100 POINTS!!! Trapezoid P'Q'R'S' is the result of a dilation with a scale factor of 0.5 and a translation to the right. Which statement is true?

A
Angle R and R’ are congruent.

B
Line RS will be half the length of Line R’S’.

C
Trapezoid P’Q’R’S’ is congruent to Trapezoid PQRS.

D
The image is an enlargement of the original trapezoid.

The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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Based on the given information, when x equals 9, the regression line predicts that log(y) will equal 3.992. To find the predicted value of y when x is 9, you will need to apply the inverse transformation to the logarithmic value.  

The inverse transformation of log(y) is achieved by using the exponential function. Specifically, you can use the formula:

y = 10^(log(y))

In this case, since log(y) = 3.992, you can plug this value into the formula:

y = 10^(3.992)

When you calculate this, you will find that y ≈ 9762.97. Rounded to the nearest whole number, the regression line predicts that y will equal 9763 when x equals 9.

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Answer: (-5, 5)

Step-by-step explanation:

x + 5y = 20...(1)

2x - 7y = -45...(2)

Multiply equation 1 by -2 and add the equations

-2x - 10y = -40

+ 2x - 7y = -45

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

- 17y =-85

-17y/-17 = -85/-17

y=5

Substitute y=5 into equation 1

x + 5y = 20

x + 5(5) = 20

x = 25-20

x=-5

Therefore the solutionto the system is (-5, 5)

Answer:

assignment for the update

Answer:

Step-by-step explanation:

The top of the wall, the bottom of the wall and the bottom of the ladder form a right triangle if connected together.

Let the length of the ladder be x, then as per Pythagorean theorem we have:

The ladder is  20.5 ft long

Answer:

x = 16

Step-by-step explanation:

Vertically opposite angles are congruent

3x - 3 = 2x + 13

Add 3 to both sides

3x = 2x + 13 + 3

3x = 2x + 16

Subtract 2x from both sides

3x - 2x = 16

x = 16

Answer:   3

Step-by-step explanation:   When you solve for x you get 2 so when you put that into the equation (2+1) you get 3.  You solve for x but solving this equation (x+5) = (x+1) Hope this helps :)

Answer:

Step-by-step explanation:

My variables are

d=big number

q=small number

My equations are

6=3q

2d+3=q

I will solve for q in first equation

6/3 = 3q/3

2=q

Now I will pluck back in to get d

2d+3=(2)

   -3   -3

2d=-1

2d/2=-½

d=-1/4

So the solution is

(-1/4, .2)

Answer:

yes

Step-by-step explanation:

a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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Answer:

where is the spinner

Step-by-step explanation:

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Let's denote the width of the rectangle by "w." We know that the diagonal of the rectangle is 5 less than 4 times the width, which can be written as 4w - 5. We also know that the length of the rectangle is 7. The width of the rectangle is approximately 3.1

       Let's start by denoting the width of the rectangle by "w." We know that the diagonal of the rectangle is 5 less than 4 times the width. In other words, we have:

diagonal = 4w - 5

We also know that the length of the rectangle is 7. Using the Pythagorean theorem, we can write an equation that relates the width, length, and diagonal of the rectangle:

w^2 + 7^2 = (4w - 5)^2

Simplifying this equation gives us a quadratic equation in standard form:

16w^2 - 64w + 39 = 0

We can solve this equation using the quadratic formula:

w = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 16, b = -64, and c = 39. Plugging in these values and solving gives us two possible solutions:

w ≈ 0.7 or w ≈ 3.1

Since the width of the rectangle cannot be negative, we discard the first solution. Therefore, the width of the rectangle is approximately 3.1, rounded to the nearest tenth.

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If A and B are mutually exclusive events, P(A ∩ B) = 0, and the general addition law can be simplified to the sum of the individual probabilities for A and B

Given data ,

If events A and B are mutually exclusive, it means that they cannot occur simultaneously. In this case, the intersection of events A and B, denoted as A ∩ B, would indeed have a probability of 0

And , P(A ∪ B) = P(A) + P(B)

Therefore , if A and B are mutually exclusive, the probability of either event A or event B occurring is equal to the sum of their individual probabilities.

Hence , the probability is solved

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In table 9.1, the marginal cost of producing the seventh unit of output is equal to $8.
Marginal cost refers to the additional cost incurred when producing one more unit of output. To find the marginal cost of producing the seventh unit of output, follow these steps:

1. Locate the total cost column in table 9.1.
2. Identify the total cost of producing 6 units of output.
3. Identify the total cost of producing 7 units of output.
4. Subtract the total cost of producing 6 units from the total cost of producing 7 units.

The difference you get from step 4 is the marginal cost of producing the seventh unit of output.

