Find the length of the third side. If necessary, round to the nearest tenth

The side of the house which the ladder will reach now is equal to 14.2 feet.

In Mathematics and Geometry, Pythagorean's theorem is represented or modeled by the following mathematical equation:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine how far up the side of the house will the ladder reach, we would have to apply Pythagorean's theorem as follows;

21² + y² = 35²

y² = 1,225 - 441

y² = 784

y = √784

y = 28 feet.

Since Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, we have:

New Length = 28 + 4 = 32 feet.

Therefore, the required length is given by;

Distance = √(35² - 32²)

Distance = 14.2 feet.

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The solution of the system of equations. -2x-y=6 over -2x+8y=-39 is the ordered pair (-0.5, -5).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

-2x-y=6     ......equation 1.

-2x+8y=-39  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-0.5, -5).

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The unit of measurement "length of a soccer field" is in yards

The unit of measurement "length of a soccer field" is typically measured in yards, which is option B.

A standard soccer field is rectangular, with a length ranging from 100 to 130 yards and a width ranging from 50 to 100 yards.

The measurement of the length of a soccer field is based on the distance between the goal lines, which is equivalent to the length of the field.

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

Step-by-step explan             456

If she worked 36 hours this week, then Corina made $486 this week.

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

Corina makes $27 for every 2 hours that she works.

So she makes:

27/2 = $13.50 per hour

If she worked 36 hours this week, she would make:

36 hours x $13.50 per hour = $486

Therefore, Corina made $486 this week.

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Answer: The point (4, 1) is a solution to this system of equations.

Step-by-step explanation:

To determine if (4, 1) is a solution to this system, you must plug it in to both of the equations. It is in the form of (x, y); so x = 4, and y = 1

Equation #1: y = -x + 5

                     1 = -(4) + 5

                     1 = 1      <————— This is part of the solution to this equation.

Equation #2: y = 2x - 7

                      1 = 2(4) - 7

                      1 = 8 - 7

                      1 = 1       <———- This is part of the solution to this equation.

The point (4, 1) is a solution to this system of equations.

Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.

A quadratic equation can be made together into perfect square trinomial simply adding or removing elements from both sides, a technique known as "completing the square."

You can use the square's completion as another mathematical tool to solve a variety of problems:

Given expression:

-3x² - 298 = 60x - 1

isolating the x values:

-3x² - 60x = 298 - 1

-3x² - 60x = 299

Taking -3 common from the left hand side:

-3(x² + 20x) = 299

x² + 20x = - 299/3

This, can be written as:

x² + 2*10x = - 299/3

add both side by 100

x² + 2*10x + 100 = - 299/3 + 100

On simplification:

(x + 10)² = (-299 + 300) /3

(x + 10)² = 1 /3

Comparing obtained expression with the given form: (x+a)²=b

a = 10 and b = 1/3

Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.

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The coordinates for the image after the translation of EFG would be E'(-2, 3), F'(-4, 0), and G'(-1, -2).

To translate a point, you simply add or subtract the specified units from its x and y coordinates. In this case, you are asked to translate the points 3 units left and 1 unit down.

To translate 3 units left, subtract 3 from the x-coordinate, and to translate 1 unit down, subtract 1 from the y-coordinate.

For point E (1, 4):

E' = (1 - 3, 4 - 1) = (-2, 3)

For point F (-1, 1):

F' = (-1 - 3, 1 - 1) = (-4, 0)

For point G (2, -1):

G' = (2 - 3, -1 - 1) = (-1, -2)

The translated points are E'(-2, 3), F'(-4, 0), and G'(-1, -2).

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Answer:

To solve the problem, we can use multiplication. We know that one classroom took 254 photos and the other classroom took 15 times as many pictures. So, we can write an equation to represent the situation:

Number of photos taken by Advocacy Project for Homeless Pets classroom = 254 x 15

We can then solve this equation using multiplication.

254 x 15 = 3810

Therefore, the Advocacy Project for Homeless Pets classroom took 3,810 photos.

Yes, we can determine the probability of one thing happening before another based on their expected time to occur.

