Solve the equation for x​

Problem 1

The circumference is the full perimeter around the circle. You can think of it as the combination of "circle" and "fence" to get "circumference", but there might be other tricks to remember the term.

Anyways, the formula to get the circumference of a circle is

C = 2*pi*r

In this case, r = 14 is our radius so,

C = 2*pi*r

C = 2*pi*14

C = 28pi .... exact circumference in terms of pi

We only want a portion of this circumference as shown by the piece of the circle darkened. The fractional portion we want is 135/360 of a circle. Divide the angle by 360 to get the fractional portion you want. If the angle was say 180 degrees, then 180/360 = 1/2 is the fractional portion.

So we take 135/360 and multiply it by the value of C found earlier

arc length = (fractional portion)*(circumference)

arc length = (135/360)*28pi

arc length = 10.5pi

That's the exact arc length in terms of pi. Use a calculator to find that

10.5pi = 32.9867228626929

Or you could use pi = 3.14 to say

10.5*pi = 10.5*3.14 =  32.97

Which is fairly close to what the calculator is saying

-----------------

Exact arc length = 28pi

Approximate arc length (using calculator) = 32.9867228626929

Approximate arc length (using 3.14 for pi) = 32.97

Units are in feet

When I write "using calculator", I mean using the calculator's stored version of pi, instead of pi = 3.14

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

Problem 2

We could use the same idea as problem 1, or we could use the formula below. The formula is just a quick way of encapsulating what I discussed earlier.

L = arc length

x = central angle

L = (x/360)*2*pi*r

L = (150/360)*2pi*13

L = (65/6)pi .... exact arc length

L = 34.0339204138894 .... approx arc length (using calculator)

L = 34.0166666666667 .... approx arc length (using 3.14 for pi)

-----------------

Exact arc length = (65/6)pi

Approximate arc length (using calculator) = 34.0339204138894

Approximate arc length (using 3.14 for pi) = 34.0166666666667

Units are in meters

Answer:

Area= 97.9 km²

Step-by-step explanation:

Angle at w = 180-119-34

Angle at w = 27°

Side XV= x

x/sin27= 26/sin119

x= sin27(26/sin119)

x= 0.454(26/0.8746)

x= 13.5 km

Side WX = y

y/sin 34= 26/sin119

y= sin34(26/sin119)

y= 0.559(26/0.8746)

y= 16.6 km

S= (16.6+13.5+26)/2

S= 56.1/2

S=28.05

Area = √(28.05(28.05-26)(28.05-13.5)(28.05-16.6))

Area=√(28.05(2.05)(14.55)(11.45))

Area=√(9579.772744)

Area=97.8763

Area= 97.9 km²

Answer:

PY = 14.5

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, thus

XZ = WY , that is

4x - 1 = x + 7 + x + 7

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = 7.5

Thus

PY = x + t = 7.5 + 7 = 14.5

Step-by-step explanation:

x+7+x+7= 4x-1

2x+14=4x-1

14= 2x-1

15= 2x (divide)

x = 7.5

wp= 7.5cm

not really sure

Answer: Hi!

Okay. So this equation we will solve using something called the distributive property. We use the distributive property to multiply the terms inside the parentheses (x and -2) by the term outside and in front of the parentheses (4). First, we would multiply 4 * x, which is 4x. Then, we would multiply 4 * -2, which is -8. Out equation now looks like this:

4x - 8 = 14

Our goal is to isolate the x, so now we'll use inverse operations to remove the -8 from the equation. The inverse operation for subtraction is addition, so we would add 8 to both sides:

4x - 8 = 14

   + 8  + 8

The eights cancel out, so we're left with this equation:

4x = 22

Last step! We're almost done. All we have to do now is divide 4 on both sides; in the term 4x, 4 is being multiplied by x, so the inverse operation would be division.

4x ÷ 4 = x

22 ÷ 4 = 5.5

Our equation now looks like this:

x = 5.5

So, 5.5 is equal to x! This would be your answer!

Hope this helps!

Answer:

  $887.50

Step-by-step explanation:

Her gross pay is the sum of the pay amounts for each of the hour amounts:

  pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)

  = (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)

  pay = 887.50

Barbara's gross pay for the week was $887.50.

