6 What is an equation in point-slope form of the
line that passess through the point (3, -2) and
has a slope -2?
A.
B.
C.
D.
y + 2 = -2(x - 3)
y - 2 = -2(x-3)
y - 2 = -2(x + 3)
y + 2 = 2(x-3)
1041
quation in point-slone form of a line

Answer:

The ordered pairs that are solution to this equation are:

(8,1) and (10,3)

Step-by-step explanation:

Given statement is:

"difference of two variables x and y is 7"

This can be mathematically written as:

\(x-y = 7\)

To solve this we have to put y = 1 and y = 3

Now,

Putting y = 1 in the equation

\(x-1 = 7\\x = 8\)

Putting y = 3 in the equation

\(x-3 = 7\\x = 7+3\\x = 10\)

Ordered pairs are of the form (x,y)

Hence,

The ordered pairs that are solution to this equation are:

(8,1) and (10,3)

Let x be the width of the rectangle. Since the length of the is 6 times as long as it is wide, the length would be 6x.Perimeter of the rectangle is given as 28 feet. So, the equation would be,2x + 2(6x) = 28.Simplifying the equation,2x + 12x = 28
14x = 28
x = 2So the width of the rectangle would be 2 feet and the length of the rectangle would be 6 times the width which would be 6(2) = 12 feet.

The perimeter of a rectangle is the sum of the length of all four sides. The formula for the perimeter of a rectangle is P = 2l + 2w where P is the perimeter, l is the length and w is the width of the rectangle. In this problem, we are given that a rectangle is 6 times as long as it is wide and its perimeter is 28 feet.

We are supposed to find the dimensions of the rectangle. Let x be the width of the rectangle.Since the length of the rectangle is 6 times as long as it is wide, the length would be 6x.Now we can use the formula for perimeter of the rectangle to form an equation as follows,2x + 2(6x) = 28Simplifying the equation,2x + 12x = 28
14x = 28
x = 2.

Therefore, the width of the rectangle would be 2 feet and the length of the rectangle would be 6 times the width which would be 6(2) = 12 feet. Thus, the dimensions of the rectangle would be 2 feet and 12 feet.

The width of the rectangle would be 2 feet and the length of the rectangle would be 12 feet.

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Answer:

where is the dot plot??

Step-by-step explanation:

Answer:

-5x + 2y=2

Step-by-step explanation:

\(- 7x + 3y = 2 \\ - 2x + y = 0 \\ subtracting \: this.we \: have \\ ( - 7x \: + 3y - 2) - ( - 2x + y) \\ - 7x + 2x + 3y - y - 2 \\ - 5x + 2y - 2 \\ therefore \: we \: have \\ - 5x + 2y = 2\)

Answer: ∞

Step-by-step explanation: ∞

7, 14, 28, 56, 112.

The 5th term is 112

Answer:

-1

Step-by-step explanation:

countdown till you reach 5 or use a\(a_{n} = d (n - 1) + c\)

Answer:

3 months

Step-by-step explanation:

the acosta family went out to dinner. the price of the meal was $79.85. if the tip was 15%.The Acosta family paid $91.83 for the meal, including the 15% tip.

To calculate the total amount paid, we need to add the original price of the meal to the tip amount. The price of the meal was $79.85, and the tip was 15% of that amount. To find the tip, we multiply $79.85 by 0.15 (or 15% expressed as a decimal), which equals $11.98. Adding the tip of $11.98 to the original price, the total amount paid is $91.83.

In more detail, a 15% tip means that 15% of the meal price is added as an extra amount to the bill. To calculate the tip, we multiply the meal price ($79.85) by 0.15 (or 15% as a decimal), resulting in $11.98. This represents the additional amount the Acosta family paid for the tip. To find the total amount paid, we add the tip amount to the original meal price: $79.85 + $11.98 = $91.83. Therefore, the Acosta family paid $91.83 for the meal, including the tip.

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The nonresponse caused the results of the survey to be biased as C. Those who did not respond caused a violation of the assumption of independence.

It should be noted that each person in a simple random sample of 1,200 received a survey, and 325 people returned their survey. How could nonresponse cause the results of the survey to be biased?