A coin has two sides: one side ("heads") is side A and the other ("tails") is side B. A coin is tossed into the air and the question is what are the chances, the "probability" if you want it to land on side A. The probability of an event occurring describes the number of chances that the event occurred. The total probability of hitting A before B is the sum: P(A before B) = p + rp + r² + r³p + r⁴p + … = p[1 + r + r² + r³ + r⁴ + … ] and this determines the result. Thus, it is possible to determine the probability of one thing happening before another, based on their expected time to occur.

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The common ratio is -1/3 and the initial term is -4, then the formula is:

A(n) = -4*(-1/3)^(n - 1)

Remember that in a geometric sequence, to get the next term we need to multiply the previous term by the common ratio.

To get the common ratio, take the quotient between two consecutive terms.

We will get:

(4/3)/(-4) = -1/3

Then the n-th term of the geometric sequence is:

A(n) = -4*(-1/3)^(n - 1)

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Answer:

[tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

The common ratio between any two terms in a geometric sequence is constant. Let this ratio be denoted by r. Then, we have:

[tex]r = \frac{\frac{4}{3}}{-4} = \frac{-\frac{4}{9}}{\frac{4}{3}} = \frac{\frac{4}{27}}{-\frac{4}{9}} = \frac{1}{3}[/tex]

Using this value of r, we can write the formula for the nth term an as:

[tex]an=[/tex][tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]

Answer: -1.12, -1^(1/2), 1^(1/8), 1^(1/2), 1^(2/3), 1.12

Step-by-step explanation:

Starting with the smallest:

-1.12

-1^(1/2) (which is equal to -1)

1^(1/8) (which is equal to 1)

1^(1/2) (which is equal to 1)

1^(2/3) (which is equal to 1)

1.12

Therefore, the numbers in order from smallest to largest are: -1.12, -1, 1, 1.12.

Answer:

the product of (3-2x)(2x+1)(x-5) is -4x^3 + 26x^2 - 19x - 75.

Step-by-step explanation:

To find the product, we need to multiply these three expressions:

(3 - 2x)(2x + 1)(x - 5)

Let's start by multiplying the first two expressions using the distributive property:

(3 - 2x)(2x + 1) = 6x - 4x^2 + 3 - 2x

Now we can multiply this result by the third expression using the distributive property again:

(6x - 4x^2 + 3 - 2x)(x - 5) = 6x^2 - 34x + 15x - 75 - 4x^3 + 20x^2

Simplifying this expression by combining like terms, we get:

-4x^3 + 26x^2 - 19x - 75

Therefore, the product of (3-2x)(2x+1)(x-5) is -4x^3 + 26x^2 - 19x - 75.

we do not have convincing statistical evidence that women pay more than men for the same transmission repair

To determine whether the data provide convincing statistical evidence that women pay more than men we do not have convincing statistical evidence that women pay more than men for the same transmission repair for the same transmission repair, we can perform a hypothesis test.

Null hypothesis: The mean repair cost for women is the same as the mean repair cost for men.

Alternative hypothesis: The mean repair cost for women is greater than the mean repair cost for men.

We can use a two-sample t-test for the difference in means, assuming equal variances.

The test statistic is given by:

t = (xbar1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))

where xbar1 and xbar2 are the sample means, s_p is the pooled standard deviation, and n1 and n2 are the sample sizes.

The degrees of freedom is given by:

df = n1 + n2 - 2

Using the data given, we have:

xbar = 2542.86, xbar2 = 2469.29

s1 = 691.27, s2 = 599.77

n1 = n2 = 7

First, we can calculate the pooled standard deviation:

s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))

s_p = sqrt(((6)*691.27^2 + (6)*599.77^2) / (7 + 7 - 2))

s_p = 644.47

Then, we can calculate the t-statistic:

t = (xbar 1 1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))

t = (2542.86 - 2469.29) / (644.47 * sqrt(1/7 + 1/7))

t = 0.97

Using a t-distribution table with df = 12 and a significance level of 0.05, the critical value for a one-tailed test is 1.7823. Since our t-statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have convincing statistical evidence that women pay more than men for the same transmission repair

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Answer:

y= 7/3x -7

Step-by-step explanation:

Slope is 7/3 (rise/run or up seven over 3) and when you continue the graph the line will eventually hit your y-intercept at -7

The quotient of 30y³ + 50y² - 35y divided by 5y is: 6y² +10y - 7

Hence option c is the correct answer.

