A line has the equation y=x+3
What are the coordinates of the point where the line intersects the y and x axis?

Answer:

X= 1/2 Y= 5

Step-by-step explanation:

8x+7y=39-------------(1)--------×2

4x-14y= -68-----------(2)-------×1

16X + 14Y = 78--------(3)

4X- 14Y = -68----------(4)

Addy equation (4) and (3)

20X = 10

dividing bothsides by 20

20X/20= 10/20

X = 1/2

substitute the value of X into equation (1)

8X+7Y = 39

8(1/2)+7Y= 39

4+7Y = 39

7Y = 39-4

7Y = 35

dividing bothsides 7

7Y= 35/7

Y = 5

For a store sells ink cartridges in packages, two packages have the same ratio of cartridges to cost are Package A and Package C.

A ratio is used to comparison of two quantities. An equivalent or same ratio means a ratio that is equal to or has the same value as another ratio. We have a store sells ink cartridges in packages. The table represents the ink cartridges, number Cartridges and total cost.

Ink World Number of Total Cost

Packages Cartridges

Package A 3 $60

Package B 6 $60

Package C 1 $20

Package D 3 $20

We have to determine two packages have the same ratio of cartridges to cost.

Now, check the ratio of cartridges to cost for each packages. For package A,

cartridges : cost = 3 : 60 = 1 : 20

For package B, cartridges : cost = 6 : 60 = 1 : 10

For package C, cartridges : cost = 1 : 20

For package D, cartridges : cost = 3 : 20 = 3 : 20

So, the packagses with same ratio are package A and C.

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The answer is 2 1/4 cupcakes

Answer:

2 1/4 cupcakes

Step-by-step explanation:

Step 1: State what is know

There are 3 people Jake, Brother 1, and Brother 2.  They all ate 3/4 of a cup cake each

Step 2: Solve

Multiple 3 by 3/4

3 x 3/4 = \(C_{Total}\)

2.25 = \(C_{Total}\\\)

0.25=1/4

2 1/4 cupcakes

Step 3: Therefore Statement

Therefore the 3 brothers ate 2 1/4 cupcakes

Answer:

the last one : the range of the function is all real numbers less than our equal to 9.

Step-by-step explanation:

it is a parabola that opens up only down. that means all the calculated y-values go deeper and deeper into lower and negative values the more right or left we go on the x-axis.

the maximum y-value we have at the vertex with y=9. no other x-value can generate a bigger y-value.

that's why the last answer option is right.

Answer:

[2, 4]

Step-by-step explanation:

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:-8 1/10

Step-by-step explanation:

-2 3/5 - 5 1/2

-13/5 -11/2

-81/10

-8 1/10

The simplified expression of the statement is -81/10

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

negative 2 and three fifths minus 5 and one half.

Express as numbers

So, we have

-2 3/5 - 5 1/2

Convert the fractions to improper fractions

So, we have

-13/5 - 11/2

Take the LCM of the above fractions

(-13 * 2 - 11 * 5)/10

Evaluate the difference

So, we have

-81/10

Hence, the value of the expression is -81/10

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Answer:

x^2+x

Step-by-step explanation:

Use the distributive property: x*x+x*1=x^2+x

Step-by-Step Solution:

Finding the product means to find what the expression would equal if it was multiplied.

In this equation, we need to multiply x to x, and 1.

x(x) + x(1) = x² + x

Answer:

- 13

Step-by-step explanation:

Step 1:

2c + 5 = c - 8     Equation

Step 2:

c + 5 = - 8   Subtract c on both sides

Step 3:

c = - 8 - 5   Subtract 5 on both sides

Answer:

c = - 13

Hope This Helps :)

Answer:

c=-13

Step-by-step explanation:

2c+5=c−8

Step 1: Subtract c from both sides.

2c+5−c=c−8−c

c+5=−8

Step 2: Subtract 5 from both sides.

c+5−5=−8−5

c=−13

hope that helps :)

The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion

This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.

A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.

To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:

Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)

where:

Using this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.

This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.

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The maximum quantity that can be reached in a quadratic model can be determined by finding the vertex of the quadratic function. In this case, with coefficients of 117t and -22.9906t^2, the maximum quantity can be calculated.

To find the maximum quantity in a quadratic model, we need to locate the vertex of the quadratic function. The vertex is the point where the quadratic curve reaches its maximum or minimum value. In a quadratic equation of the form ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / (2a). In this case, the coefficients of the quadratic model are 117t and -22.9906t^2. Since there is no constant term, we can disregard it in this calculation. By substituting the values into the formula, we find that the x-coordinate of the vertex is -117 / (2 * -22.9906) = 2.5415.

To determine the maximum quantity, we need to substitute this value back into the quadratic equation. However, since the problem statement does not provide the complete quadratic equation or the context for the variable t, we cannot calculate the exact maximum quantity. Therefore, the specific value of the maximum quantity cannot be determined without additional information.

