What does B x h stand for?

The proof of  C(3)= C(6) is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

We have the function C(x) = 10 (1/x + x/ (x+3))

So, we have to prove that C(3)= C(6)

Then, C(3)= 10 (1/x + x/ (x+3))

= 10 (1/3 + 3/ (3+3))

= 10 (1/3 + 3/ 6)

= 10 (1/3 + 1/2)

= 10 (5/6)

= 50/6

= 25/3

and, C(6)= 10 (1/x + x/ (x+3))

= 10 (1/6 + 6/ (3+6))

= 10 (1/6 + 6/ 9)

= 10 (1/6 + 2/3)

= 10 (5/6)

= 50/6

= 25/3

Thus, C(3)= C(6).

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Based on the above, David must save $150 each month to cover the money left over for his first year of college.

To calculate the savings that David must make monthly for the next 5 years we must carry out the following procedure:

His uncle gave him $12,000 so we must subtract this value from the total he needs.

So he must save $9,000 in 5 years.

According to the above, he must save $1,800 per year, so each month he should save $150.

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Answer:

From the given diagram

m∠1 = 117° (Vertically opposite angles)

m∠2 = 117° (Corresponding angles)

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

divide 2 by y and 18 and the the 2divided by 2 cancel out. then divide 18 by 2 and you get y = 9

Answer:

14 weeks

Step-by-step explanation:

14 times 245= 3430+ 500=3930 (carrie)

14 times 230= 3220+ 710= 3930 (jose)

Answer:

A ≈ 346.36

Step-by-step explanation:

To find the answer, you must use the formula, A=πr²

Since only the diameter was provided, you need to divide it by 2 to find the radius. 21 divided by 2 equals 10.5, so that will be your radius.

Another formula that can be used while using only the diameter would be A= 1/4 π d²

Answer: 235,000,000

Step-by-step explanation:

Answer:

5 units

Step-by-step explanation:

if they are congruent that means that the corresponding sides have the same lenghts. in this case ad's corresponding side is bc, which is 5 units and so is ad respectively

Answer:

\(-4\)

Step-by-step explanation:

So we have the two functions:

\(h(x)=4x+5\text{ and } g(x)=3x+5\)

And we want to find:

\((h+g)(-2)\)

This is the same as:

\(h(-2)+g(-2)\)

Let's substitute them for their functions:

\(=(4(-2)+5)+(3(-2)+5)\)

Multiply:

\(=(-8+5)+(-6+5)\)

Add:

\(=-3-1\)

Subtract:

\(=-4\)

And we're done!

Answer:

4 miles

Step-by-step explanation:

30-18=12

12÷3=4

hope this helped :)

The value of the composite function (f o g)(3) is 1603

The functions are given as

f(x) = 3x² - 7x - 3

g(x) = -4x - 10

Next, calculate (f o g)(x) using

(f o g)(x) = f(g(x))

So, we have

(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3

Substitute 3 for x.

So, we have

(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3

Evaluate

(f o g)(3) = 1603

Hence, the value of the composite function (f o g)(3) is 1603

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answer:

they will never cross....

Answer:

5 hope this helps

<3

Step-by-step explanation:

ok so this will turn into an algebraic equation, x4-7=13

these are hard because you have to figure out the order first then you just solve like a normal problem..

x4-7=13

x4=20

x=5

Answer:

5

Step-by-step explanation:

x-7•4=13

13+7=20

20/4=5

5•4-7=13

Answer:

303.75

Step-by-step explanation:

135/20=6.75

6.75•45= 303.75

Solution:

Given that;

The line y=−2x+7 together with the coordinate axes forms a triangle.

Using a graphing tool, the graph of the line is shown below

From the graph above,

The height, h, of the triangle formed is 7 units

The base, b, of the triangle formed is 3.5 units

To find the area, A, of a triangle, the formula is

Substitute the values of b and h into the formula above

Hence, area, A, of the triangle is 12.25 square units

\(P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} \)

\(P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407\)

\(P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} \)≈0.999787

Answer:

Step-by-step explanation:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

5.5pi = angle/360 * pi * 9

5.5 = angle/360 * 9

angle = (5.5 * 360)/9 = 40 * 5.5 = 220

Step-by-step explanation:

Range -6

Range is a higherd number

10-4=6

Answer:

In a rectangle ABCD of 3 mx 4 m, starting from A and D, along the sides AB and DC after every 30 cm, a square shape of 10 cm is taken out as shown below. What will be the perimeter (in cm)

Step-by-step explanation:

12 CM And 300 CM is the answer

a. Assume a is even, so a = 2k for some integer k. Now let a and b be integers such that a divides b and a + b is odd.

Since a divides b, b = an for integer n, and in turn b = 2nk, which means b is even and hence a + b is also even. But this contradicts our initial assumption, so a must be odd.

b. Let n be even, so that n = 2k for some integer k. Then

n² = (2k)² = 4k²

so that n² ≡ 0 (mod 4).

Now let n be odd, so n = 2k + 1 for integer k. Then

n² = (2k + 1)² = 4k² + 4k + 1

so that n² ≡ 1 (mod 4).

Therefore n² is never congruent to 2 (mod 4).

Answer:

110

Explanation:

First move the decimal point over to the left twice.

.375

Then multiply 80 by .375 like this :

.375 x 80 = 30

Lastly, add 30 to 80 and put the dollar sign.

$110

To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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Step-by-step explanation:

Scatter plot is the correct answer

Answer:

d -3

Step-by-step explanation:

Answer:

5356$

Step-by-step explanation:

206*26=5356

There are 21 different city combinations possible for Peter's summer traveling.

To determine the number of different city combinations possible for Peter's summer traveling, we need to calculate the number of combinations of choosing 5 cities out of the 7 available cities.

Since the order in which he visits the cities does not matter, we are dealing with combinations rather than permutations.

The formula to calculate the number of combinations is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k) or (nCk).

In this case, we have 7 cities to choose from, and Peter will visit 5 cities. Thus, we can calculate the number of city combinations as follows:

C(7, 5) = 7! / (5! * (7-5)!)

= 7! / (5! * 2!)

= (7 * 6 * 5!) / (5! * 2)

= (7 * 6) / 2

= 42 / 2

= 21

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Answer:

L = 131 feet

Step-by-step explanation:

Right Triangles

The cable, the ground, and the radio tower form a right triangle with an angle of 90° located where the ground and the tower meet.

The cable is the hypotenuse of the triangle and the angle of 50° is opposite to the height of the radio tower.

To find the hypotenuse L we use the sine ratio:

\(\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}\)

\(\displaystyle \sin 50^\circ=\frac{100}{L}\)

Solving for L:

\(\displaystyle L=\frac{100}{\sin 50^\circ}\)

Calculating;

L = 131 feet

f(x) = x^4 - 5x^3 + x^2 + 21x - 18

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

Explanation:

The root x = -2 means x+2 is a factor. This is because we add 2 to both sides of x = -2 to get x+2 = 0.

Similarly, x = 3 leads to x-3 being another factor. It's a double root so we really have two copies of (x-3)

The last root is x = 1 which gives the factor x-1.

The four factors are: (x+2)(x-3)(x-3)(x-1)

Let's use the FOIL rule to expand out the first two factors

(x+2)(x-3) = x^2-3x+2x-6 = x^2-x-6

Do the same for the last two factors

(x-3)(x-1) = x^2-1x-3x+3 = x^2-4x+3

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

So far we have:

(x+2)(x-3) = x^2-x-6

(x-3)(x-1) = x^2-4x+3

which leads to  

(x+2)(x-3)(x-3)(x-1) = (x^2-x-6)(x^2-4x+3)

From here I'll use the box method to multiply these trinomials. Check out the diagram below. Each inner cell is the result of multiplying the headers. Example: x^2 times x^2 = x^4 in the upper left corner.

I've color-coded the inner cells to show the like terms. Add up those like terms:

Therefore we end up with

(x^2-x-6)(x^2-4x+3) = x^4 - 5x^3 + x^2 + 21x - 18 which is choice B

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

To verify this answer, plug in x = 0 and you should get y = -18 to show that we have the correct y intercept. If we tried this with choice A, then we'd get y = 18 which helps eliminate choice A.

Furthermore, plug in x = -2 into choice B and you should get y = 0 as an output. The same applies to x = 3 and x = 1. This confirms that they are roots or x intercepts of the polynomial.

Another way to verify the answer is to use something like WolframAlpha to type in (x+2)(x-3)(x-3)(x-1). Under the "expanded form" subsection, it says x^4 - 5x^3 + x^2 + 21x - 18