A picture 8 3/4 feet long is to be centered on a wall that is 12 1/2 feet long. How much space is there from the edge of the wall to the picture?

Answer:

|x - 8| = 6

Step-by-step explanation:

   |x - b| = c

⇒ (x - b)² = c²

Given:

Substitute the values of x into (x - b)² = c²:

(2 - b)² = c²

(14 - b)² = c²

Equate and solve for b:

(2 - b)² = (14 - b)²

⇒ 4 - 4b + b² = 196 - 28b + b²

⇒ 4 - 4b = 196 - 28b

⇒ 24b = 192

⇒ b = 8

Substitute b = 8 into the equations to find c:

x = 2 ⇒ |2 - 8| = 6

x = 14 ⇒ |14 - 8| = 6

Therefore, c = 6

Final equation:  |x - 8| = 6

Answer:

A = 390

Step-by-step explanation:

l=14

w= 3

h= 9

A= 2 (wl+hl+hw) = 2 (3.14+9.14+9.3) = 390

Answer: 390in^2

Step-by-step explanation:

2(14 x 3) + 2(9 x 3) + 2(14 x 9)

84 + 54 + 252 = 390 in^2

Answer:

92 boys

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

Answer:

42 boys

Step-by-step explanation:

Represent the number of boys with 'b' and that of girls with 'b + 23.'

Then b + (b + 23) = 207.

Simplifying, we get 2b =   84, so that b is 42.  There are 42 boys and

(42 + 23) girls, or 65 girls.

Answer:

The probability of each is 50-50.

Step-by-step explanation:

With the marbles, there are four different outcomes: red-blue, blue-red, red-red, and blue-blue. Because one outcome is for same colors and the other is different colors, the probability of either is 2/4, or 1/2, or 50%. This is the same as tossing a coin. Hope this helps!

Answer:

A.128

Step-by-step explanation:

First you break the prism apart so that you have one 7x4x2 rectangular prism and one 12x3x2 prism. Find the volume of both, then add them together.

Volume of 12x3x2:

12 x 3 = 36.          36 x 2 = 72.

Volume of 7x4x2:

7 x 4 = 28.            28 x 2=56.

Then add both volumes: 72 + 56 = 128.

Answer:

722.5792 cm²

Step-by-step explanation:

1 in ≈ 2.54 cm

Squaring both sides:

⇒ (1 in)² ≈ (2.54 cm)²

Apply exponent rule (ab)² = a²b²

⇒ (1)² in² ≈ (2.54)² cm²

⇒ 1 in² ≈ 6.4516 cm²

Therefore, to convert an area measured in inches squared to centimeters squared, multiply by 6.4516:

⇒ 112 in² ≈ (112 × 6.4516) cm²

               = 722.5792 cm²

The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.

Data;

Using poission formula,

[tex]P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute[/tex]

Let's substitute the values into the formula.

For 50 calls in 150 hours

For 150 hours = x = 0.3 * 150 = 45

[tex]p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431[/tex]

b)

The probability the next call arrives after 2 hours.

[tex]\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488[/tex]

c)

The number of calls recieved each day is recorded for 50 consecutive days.

for 50 days;

[tex]\lambda = 0.3 * 50 * 24 = 360[/tex]

The mean = 360

The standard deviation is given as

[tex]S.D = \sigma =\sqrt{360} = 18.974\\[/tex]

The probability the sum of these 50 number is less than 356 is

[tex]p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165[/tex]

Learn more on poission formula here;

https://brainly.com/question/7879375

Answer:

Cubic centimetres

Step-by-step explanation:

Cubic centimetres is perfect

As

Answer:

5 students did.

Step-by-step explanation:

20 students. 1/4 of 20 is 5

Answer:

B

Step-by-step explanation:

The 1st quartile is 135. The 3rd quartile is 195. To find the interquartile, you would subtract the 3rd quartile from the 1st quartile. 195-135=60. The interquartile range for the spring musical is 60

Answer:

[tex] \: [/tex]

Step-by-step explanation:

In the question, it is given that a cone has a diameter of 14 feet and a height of 11 feet and we have to find the volume of the cone.

