use the following table to find the value of h'(3) if h(x)=g[f(x)]

Answer:

[tex]C=9.4\pi[/tex] meters

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex].

We start by substituting 4.7m for r in the second circumference formula.

[tex]C=2\pi r\\C=2\pi (4.7)\\C=9.4\pi [/tex]. We input this value of r into the area formula.

Answer:

its C.

Step-by-step explanation:

Answer:

F(x)=4-x^2

Step-by-step explanation:

I am assuming that x=3 and y=-5

Put in x =3

F(3)=4-3^2 = 4-9  =-5    Yes

F(3)=3-5   = -2  No

F(3)=-3+2 = -1  No  

F(3)=3+8=11  No

Answer:

(-6, 24) and (2, -8)

(-6, 24) and (2, -8) is the answer.

There are three strategies used to resolve structures of equations: graphing, substitution, and elimination. To solve a gadget via graphing, you honestly graph the given equations and locate the factor(s) in which they all intersect. The coordinate of this point will provide you with the values of the variables that you are fixing.

To remedy a machine of linear equations without graphing, you may use the substitution technique. This method works by way of solving one of the linear equations for one of the variables, then substituting this price for the same variable in the different linear equation and solving for the other variable.

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Answer:

9(m+H) = a

Step-by-step explanation:

m=a/9-H

The first step is to add H to each side.

m+H = a/9 -H+H

m+H = a/9

Now multiply both side by 9

9(m+H) = a/9*9

9(m+H) = a

Answer:

x<44

Step-by-step explanation:

Answer:

x<-28

Step-by-step explanation:

Answer:

Because -3-/8 itself is an irrational number. No matter the operation it wil always be irrational

Step-by-step explanation:

Answer:

£72

Step-by-step explanation:

Firstly, if half of 96 coins are £1 coins then:

96/2 * 1 = value of half the coins = £48

Now, we simply need to multiply 96/2 by 0.5 to find the value of these coins:

48 * 0.5 = 24

Now we can add the two:

48 + 24 = 72

So the value of the 96 coins are £72.

Answer:

14 pieces

Step-by-step explanation:

We will divide 6 m into 3/7 m pieces

6 ÷ 3/7

Use copy dot flip

6 * 7/3 =

42/3

14

She will have 14 pieces

Answer:

A: 15.23 ft, B: 7.75 ft

Step-by-step explanation:

A:

√(14² + 6²)

√(196 + 36)

√232 = 15.23

B:

√(16² - 14²)

√(256 - 196)

√60 = 7.75

NOTES:

Since Q is a right angle then PQ and QR are the legs and PR is the hypotenuse.  Use the Pythagorean Theorem to solve.

********************************************************************************

Part A Answer: PR = 15.23

Step-by-step explanation:

PQ² + QR² = PR²

6² + 14² = PR²

36 + 196 = PR²

    232    = PR²

     15.23 = PR

************************************************************************************

Part B Answer: PR = 7.75

Step-by-step explanation:

PQ² + QR² = PR²

PQ² + 14² = 16²

PQ² + 196 = 256

PQ² = 60

PQ = 7.75

Answer:

1A/3 OR 1/3A

Step-by-step explanation:

Substitute y = 15x to the equation y = 25 + 12.5x:

15x = 25 + 12.5x     subtract 12.5x from both sides

2.5x = 25    divide both sides by 2.5

x = 10

Substitute the value of x to the equation y = 15x:

y = (15)(10)

y = 150

Answer:

The correct answers would be

vertex A' (-8,4)

vertex B' (-12,12)

vertex C' (-4,12)

Step-by-step explanation:

I'm not 100% sure but I took this test a couple days ago and didn't do terribly:).

Start by distributing:

-12(x+5) = (-12 * x) + (-12 * 5) = -12x - 60

144 = -12x - 60

Add 60 to both sides to start isolating your variable:

204 = -12x

Solve for x by dividing both sides by -12:

x = -17

Step-by-step explanation:

multiply -12 with x and 5, after you get the answer. subtract 60 on the left and right, after getting 84 divide it by -12 and the final answer will be -7

Answer:

The distance from A to C is 12600 ft

Step-by-step explanation:

We can use similar triangles to help us solve the problem.

5600 ft          AC

-------------  = --------------

5200 ft          5200 + 6500

5600 ft          AC

-------------  = --------------

5200 ft          11700

We can solve using cross products

11700* 5600 = AC *5200

65520000=5200 AC

Divide each side 5200

65520000/5200 = AC

12600 =AC

Answer:

12600

Step-by-step explanation:

Final answer:

To determine 'a' and 'd' for tn = a + (n-1)x, substitute the values of 'n' and 't' into the equations and solve the system of equations.

Explanation:

To determine 'a' and 'd' for tn = a + (n-1)x, we need to find the values of 'a' and 'd' that satisfy both t7 = 3 + 5x and t11 = 3 + 23x.

