What is the area of this trapezoid

Geometry

P=2l+2s

Plugin both numbers.

P=24+38

P=62

Answer:

[tex]11, 13, 15[/tex]

B) 6x + 16 = 82

Note: I just kept my wrong approach.

Step-by-step explanation:

Let first define an odd integer.

Considering [tex]x\in\mathbb{Z}: 2k+1[/tex], [tex]x[/tex] is an odd integer.

Now, three consecutive odd integers are [tex]a_1 = 2k+1[/tex] , [tex]a_2 = 2k+3[/tex] and [tex]a_3 = 2k+5[/tex]

The sum of the​ first, two times the second and three times the third can be written as

[tex]a_1 + 2a_2 + 3a_3 = 2k+1 + 2(2k+3)+3(2k+5)[/tex]

Expanding and simplifying

[tex]2k+1 + 2(2k+3)+3(2k+5) = 2k+1 +4k+6+6k+15 = 12k+22[/tex]

This is what I have done initially, but considering [tex]x[/tex] to be an odd integer, three consecutive integers can be written as

[tex]x, x+2, x+4[/tex] such that [tex]x\in\mathbb{Z}: 2k+1[/tex]

Therefore,

[tex]x+2(x+2)+3(x+4)=82 \implies x+2x+4+3x+12 = 82 \implies 6x+16 = 82[/tex]

and [tex]6x+16 = 82 \implies 6x = 66 \implies x = 11[/tex]

The three consecutive odd integers such that the sum of the​ first, two times the second and three times the third is 82 are [tex]11, 13, 15[/tex]

Answer:

12 units²

Step-by-step explanation:

A(triangle) = 1/2(2)(2) = 2 units²

A(triangle) = 1/2(2)(6) = 6 units²

A(Square) = 2(2) = 4 units²

A(Shape) = 2 + 6 + 4 = 12 units²

Answer:

r≈4.5 ft

Step-by-step explanation:

r≈4.5 ft

\text{Volume of a Sphere:}

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

V=

3

4

​

πr

3

384=

384=

\,\,\left(\frac{4}{3}\pi\right) r^3

(

3

4

​

π)r

3

384=

384=

\,\,(4.1887902)r^3

(4.1887902)r

3

Evaluate 4/3pi in calc

\frac{384}{4.1887902}=

4.1887902

384

​

=

\,\,\frac{(4.1887902)r^3}{4.1887902}

4.1887902

(4.1887902)r

3

​

Evaluate \frac{4}{3}\pi

3

4

​

π in calc

91.6732472=

91.6732472=

\,\,r^3

r

3

\sqrt[3]{91.6732472}=

3

91.6732472

​

=

\,\,\sqrt[3]{r^3}

3

r

3

​

Cube root both sides

4.5090066=

4.5090066=

\,\,r

r

\text{Final Answer:}

Final Answer:

r\approx 4.5\text{ ft}

r≈4.5 ft

Round to nearest tenth

The radius of the sphere is approximately 4.2 feet.

To find the volume of a specific sphere, we need to know its radius. Once we have the radius, we can plug it into the formula and calculate the volume.

The formula for the volume of a sphere is:

V = (4/3) x π x r^3

where V is the volume of the sphere, r is its radius, and π is a mathematical constant approximately equal to 3.14.

We are given the volume of the sphere, so we can plug it into the formula and solve for the radius:

384 = (4/3)  x π  x r^3

Dividing both sides by (4/3) x π, we get:

r³ = 384 / ((4/3) x π)

r³ = 72.825

Taking the cube root of both sides, we get:

r ≈ 4.243

The radius of the sphere is approximately 4.2 feet.

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Answer:

1.) 113 degrees and 2.) 67 degrees

Step-by-step explanation:

(x + 33) + (x - 13) = 180

Add like terms:

2x + 20 = 180

2x = 160

x = 80

x + 33 =

80 + 33 =

113 =

x - 13 =

80 - 13 =

67 =

Answer: 7m⁴n²

Step-by-step explanation:

Find the GCF of 21m⁵n² and 28m⁴n².

