3}{4}[/tex]

Therefore the value of P(S or T) is 3/4.

Answer:

  x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n

Step-by-step explanation:

Multiplying by the denominator, the equation becomes ...

  sin((x -3)°) = cos((2x+6)°)

The sine and cosine are equal when ...

  (x -3) + (2x +6) = 90 + n·360 . . . . . for any integer n

  3x +3 = 90 + n·360 . . . . . . . . . collect terms

  x +1 = 30 +n·120 . . . . . . . . . . . .divide by 3

  x = 29 + n·120 . . . . . . . . . . . . . . subtract 1

__

The sine and cosine are also equal when ...

  (x -3) -(2x +6) = 90 + n·360

  -x -9 = 90 +n·360

  x = -99 -n·360

Since n can be any integer, this can also be written as ...

  x = 261 + n·360

Possible values of x include {29, 149, 261, 269} +n·360 for any integer n.

_____

The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.

Answer:

yes

Step-by-step explanation:

6 times 6 = 36

Answer: Yes

Step-by-step explanation: Yes, it is a perfect square of 6. 6 x 6 = 36.

Answer:

y = 2x - 5

Step-by-step explanation:

We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).

Finding the slope:

Slope = [tex]\frac{3-(-1)}{4-2} =2[/tex]

Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.

[tex]y=mx+c[/tex]

[tex] -1 = 2 (2) + c \\\\ c = - 5 [/tex]

So the equation of the line would be [tex]y=2x-5[/tex]

Answer: first option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

To find "m", we need to substitute the coordinates of the points  (4, 3) and (2, -1) into this formula:

 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We can identify that:

[tex]y_2=-1\\y_1=3\\x_2=2\\x_1=4[/tex]

Then:

[tex]m=\frac{-1-3}{2-4}\\\\m=2[/tex]

To find "b" we must substitute the slope and one of the given points into [tex]y=mx+b[/tex] and solve for "b". Then, this is:

[tex]3=2(4)+b\\\\3-8=b\\\\b=-5[/tex]

Therefore, the equation of this line is:

[tex]y=2x-5[/tex]

Answer:

Last choice. d.

Step-by-step explanation:

We are given the first term and the sixth term.

The first term is [tex]a_1=-9[/tex].

The sixth them is [tex]a_6=a_1r^5=-9216[/tex].

Let's solve for the common ratio, r.

[tex]-9r^5=-9216[/tex]

Divide both sides by -9:

[tex]r^5=1024[/tex]

Take the fifth root of both sides:

[tex]r=1024^{\frac{1}{5}}[/tex]

[tex]r=4[/tex]

So the common ratio is 4.

[tex]a_1=-9[/tex]

[tex]a_2=-9(4)=-36[/tex]

[tex]a_3=-9(4)^2=-144[/tex]

[tex]a_4=-9(4)^3=-576[/tex]

[tex]a_5=-9(4)^4=-2304[/tex]

[tex]a_6=-9(4)^5=-9216[/tex]

Answer:

Step-by-step explanation:

The polynomial y = (x + 4)(x - 2)(x + 7) has 3 roots.

y = 0 ⇒ (x + 4)(x - 2)(x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0

x + 4 = 0   subtract 4 from both sides

x = -4

x - 2 = 0      add 2 to both sides

x = 2

x + 7 = 0      subtract 7 from both sides

x = -7

The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots: -4, 2, and -7.A. 3

The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots, which can be found by setting y to zero and solving for the values of x that make the function equal to zero. When you set y to zero, the equation becomes 0 = (x + 4)(x - 2)(x + 7), and the roots are x = -4, x = 2, and x = -7. Hence, the correct answer to the question of how many roots the polynomial function has is:

A. 3

Answer: C: 3rd degree polynomial wit 3 terms.

Step-by-step explanation: The polynomial has 3 terms and the highest degree is 3.

C. Third degree polynomial with three terms.

Terms are, by definition, the number of nonzero coefficients for powers of x. In this case, there are 3 nonzero coefficients (3 terms) because [tex]-1=-1x^0[/tex]. For example, [tex]2x^3[/tex] has one term, but [tex]0[/tex] has 0 terms.

The degree of a polynomial is the highest power involved in the expression. In this case, it's [tex]4x^3[/tex], so the degree is 3.

Answer:

16 N

Step-by-step explanation:

If the 7 N force is at 0°, and the 11 N force is at 60°, then the components of the resultant force are:

Fₓ = 7 cos 0° + 11 cos 60° = 12.5

Fᵧ = 7 sin 0° + 11 sin 60° ≈ 9.53

The magnitude of the resultant force is:

F = √(Fₓ² + Fᵧ²)

F ≈ 15.7

Rounded to the nearest whole number, the magnitude is 16 N.