Answer:

There are 3 ways

Step-by-step explanation:

The formula for a sector's area is:

1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2)

3. A = (fraction of the circle) * (pi * r2)

Answer:  D

Step-by-step explanation:

To find how much time she need on each project divide the time by 3 because there are 3 projects and to get to 1 project you will need to divide by 3.

16 3/4 =  67/4

[tex]\frac{67}{4}[/tex] ÷ [tex]\frac{3}{1}[/tex]  = [tex]\frac{67}{12}[/tex]   = 5 7/12

Answer:

Step-by-step explanation:

Answer:

From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.

Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).

Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).

Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.

Answer:

k) the product of ant 2 odd numbers is odd

I don't know.

Let's check um out.

For each choice, I'll try to find an example to show that it's false.

F. The sum of any 2 even numbers is odd.  

    2+2=4. 4 is even. This one is false.

G. The sum of any 2 odd numbers is ood.

    3+3=6.  6 is even.  This one is false.

H. The quotient of any 2 even numbers is odd.

    8÷4=2. 2 is even. 10÷4=2.5.  2.5 is neither odd nor even. This one is false.

J. The quotient of any 2 even numbers is even.

   10÷2=5.  5 is odd.  This one is false.

K. The product of any 2 odd numbers is odd.

    I can't find an example where this is false.

    So I'm gonna say that this is the true one.

Answer:

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Step-by-step explanation:

Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.

Therefore:

x + y = z                                  (1)

Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:

Cost of buying = Price it was sold for

The cost of the mango = 5z and the price it was sold for = 3x + 6y

3x + 6y = 5z                            (2)

Substituting z = x + y in equation 1

3x + 6y = 5(x + y)

3x + 6y = 5x + 5y

6y - 5y = 5x - 3x

y = 2x

x / y = 1/ 2 = 1 : 2

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Answer:

Which term is a term in this expression?

Step-by-step explanation:

Which term is a term in this expression?Which term is a term in this expression?Which term is a term in this expression?Which term is a term in this expression?Which in this expression?Which term is a term in this expression?

Answer:

  range = {5, 2, -1, -4}

Step-by-step explanation:

Maybe you want the corresponding range.

  f({-1, 0, 1, 2}) = 2 -3{-1, 0, 1, 2} = 2 +{3, 0, -3, -6} = {5, 2, -1, -4}

Answer:

6

Step-by-step explanation:

the solution in photo :)

Answer:

6

Step-by-step explanation:

→ Prime factorise each number

12 = 2² × 3 ⇒ 2 × 2 × 3

18 = 2 × 3² ⇒ 2 × 3 × 3

24 = 2³ × 3 ⇒ 2 × 2 × 2 × 3

→ Find which number there are in each one

2 and 3

→ Multiply them together

2 × 3 = 6

Answer:

3,060

Step-by-step explanation:

Given:

18C4

nCr=n! / r!(n-r)!

=18! / 4!(18-4)!

18!=18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

=6,402,373,705,728,000

4!=4*3*2*1

=24

(18-4)!=14!

=14*13*12*11*10*9*8*7*6*5*4*3*2*1

=87,178,291,200

18! / 4!(18-4)!

=6,402,373,705,728,000 / 24*87,178,291,200

=6,402,373,705,728,000 / 2,092,278,988,800

=3,060

Answer:

[tex]\huge \boxed{16}[/tex]

Step-by-step explanation:

4 raised to 2 is 4 squared or 4 to the power of 2.

[tex]4^2 =4 \times 4 = 16[/tex]

Answer:  x = 4/5

Step-by-step explanation:

[tex]\tan\ y=\dfrac{\text{side OPPOSITE y}}{\text{side ADJACENT to y}}=\dfrac{1}{6}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \dfrac{x}{x+4}=\dfrac{1}{6}\\\\\\\text{Cross multiply, distribute, and solve for x:}\\6(x)=1(x+4)\\6x=x+4\\5x=4\\\\\large\boxed{x=\dfrac{4}{5}}[/tex]

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] \sf{ \frac{3}{5} = \frac{x - 1}{8} }[/tex]

Apply cross product property

⇒[tex] \sf{ 5(x - 1) = 3 \times 8}[/tex]

Distribute 5 through the parentheses

⇒[tex] \sf{5x - 5 = 3 \times 8}[/tex]

Multiply the numbers

⇒[tex] \sf{5x - 5 = 24}[/tex]

Move 5 to right hand side and change it's sign

⇒[tex] \sf{5x = 24 + 5}[/tex]

Add the numbers

⇒[tex] \sf{5x = 29}[/tex]

Divide both sides of the equation by 5

⇒[tex] \sf{ \frac{5x}{5} = \frac{29}{5} }[/tex]

⇒[tex] \sf{x = \frac{29}{5} }[/tex]

Hope I helped!