In this case, the nonresponse caused rhe results of the survey to be biased as those who did not respond caused a violation of the assumption of independence. Those who did not respond may differ in some important way from those who did respond

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For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

The "Rule of 72" is a quick estimation method to determine the time it takes for an investment or savings to double in value. By dividing 72 by the interest rate, you can obtain an approximation of the doubling time. For an interest rate of 3%, it would take approximately 24 years for the savings to double. For an interest rate of 8%, it would take around 9 years for the savings to double.

To calculate the doubling time using the Rule of 72, divide 72 by the interest rate. This provides an approximation of the number of years it takes for an investment or savings to double in value.

For an interest rate of 3%, we divide 72 by 3: 72 / 3 = 24. Therefore, it would take approximately 24 years for the savings to double.

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

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5/6, five sixths is the answer

To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations.

Kathleen's prediction is flawed because she assumed that the average number of pets per household would remain the same for all households in the state, which may not necessarily be true. The sample size of 200 households may not be representative of the entire population of households in the state, and there may be variations in the number of pets per household across different regions or socioeconomic groups.

To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations. Alternatively, she could use data from existing sources, such as census data, to estimate the number of pets per household in different regions of the state and adjust her prediction accordingly. It's also worth noting that factors such as pet ownership trends, cultural attitudes towards pets, and population growth may also impact the accuracy of Kathleen's prediction and should be taken into account.

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A) Sample size of compound event = 25

B) New Sample size = 36

What is Compound event?

A compound event is one that has more than one sample point. Simple events are less complicated than compound events. These occurrences entail the possibility of multiple occurrences. One is the probability of all possible outcomes of a compound event.

An event that consists of two or more simple events is called a compound event. Simple events are those that can only have one result, whereas complex events can have a variety of distinct results. Compound events can consist of several independent or dependent occurrences, where the result of one event has no bearing on the likelihood of the other.

Given,

Number of buttons in a container = 5

Lucas picks one button, replaces it and then picks another.

Therefore,

Sample size of the compound event

                 n = 5\(\times\)5

                 n  = 25

Now, one more button is added in the container and in total there are 6 buttons.

Lucas repeats the same process again and hence,

Sample size of the new compound event will be,

                  n = 6\(\times\)6

                  n = 36

Full Question is - Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is  ___  Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be ____

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40,000 in scientific notation can be represented by the expression

4 × 10⁴ .

The number 40000 can be written in the scientific notation as 4 × 10⁴ .

Scientific notation must be used when a number is either too large or too little to be stated in decimal form, which typically yields a long string of digits. It's also known as standard index form or scientific form.

460000000 = 4.6×10⁸

6230000000 = 6.23×10⁹

60500000 = 6.05 x 10⁷

Since it may make a number of mathematical operations simpler, this base ten notation is frequently employed by scientists, mathematicians, and engineers. A digit that improves a number's correctness is referred to as an essential figure. This includes all non-zero values, significant zeroes, and zeros in significant intervals between significant digits.

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The rate of change (slope) to match the line include the following: B. -3/2.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 - 1)/(2 - 0)

Slope (m) = -3/2

Slope (m) = -1.5.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

12.60.

Step-by-step explanation:

12.00 × 5%=.6

,6 + 12.00= 12.60

Step-by-step explanation:

Volume of a sphere is given by the formula

4/3 pi r^3       diameter = 6.3 cm  so radius, r = 3.15 cm

4/3 * pi * (3.15)^3 = 130.9 cm^3

Answer:

Unknown number = 36

Step-by-step explanation:

Equivalent ratio means,

\(\frac{x_1}{y_1}=\frac{x_2}{y_2}\)

If \(x_1=2, y_1=9\) and \(x_2=8\),

\(\frac{2}{9}=\frac{8}{y_2}\)

By cross multiplication,

2 × y₂ = 8 × 9

2y₂ = 72

\(\frac{2y_2}{2}=\frac{72}{2}\)

y₂ = 36

Therefore, missing number in the denominator of the fraction will be 36.