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Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.

In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.

Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:

Profit = Revenue - Cost

In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.

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Answer:

Step-by-step explanation:

1. Figure out which terms are alike. I have separated the like terms using parenthesis for clarification, however, this is not necessary when solving by yourself.

(3y + 4y) + (8 + 2)

2. Combine both sets of like terms however the signs dictate. In this case, add all the signs.

3y + 4y = 7y  

(solve as if there was no constant so if 3 + 4 = 7 then 3y + 4y = 7y)

8 + 2 = 10

3. Put it all together

Final answer: 7y + 10

Note: Understanding how to combine and simplify like terms will be very helpful when you eventually will have to solve for y. When solving an equation you will always want to start by combing and simplifying like terms first.  

Most psychological research is undertaken with the hope of discovering the ultimate truth.

What is the main purpose of hypothesis testing?

What is null and alternative hypothesis?

What is null hypothesis in research?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

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The overall average of the 9 numbers is 13 and the average of the last 4 numbers is 20.

To find the overall average of the 9 numbers, we can use the formula for the weighted average:

overall average = (sum of all numbers) / (number of numbers)

We know that the average of the first 5 numbers is 10, so their sum is 5 * 10 = 50. We also know that the average of the next 4 numbers is 15, so their sum is 4 * 15 = 60. The sum of all 9 numbers is then 50 + 60 = 110. Therefore, the overall average is:

overall average = 110 / 9 ≈ 13

To find the average of the last 4 numbers, we can subtract the sum of the first 5 numbers from the sum of all 9 numbers, and then divide by 4:

average of last 4 numbers = (sum of all 9 numbers - sum of first 5 numbers) / 4

= (110 - 50) / 4

= 60 / 4

= 15

Therefore, the average of the last 4 numbers is 15, which is option C.

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Answer:

y = 2x + 3

Step-by-step explanation:

Given:

(2, 7) and (0, 3)

Find the slope between the two points:

(x1, y1) = (0, 3)

(x2, y2) = (2, 7)

(y2 - y1)/(x2 - x1)

(7 - 3)/(2 - 0)

4/2 = 2

m = 2

y = mx + a

y = 2x + a

Use one of the two points to find a (I will use point (2, 7):

7 = 2(2) + a

7 = 4 + a

a = 3

Slope-intercept Form: y = 2x + 3

Point-slope Form: y - 3 = 2x

Point-slope Form: y - 7 = 2(x - 2)

General equation: 2x - y + 3 = 0

Answer:

40g butter

20g sugar

60g flour

Step-by-step explanation:

8 is 24/3

then divide all measured by 3

120/3 =40

60/3=20

180/3=60

Answer:

40g butter

20g sugar

60g flour

Step-by-step explanation:

8 is 24/3

then divide all measured by 3

120/3 =40

60/3=20

180/3=60

The most commonly shaped base in pin curls is the rectangular base.

This is the main answer to your question. An explanation for this is that the rectangular base is versatile and can be used for creating various sizes of curls. Additionally, it allows for easy control of the curl direction. In conclusion, when creating pin curls, the rectangular base is the most commonly used due to its versatility and ease of use.


The arc base, also known as the half-moon or C-shape base, is the most popular base shape for pin curls because it allows for better distribution of the hair and provides more natural-looking curls. This shape helps prevent splits in the finished hairstyle, ensuring a smoother and more cohesive appearance.

In pin curls, the arc base is the most commonly used base shape due to its ability to create natural-looking curls and prevent splits in the hairstyle.

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Let Xk be independent and normally distributed with common mean 22 and standard deviation 11 (so their common variance is 1.1.). The value of p(-[infinity] ≤ ∑k=181 Xk ≤ 172.89) ≈ 0.0265.

The common variance of independent and normally distributed random variables with a common mean can be computed with the formula

σ² = Var[Xk]

= 1.1.

This can be solved by finding the standard deviation, which is equal to the square root of the variance as

σ = sqrt(1.1)

= 1.0488.

The sum of the independent and identically distributed normal random variables can be expressed as a normal random variable with a mean equal to the sum of the individual means and a variance equal to the sum of the individual variances.

Thus, we can express this random variable as ∑k=181 Xk ~ N(22 * 181, 1.1 * 181).

To solve the given problem, we need to compute the probability that the sum of the random variables lies between -infinity and 172.89.

Since the sum of normal random variables follows the normal distribution, we can standardize the sum by subtracting the mean and dividing by the standard deviation.

Let Z be the standardized random variable.

Then Z = (X - μ)/σ

Z = (∑k=181 Xk - μ)/σ, where μ = 22 * 181 and σ = sqrt(1.1 * 181).