Best regards!!

Hi there! :)

Answer:

[tex]\huge\boxed{m\leq 2}[/tex]

Equation:

8m - 6 ≤ 10

Add 6 to both sides:

8m ≤ 16

Divide both sides by 8:

8m/8 ≤ 16/8

m ≤ 2

Answer:

8m - 6≤ 10

m≤2

Step-by-step explanation:

8m - 6≤ 10

Add 6 to each side

8m - 6+6≤ 10+6

8m ≤ 16

Divide each side by 8

8m/8 ≤16/8

m≤2

Answer:  A & C

Step-by-step explanation:

HL is Hypotenuse-Leg

A) the hypotenuse from ΔABC ≡ the hypotenuse from ΔFGH

   a leg from ΔABC ≡ a leg from ΔFGH

   Therefore HL Congruency Theorem can be used to prove ΔABC ≡ ΔFGH

B) a leg from ΔABC ≡ a leg from ΔFGH

   the other leg from ΔABC ≡ the other leg from ΔFGH

   Therefore LL (not HL) Congruency Theorem can be used.

C) the hypotenuse from ΔABC ≡ the hypotenuse from ΔFGH

   at least one leg from ΔABC ≡ at least one leg from ΔFGH

   Therefore HL Congruency Theorem can be used to prove ΔABC ≡ ΔFGH

D) an angle from ΔABC ≡ an angle from ΔFGH

   the other angle from ΔABC ≡ the other angle from ΔFGH

   AA cannot be used for congruence.

Answer:

197

Step-by-step explanation:

Sample proportion is; p^ = 12/50 = 0.24

Margin of error of 5% is given by the formula;

ME = (z_0.05) √[p^(1 - p^)/n]

Let's make n(number of sample) the subject.

n = ((z_0.05)/ME)²((p^)(1 - p^))

From tables, the z-score of 0.05 is 1.645

Thus;

n = ((1.645)/0.05)²(0.24(1 - 0.24))

n ≈ 197

Answer:

Top left: 6

Bottom left: 8

Top right: 7

Bottom right: 3

Step-by-step explanation:

To solve this problem, we need to look at the table to see what missing information we need to solve for. On the table, it asks us how many students:

On the first intersection (top left), we are asked how many students played an instrument and sport. That is easy to solve because the information they provide us already gives us that number: 6.

On the second intersection (bottom left), things get a little more challenging. The information states that 14 students in total play sports, so that is not the number of people who only play sports. Since 14 people in total play sports and 6 people play both an instrument and sport, we subtract 6 from 14 to get our answer, 8.

On the third intersection (top right), it asks us how many people play an instrument but doesn't play a sport. Let's look at the remaining values first. There is: 6, 8, 3. When we add those together, we get 17, and when we subtract that from the total (24), we get our answer: 7.

On the last intersection (bottom right), the information already provides us with the answer to how many people don't play anything: 3.

Answer:

A) 10th of August

B) $1780.03

Step-by-step explanation:

A) From the payment terms of 2/10 EOM, Melissa is to receive a 2% discount if she pays within 10 days from the end of the month

From the date on the invoice, July 26, the date at which Melissa has to pay to take the cash discount is before the 10th of August

B) The payment amount will be 2% off the original payment amount

The total cost of the four new gas mowers less the trade discount = 499 × 4 × (100 - 9)/100 =$1816.36

The 2% discount will then be $1816.36 × (100 - 2)/100 = $1780.03

The payment amount assuming Melissa pays before the end of the discount period = $1780.03.

