6x^2 - 19x + 10
Factor

Answer:The answer will be 35ft

Step-by-step explanation:

One way that you can answer this is by using sin law. You will put the length of a side on top and the corresponding angle that faces towards that side at the bottom of a fraction. So for this one it will be 30/sin(70) = x/sin(90) The 90 comes from the bottom of the building with the ground. And the side the angle faces is the ladder. After that you put 30sin(90)/sin(70) to find x. And you get 34.655 which rounds to 35 ft.

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

The standard normal distribution has the largest variance.

The variance of a normal distribution determines the spread or dispersion of the data.

A larger variance indicates a wider spread of values around the mean. The standard normal distribution is a specific case of the normal distribution with a mean of 0 and a variance of 1. Since the variance is fixed at 1 for the standard normal distribution, it has the largest variance compared to any other normal density with different variances.

The variance of a normal distribution measures how much the data values deviate from the mean.

It is calculated as the average of the squared differences between each data point and the mean. A higher variance implies a greater dispersion of values, indicating a wider range of possible outcomes.

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Answer:

2 more classes than Ha? Provide more information, please.

Answer:

NEED MORE INFO

Step-by-step explanation:

(a) Using a left-endpoint Riemann sum, we can estimate the integral of f(x) over the interval from 0 to 10.

The left-endpoint Riemann sum is obtained by multiplying the width of each subinterval by the function value at the left endpoint of that subinterval and summing all the products. In this case, the width of each subinterval is 2 units. Evaluating the sum: (2 * 45) + (2 * 44) + (2 * 42) + (2 * 37) + (2 * 27) + (2 * 7) gives us 212. Therefore, the estimate for the integral of f(x) using the left-endpoint Riemann sum is 212.

(b) Using a right-endpoint Riemann sum, we can estimate the integral of f(x) over the same interval. The right-endpoint Riemann sum is obtained by multiplying the width of each subinterval by the function value at the right endpoint of that subinterval and summing all the products. In this case, the width of each subinterval is still 2 units. Evaluating the sum: (2 * 44) + (2 * 42) + (2 * 37) + (2 * 27) + (2 * 7) + (2 * 0) gives us 202. Therefore, the estimate for the integral of f(x) using the right-endpoint Riemann sum is 202.

(c) To find the average of the left- and right-endpoint Riemann sums, we add the results from parts (a) and (b) and divide the sum by 2. (212 + 202) / 2 equals 207. Therefore, the average of the left- and right-endpoint Riemann sums gives us an estimate of 207 for the integral of f(x) over the interval from 0 to 10.

Using a left-endpoint Riemann sum, the estimated integral of f(x) over the interval from 0 to 10 is 212. Using a right-endpoint Riemann sum, the estimated integral is 202. The average of these two sums gives an estimate of 207 for the integral of f(x) over the same interval.

Riemann sums are methods used to approximate the area under a curve by dividing the interval into subintervals and summing the areas of rectangles. In this case, the table provides us with discrete values of f(x) at specific points. To estimate the integral, we divide the interval from 0 to 10 into subintervals of equal width, which is 2 units in this case. In a left-endpoint Riemann sum, we multiply the width of each subinterval by the function value at the left endpoint of that subinterval and sum all the products. The right-endpoint Riemann sum follows a similar principle, but we use the function value at the right endpoint of each subinterval. Taking the average of the left- and right-endpoint Riemann sums provides a more balanced estimate. In this example, the left-endpoint Riemann sum yields an estimate of 212, the right-endpoint Riemann sum gives 202, and their average is 207. These estimates provide approximations for the integral of f(x) over the given interval.

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To simplify a radical expression, we aim to simplify the radical itself by finding perfect square factors and then simplify any remaining factors outside the radical.

For example, if you have the expression √(12x^3), you can simplify it as follows:

√(12x^3) = √(4 * 3 * x^2 * x) = 2x√(3x)

So the simplified form of √(12x^3) is 2x√(3x).

By following these steps, you can simplify radical expressions and write them in a more simplified and concise form.

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Answer:(9,-3)

Step-by-step explanation:

You just have to flip the numbers

Answer:

maybe 15?? sorry if I'm wrong

Answer:

800,653,284

Step-by-step explanation:

859*612 = 525,708

525,708*1523 =

800,653,284

Answer:

859 x 612 x 1523 =

Step-by-step explanation:

800653284  

hope this helps! :)

Answer:

32

Step-by-step explanation:

This is because you would want the feet and the radium kinda meeting up in a way and would need to make sure you can fill it in with th e drive way as it will be on a horizontal base so you would need X2 of the driveway to make it into a standing up horizontal base

Hope this helps

If this seems incorrect please comment with the answer that it should be and I shall change my answer thanks you :)

The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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Answer:

∠6 = 78°.