Find the prime factors of each term in order to find the greatest common factor (GCF).

21m⁵n² = 7 · 3 · m · m · m · m · m · n · n

28m⁴n² = 7 · 2 · 2 · m · m · m · m · n · n

The product of these common prime factors will be  the Greatest Common Factor: 7 · m · m · m · m · n · n = 7m⁴n²

Answer:

$38,025.04

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 8.4/100

r = 0.084 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 1,200.00(1 + 0.084/2)(2)(42)

A = 1,200.00(1 + 0.042)(84)

A = $38,025.04

Answer:

Vertical

Step-by-step explanation:

/_

Answer:

-3(6/8+9/8)+4 2/5

Step-by-step explanation:

You convert decimal, you find common denominator, calculate sum of distance, rewrite, write as fraction, it is long tiresome process.

Answer:48.013

Step-by-step explanation: just found it

9514 1404 393

Answer:

  -9

Step-by-step explanation:

You are given a point and a slope, so you can write the equation of the line in point-slope form:

  y -k = m(x -h) . . . . . line of slope m through point (h, k)

  y -7 = 4(x +5) . . . . using the given point

Putting in the x- and y-values of the other point, we have ...

  -9 -7 = 4(w +5)

  -4 = w +5 . . . . . . . . . divide by 4

  -9 = w . . . . . . . . . . subtract 5

The value of w is -9.

Answer:

(8,6)

Step-by-step explanation:

See image below:)

FYI you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free:)

Answer:

144 un²

Step-by-step explanation:

Front Parallelogram = 5 x 11 = 55

Two triangles = 3 x 4 = 12

Back Parallelogram = 3 x 11 = 33

Bottom rectangle = 4 x 11 = 44

Total =

55 + 12 + 33 + 44 = 144

units = un²

144 un²

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

There's is a 25% chance on having all 6 births be girls. There is a 50-50 chance of a boy nor a girl. However, it is possible.

The probability of having 6 ​girls will be 1/64.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

In a family with 6 ​children, excluding multiple​ births.

Then the probability of having 6 ​girls will be

Leaving out the third gender, let's suppose that there is an equal chance of having a girl or a boy.

Any child can be either a boy or a girl, with each having equal probability of = 1/2

Each of these blank spaces can be filled in 2 ways : B and G (denoting 'B' and 'G' respectively)

Probability of first blank being a ''G' is = 1/2

and second blanks too being a “G” is = 1/2

Thus, probability of each blank individually being a “G” = 1/2

Thus, probability of all being a “G” = (1/2) (1/2)  (1/2) (1/2) (1/2)* (1/2) = (1/2)6 = 1/64

Thus, probability of 6 children being all 6 girls = 1/64

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Answer:

-60

Step-by-step explanation:

-42+3*-6

-42-18

-60

Answer:

34 gallons

Step-by-step explanation:

Water in tank = starting amount - rate * time

water in tank   = 50 - 2 * time

Let the time = 8 minutes

water in tank   = 50 - 2 * 8

                        = 50 - 16

                        = 34

Answer:

34 gallons still remain after 8 minutes.

Step-by-step explanation:

Variable x = gallons of water after 8 mins

2 gallons = 1 min

x gallons = 8 mins

Set up an equation:

2/1 = x/8

Cross multiply:

2 × 8 = 1 × x

16 = x

16 gallons of water are drained after 8 minutes.

Find the difference:

50 - 16 = 34

34 gallons still remain after 8 minutes.

9514 1404 393

Answer:

  A)  B. 18-6

  B)  20÷4

  C)  20

Step-by-step explanation:

Part A

The order of operations tells you that the first step is to evaluate any expressions in parentheses. Here, that means you first evaluate (18 -6).

__

Part B

After parentheses have been removed, the next step is to perform multiplication and division. Here, there is only one term involving division, so you divide 20 by 4 as your second step.

__

Part C

After you have done parts A and B, your expression is ...

