Base=30cm
Heights=20cm
Find the X?

Check the picture below.

The sum of first 10 terms is 620.

Arithmetic Progression (AP) is a numerical series in which the difference between any two subsequent numbers is always the same.

Here a1= 8,a2 = 20,a3  = 32 and a4= 44

Find the difference between two terms

a2 - a1 = 20 - 8 = 12

a3 - a2 = 32 - 20 = 12

a4 - a3 = 44 - 32 = 12 sum of n terms is = n/2[2a1 + (n-1)d]

For the given sequence we have n = 10, a1= 8 and d = 12

substituting values of a1 and n in S = 10/2[2x8 + (10-1)x12]

S = 5[16+9x12]

S = 5[16+108]

S = 5[124]

S = 5x124

S = 620

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The volume of the cylinder is:

3.14 x 0.3^2 x 0.75 = 0.21 cubic meters.

Multiply the density of the kerosene by the volume of the cylinder:

0.21 x 815 = 17.85 kg.

Answer:

173

Step-by-step explanation:

Answer: 432 units²

Step-by-step explanation:

The figure is composed by two trapezoids.

The formula for calculate the area of a trapezoid is:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where "B" is the larger base, "b" is the smaller base and "h" is the height.

Let be [tex]A_f[/tex] the area of the figure, [tex]A_1[/tex] the area of the trapezoid on the left and [tex]A_2[/tex] the area of the trapezoid of the right. Then the area of the figure will be:

 [tex]A_f=A_1+A_2[/tex]

[tex]A_f=\frac{h_1}{2}(B_1+b_1)+\frac{h_2}{2}(B_2+b_2)[/tex]

Substituting values, you get:

[tex]A_f=\frac{16units}{2}(25units+4units)+\frac{10units}{2}(25units+15units)=432units^2[/tex]

Answer:

Area of given figure = 432 unit ²

Step-by-step explanation:

Points to remember

Area of trapezoid = h(a + b)/2

Where h - height  and a and b  are two parallel sides

To find the area of given figure

It is given two trapezoid

Area of 1st trapezoid

h = 16, a = 25 and b = 4

Area = h(a+ b)/2

 = 16(25 + 4)/2

 = 232 units ²

Area of 2nd trapezoid

h = 10, a = 25 and b = 15

Area = h(a+ b)/2

 = 10(25 + 15)/2

 = 200 units ²

Total area = 232 + 200 = 432 units²

Answer:

All positive integers and zero

A is correct

Step-by-step explanation:

A box of pencils costs $10

The total cost (c) as a function of the number of boxes (b) is expressed as

c = f(b) = 10b

The function, f(b) = 10b

b is independent variable and c is dependent variable.

For any function find domain using independent variable.

b represents number of boxes.

Number of boxes neither be negative nor decimal.

Possible value of b: {0,1,2,3,4,5,.......}

All positive integers and zero.

Domain: All positive integers and zero

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}\dfrac{1}{3}x+y=\dfrac{0}{3}&\text{multiply both sides by 3}\\\\\dfrac{1}{6}x+\dfrac{1}{5}y=\dfrac{9}{10}&\text{multiply both sides by 30}\end{array}\right\\[tex]\left\{\begin{array}{ccc}x+3y=0&\text{multiply both sides by (-2)}\\5x+6y=27\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-6y=0\\5x+6y=27\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=27\qquad\text{divide both sides by 3}\\.\qquad\boxed{x=9}\\\\\text{Put the value of x to the first equation:}\\\\9+3y=0\qquad\text{subtract 9 from both sides}\\3y=-9\qquad\text{divide both sides by 3}\\\boxed{y=-3}[/tex][/tex]

Answer:

A)13.3

Step-by-step explanation:

20² + y² = 24²

400 + y² = 576

y²  = 176

y=13.3

By Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.

According to Pythagoras theorem, the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Mathematically,

(Hypotenuse)² = (Base)² + (Height)² .

For the given triangle, length of hypotenuse is 24ft., height is 20ft and base is y ft.