Applying long division rule to find quotient,

Dividend is  30y³ + 50y² - 35y and divisor is 5y

Dividing   30y³ + 50y² - 35y  by 5y step by step we get ( +) 30y^3  is divisible by 5y as the remainder is zero and the quotient is (+) 6y^2.

Then at second step we get (+) 50y^2 is divisible 5y as the remainder is zero and the quotient is (+) 10y.

And at the last step we get (-) 35y is divisible by 5y as the remainder is zero and the quotient is (-) 7.

Thus adding up the quotients found at each step of division of   30y³ + 50y² - 35y by 5y is 6y² +10y - 7.

Hence option c is the correct answer.

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The circle with equilateral triangle is constructed.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Here we need to construct the circle  with center D.

Now we know that in equilateral triangle , side length of the all sides are equal.

Then, AB=BC=CA.

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The probability that the cost will exceed $600 is approximately 0.057, or 5.7%. which is relatively small, so it is highly unlikely that the cost of conducting the test will exceed $600.

we need to use the information provided to calculate the probability that the test execution cost will exceed a certain value.

Let X be the cost of conducting a test to find three of her employees with positive signs of asbestos poisoning. From the information provided, we can see that:

E(X) = $550

Var(X) = $500

Using these values, we can standardize X to a standard normal distribution.

Z = (X - E(X)) / sqrt(Var(X))

= (X - $550) / square meters ($500)

Accepting that the costs take after an ordinary conveyance, able to utilize the standard ordinary conveyance to compute the likelihood that the fetched surpasses a certain esteem. For case, to find the likelihood that the taken toll surpasses $600, we are able to compute:

P(X > $600) = P(Z > ($600 - $550) / square meters ($500))

= P(Z > 1.58)

Using a standard normal table or calculator, we find that P(Z > 1.58) is approximately 0.057. hence, the probability that the cost will exceed $600 is approximately 0.057, or 5.7%.

This likelihood is generally little, so it is profoundly impossible that the fetch of conducting the test will surpass $600.

Be that as it may, the precise limit for what is considered exceedingly improbable may change depending on the setting and the particular criteria utilized. 

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Answer: 1,200

Step-by-step explanation: 1,300 - 100 = 1,200

The statement " Time plots are special scatterplots where the explanatory variable, x, is a measure of time" is true because time plots are scatterplots where the x-axis represents time, and they are commonly used to visualize trends and patterns in time series data.

A time plot is a type of scatterplot where the x-axis represents time and the y-axis represents a response variable. Time plots are useful for displaying data that change over time and can reveal trends, patterns, and seasonality in the data. They are commonly used in fields such as economics, finance, and social sciences to analyze time series data.

By visualizing data over time, time plots can help to identify relationships, outliers, and potential forecasting models. Overall, time plots are a powerful tool for analyzing and understanding trends and patterns in time series data.

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The given question is incomplete, the complete question is:

Time plots are special scatterplots where the explanatory variable, x, is a measure of time. True or false

The quotient of the expression (6x​-24)÷x^2-16/6x is 36x/(x + 4)

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

(6x​-24)÷x^2-16/6x

Assume that no denominator has a value of 0, we have

(6x​-24)÷x^2-16/6x = 6(x - 4)  ÷ (x - 4)(x + 4)/6x

Express as products

So, we have the following representation

(6x​-24)÷x^2-16/6x = 6(x - 4)  * 6x/(x - 4)(x + 4)

When the factors are evaluated, we have

(6x​-24)÷x^2-16/6x = 36x/(x + 4)

Hence, the solution is 36x/(x + 4)

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Answer:

(1/256)

Step-by-step explanation:

[tex](\frac{1}{4})^{4} = \frac{1^{4} }{4^{4} } = \frac{1}{256}[/tex]

Using laws of exponents I distributed the exponent to the fraction and solved.