  3 + 12 + 5

The value of this sum is 20.

Answer:

The answer is "300".

Step-by-step explanation:

Please find the complete solution in the attached file.

Answer:300

Step-by-step explanation:

Answer:

0.48

0.52

No

Yes

Step-by-step explanation:

Result of experiment :

Point up = 48

Point down = 52

Total number of trials = 100

Recall :

Experimental probability = number of outcomes / number of trials

1.)

P(Landing point up) = 48 / 100 = 0.48

2.)

P(Landing point down) = 52 / 100 = 0.52

3.)

The same result will not occur has the outcomes of trials aren't fixed.

4.) Yes, nearly the same result could occur on the second trial, as the number of possible outcubes are just 2 and the number if trials is high.

Answer:

15014.57

Step-by-step explanation:

effective rate: .05/12= .004166667

[tex]450*\frac{1-(1+.004166667)^{-36}}{.004166667}=15014.5655[/tex]

Step-by-step explanation:

15014.57

Step-by-step explanation:

effective rate: .05/12= .004166667

450*\frac{1-(1+.004166667)^{-36}}{.004166667}=15014.5655450∗

.004166667

1−(1+.004166667)

−36

=15014.5655

Answer:

b=-18

Step-by-step explanation:

If a line that passes through the point [tex]P(x_o,y_o)[/tex]and it has slope [tex]m[/tex], the equation of the line is:

[tex]y-y_o=m(x-x_o)~=>y=mx+y_o-mx_o~=>b=y_o-mx_o\\\\b=-6-4(3)=-18[/tex]

Answer:

-18

Step-by-step explanation:

Answer:

33.1

Step-by-step explanation:

cos(65)=14/x

x=33.1

Answer:

Step-by-step explanation:

A.-5+(n-1)*2 and n belong to 1 to ponitive infinity

Answer:

y= -1/3(x) + 8

Step-by-step explanation:

slope of the 1st line = 3

slope of the line perpendicular to the first is its opposite reciprocal, so

slope of the 2nd line = -1/3

now we have a point and the slope of the perpendicular line, so we use the point slope formula to get:

y-7=-1/3(x-3)

y= -1/3(x) + 1 + 7

y= -1/3(x) + 8

Answer:

X = -6 - 3y

Y = -1

Step-by-step explanation: Solve for X first using basic algebra. Plug in X vaalue to original equation and solve. -6 - 3y + 3y = -6. Solve by adding 6 to both sides of the equation and dividing -3y by 3y.

Answer:

[tex] D)\displaystyle \rm \frac{ \sqrt{3} }{12} cis \left( \frac{19\pi}{15} \right)[/tex]

Step-by-step explanation:

remember that

[tex] \displaystyle a \rm cis( \theta) \times b cis( \theta _{2}) = ab \cdot cis( \theta + \theta _{2})[/tex]

so we acquire:

[tex] \displaystyle \frac{ \sqrt{2} }{6} \rm cis \left( \frac{3\pi}{5} \right) \times \frac{ \sqrt{6} }{4} cis \left( \frac{2\pi}{3} \right) = \frac{ \sqrt{2} }{6} \times \frac{ \sqrt{6} }{4} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]

simplify the left hand side

[tex] \displaystyle \rm \frac{ \sqrt{12} }{24} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]

[tex] \displaystyle \rm \frac{2 \sqrt{3} }{24} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]

reduce fraction:

[tex] \displaystyle \rm \frac{ \sqrt{3} }{12} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]

simplify addition:

[tex] \displaystyle \rm \frac{ \sqrt{3} }{12} cis \left( \frac{19\pi}{15} \right)[/tex]

hence our answer is D

The value of x will be 2.067.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ eˣ = 7.9

Now,

Since, The expression is,

⇒ eˣ = 7.9

Take natural log both side, we get;

⇒ ln eˣ = ln 7.9

⇒ x = ln 79 - ln 10

⇒ x = 4.369 - 2.302

⇒ x = 2.067

Thus, The value of x = 2.067

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