If
F(x) = f(xf(xf(x))),
where
f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5,
and
f '(5) = 6,
find
F '(1).

F '(1) =

The scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.

Now,

That means that 1 inch corresponds to 7ft +7ft= 14ft.

Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.

Answer: The scaled figure will fit in the billboard.

Answer:

  x = 8

Step-by-step explanation:

You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².

The area of a triangle is given by the formula ...

  A = 1/2bh

Then the area of this triangle is ...

  22.5 = 1/2(x -3)(x +1)

  45 = x² -2x -3

  48 = x(x -2) . . . . . . . add 3 and factor out x

We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.

__

Additional comment

x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.

Let the price of black and white brouchers be x

The price of color brochures be y.

A/q,

4x+4y=148.....(1)

4x+3y=125 .....(2)

The equation (1) becomes,

x+y=37

y=37-x.......(3)

Putting (3) in (2) we have,

4x+3(37-x)=125

4x+111-3x=125

x=14

Putting the value of x in (3) we have,

y=37-14=23

The price of black and white brouches is $14

The price of color brouchers is $23.

The total possible outcome for the experiment is 36.

The ossible outcomes for same number on each dice is 6.

So probability for the same number on dice is,

So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.

Answer:

Step-by-step explanation:

Answer: You can add 5. The question is asking you what can you do to make both sides equal 8. I am not a professional but I hope that helped.

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

The given system of equations:

x  +  2y  =  8              (Equation - 1)

-3x - 2y  =  12            (Equation - 2)

This can be written in matrix form as shown:

[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]

Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]

We can use cross multiplication,

= (-2)(1) - (-3)(2)

= -2 + 6

= 4 ≠ 0

So the system has a unique solution,

Then,

[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]

[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]

So, they can solve the X and Y values,

X = D1 / D

X = -40/4

X = -10

Y = D2 / D

Y = 36/4

Y = 9

Therefore,

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

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Step-by-step explanation:

Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.

How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?

..

please post full questions

The dilated polygon image is attached below under a dilation with a scale factor of 3 and center of dilation (0,0)​

In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.

Transformation is the movement of a point from one location to another. Transformations include rotation, reflection, translation, and dilation.

Dilation is the process of increasing or decreasing the size of a figure by a factor k. If a point A(x, y) is dilated about the origin by a factor k, the new point is A' (kx, ky).

Assume the polygon has vertices at A(0, 0), B(3, 3) and C. (-3, 3). If the polygon is dilated by a factor of three with the center of dilation at (0, 0), the new vertices are as follows:

A'(0,0), B'(1, 1) and C'(-1, 1)

Therefore, the polygon graph is attached in which the polygon is dilated by a factor of three with the center of dilation at (0, 0),

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Answer:

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

Step-by-step explanation:

ASA: Angle, Side, Angle

AAS: Angle, Angle, Side

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

I am going to use the drawer to show the differences:

Based on the slope formula for a line, the value of a is: a = -3.

If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:

Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.

The given line has the following:

(-10, 0) = (x1, y1)

(a, -6) = (x2, y2)

Slope (m) of the line = -6/7.

Plug in the values into the slope formula for a line:

(-6 - 0) / (a - (-10)) = -6/7

-6/(a + 10) = -6/7

Cross multiply and solve to find the value of a in the equation:

-6(a + 10) = -6(7)

Apply the distributive property

-6a - 60 = -42

Add 60 to both sides

-6a - 60 + 60 = -42 + 60 [addition property of equality]

-6a = 18

Divide both sides by -6

-6a/-6 = 18/-6 [division property of equality]

a = -3

Therefore, the value of a is -3.

The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).

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The original price for the desk is $980.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

Given:

Sale price = 343

price was 35% of the original price.

let the original price be x

35% of x = 343

35 / 100 * x = 343

x= 343 * 100/ 35

x=980

Hence, the original price of the desk was $980.

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The z-score of the given expression P(-a < z < a) = 0.4314 is; 0.55

We are told that P(-a < z < a) = 0.4314. Thus;

P(-a < z < a) = 0.4314 is represented by the area about mean. This means that; 0.4314/2 = 0.2157 is the area each on the left side and right side of mean.

Now, from online z-score calculator, we see that the z value corresponding to 0.2157 is 0.55.

Assume that ​z-scores are normally distributed with a mean of 0 and a standard deviation of 1, if P(-a < z < a) = 0.4314, then it means that the z score is 0.55.

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Complete question is;

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−a < z < a) = 0.4314, find d a. Round to two decimal places

The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.

A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.

It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.

The balance sheet is illustrated below:

Current Assets  

Accounts Receivable  26500

Cash    20500

Merchandise Inventory  26300

Total Current Assets  73300

Property, Plant and Equipment  

Land    10000

Total Property, Plant and Equipment 10000

Total Assets   83300

Current Liabilities    

Accounts Payable   12200

Long Term Liabilities  

Long-Term Notes Payable  17500

Stockholders' Equity  

Common Stock  30000  

Retained Earnings  23600  

Total                                 53600

Total Liabilties          83300

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Answer:

y = 1

The graph has no gradient and only intersects at the y-axis.

ive n

lan A

Plan B

Monday: 3 clients - Plan A

5 clients - Plan B

Total 10 hours

Tuesday

6 clients - Plan A

2 clients - Plan B

Total 10 hours

rocedure

Let's define a system of linear equations that represents the above problem.

A: Number of hours of workout in plan A

B: Number of hours of workout in plan B

The goal here is to solve

3A+5B=10 and

6A+2B=10 for the variables A and B.