Therefore, the temperature at the summit of the 3,000-foot mountain on a sunny day is estimated to be 10.8 F°.

In mathematics, an equation is a statement that indicates the equality of two expressions. An equation typically contains one or more variables, which are placeholders for unknown values or quantities. The variables can take on different values, and the goal is often to find the values that satisfy the equation.

Here,

Let's start by calculating the rate of change of temperature with respect to elevation:

=-5.4 F° / 1,000 ft

This means that for every 1,000-foot increase in elevation, the temperature will decrease by 5.4 F°.

Next, we can calculate how much the temperature will decrease from the base of the mountain to the summit:

3,000 ft / 1,000 ft = 3

This means that the elevation difference between the base of the mountain and the summit is 3,000 - 0 = 3,000 ft.

So, the temperature decrease from the base to the summit is:

-5.4 F° / 1,000 ft * 3,000 ft = -16.2 F°

This means that the temperature at the summit will be:

27 F° - 16.2 F° = 10.8 F°

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The solution for the value of x is 55.

Since the segments of the secant segment and the tangent segment share an endpoint outside of the circle.

According to Tangent-Secant Theorem, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. That is:

x² = 5 * (5 + 6)

x = 5 * 11

x = 55

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Answer:

b, c, d, f

Step-by-step explanation:

Which ordered pairs are solutions to the inequality?

 2x+3y≥−1?

a≥b means that A must be equal to or greater than B.

Let's do this the long, but easy way, by plugging it in!

(x,y)

a. (0,-1) -> -3≥-1 -> false

b. (5,-1)-> 7≥-1 -> true

c. (-2,1) -> -1≥-1 -> true

d. (0,1) -> 3≥-1 -> true

e. (-6,0) -> -12≥-1 - > false

f. (2,-1) -> 1≥-1 -> true

Let me know if it is incorrect!

- a friendly 8th grader :)

Answer:  The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials.

In this case, the number of cinnamon jelly beans in the scoop is 6. The total number of jelly beans in the scoop is 5+22+6=33.

Therefore, the experimental probability of scooping a cinnamon jelly bean from the bin is:

P(cinnamon) = number of cinnamon jelly beans / total number of jelly beans

P(cinnamon) = 6 / 33

P(cinnamon) = 2 / 11

So the experimental probability of scooping a cinnamon jelly bean from the bin is 2/11, which can be written as a fraction.

Step-by-step explanation:

Answer: Let's call the time it takes for Mrs. Cunningham to overtake Mr. Cunningham "t".

In that time, Mr. Cunningham will have traveled for 4 more hours than Mrs. Cunningham, so he will have traveled 4 + t hours.

We can set up an equation to represent the distance each person traveled:

distance = rate x time

For Mr. Cunningham:

distance = 46 mph x (4 + t) hours

For Mrs. Cunningham:

distance = 62 mph x t hours

Since they end up at the same place, their distances must be equal:

46 mph x (4 + t) = 62 mph x t

Simplifying this equation:

184 + 46t = 62t

16t = 184

t = 11.5

Therefore, it will take Mrs. Cunningham 11.5 hours to overtake Mr. Cunningham.

Step-by-step explanation:

Since 1 gallon = 4 quarts → (1/2) gallons = 2 quarts

1 gallon = 8 pints → (1/2) gallons = 4 pints

1 gallon = 16 cups → (1/2) gallons = 8 cups

Therefore from the given relation with gallons we can describe the relation between the cups, quarts and pints.

(1/2) Gallon > quarts > pints > cups

If we need 1 cup of milk then a pint container will be the best choice at a grocery store.

Answer: 1  pint would because a quart has 4 cups and 1/2 a gallon would be way to much. and a pint would be 2.

Step-by-step explanation:

1 pint  would be because a quart has 4 cups and 1/2 a gallon would be way to much. and a pint would 1 cup more than you need so 1 pint is right

Step-by-step explanation:

Radius = 70 cm    then diameter = 140 cm

Circumference = rope length = pi * diameter

                       = 140 * pi = 439.8 cm long   (round as needed)