Answer:

A) -20

Step-by-step explanation:

\(4y(4y-4)-4(-4y+5+4y^2)\\\\16y^2-16y + 16y-20-16y^2\\\\-20\\\)

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Step-by-step explanation:

a

\(9 \times {10}^{ - 7} = \frac{9}{10000000} = 0.0000009\)

b

\(6.130 \times {10}^{ 9} = 6.13 \times {10}^{9} = 6130000000\)

c

\(1 \times {10}^{15} = 1000000000000000\)

d

\(1 \times {10}^{ - 5} = \frac{1}{100000} = 0.00001\)

e

\( {10}^{ - 7 } = 1 \times {10}^{ - 7} = \frac{1}{10000000} = \\ = 0.0000001\)

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Tyler made an error in his analysis by assuming the supplementary angle, m<1 = 72, was the same as the angle opposite it. Tyler's mistake was in assuming that the same-side exterior angles theorem and the definition of supplementary angles were interchangeable.

Tyler assumes that because the theorem states that same-side exterior angles are supplementary, then any supplementary angles must be same-side exterior angles. Therefore, he concludes that m<2 is also 72 degrees, and that m<3 is 180-72 = 108 degrees. However, this assumption is incorrect. Supplementary angles can be any two angles that add up to 180 degrees, and they do not have to be same-side exterior angles. Therefore, Tyler's analysis is incorrect. The correct way to solve this problem would be to recognize that the angle opposite m<1 is m<3, and therefore, m<3 = 72 degrees.

In summary, Tyler's error in his analysis was to assume that the same-side exterior angles theorem and the definition of supplementary angles were interchangeable. This assumption led him to conclude that m<2 and m<3 were both same-side exterior angles and therefore both 72 degrees. However, this assumption is incorrect, and Tyler's analysis is flawed. The correct way to solve the problem is to recognize that m<1 and m<3 are supplementary angles, and therefore, m<3 is 72 degrees. Then, because m<2 and m<3 form a straight line, m<2 is 108 degrees. In conclusion, Tyler's error shows the importance of understanding the definitions of basic geometric concepts and not making assumptions based on incomplete knowledge.

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Step-by-step explanation:

option C is the answer

hope it helps

To calculate the present value of $51,270 payments to be made at the end of each period for 17 periods at a 9% interest rate, we need to find the discounted value of each payment and sum them up.

The present value (PV) is calculated by discounting each future payment back to its current value using the interest rate. The formula to calculate the present value of a series of payments is:

PV = Payment × [1 - (1 + interest rate)^(-number of periods)] / interest rate.

In this case, the payment is $51,270, the interest rate is 9% (or 0.09 as a decimal), and the number of periods is 17.

Using the provided formula and rounding the factor values to 5 decimal places, we can calculate the present value as follows:

PV = $51,270 × [1 - (1 + 0.09)^(-17)] / 0.09.

Evaluating this expression will give us the present value of the payments. It's important to round the final answer to 0 decimal places, as stated in the question.

By substituting the values and calculating the expression, we can determine the present value of the $51,270 payments made over 17 periods at a 9% interest rate.

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Answer:

P = 0.015x + 60

Since Carson's base pay is $60, he would earn $60 even for selling $0 worth of computers, meaning P= 60 when x=0, which is the y-intercept.

(0,60) is a point on the graph

Since Carson makes a commission of 1.5% for all sales, the amount of money earned in a given day increases $0.015 for each $1 of sales made (multiply 1 by 0.015). This means the slope of P is equal to 0.015.

Step-by-step explanation:

Answer:

Step-by-step explanation:

For one flower, the following shapes are used;

6 yellow hexagons, 2 red trapezoids and 9 green triangles

If we are given 30 yellow hexagons 50 red trapezoids and 60 green triangles, to get the number of flowers we can make, we will find the greatest common factor of 30, 50 and 60

30 = 6*5

50 = (2*5)+40

60 = (9*5)+15

We can see that 5 is common to all the factors. This means that we can make 5 flowers if they were changed to 30 yellow hexagons 50 red trapezoids and 60 green triangles.

Since there are 40 trapezoids left and 15 green triangles left, hence the shape that would have n as left over most is trapezoid (40 left over)