Using Pythagoras theorem,

⇒ (24)² = y² + (20)²

⇒ y² = 24² - 20²

⇒ y² = 176

∴ y = √176 = 13.2665 ≈ 13.3 ft.

Thus, by Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.

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Answer: Option A

[tex]P = 5.3 + 0.09125t[/tex]

Step-by-step explanation:

Note that for the initial year, 1990, the population was 5.3 billion.

The exchange rate is 0.09125 billion per year. In other words, each year there are 0.09125 billion more people.

In year 2 there will be 0.09125 * 2 billion people

In year 3 there will be 0.09125 * 3 billion people

In year 4 there will be 0.09125 * 4 billion people

In year t there will be 0.09125 * t billion of people

So the equation that models the number of people that there will be as a function of time is:

[tex]P = P_0 + rt[/tex]

Where [tex]P_0[/tex] is the initial population

[tex]P_0 = 5.3[/tex] billion

r is the rate of increase

[tex]r = 0.09125[/tex] billion per year

finally the equation is:

[tex]P = 5.3 + 0.09125t[/tex]

The correct answer is option A.

#17: Domain: [−4,∞),{x|x≥−4}

Range: [−2,∞),{y|y≥−2}

#18 g(2)=4(2)+2

g(2)=10

f(10)=3(10)^2-2

f(10)=298

For this case we have:

Question 1:

We have the following functions:

[tex]f (x) = 2x-1\\g (x) = x ^ 2-2[/tex]

We must find (g_ {0} f) (x).

By definition of composition of fusions we have to:

[tex](g_ {0} f) (x) = g [f (x)]\\(g_ {0} f) (x) = g [2x-1]\\(g_ {0} f) (x) = (2x-1) ^ 2-2\\(g_ {0} f) (x) = 4x ^ 2-2 (2x) + 1-2\\(g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]

Answer:

[tex](g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]

Question 2:

For this case we have a function of the form[tex]y = f (x)[/tex], where: [tex]f (x) = \sqrt {x + 4} -2[/tex]

We must graph the given function.

By definition, the domain of the function will be given by the values for which the function is defined. The function is not defined when the root is negative, that is to say for values of "x" less than -4. Then, the domain is:

[-4, ∞)

For its part, the range is the set of values that correspond to the domain. When replacing the values from -4 to infinity we have the following range:

[-2, ∞)

Answer:

See attached image

Domain: [-4, ∞)

Range: [-2, ∞)

Question 3:

For this case we have the following functions:

[tex]f (x) = 3x ^ 2-2\\g (x) = 4x + 2[/tex]

We must find, (f + g) (x):

By definition, we have to:

[tex](f + g) (x) = f (x) + g (x)\\(f + g) (x) = 3x ^ 2-2 + (4x + 2)\\(f + g) (x) = 3x ^ 2-2 + 4x + 2\\(f + g) (x) = 3x ^ 2 + 4x[/tex]

Now, we must find [tex](f + g) (2):[/tex]

[tex](f + g) (2) = 3 (2) ^ 2 + 4 (2)\\(f + g) (2) = 3 (4) +4 (2)\\(f + g) (2) = 12 + 8\\(f + g) (2) = 20[/tex]

Answer:

[tex](f + g) (2) = 20[/tex]

The answer is:

The function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0).

To find where the function is greater or equal to 0, we need to look (using the graph) where the function is above the x-axis

So, we can see that the function is above the x-axis from the point (-3,6)  to the point (4,0), for these points, the function is greater or equal to 0.

Hence, the function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0), or the function is greater or equal to 0,  from -3 to 4 (x-axis values or input).

We have that:

[tex]f(-3)=6\\6\geq 0\\\\f(-2)=0\\0=0\\\\f(0)=6\\6\geq 0\\\\f(4)=0\\0=0[/tex]

Have a nice day!

Answer:-250

Step-by-step explanation:

Answer:

The coefficients would be 4 and/or 3.

Step-by-step explanation:

The coefficient is always the number before the variable.