Answer:

Step-by-step explanation:

a) 5.6 x 10∧-8

b) 5.678 x 10∧10

c) 1.9238 x 10∧3

[tex]f(x)[/tex] passes through origin, i.e. $(0,0)$

if you move 5 units up, it should pass through $(0,5)$

so you'll add 5 to $y$ i.e. $y+5=x^2$ this satisfies $(0,5)$

and to move right, it should pass through $(7,0)$ so you'll subtract $7$ from $x$ i.e. $y=(x-7)^2$

now combine both translations

$g(x)=(x-7)^2-5=x^2-14x+45$

Answer:

-8

Step-by-step explanation:

2(-2) +3(-2) +2

-4 -6 +2

-10 +2

-8

Answer:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Step-by-step explanation:

Given that

Radius of a circle is doubled.

Diameter of circle is doubled.

To study:

The effect on circumference and area on doubling the radius and diameter.

Solution/explanation:

Let us discuss about the formula for circumference and area.

Formula for Circumference of a circle in form of radius:

[tex]C =2\pi r[/tex]

It is a linear equation in 'r'. So by doubling the radius will double the circumference.

Formula for Area of a circle in form of radius:

[tex]A =\pi r^2[/tex]

It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.

Testing using example:

Let the initial radius of a circle = 7 cm

Initial circumference = [tex]2 \times \frac{22}{7} \times 7 = 44 cm[/tex]

Initial area = [tex]\frac{22}{7} \times 7 \times 7 =154 cm^2[/tex]

After doubling:

Radius = 14 cm

circumference = [tex]2 \times \frac{22}{7} \times 14 = 88 cm[/tex]   (Twice the initial circumference)

area = [tex]\frac{22}{7} \times 14 \times 14 =616 cm^2[/tex] (4 times the initial area)

------------------------------------

Formula for Circumference of a circle in form of Diameter:

[tex]C =\pi D[/tex]

It is a linear equation in 'D'. So by doubling the diameter will double the circumference.

Formula for Area of a circle in form of diameter:

[tex]A =\dfrac{1}{4}\pi D^2[/tex]

It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.

Testing using example:

Let the initial diameter of a circle = 28 cm

Initial circumference = [tex]\frac{22}{7} \times 28 = 88 cm[/tex]

Initial area = [tex]\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2[/tex]

After doubling:

Diameter = 56 cm

circumference = [tex]\frac{22}{7} \times 56= 176 cm[/tex]   (Twice the initial circumference)

area = [tex]\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2[/tex] (4 times the initial area)

So, the answer is justified:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Answer:

[tex]\boxed{y=2x-2}[/tex]

Step-by-step explanation:

Pick values from the table.

When x = 1, y = 0.

The third option seems right.

[tex]y=2(1)-2[/tex]

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

[tex]y=0[/tex]

True.

Answer: x=1/9

Step-by-step explanation:

[tex]2\left(\frac{1}{9}\right)x=\frac{2}{81}[/tex]

[tex]\frac{2}{9}x=\frac{2}{81}[/tex]

multiply both sides by 9

[tex]9\cdot \frac{2}{9}x=\frac{2\cdot \:9}{81}[/tex]

[tex]2x=\frac{2}{9}[/tex]

divide 2 on both sides

[tex]x=\frac{1}{9}[/tex]

Answer:

The correct option is;

D. 6,5

Step-by-step explanation:

TS and TU are midsegments

Segment PR = 18.2

Segment TS = 6.5

Given that TS is the midsegment of PR and PQ, therefore, TS = 1/2×QR

Which gives;

Segment QR = 2×TS = 2 × 6.5 = 13

Segment QR = 13

Given that TU is a midsegment to PQ and QR, we have that QU = UR

Segment QR = QU + UR (segment addition postulate)

Therefore, QR = QU + QU (substitute property of equality)

Which gives;

QR = 2×QU

13 = 2×QU

Segment QU = 13/2 = 6.5

The length of segment QU is 6.5.

Answer:

  −13.8654599313 and 0.8654599313

Step-by-step explanation:

The two numbers of interest will be the solutions to ...

  xy = -12

  x +y = -13

Substituting for y, this becomes the quadratic ...

  x(-13 -x) = -12

  x^2 +13x = 12 . . . . . multiply by -1

  x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square

  (x +6.5)^2 = 54.25

  x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5

  x ≈ -13.865499313 or 0.8654599313

The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.