Answer:

[tex]5\sqrt{5}[/tex]

Step-by-step explanation:

We start by factoring 125 and look for a perfect square:

125= 5*5*5=[tex]5^{2} *5[/tex].

This allow us to simplify the radical:

[tex]\sqrt{125} = \sqrt{5^{2} *5}[/tex]

So we have:

[tex]\sqrt{5^{2} *5} =5\sqrt{5}[/tex]

Step-by-step explanation:

solve the equation:

5x-10=4x+20

Answer:

The correct answer is option B. 140

Step-by-step explanation:

From the figure we can see that,

AB ║ CD

To find the value of x

From the figure we can see that,

<CFE = <BEF      [Alternate interior angles are equal]

4x + 20 = 5x - 10

5x - 4x = 20 + 10

x = 30

To find the measure of <BEF

m<BEF = 5x - 10

 = (5*30) - 10

 = 150 - 10

 = 140°

Therefore the correct answer is option B. 140

[tex]\huge\boxed{1 \frac{4}{5}\ \text{ft}}[/tex]

Change [tex]\frac{1}{5}[/tex] so that is has a common denominator.  [tex]\frac{1*2}{5*2}=\frac{2}{10}[/tex]

Make an equation.  [tex]\frac{7+7+2+2}{10}[/tex]

Add.  [tex]\frac{14+4}{10}[/tex]

Add.  [tex]\frac{18}{10}[/tex]

Divide both sides by 2.  [tex]\frac{9}{5}[/tex]

Convert to a mixed number.  [tex]1 \frac{4}{5}[/tex]

Answer:

1 4/5 ft.

Step-by-step explanation:

Change 7/10 into 70

Change 1/5 into 20

( It will be easier to find perimeter this way )

Formula: P=2(l+w)

P=2(l+w)=2·(70+20)=180

Then, you change the 180 back into a fraction to get 1 4/5.

Answer:

3/6 or 50%

Step-by-step explanation:

The probability of rolling an odd number from the dice numbered,  {1,2,3,4,5,6} is 3/6.

6 numbers in all.

3 odd numbers.

3 even numbers.

Therefore, 3/6 or 50%.

Answer: 3/2 (simplified: 1.5)

Step-by-step explanation:

X=pi

X=3pi/2

Remove pi from both equations because pi will cancel out each other then you will be left with the equation 3/2. So therefore the rate of change would be 3/2 simplified would be 1.5

Answer:

pi/2

Step-by-step explanation:

Arccos(tan(0))

Arccos( 0) since tan(0)=0

Arccos(0)=pi/2 since cos(pi/2)=0 and the restricted domain of cosine is [0,pi].

Answer:

1

Step-by-step explanation:

First of all go one step at a time. Find tan(0). For this question, you can use your calculator.

Tan(0) = 0 That's because the opposite side has a length of 0 and the tangent's definition is

Tan(x ) = opposite side / adjacent side. The opposite side and the adjacent side are part of the same length. There is no real opposite side.

=========

Now you are down to cos-1(0)

If you put that into your calculator like this

2nd Function

cos-1(

0

)

=

You will get 1

Answer:

C.WXYZ equal to PNLM

Step-by-step explanation:

Look at the given statement, WZYX is equal to PMLN.

WZYX is equal to PMLN.   W corresponds to P.

WZYX is equal to PMLN.   Z corresponds to M.

WZYX is equal to PMLN.   Y corresponds to L.

WZYX is equal to PMLN.   X corresponds to N

Now look in the choices. The letters must correspond like they do above.

W must correspond to P.

WXYZ equal to P...

X must correspond to N.

WXYZ equal to PN...

Y must correspond to L.

WXYZ equal to PNL...

Z must correspond to M.

WXYZ equal to PNLM

Answer: C.WXYZ equal to PNLM

Answer: C.WXYZ equal to PNLM

Answer:

[tex]\frac{60c}{m}[/tex]

Step-by-step explanation:

We can use the unity rule to solve this problem.

Number of toys made in m minutes = c

Number of toys made in 1 minute = [tex]\frac{c}{m}[/tex]

Number of toys made in 60 minutes = [tex]\frac{c}{m} \times 60 = \frac{60c}{m}[/tex]

Since 60 minutes = 1 hours, we can write:

Number of toys made in 1 hour = [tex]\frac{60c}{m}[/tex]

Therefore, we can say that Kevin makes [tex]\frac{60c}{m}[/tex] toys per an hour.