[tex] \: [/tex]

To Find the volume of the cone, we must know this formula :

[tex] \\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(cone) }= \dfrac{1}{3} \: \pi {r}^{2}h }}}}}}} \\ \\[/tex]

Where,

Now, we will substitute the values in the formula :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times {(7)}^{2} \times 11 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 49 \times 11 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 539 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1692.46 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1692.46}{3} }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \: \: \underline{ \boxed{ \frak{564.15 } }} }}}}}}} \: \: \bigstar \\ \\[/tex]

Therefore,

Step-by-step explanation:

Given :-

To Find :-

Solution:-

Formula for volume of cone = 1/3πr²h

Volume = 1/3×3.14×7²×11 cubic ft.

Volume = 564.15 cubic ft.

Answer:

Question 1

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, or a right triangle)

Given:

⇒ BC² + 8² = 10²

⇒ BC² = 36

⇒ BC = 6 cm

Question 2

Given:

⇒ MB = AB - AM = 8 - x

As ΔABC ~ ΔMBN

⇒ AB : AC = MB : MN

⇒ 8 : 10 = (8 - x) : MN

[tex]\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}[/tex]

[tex]\sf \implies \dfrac45=\dfrac{(8-x)}{MN}[/tex]

[tex]\sf \implies MN=\dfrac54(8-x)[/tex]

Question 3

D = (6, 8)

As ΔBAD ~ ΔMAP

⇒ AB : AD : BD = AM : AP : MP

⇒ 8 : 6 : 10 = x : AP : MP

[tex]\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}[/tex]

[tex]\sf \implies AP=\dfrac34x[/tex]

[tex]\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}[/tex]

[tex]\sf \implies MP=\dfrac54x[/tex]

Question 4

Perimeter of MNCDP = MN + NC + CD + PD + MP

As ΔABC ~ ΔMBN

⇒ AB : BC : AC = MB : BN : MN

⇒ 8 : 6 = (8 - x) : BN

[tex]\sf \implies \dfrac86=\dfrac{(8-x)}{BN}[/tex]

[tex]\sf \implies BN=\dfrac34(8-x)[/tex]

NC = BC - BN

[tex]\sf \implies NC=6-\dfrac34(8-x)[/tex]

PD = 6 - AP

[tex]\sf \implies PD=6-\dfrac34x[/tex]

Perimeter of MNCDP = MN + NC + CD + PD + MP

[tex]\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x[/tex]

[tex]\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x[/tex]

[tex]\sf \implies perimeter=10+8+6=24[/tex]

Answer:

168

Step-by-step explanation:

The elevation and the top of the tree form a right triangle

The height of the tree is 104.96 feet

The given parameters are:

The height (h) of the tree is calculated using the following trigonometry ratio

tan(α) = h/b

Make h the subject

h = b * tan(α)

Substitute known values

h = 82* tan(52)

Evaluate the product

h = 104.96

Hence, the height of the tree is 104.96 feet

Read more about right triangles at:

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Answer:

Step-by-step explanation:

tan 52 = x/82

x= 82 x tan 52

x=104.96

Answer:

the question is blurry, please resend it

Answer:

183 cm^2

Step-by-step explanation:

the line through the shape line means that they are equivalent meaning the side that is empty not making the trapezoid would be 9 as well. moving the 3 over since it is right next to it. 3 times 9 equal 27cm^2. later we are gonna use this number to subtract

then make a different equation with 3+9 to the the full height of the trapezoid pretending it is not missing anything. 3+9=12

then use the formula to find the area of the trapezoid which is 1/2(h)(b1+b2)

add the 2 bases together to get 35. how did i get 35. 12+14=26 yes then include the 9 to get 35.

1/2(height=12)(35)=6(35)=210cm^2

then you used 210-27 to get 183cm^2

Answer:

[tex]78 \frac{5}{8} [/tex]

Step-by-step explanation:

[tex]for \: the \: width = 8 \tfrac{1}{2} \\ = \frac{17}{2} \\ sine \: the \: width \: is \: 9 \frac{1}{4} a \: long \\ 9 \ \frac{1}{4} = \frac{37}{4} \\ lenht \: of \: the \: plot = \ \frac{17}{2} \times \frac{37}{4} = \frac{629}{8} = 78 \ \frac{5}{8} \\ it \: will \: be78 \ \frac{5}{8}long [/tex]

Answer:

Step-by-step explanation:

the slopes are perpendicular

find a slope perpendicular to 3/2

how to find:

change the sign of the slope and flip the fraction

-2/3 is the slope

The slope of BD is -2/3.

Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it.

Given:

BD is a diameter of circle A. If the slope of BE is 3/2.

We have to find the slope of BD.

According to given question we have

We know that the slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is [tex]m_{1}[/tex] and the slope of a perpendicular line is [tex]m_{2}[/tex] then we have

[tex]m_{2} = -1/m_{1}[/tex]

So, the slope of BD is -2/3.

Therefore, the slope of BD is -2/3.

Learn more details about slope here:

https://brainly.com/question/3605446

#SPJ1

Perpendicular lines have negative reciprocal slopes. That means the fraction is flipped and multiplied by negative 1. So if one line has a slope of 3/5, then a line perpendicular to it has a slope of -5/3.

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line

Now

Answer:

I got 15.6

Step-by-step explanation:

I subtracted 28.8 percent from 68.4 then subtracted that number from 68.4

Answer:

73.81

Step-by-step explanation:

You know that the formula for circumeference is 2(pi)r.

2x3.14x11=69.08;

However, a part of the circle is cut off, leaving 3/4 of it.

3/4x69.08=51.81.

However, you add the 11+11 to it because of the slice.

22+51.81=73.81

Answer:

55 degrees

Step-by-step explanation:

well, x is on the same line as 125, and a line is always a straight 180 degrees, so you subtract 180-125=55, and angle x and angle y are corrisponding angles, so y also equals 55 degrees.

hope that helps!

Answer: 75

Step-by-step explanation:

Separate the parallelogram into two identical triangles (0.5 length by 10 height) and a rectangle (8 length by 10 height).

Work out the area of the rectangle - 8 * 10 = 80

Work out the area of the triangle - 0.5 * 10 = 5 (you don't need to halve it as you have two triangles)

Work out the area of the parallelogram - 80 + 5 = 85

Work out the area of the purple rectangle? (it says triangle in your description but I'm pretty sure that's not a triangle) - 5 * 2 = 10

Work out final area of the parallelogram - 85 - 10 = 75

I'm not sure if this is right but either way I hope you get your answer :)

The given expression [tex]\rm 12x^2-13x+3[/tex]equivalent to (3x - 1)(4x - 3) option second is correct.

A quadratic expression is a second-degree algebraic expression represented by the:

[tex]\rm f(x)=ax^2+bx+c[/tex] ........(1)

Where a, b, and c are the constants and  

We have the quadratic expression:

[tex]\rm f(x)=12x^2-13x+3[/tex]

[tex]\rm f(x)=12x^2-9x-4x+3[/tex]  (we can write -13x as a sum of -9x and -4x)

After taking common term, we get:

[tex]\rm f(x)=3x(4x-3)-(4x-3)[/tex]

[tex]\rm f(x)=(4x-3)(3x-1)[/tex]  or

[tex]\rm f(x)=(3x-1)(4x-3)[/tex]

Thus, the given expression [tex]\rm 12x^2-13x+3[/tex]  is equivalent to (3x - 1)(4x - 3).

Learn more about quadratic equations here:

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$37.51 - the third option above

Step-by-step explanation:

A

1600 x 1.053^3= 1868.12

B

1600x1.06^3 =1905.63

Difference

1905.63-1868.12= 37.51

$37.51

Hope this helps!

Answer:

y = ¼(x-4)

Step-by-step explanation:

Before solving the question, let's look at one example,

In this case, y is directly proportional to (x-4) means that y∝(x-4) which can also mean that y=k(x-4).

Hence, to find the value of k, substitute x=16, y=3 into y=k(x-4),

3=k(16-4)

k=3/12

k=1/4

After that, substitute the k value into the equation,

Answer:

Hiroko removed common factors, which leads to smaller numbers, which can be easier to work with.

Step-by-step explanation:

However, this step is not entirely needed in the grand scheme of solving the problem. It simply uses smaller numbers to digest.

Do the opposite of PEMDAS when isolating the variable, d. Note the equal sign, what you do to one side of the equal sign, you do to the other.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)
Multiplication

Division

Addition

Subtraction.

First, subtract 490 from both sides of the equation:

10d + 490 (-490) = 2500 (-490)

10d = 2500 - 490

10d = 2010

Next, divide 10 from both sides of the equation:

(10d)/10 = (2010)/10

d = 2010/10

d = 201

201 is your value for d.

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