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The unit of the rate of change is (b) dollars per month

From the question, we have the following parameters that can be used in our computation:

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

substitute the known values in the above equation, so, we have the following representation

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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Answer:

Step-by-step explanation:

The student makes a mistake between the Given and Step 1.

The true statement is

Step 2. Between Steps 1 and 2, the student makes a mistake.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x+1 /√3=3

Step 1: (x+1/√3)3=(3)3

Step 2: x+1=9

Step 3: x=8

From the above steps the student made the mistake in step 1.

This is because

(x+1/√3)3

=  (x+1)√3, the term of √3 cannot be vanished easily.

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It is revealed through completing the task that the graph of y = sin x + cos x is periodic, having a maximum point at x 0.94 and y 2.24. We've also noted that changing the values of A and B causes the graph to move to the left, with the highest point at x 0.44 and y 2.84. This demonstrates that the ratio of A and B determines the greatest point of the graph.

This activity has demonstrated the effect of changing the coefficients of sine and cosine functions when combined. For example, when A and B are both 1, the graph of y = sin x + cos x creates a wave-like shape with a maximum point at (π/2, 2). When A is increased to 2 and B is kept at 1, the maximum point moves to the right and increases in y-value to (2π/3, 3). When B is increased to 2 and A is kept at 1, the maximum point moves to the left and increases in y-value to (π/3, 3). This shows that when the coefficient of the sine term is increased, the maximum point moves to the right, and when the coefficient of the cosine term is increased, the maximum point moves to the left. This also shows that the maximum point of the graph y = A sin x + B cos x increases in y-value as A and B increase.

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The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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The derivative is f'(x) = (4x - 1) / (2x² - x).

To find the derivative of the function f(x) = ln(2x² - x), we can use the chain rule.

Begin by identifying the function to be differentiated, which is f(x) = ln(2x² - x).

Apply the chain rule, which states that if we have a composition of functions, f(g(x)), the derivative is given by (f'(g(x))) g'(x).

Let's consider the inner function g(x) = 2x² - x.

To differentiate g(x), we need to apply the power rule and the constant rule. The derivative of 2x² is 4x, and the derivative of -x is -1.

Now, we differentiate the outer function f'(g(x)). The derivative of ln(x) is 1/x.

Finally, we multiply the derivatives obtained in steps 3 and 4. Thus, the derivative of f(x) = ln(2x² - x) is:

f'(x) = (1 / (2x² - x)) * (4x - 1)

Simplifying further, we have:

f'(x) = (4x - 1) / (2x² - x)

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The IQ score given the mean and the standard deviation, can be found to be 105. 25.

To find the indicated IQ score corresponding to a right tail area of 0.3694, we can use a standard normal distribution table or calculator. Using a calculator, we can find that the z-score corresponding to a right tail area of 0.3694 is approximately 0.35.

Once we have the z-score, we can use the formula z = (x - μ) / σ to solve for the IQ score :

0.35 = (x - 100) / 15

Solving for x, we get:

x = 0.35 x 15 + 100

= 105.25

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The line equation is y = 8/3(x - 1) + 4

The given parameters are:

Slope, m = 8/3

Point (x, y) = (1, 4)

The line equation is calculated as:

y = m(x - x1) + y1

So, we have:

y = 8/3(x - 1) + 4

Hence, the line equation is y = 8/3(x - 1) + 4

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Answer:

110

Step-by-step explanation:

Divide 176 by 8 to get 22 and then multiply 22 by 5 to get 110

Answer:

110

Step-by-step explanation:

176/8 is 22 so there are 22 slices per loaf.

To find the amount of slices in 5 loaves you multiply 22 and 5 to get 110.

Hope this helped :)

Answer:

96

Step-by-step explanation:

1 sticker pack has 28 stickers

3(28) = 84

84+12

96

Answer:

96

Step-by-step explanation:

28 × 3 = 84 + 12 = 96 I think, I'm not sure

Answer:

It is 390.5 (volume, not surface area)

Step-by-step explanation:

Answer:

1) y = -3x + 6  

Step-by-step explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula \(y-y_1 = m (x-x_1)\) and substitute values for \(m\), \(x_1\), and \(y_1\).  

Since \(m\) represents the slope, substitute -3 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:

\(y+6 = -3(x-4)\)

2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.

\(y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6\)

So, the first option is correct.

Answer:

(a) A = -36

(b) B = -4

(c) 32

Step-by-step explanation:

(a) Isolate the A variable to solve for A. Here you divide.