Step 1: Set up two equations

t7 = 3 + 5x

t11 = 3 + 23x

Step 2: Use the formula tn = a + (n-1)x to substitute the values of 'n' and 't' in the equations.

a + 6d = 3 + 5x (equation 1)

a + 10d = 3 + 23x (equation 2)

Step 3: Solve the system of equations.

Subtract equation 1 from equation 2: (a + 10d) - (a + 6d) = (3 + 23x) - (3 + 5x)

Cancel out the 'a' terms and simplify the 'd' and 'x' terms: 4d = 18x

Divide both sides by 18: d = 4.5x

Substitute the value of 'd' in equation 1 to solve for 'a': a + 6(4.5x) = 3 + 5x

Expand and simplify the equation: a + 27x = 3 + 5x

Subtract 5x from both sides: a + 22x = 3

Subtract 22x from both sides: a = 3 - 22x

So, the values of 'a' and 'd' are a = 3 - 22x and d = 4.5x.

The Mathematics problem involves adding areas in different units and converting them appropriately. After conversion and addition, the correct answer from the options provided is 1 acre, 7 square feet, and 119 square inches: (a) 1a 7 sqft 119 sqin.

The subject of this question is Mathematics, specifically dealing with area measurements in different units and their conversions. The student needs to solve an addition problem that involves square yards, square feet, and square inches. To solve this problem, we must first understand that there are 9 square feet in one square yard, and we use this knowledge to convert all measurements to the same unit before summing them up.

To answer the student's question, we must add the areas given in the problem:

First, we convert square yards to square feet using the conversion 1 sq yd = 9 sq ft:

4,839 sq yd = 4,839 × 9 sq ft = 43,551 sq ft

Now we add the square feet:

43,551 sq ft + 8 sq ft + 7 sq ft = 43,566 sq ft

Lastly, we add the square inches:

139 sq in + 124 sq in = 263 sq in

Since there are 144 square inches in one square foot, we must convert the excess square inches into square feet and square inches:

263 sq in = 1 sq ft (144 sq in) + 119 sq in

Adding the converted square inches to the total square feet:

43,566 sq ft + 1 sq ft = 43,567 sq ft 119 sq in

Next, we convert the total square feet to acres, understanding that 1 acre = 4,840 sq yd or approximately = 43,560 sq ft.

43,567 sq ft ÷ 43,560 sq ft per acre ≈ 1 acre 7 sq ft 119 sq in

Thus, the correct answer is (a) 1a 7 sqft 119 sqin.

Complete question is here:

Solve the following problem 4,839 sq yd 8 sq ft 139 sq in + 7 sq ft 124 sq in Select one of four

a)1a 7 sqft 119 sqin

b)4a 10 sqft 145 sqin

c)3a B sqft 130 sqin

d)2a 9 sqft 150 sqin

The question asks for the addition of different area units, which requires unit conversion. Square yards are converted to square feet and then to square inches, ensuring all areas are in the same units before adding them together.

The question involves adding areas measured in different units (square yards, square feet, and square inches) and converting between these units. To perform the calculation correctly, we need to convert all areas to the same unit. One square yard is equivalent to 9 square feet, and one square foot is equivalent to 144 square inches. Thus, to add the areas given in the question, we should first convert the 8 sq. ft. 139 sq. in. to sq. in. by multiplying 8 by 144 and then adding 139. After that, we would need to convert this total area into square yards if required. For the second part, we convert 7 sq. ft. 124 sq. in. to square inches similarly. Once both areas are in square inches, they can be added together. Additionally, it's important to remember that there is no direct conversion between square inches and square yards, so a two-step conversion is needed via square feet.

Answer:

x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]

Step-by-step explanation:

We have

7x²=9+x

Subtracting x from both sides, we get

7x²-x=9+x-x

Cancelling out +x and -x from the right side, we get

7x²-x=9

Subtracting 9 from both sides, we get

7x²-x-9=9-9

Cancelling out 9 and -9 from the right side, we have

7x²-x-9 = 0

The above equation is in the form ax²+bx+c=0 where upon comparing we get a= 7 , b = -1 and c= -9

We can solve for x using the below quadratic formula:-

x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]

Upon solving we'll get two values for x, one positive an the other negative.

Answer:

Step-by-step explanation:

x^2 + 3x - 18 = 0

(x+6)(x-3)=0

x=-6 x=3

i had this on my book so i just wanted to help.

Final answer:

The quadratic equation x^2 + 3x - 18 = 0 can be solved using the quadratic formula, resulting in two solutions, x = 3 and x = -6.