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Answer: mg they left u hanging for some time here hol up,

y=−25

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y/5-2-(-7)=0

y/5          

(y/5 -  2) -  -7  = 0  

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

   2 =  2/1=2.5/5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

y - (2.5/5 5)=y - 10

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 y+25

 ———— • 5 = 0 • 5

  5  

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  y+25  = 0

4.2      Solve  :    y+25 = 0  

Subtract  25  from both sides of the equation :  

                     y = -25

Answer:

4.2

Step-by-step explanation:

84 divided by 20  4.2

Answer:

the angle of CAD is 100°

Step-by-step explanation:

all of the angles inside of the triangle should add up to 180°

so 180=x+80+20, which equals 80°

the angle of a straight line is 180° so use the inside angle of the triangle 80°

180=x+80, now the angle CAD equals 100°

Kareem should write the length of the Nile River in standard form as 4160 miles.

To write the length of the Nile River in standard form, we need to express it as a number multiplied by a power of 10.

Given: Length of the Nile River = 4.16 × 10³ miles

In standard form, we want a number between 1 and 10 multiplied by a power of 10. To achieve this, we can move the decimal point three places to the right since we have a positive exponent of 10³.

Moving the decimal point three places to the right gives us:

4.16 × 10³ = 4160

Therefore, Kareem should write the length of the Nile River in standard form as 4160 miles.

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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The first five terms of the sequence  are: 3/5, 3/4, 9/7, 3/2, 15/9.

To find the first five terms of the sequence  aₙ = 3n/(n+4)

we need to substitute the values of n from 1 to 5 and solve for .

a₁ = 3×1/(1+4) = 3/5

a₂ = 3×2/(2+4) = 3/4

a₃ = 3×3/(3+4) = 9/7

a₄ = 3×4/(4+4) = 12/8 = 3/2

a₅ = 3×5/(5+4) = 15/9

Hence, the first five terms of the sequence  are: 3/5, 3/4, 9/7, 3/2, 15/9.

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Answer:

1 pizza

Step-by-step explanation:

(5/6) × (1 1/5) = 1

put 62  it does have instructions right

Answer:

8 hours. maybe 8×4

Step-by-step explanation:

I'm not sure on the last part though

Answer:

Here the ratio of length of the shadow to the height of the object (in this case a yardstick) is 15:36. The ratio of shadow to the height of tree will also be the same. the shadow of tree is 25 feet long. So the height of tree will be (25*36)/15, that is 60 feet.

(I really hope this helps!)

Answer:

G. 60m

H. 7.5cm

Step-by-step explanation:

0.8 = \(\frac{8}{10}\)

Perimeter of figure = (12 + 10 + 16 + 10) × \(\frac{10}{8}\)

                                = 48 × \(\frac{10}{8}\)

                                = 60m

1.5 feet --- 0.75cm

15 feet --- \(\frac{15}{1.5}\) × 0.75cm = 7.5cm

Answer:

Step-by-step explanation:

BC= 9.6

CD=8

BA=8

AD= 12.8

New perimeter is 38.4

And the statue is 7.5 cm tall

The common difference is 5

The formula for the nth term of an arithmetic sequence is ;

Tn = a + ( n - 1)d

Given that the parameters are;

Substitute the values

T₆ = 10 + ( 6-1) d

Subtract the values

35 = 10 + 5d

collect like terms

25 = 5d

Divide the values, we have;

d = 5

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Answer:

\(y = x \div 3 - 3 \div 4\)

Step-by-step explanation:

\(y = mx + c \\ - 12y = 9 - 4x \\ 4 x - 9 = 12y \\y = 4x \div 12 - 9 \div 12 \\ reduce \\ y = x \div 3 - 3 \div 4\)

kindly follow me if I am correct

The main difference between everyday logic and mathematical logic is that everyday logic is based on general observations and opinions, while mathematical logic is based on precise statements and facts.

Differences:
- Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.
- Everyday logic is often used to make decisions or solve problems in daily life, while mathematical logic is used to solve complex mathematical problems.
- Everyday logic can be subjective and influenced by personal beliefs or experiences, while mathematical logic is objective and follows a set of universally accepted principles.

Similarities:
- Both everyday logic and mathematical logic use reasoning to draw conclusions.
- Both everyday logic and mathematical logic rely on evidence and facts to support their conclusions.
- Both everyday logic and mathematical logic can be used to solve problems and make decisions.

In conclusion, while everyday logic and mathematical logic have some similarities in terms of their use of reasoning and evidence, they differ in their approach and application. Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.

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Answer:

565,482

Step-by-step explanation:

As the mosquito population grows by a constant rate of 6% each day, we can use the exponential growth formula to create an equation to find the number of mosquitoes in the city "t" days after May 10th.

\(\boxed{y=a(1+r)^t}\)

where:

Given the size of the mosquito population on May 10th is 210,000:

Given the growth rate is 6%:

Substitute the values of a and r into the formula to create an equation for the number of mosquitos in the city "t" days after May 10th.

\(y=210000(1+0.06)^t\)

\(y=210000(1.06)^t\)

To calculate how many mosquitoes will inhabit the city on May 27th, substitute t = 17 into the equation.

\(\implies y=210000(1.06)^{17}\)

\(\implies y=210000(2.69277278...)\)

\(\implies y=565482.285011...\)

\(\implies y=565482\; \sf(nearest\;whole\;number)\)

Therefore, the number of mosquitoes that will inhabit the city on May 27th is approximately 565,482 to the nearest whole number.