2/3A = -24

A = -24 / (2/3)

A = -36

(b) Here, you multiply then divide by -1 to get rid of the negative on the variable

20 = -B / 0.2

20 x 0.2 = -B

4 = -B

4/-1 = -B / -1

-4 = B

(c) The difference between these two numbers is found by subtracting them. Since the answer is negative, put it in absolute value to get a positive answer since distance cannot be negative.

-36-(-4)

= -32

absolute value = 32

Answer:

0

Step-by-step explanation:

3r-9=3(r+3)

3r-9=3r+9

collect like terms

3r-3r=9-9

r=0

Answer:

\(\large\boxed{\textsf{No Solutions.}}\)

Step-by-step explanation:

\(\textsf{We are asked to identify how many solutions are possible for r.}\)

\(\textsf{First, we should simplify the given equation.}\)

\(\textsf{For one part of the equation, we have to use the \underline{Distributive Property}.}\)

\(\Large\underline{\textsf{What is the Distributive Property?}}\)

\(\textsf{The \underline{Distributive Property} is a property used to distribute the \underline{multiplier} into}\)

\(\textsf{values \underline{inside} the parentheses.}\)

\(\textsf{Let's begin simplifying the equation.}\)

\(\large\underline{\textsf{Simplify.}}\)

\(\mathtt{3r-9=3(r+3)}\)

\(\large\underline{\textsf{Distribute:}}\)

\(\mathtt{3r-9=(3 \times r)+(3 \times 3)}\)

\(\mathtt{3r-9=3r+9}\)

\(\large\boxed{\textsf{No Solutions.}}\)

\(\large\underline{\textsf{Why?:}}\)

\(\textsf{Any value that is substituted into r will \underline{never} make the equation true.}\)

Answer: 11/15

Step-by-step explanation:

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

24.49

Step-by-step explanation:

Answer:

24.489%, but most of the time they only go to 2 decimal places so 24.49%

Step-by-step explanation:

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

p=32

Step-by-step explanation:

Answer:

Step-by-step explanation:

p+19=51

p=51-19

p=32

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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Answer:

Part A:

The probability of hitting the black circle is the ratio between the area of the black circle and the white square (including the black circle)

Area of circle:

Ac = pi x r^2 = pi x (2/2)^2 = pi (diameter = 2)

Area of square:

As = side^2 = 11^2 = 121 (side = 11)

=> P = pi/121 = ~0.025 (P = 0.025 < 0.5 => P is closer to 0 than 1)

Part B:

The probability of hitting the white portion could be calculated in a similar way as shown in part A. However, the event of hitting the white portion is the complement event of the event of hitting the black circle.

Because P(event) + P(complement of event) = 1

=> P = 1 - 0.025 = 0. 975 (P = 0.975 > 0.5 => P is closer to 1 than 0)

Answer:

Adding +6 in turn

Step-by-step explanation:

-13+6=(-7)

(-7)+6=(-1)

(-1)+6=5

5+6=11

11+6=17

17+6=23

23+6=29

29+6=35

........... And so on

Answer:

\(-73\frac{1}{9}\)

Step-by-step explanation:

We know that z varies directly as √√x and inversely as y, which can be written as:

z = k(√√x)/y

where k is the constant of proportionality.

To find the value of k, we can use the values given when x = 25 and y = 7:

179 = k(√√25)/7

179 = k(5/7)

k = (179*7)/5

k = 250.6

Now we can use this value of k to find z when x = 64 and y = 4:

z = 250.6(√√64)/4

z = 250.6(2)/4

z = 125.3

Therefore, z ≈ 125.3 when x = 64 and y = 4.

Answer:

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

The range of the given function has one restriction, its denominator can't be zero, hence:

Therefore the function can get any value but zero:

The matching answer choice is D.

Linear function is f(x) = mx + b.

Reciprocal of a function f(x)  is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Substitute x = - 5/3 into function to get:

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.

The length of the rectangle is 96 inches.

Given,

James fenced in his backyard.

The perimeter of his fence is 20 feet, and the width of his yard is 2 feet wide.

Use the perimeter formula to find the length of his rectangular yard in inches:

P = 2L + 2W.

The area of a rectangle is given by:

= Length x width

The perimeter is given by:

= 2 ( Length + width )

We have,

Perimeter = 20 feet

Width = 2 feet

Perimeter = 20 feet

2 ( length + width ) = 20

length + width = 20 / 2

length + 2 = 10

length = 10 - 2 = 8 feet

We know that,

1 feet = 12 inches

8 feet = 12 x 8 inches = 96 inches

Thus the length of the rectangle is 96 inches.

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Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.