The solutions to your equations are:

A = 5/4 hour

B = 5/4 hour

1. The value of the expression when q = 13 in q - 10 is 3.

2. The value of the expression when x = 4.2.

34.5x is 144.9

3. The interest will be $5.25.

It should be noted that an expression is simply used to show the relationship between the variables.

1. The expression when q = 13 in q - 10 will be:

= q - 10

= 13 - 10

= 3

2. The value in the expression when x = 4.2 will be:

= 34.5x

= 34.5 × 4.2

= 144.9

3. Principal = $70

Rate = 3%

Time = 2.5 years

Interest = PRT / 100

= (70 × 3 × 2.5) / 100

= $5.25

The simple interest would you earn in 2.5 years is $5.25.

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Answer:

x + 15 - 30

x -15

Step-by-step explanation:

Answer:

578.0 yd^2

Explanation:

The formula for finding the surface area of a cylinder is given as;

where A = surface area

pi = 3.14

r = radius of the base of the circle = diameter/2 = 8/2 = 4 yd

h = height = 19yd

Let's go ahead and substitute these values into our formula and solve for A;

7r³ + 11r²s  -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).

The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.

Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.

Let's review some of the crucial words used during expression simplification:

In an algebraic expression, a variable is a letter with an undetermined value.

We have been asked to simplify the expression

(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)

Let's simplify

⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)

⇒ 7r³ + 10r²s  −3rs² − 8s + r²s -6rs²

⇒ 7r³ + 11r²s  -9rs² - 8s³

Thus, 7r³ + 11r²s  -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).

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Using the law of Sines, the length of side AD, |AD|, is 7.44

From the question, we are to determine the length of side AD

From the given information, we have that

u = 17 and v = 17

Then,

ΔBCD is an isosceles triangle

∴ m ∠DBC = m ∠ BCD

m ∠DBC = x = 25°

∴ m ∠BCD = 25°

Also,

m ∠BCA = ∠y + m ∠BCD

m ∠BCA = 25° + 25°

m ∠BCA = 50°

Now, we will determine the measure of ∠CAD.

m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)

m ∠CAD + 25° + 50° = 180°

m ∠CAD = 180° - 25° - 50°

m ∠CAD = 105°

Now,

From law of Sines, we can write that

|AD| / sin DCA = |DC| / sin CAD

|AD| / sin y = u / sin CAD

|AD| / sin 25° = 17 / sin 105°

|AD| = (17 × sin 25°) / sin 105°

|AD| = 7.43795

|AD| ≈ 7.44

Thus,

Length AD is 7.44

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SOLUTION

Step1:

hence from the diagram above, the dimension of the rug is

Since we have area of the rug,

then we have

We now solve the equation above quadratically

Then we have

Solve using factor method we obtain

Equating each factor to zero we have

Since x can not be 28, the value of x is 1

The Dimension of the rug becomes

Hence the dimension of the rug is 32 ft by 22ft (22,32)

SOLUTION

f(x) = x + 3

Matching the given mathematical operation equations to the specified choices, gives;

A•B = B•A ; Commutative Property of Multiplication

A + B = B + A ; Commutative Property of Addition

(A•B)•C = A•(B•C); Associative Property of Multiplication

A•0 = 0; Multiplicative Property of 0

(A + B) + C = A + (B + C); Associative Property of Addition

A•1 = A; Multiplicative Identity

A + 0 = A; Additive Identity

The properties of mathematical operations includes; inverse, associative, distributive, associative and commutative properties

Commutative property in mathematics is one in which for a binary operation, the result of an operation remains unchanged when the order in which the operands appears in the expression is changed.

Therefore;

Commutative property of multiplication is therefore; A•B = B•A

Commutative property of addition is; A+B = B+A

Associative property relates with operations that have results which remains the same when the parentheses in the expressions are rearranged.

Therefore;

(A•B)•C = A•(B•C) represents the associative property of multiplication

The associative property of addition is represented by (A+B)+C = A+(B+C)

The multiplicative property of 0, which can be understood as the zero product property, states that the product of any number and 0 is 0

Therefore, the equation, A•0 = 0, represents the multiplicative property of 0

The multiplicative and additive identity states that an expression remains the same following the product of the expression with an identity element such as 1, or following the addition of the expression with an identity element such as 0

The multiplicative and additive identity are therefore represented by A•1 = A and A + 0 = A respectively

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Answer:

In order, the answers are d, b, c, a

Step-by-step explanation:

[tex] \frac{ {x}^{7} }{ {x}^{4} } = {x}^{3} [/tex]

[tex] {x}^{ - 3} = \frac{1}{ {x}^{3} } [/tex]

[tex] {x}^{0} = 1[/tex]

[tex] \frac{ {x}^{4} }{ {x}^{3} } = x[/tex]

The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true

The functions are given as

f(x) = c

Also, we have

f(-x) = c

In the above function definitions, we can see that

The functions f(x) and f(-x) have the same value

i.e. f(x) = f(-x) = c

This means that f(x) =f(-x)

By the symmetric property of an equation, the above can also be rewritten as

f(-x) = f(x)

Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true

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EXPLANATION:

Solution first(a) exercise part b:

All the internal angles of a right triangle must add up to 180, so to order the internal angles from least to greatest we must find the missing angle;

The exercise is as follows:

Now we must order them from lowest to highest, the order is as follows:

Answer:

400 < m< 430 kg

Step-by-step explanation:

the mass of horse is 429 kg

estimated to the nearest hundred is 400  kg

estimated to the nearest  tens is 430 kg

thus the value of m mass lies between 400 to 430

therefore

400 < m< 430 kg

The answer is 400 < m< 430 kg