Explanation:

To solve the quadratic equation x^2 + 3x - 18 = 0 using the quadratic formula, we must first identify the coefficients a, b, and c in the standard form ax2 + bx + c = 0. In our equation, a = 1, b = 3, and c = -18. Substituting these values into the quadratic formula gives us:

x = [-b ± √(b^2 - 4ac)] / (2a)

By substituting the values we have:

x = [-(3) ± √((3)^2 - 4(1)(-18))] / (2(1))

Which simplifies to:

x = [-3 ± √(9 + 72)] / 2

x = [-3 ± √(81)] / 2

x = [-3 ± 9] / 2

Therefore, we have two possible solutions for x:

x = (-3 + 9) / 2 = 3

x = (-3 - 9) / 2 = -6

So, the solutions to the equation x2 + 3x - 18 = 0 are x = 3 and x = -6.

Answer:

The Pythagorean theorem shows that one leg squared plus the other leg squared is equal to the hypotenuse squared

Step-by-step explanation:

Answer:

She has 11/20 yds left

Step-by-step explanation:

We take what she had and subtract what she gave away

9/10 - 7/20

We need to get a common denominator of 20

9/10 *2/2 - 7/20

18/20 - 7/20

11/20

She has 11/20 yds left

Answer:

Step-by-step explanation:

We are given that a shade of green is prepared using 2 cups of yellow and 3.5 cups of blue.

We want to make the same shade of green, but lesser quantity. We can assume a smaller value for either of the yellow or the blue colors, and find the corresponding value of the other to figure out the answer.

Let us assume that 1 cup of yellow is mixed with x cups of blue to prepare the same shade of the green. Now we can set up the ratios as shown below:

[tex]\frac{1}{x}=\frac{2}{3.5}\\2x=3.5\\x=1.75[/tex]

Therefore, 1 cup of yellow and 1.75 cups of blue color will also make the same shade of green

Among the given equations, only 'y = 6/13x' shows a proportional relationship because the ratio between x and y remains constant. The other two equations-'y = x + 2.3' and '7 - y = 2x' are not showing proportional relationships because the ratio between the variables doesn't remain constant.

A proportional relationship is one where the ratio between two variables remains constant. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.

a) The equation y = x + 2.3 is not a proportional relationship because it involves an added constant. If x is zero, y is not zero, thus it's not proportional.

b) The equation y = 6/13x is a proportional relationship, because there is a direct proportion between x and y. If x is multiplied by a certain factor, y will be multiplied by the same factor, thus maintaining the ratio.

c) The equation 7 - y = 2x rearranges to y = 7 - 2x, which is not a proportional relationship. Again, if x is zero, y is not zero, thus it's not proportional.

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Answer:

[tex]\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg][/tex]

General Formulas and Concepts:
Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                          [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                        [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:                                                                            [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                               [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle f(x) = (x + 8)^{3x}[/tex]

Step 2: Differentiate

∴ we have found the derivative of the given function.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Charlene, Mark, and Paul sold a combined total of 44 magazine subscriptions for their fundraiser.

In this problem, Charlene, Mark, and Paul collectively sold magazine subscriptions. We need to find the total number of subscriptions sold. We can do this using simple addition: Charlene sold 15 subscriptions, Mark sold 17 subscriptions, and Paul sold 12 subscriptions. Therefore, using s to represent total subscriptions, our equation would be: s = 15 (Charlene's sales) + 17 (Mark's sales) + 12 (Paul's sales). Summing the numbers, s = 44. Hence, they sold 44 subscriptions in total.

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By adding Janelle's spending to what she came home with and dividing by the hours worked, we find that she earned $8 per hour babysitting.

To find out how much Janelle made per hour babysitting, we need to add the money she spent at Walmart to the money she came home with.

This gives us the total amount she earned.

Since she spent $12 at Walmart and came home with $36, we add these two amounts together to get $48.

Janelle babysat for 6 hours, so to find out her hourly wage, we divide the total amount she earned ($48) by the number of hours she worked (6 hours).

= $48 / 6 hours = $8 per hour

Thus, Janelle earned $8 per hour for her babysitting.

Answer:

c

Step-by-step explanation:

Answer:

(A) 2x + 4y = –26

(D) y = 0.5x – 7

The equations satisfying the points  (0.5, –6.75) will be  2x + 4y = –26 and y = 0.5x – 7. The correct options are A and D.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given point is (0.5, –6.75). Check whether all the equations satisfy the point or not.

A) 2x + 4y = –26

2 x 0.5 + 4 x -6.75 = -26

1 - 27 = -26

-26 = -26

Satisfying

B) y = x – 7.5

-6.75 = 0.5 - 7.5

-6.75 ≠ -7

C) 2y = x + 13

2 x -6.75 = 0.5 + 13

-13.5 ≠ 13.5

y = 0.5x – 7

-6.75 = 0.5 x 0.5 -7

-6.75 = -6.

Satisfying.

Therefore, the equations satisfying the points  (0.5, –6.75) will be  2x + 4y = –26 and y = 0.5x – 7. The correct options are A and D.

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Answer:

He could build 30 houses.

Step-by-step explanation:

7 1/2 divided by 1/2 equals 30!

Answer: 30 houses can be built

Step-by-step explanation: