Find (a) arc length and (b) Area of a sector.

Assuming that you want the product of the two factors given in each problem:

 ⇒ we solve this problem by timing each unit of a factor to every unit

     of the other factor

   ⇒then add each one of them who shares a common like-term

      ⇒to get the answer

Let's solve:

            [tex](4m+n)(m-2n)=4m*m+(-2n)*4m+n*m+n(-2n)\\=4m^2-7nm-2n^2[/tex]

            [tex](2a-4b)(7a-2b)=2a*7a+(-2b)(2a)+(-4b)7a+(-4b)(-2b)\\=14a^2-4ab-28ab+8b^2\\=14a^2-32ab+8b^2[/tex]

            [tex](4m+1)^2=(4m+1)(4m+1)=4m*4m+4m*1+1*4m+1\\=16m^2+4m+4m+1\\=16m^2+8m+1[/tex]

            [tex](2w+1)(2w-1)=2w*2w+2w(-1)+1*(2w)+1(-1)\\=4w^2-1[/tex]

            [tex](m+3)(m^2+4m+7)\\=m*m^2+m*4m+m*7+3m^2+3*4m+3*7\\=m^3+4m^2+7m+3m^2+12m+21\\=m^3+7m^2+19m+21[/tex]

           [tex](3x+2)(5x^2-12x-2)\\=3x*5x^2+3x(-12x)+3x(-2)+2(5x^2)+2(-12x)+2(-2)\\=15x^3-36x^2-6x+10x^2-24x-4\\=15x^3-26x^2-30x-4[/tex]

Hope that helps!

[tex]area = l \times w \\ area = 34 \times 17 \\ area = \: 578 {mm}^{2} [/tex]

[tex]Area \: of \: the \: triangle = ½× width×height. \\ area \: = \frac{1}{2} \times 34 \times 6 \\ area = 34 \times \frac{ {\cancel6} {}^{ \: \: 3} }{ \cancel2} \\ area = 34 \times 3 \: {mm}^{2} \\ area = 102 {mm}^{2} [/tex]

[tex]volume \: = area \: \times length \\ vol = 102 \times 17 \: \: {mm}^{3} \\ vol \: = 1734{mm}^{3} [/tex]

Answer:

1734 mm² = volume

[tex] \\ \\ \\ \\ [/tex]

The mathematical expression represents C(x(y)) will be C(x(y)) = 70y + 325. Then the correct option is B.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The daily cost of manufacturing x comic books at a small custom printing shop is C(x) = 2x + 325, and the number of comic books assembled in y hours is x(y) = 35y.

The composition function, C(x(y)), identifies the cost of assembling comic books in a y-hour day.

Then the mathematical expression represents C(x(y)) will be

C(x(y)) = 2(35y) + 325

C(x(y)) = 70y + 325

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

Answer:  3

Step-by-step explanation:

3/1 or 3

hope it helps...!!!

Answer:

Mean = 92

Median = 95.5

There is no mode.

What is mean, median, and mode?

Mean, median, and mode are terms in math when it comes to looking at charts and sets/groups of numbers.

1. The mean is the average of a data set.

2. The median is the middle of a data set.

3. The mode is the most common number in a data set.

Mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Before we start, let's put the set of numbers in order from least to greatest,

95, 97, 100, 86, 78, 96

78, 86, 95, 96, 97, 100

Now that we have done that let's find the mean,

78 + 86 + 95 + 96 + 97 + 100 = 552

There are 6 numbers in this set so we need to divide 552 by 6,

552 ÷ 6 = 92

92 is the mean/average of this data set,

Now let's find the median,

If we take a look at the data set we can see that there are two numbers in the middle because there are 6 in total,

78, 86, 95, 96, 97, 100

Because there are two values that are in the middle we need to add them up and divide the sum of them by 2,

95 + 96 = 191

191 ÷ 2 = 95.5

95.5 is the median of this data set,

Now let's find the mode,

If we take a look at the date set we can see that none of the numbers are repeated,

So this means there is no mode to this data set,

Therefore the mean is 92, the median is 95.5, and there is no mode.

Step-by-step explanation:

number 2)

3√2/3√4=

=3√2/3×2

=3√2/6

=3√2/6 ×3/3

=1√2/2

=√2/2

Answer:

754 divided by 13= 58

I hope this Helps! ;)

Given,

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf∠DBC= 55° and ∠BAC = 45°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf∠CAD = ∠DBC= 55° (Angles \: in \: the \: same \: segment)[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

Thus,

[tex] \sf∠DAB=∠CAD + ∠BAC[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= 55° + 45° [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \sf= 100°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

We know that the opposite angles of a cyclic quadrilateral are supplimentary.

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf ∠DAB +∠BCD = 180°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf∠BCD = 180°-100° =80°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \pink{\boxed{\sf{∠BCD = 80°}}}[/tex]

Answer:

∠BCD = 80°

Step-by-step explanation:

ABCD is a cyclic Quadrilateral.

∠DBC = 55°

∠BAC = 45°

∠BDC

=> ∠BAC = ∠BDC

=> 45° = ∠BAC { Angles of same segment BC}

In Triangle BCD

=> ∠BDC + ∠DBS + ∠BCD = 180°

=> 45° + 55° + ∠BCD = 180°

=> 100° + ∠BDC = 180°

=> ∠BDC = 180-100

=> 80° ans.

Answer:

Volume of Cone=1/3πd²/4×h

= 1/3π×7²/4×9

= 36.75cm³

answer : 9.5 because you subtract and then divide by 2

the answer is B, D and F. I hope this was helpful

Answer:

Exponential Graph

Step-by-step explanation:

The exponential graph of a function represents the exponential function properties.

Another way to known of if the graph's domain is all real numbers

Answer:

Exponential

Step-by-step explanation:

The listed points are :

The y-values are powers of 3 which decrease. Hence, it is exponential.

Answer:

y=|x|

Step-by-step explanation:

We know

general modulus function passes through origin as |0| is 0

And it's symmetric on both sides of y axis .

As it's not one -one function

Means

So the graph is y=|x|

Answer:

y = |x|

Step-by-step explanation:

The equation for the part of graph to the right of the y-axis is:  

y = x  where y ≥ 0

The equation for the part of graph to the left of the y-axis is:  

y = -x  where y ≥ 0

So we can see that both a positive and negative value of x gives the same positive value of y.

Therefore, we can create an equation for the graph by using the absolute value of x:

⇒ y = |x|

Absolute value means how far away a number is from zero.

"x" is x away from zero and "−x" is also x away from zero.

So the absolute value of x is x, and the absolute value of −x is also x.

The bars either side of the x shows that we want the absolute value of x.

In practice, think of "absolute value" as removing any negative sign in front of a number.

With y = x  →  when x = 1, y = 1  and  when x = -1, y = -1

With y = |x|  →  when x = 1, y = 1  and  when x = -1 we think of it as x = 1, so y = 1

Answer:

15/56

Step-by-step explanation:

5 people have a license

3 people don't

? = Probability that first person has a license and second does not

We can divide the problem into two sections, the first being the probability of the first person having a license, and the second section is the probability that the second person doesn't have a license.

P1 = Probability of the first person having a license, there are 5 out of 8 person having a license, thus P1 = 5/8.

P2 = Probability of the second person having a license. There are 3 people not having a license, out of 8-1 = 7 persons available, since one is taken already from the first choice, therefore P2 = 3/7.

P1 and P2 are dependent events, thus P(1,2) = P1 * P2.

P(1,2) = P1 * P1 = 5/8 * 3/7 = 15/56

Answer:

The sophomore in her school is 75

Step-by-step explanation:

Solution

The plot shows the distribution of 30 sophomores

We can see that there are 3 main vertical

line in red pen in the picture above.( distribution)

The first line means Minimum

The third line means the maximum

The second line means the medium

So the Medium is 75. And 30 sophomores in her

School took the survey.

So the medium belongs to them

Answers:  

===================================================

Explanation:

Each term is separated by a plus sign or a minus sign. We could rewrite the 4ab-5b portion as 4ab + (-5b) to help get everything separated by a plus sign.

The five terms are

The coefficients are the numbers just to the left of the variable. For a term like 4ab, the coefficient is 4. For the term "m", we can think of it as 1m so we can see it has a coefficient of 1.

The constant term is the term that doesn't have any variable attached to it. That would be the "3" as the first term.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 1) \ \left\{\begin{matrix} 5x-3y-z=1&\\ x+4y-6z=-1& \\ 2x+3y+4z=9& \end{matrix}\right. \end{gathered}$}[/tex]

The coefficient matrix associated with the system is constructed and the columns and rows are reduced.