Answer:

a = 4, b = 3, and c = -3

Step-by-step explanation:

A quadratic equation of a variable is an equation that has the general form of:

[tex]ax^{2}+bx+c=0[/tex], [tex]a\neq 0[/tex]

Where x is the variable, and a, b and c constants; a is the quadratic coefficient (other than 0), b the linear coefficient and c is the independent term. This polynomial can be interpreted by means of the graph of a quadratic function, that is, by a parabola. This graphical representation is useful, because the abscissas of the intersections or point of tangency of this graph, in the case of existing, with the X axis are the real roots of the equation. If the parabola does not cut the X axis the roots are complex numbers, they correspond to a negative discriminant.

So, the coefficients are  a = 4, b = 3, and c = -3

Answer:

This is frankly impossible.

Step-by-step explanation:

What you have given me are three x-intercepts. And it is impossible for a quadratic function to have more than two roots. However, if this was an cubic function, we could multiply (x+5)(x-1)(x-4) which results in the equation which simplifies into x^3 -21x + 20. However, this is a cubic function, not a quadratic function, so something must be wrong with this problem all together.

For the equation to work, you have to have the same number on both sides of the equal sign

so to find ?, you can do:

13 - 2 = 12 - ?       Simplify

11 = 12 - ?       Subtract 12 on both sides

-1 = - ?     Multiply -1 on both sides

1 = ?

To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.

To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.

In the equation 13-2=12-x, we need to find the missing number x.

We can solve this equation by subtracting the known numbers on both sides.

Using the concept of simple mathematics, we found the subtraction of the given number.

So the missing number in the equation 13-2=12-x is 11.

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Answer:

There are 50 multiples of 8 between 100 and 500

Step-by-step explanation:

1. We need to find out the multiple of 8 closest and higher than 100.

......80, 88, 96, 104, 112, 120..... It's 104

2. We need to find out the multiple of 8 closest and lower than 500.

....480, 488, 496, 504, 512, 520......It's 496

3. Now, we use 104 and 496, this way:

(496 - 104)/8 + 1 =

392/8 + 1 =

49 + 1 = 50

There are 50 multiples of 8 between 100 and 500

Answer:

50

Step-by-step explanation:

The smallest multiple of 8 in this range is 13 ∙ 8 = 104, and the largest is 62 ∙ 8 = 496. The number of multiples of 8 in this range is the same as the number of numbers in the list

13, 14, 15, ...,60, 61, 62.

To count these, we subtract 12 from each, obtaining the new list

1, 2, 3, ..., 48, 49, 50,

which clearly contains 50 integers. There is one number in the original list for each number in the revised list, so the original list has 50 numbers in it, and there are 50 multiples of 8 between 100 and 500.

Answer:

[tex]\boxed{\text{160 ft}}[/tex]

Step-by-step explanation:

The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).

The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC  of the right triangle ABC.

sin 30 = 80/AC

AC  = 80/sin30 = 80/0.5 = 160 ft

The distance is [tex]\boxed{\textbf{160 ft}}[/tex]

Answer:

122

Step-by-step explanation:

The average of her two scores is calculated by the sum of her two scores divided by 2.

[tex]\boxed{\text{Average}=\frac{\text{sum of data}}{\text{number of data sets}} }[/tex]

Total score= 116(2)

Total score= 232

Total score= score of 1st game +score of 2nd game

Substituting value of first score and total score:

110 +score of 2nd game= 232

Subtract 110 from both sides:

score of 2nd game

= 232 -110

= 122

Additional:

To learn more about average, do check out the following!

Answer: $450,000

Step-by-step explanation:

Answer: $450,000

Step-by-step explanation:

We know that Jerome's earnings were from $150,000

And we know that this was 1/3 of the company's overall earnings.

Then let's call "x" to the company's general earnings

So a third multiplied by x must equal Jerome's earnings

[tex]\frac{1}{3}x=150,000[/tex]

Now we solve the equation for the variable x

[tex]x=150,000*3\\\\x= \$450,000[/tex]

Finally, the general earnings of the company were $450,000

I believe we would need some more information to help you answer

Answer:

ATP is an unstable molecule

Explanation:

Recall that ATP and ADP are too unstable to serve as long-term energy storage units. In contrast, glucose has a stable molecular structure, so it stores energy more efficiently than ATP.