We need to compute P(-infinity ≤ Z ≤ (172.89 - μ)/σ) = P(Z ≤ (172.89 - μ)/σ) .

Since the standard normal distribution is symmetric about zero.

This can be solved using standard normal tables or a calculator to obtain P(Z ≤ -1.9309) ≈ 0.0265 (rounded to four decimal places).

Therefore, p(-[infinity] ≤ ∑k=181 Xk ≤ 172.89) ≈ 0.0265 (rounded to four decimal places).

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According to the questions there are 5000 students at mountain high school, and 3/4 of these students are seniors. Then, 2125 students do not favor the idea of forming a debate team

To find the number of students who do not favor the idea of forming a debate team, we need to calculate the following:

Number of senior students: 3/4 * 5000 = 3750

Number of senior students in favor: 1/2 * 3750 = 1875

Number of non-senior students: 5000 - 3750 = 1250

Number of non-senior students in favor: 4/5 * 1250 = 1000

Number of students not in favor: Total students - (Senior students in favor + Non-senior students in favor)

Number of students not in favor: 5000 - (1875 + 1000) = 2125

Therefore, 2125 students do not favor the idea of forming a debate team.

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The line's 31 y-intercept is, in accordance with the provided assertion, as follows: 

By changing the numbers of the slope, m, and the coordinates of a location on the line, (x, y), in the equation y = mx + b, one can determine the y-intercept of a linear function.

Given the following:

A point on the line (x, y) = (7, 108)

The slope of the line, m = 11

Therefore, substitute the values of m, x, and y into the equation, y = mx + b:

108 = 11(7) + b

Solve for b:

108 = 77 + b

Subtract 7 from both sides:

108 - 77 = 77 + b - 77

31 = b

b = 31

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The required factor each polynomial by grouping are factored.

A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.

1) \(x^3+4x^2+2x+8\)

can be factored by grouping as:

\(x^3 + 2x + 4x^2 + 8\)

= \(x(x^2+2) + 4(x^2+2)\)

= \((x+4)(x^2+2)\)

2) \(4b^3-6b^2+10b-15\)

can be factored by grouping as:

\(2b^2(2b-3)+5(2b-3)\)

=\((2b-3)(2b^2+5)\)

3)\(2m^3+4m^2+6m+12\)

can be factored by grouping as:

\(2m^2(m+2) + 6(m+2)\)

= \((2m^2+6)(m+2)\)

= \(2(m^2+3)(m+2)\)

4) \(7r^3-35r^2+6r-30\)

can be factored by grouping as:

\(7r^2(r-5)+6(r-5)\)

=\((7r^2+6)(r-5)\)

\(10a^3+4a^2+5a+2\)

can be factored by grouping as:

\(2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)\)

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Answer: x<7

Step-by-step explanation:

Given

12x>9(2x-3)-15

Distributive property

12x>18x-27-15

Combine like terms

12x>18x-42

Subtract 18x on both sides

12x-18x>18x-42-18x

-6x>-42

Divide -6 on both sides (REMEMBER you need to change the [<,>] sign when multiplying or dividing negative numbers)

-6x / -6 < -42 / -6

EXTRA (Graph the solution)

Answer: x<7

Step-by-step explanation:

First distrubite factors. ( 9(2x-3) = 18x-27)

1) 12x>18x-27-15

Combine like terms. (-27-15)

2) 12x>18x-42

Subtract 18x from both sides.

3) -6x>-42

Isolate the variable. (divide -6 on each side)

4) x>7

Flip the sign since your dividing.

5) x<7

Final answer: X<7

p(0)=2

p(1)=2+1+2-1=4

p(2)=2+2+8-8=4

The sets that represent possible input and output of the function represented as ordered pairs is {(−1, −8), (0, −3), (3, 12)}.

A linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the sets that represents the possible inputs and outputs of the function represented as ordered pairs are as follows:

Using y = 5x - 3

Let's test the ordered pair for option D.

{(−1, −8), (0, −3), (3, 12)}

(-1, -8)

y = 5(-1) - 3 = -5  - 3 = - 8

(0, −3)

y = 5(0) - 3 = 0 - 3 = - 3

(3, 12)

y = 5(3) - 3 = 15 - 3 = 12

Therefore, the right option is D.

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ANSWER

EXPLANATION

We want to find the discrimininant of the equation:

The general form of a quadratic equaion is given as:

The discriminant is given as:

Therefore, we need to find that.

From the given equation:

Therefore, we have that the discriminant is:

That is the discriminant.

Since the discriminant is less than 0, then there are no real solutions of the equation.

Answer:

x=18

Step-by-step explanation:

3(x-4)=2x+6

3x-12=2x+6

3x-2x=6+12

x=18

Answer:

\(3(x - 4) = 2x + 6 \\ 3x - 12 = 2x + 6 \\ 3x - 2x = 6 + 12 \\ x = 18\)

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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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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