                [tex]\left ( \begin{array}{ccc|c} 5 & -3 &-1 &1\\ 1 & 4 & -6 &-1\\ 2 & 3 & 4 & 9 \end{array} \right ) \begin{array}{c} \xrightarrow[\textup{F}_3- 2\textup{F}_2]{\textup{F}_1 - 5\textup{F}_2} \end{array} \left ( \begin{array}{ccc|c} 0 & -23& 29 &6\\ 1 & 4& -6 &-1\\ 0 & -5 &16 & 11 \end{array} \right )\\ \ \\ \ \\ \begin{array}{c} \xrightarrow[]{23\textup{F}_3 - 5\textup{F}_1} \end{array} \left ( \begin{array}{ccc|c} 0 & -23& 29 &6\\ 1 & 4& -6 &-1\\ 0 & 0 & 223 & 223 \end{array} \right )[/tex]

So, z=1. Translating the last matrix to the associated system of equations, we have that x=1, y=1, since:

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} y&=\dfrac{6-29}{-23}=\dfrac{-23}{-23}=1\\ x = -1+6-4=1 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{2) \ \left\{\begin{matrix} x+y=7& \\ x\times y=12& \end{matrix}\right. } \end{gathered}$}[/tex]

Clear an unknown in the first equation and substitute the resulting expression in the second. Next, the quadratic equation is solved.

             [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ y=7-x \quad \Longrightarrow \quad 12=x(7-x)=7x-x^2 } \end{gathered}$}[/tex]

                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ 0=x^2-7x+12=(x-4)(x-3); } \end{gathered}$}[/tex]

                [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x_1=4\qquad x_2=3 \Longrightarrow y_1=3 \qquad y_2=4 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{3) \ \left\{\begin{matrix} x^2+y^2=169& \\ x+y=17& \end{matrix}\right. } \end{gathered}$}[/tex]

Clear an unknown in the first equation and substitute the resulting expression in the second. Next, the quadratic equation is solved.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ y=17-x \quad \Longrightarrow \quad 169=x^2 +(17-x)^2=x^2+x^2 -34x+289 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ 0=2x^2-34x+120=2(x^2-17+60)=2(x-12)(x-5); } \end{gathered}$}[/tex]

               [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ x_1=4\qquad x_2=3 \Longrightarrow y_1=3 \qquad y_2=4 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{4 \ \left\{\begin{matrix} y^2-2y+1=x & \\ \sqrt{x}+y=5 & \end{matrix}\right. } \end{gathered}$}[/tex]

Substitute the expression that represents x into the second equation. Then both sides of the equation are squared and solved.

   [tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ \sqrt{y^2-2y+1}+y=5\quad \Longrightarrow\quad \left ( \sqrt{y^2-2y+1} \right )^2=(5-y)^2 } \end{gathered}$}[/tex]

                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ y^2-2y+1=y^2-10y+25\quad \Longrightarrow\quad 8y=24; } \end{gathered}$}[/tex]

                                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ y=6 \qquad x=4 } \end{gathered}$}[/tex]

Step-by-step explanation:

8-3 = 5,

3-5 = -2 = the x coordinate of B

-2-4 =-6,

-2-6 =-8 = the y coordinate of B

(-2,-8) is the point B

A is 5 to the right of the midpoint, so B is 5 to the left of the midpoint

A is 6 up from the midpoint so B is 6 down from the midpoint

Answer:

y = 96

Step-by-step explanation:

given that y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

to find k use the condition when y = 24 , x = 2 , then

24 = k × 2² = 4k ( divide both sides by 4 )

6 = k

y = 6x² ← equation of proportion

when x = 4 , then

y = 6 × 4² = 6 × 16 = 96

Answer: n=-3 and n=3/2

Step-by-step explanation:

To solve the expression, we want to find the values of n. Since there are no common factors in 2, 3, -9, we directly multiply the "a" and "c" values.

2×(-9)=-18

This means, we want to find two numbers that multiply to -18 and adds to 3. This can also be known as the cross method.

We will find that 6 and -3 multiply to -18, and adds to 3.

In our box method, we want to find the common factors.

|2n²|6n|

|-3n|-9|

Note: Just pretend the lines line up and form a square box, with a term in each box.

After finding that is in common between the boxes, we get (n+3)(2n-3)=0

To solve, we set each factor equal to 0.

n+3=0

n=-3

2n-3=0

2n=3

n=3/2

35° + 60° + x° = 180°

95° + x° = 180°

x° = 180° - 95°

x° = 85°

In any triangle, the sum of its interior angles measures 180º.

Answer: y = 1/2x + 1/2

Step-by-step explanation:

hope it helps if there's any questions feel free to ask me but I'm sure that's how that question is hanled

Answer:

164°

Step-by-step explanation:

596/1000 and 59.6%

Step-by-step explanation:

because when we make 596/1000 is 0.596

Answer:

it is the answer on the top

Answer:

Step-by-step explanation:

4 cups = 1 pint

$3.28/4 = .82 per pint