#pennfosternotes

See page Biology (v2): Lesson 2: Page 65 in Biology_Lesson 2.pdf

Thanks so much! I hope this helps! =)

The answer is:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.

So, let be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

[tex]x_{FirstCar}=x_o+v*t[/tex]

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]

Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles,  so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]

Then, since we know that they covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we  have:

[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]

Writing the equation, we have:

[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]

We have that the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]

Hence, we have that:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

Have a nice day!

Answer:

55 miles per hour and 41 miles per hour.

Step-by-step explanation:

Enjoy...It is correct because RSM told me so.

Answer:

Jasmine ran last week 37.2 miles

Step-by-step explanation:

Let

x ----> number of miles Rob ran last week

y ----> number of miles Jasmine ran last week

we know that

x=y-27.2 ----> equation A

x=10 ----> equation B

Substitute equation B in equation A and solve for y

10=y-27.2

y=10+27.2

y=37.2 miles

Answer: d

Step-by-step explanation:

Answer is..

ab= 18

Explanation..

a + b = 11...---> a= 11-b

a -b = 7

11 - b - b = 7

11 - 2b = 7

2b = 18

b = 9

and a = 11 - 7

a = 2

So

ab = 2 * 9 =18

Answer:

3x² - 9x + 5

Step-by-step explanation:

Given

(5x² - 3x + 4) - (2x² + 6x - 1)

Distribute the first parenthesis by 1 and the second by - 1

= 5x² - 3x + 4 - 2x² - 6x + 1 ← collect like terms

= (5x² - 2x²) + (- 3x - 6x) + (4 + 1)

= 3x² - 9x + 5

Add by positive 3 for each of the numbers

-6+3=-3

-3+3=0

0+3= 3

3+3= 6

Answer is 6

ANSWER

The next term is 6.

EXPLANATION

The given arithmetic sequence is -6,-3,0,3,

There is a constant difference of 3.

That is,

-3--6=-3+6=3

This means that, we need to add 3 to the previous terms to get the subsequent terms.

To get the next term after 3, we add 3 to obtain 3+3=6

Therefore the next term of the sequence is 6.

Answer:

k = 25

Step-by-step explanation:

Step 1: Isolate k by adding 2 on both sides.

1/5k = 5

Step 2: Simplify by multiplying 5 on both sides.

k = 25

I believe the answer is B

Final answer:

The slope of the line containing the points (4,8) and (9,8) is 0, indicating that it is a horizontal line. The correct answer is B. Slope = 0; horizontal line.

Explanation:

The slope of a line is calculated by taking the difference in the y-values of two points on the line (rise) and dividing by the difference in the x-values (run). Using the points (4,8) and (9,8), we can calculate the slope as follows:

Slope (m) = rise / run = 0 / 5 = 0.

Since there is no change in the y-value as we move from one point to the other, the line is horizontal. Thus, the line has a slope of 0. The correct answer to the student's question is B. Slope = 0; horizontal line.

Answer:

y= (.37)x + 3

Step-by-step explanation:

1. Best thing to use would be y=mx + b.

2. Flat fee is $3 so that is your b.

3. Every additional message is $0.37, that is your slope(m)

4. That is your answer, x represents the number of text messages

Answer:

The monthly cost for x messages is (3 + 0.37x)$.

Step-by-step explanation:

We are given the following information in the question:

Monthly cost for text message = $3 per month

Cost of each text message = $0.37

Let x be the number of total text messages.

Monthly cost for x messages =

Formula:

[tex]\text{Monthly charges} + (\text{Text messages}\times \text{Cost of each message})\\\text{Putting the values, we get}\\= 3 + (0.37\times x)\\=3 + 0.37x[/tex]

Hence, the monthly cost for x messages is (3 + 0.37x)$.

Answer:

$432.00

Step-by-step explanation:

$12.00x36= $432.00