Step-by-step explanation:

∠3 = 78°

∠2 and ∠3 are vertical angles, => ∠2 = ∠3 = 78°.

∠2 and ∠6 are corresponding angles, => ∠6 = 78°.

Answer:

\(\displaystyle 78° = m\angle{6}\)

Explanation:

As you can see, angles \(\displaystyle 6\:and\:3\)are alternate interiour angles, and accourding to the Alternate Interiour Angles Theorem, these angles are considered congruent, therefore seventy-eight degrees is also the measure of the sixth angle.

I am joyous to assist you at any time.

To find the equation, First step is to find the slope which we can use in the formula and then we will find the equation using the specific formula...

\( \boxed{ \sf \:m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}} }\)

\( \tt \to \: m = \frac{ - 2-( - 5)}{ - 8 -(- 4)} \)

\( \tt \to \: m = \frac{ -2+5}{ -8+4} \)

\( \tt \to \: m = - \frac{3}{4} \)

\( \boxed{ \sf \:y - y_{1} = m(x - x_{1}) }\)

\( \tt \nrightarrow \: y - ( - 5) = - \frac{3}{4} (x - ( - 4))\)

\( \tt \nrightarrow \: y + 5 = - \frac{3}{4} (x + 4)\)

\( \tt \nrightarrow \: y + 5 = - \frac{3}{4} x - 3\)

\( \tt \nrightarrow \: y = - \frac{3}{4} x - 3 - 5\)

\( \bf\nrightarrow \: y = - \frac{3}{4} x - 8\)

The solution is, The equation the line is,  y = -3x/4 -8

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have

two points (-4, -5) and (-8, -2)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y+5)/(x+4)=(-2+5)/(-8+4)

=>(y+5)/(x+4)= 3/ -4

=>-4y - 20 = 3x +12

=> -4y = 3x + 32

=> y = -3x/4 -8

Hence, the required equation is,   y = -3x/4 -8

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The sampling distribution model for figuring out how many people in this group might not pay on time is:

E. mean = 8%; standard deviation = 1.1%.

The steps to determine the mean and standard deviation of the sampling distribution of the proportion of clients who may not make timely payments would be:

Start with the idea that 8% of the loans will have payments that are late. So the percentage of people who pay late is p = 0.08.

Calculate the sample size, which is given as n = 600.

Determine the mean of the sampling distribution. The mean of the sampling distribution of the proportion of late payments is equal to the population proportion, which is 0.08.

Find the standard deviation of the distribution of the samples. The standard deviation is discovered by taking the square root of the commodity of the sample size and the percentage of late payments in the whole population (1 - percentage of late payments in the whole population) and dividing it by the sample size:

σ = √( (p * (1-p)) / n )

σ = √( (0.08 * 0.92) / 600 ) ≈ 0.011

So, the answer will be option E. mean = 8%; standard deviation = 1.1%.

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The interval of convergence is (-2, 14)., the radius of convergence is 8.

To find the radius of convergence, we take half the length of the interval of convergence: Radius of Convergence = (14 - (-2))/2 = 16/2 = 8. Hence, the radius of convergence is 8.

To find the radius of convergence and interval of convergence of the series, we will use the ratio test. Consider the series:

∑ [(√n)/(8^n)] * [(x-6)^n]

Let's apply the ratio test:

lim┬(n→∞)⁡(|(√(n+1))/(8^(n+1)) * ((x-6)^(n+1))| / |(√n)/(8^n) * ((x-6)^n)|)

Simplifying this expression, we get:

lim┬(n→∞)⁡(|√(n+1)/(√n) * ((x-6)/(8))|)

Since we are interested in finding the radius of convergence, we want to find the limit of this expression as n approaches infinity:

lim┬(n→∞)⁡(|√(n+1)/(√n) * ((x-6)/(8))|) = |(x-6)/8| * lim┬(n→∞)⁡(√(n+1)/(√n))

Now, let's evaluate the limit term:

lim┬(n→∞)⁡(√(n+1)/(√n)) = 1

Therefore, the simplified expression becomes:

|(x-6)/8|

For the series to converge, the absolute value of (x-6)/8 must be less than 1. In other words:

|(x-6)/8| < 1

Simplifying this inequality, we have:

-1 < (x-6)/8 < 1

Multiplying each part of the inequality by 8, we get:

-8 < x-6 < 8

Adding 6 to each part of the inequality, we have:

-8 + 6 < x < 8 + 6

Simplifying, we obtain:

-2 < x < 14

Therefore, the interval of convergence is (-2, 14).

Finally, to find the radius of convergence, we take half the length of the interval of convergence:

Radius of Convergence = (14 - (-2))/2 = 16/2 = 8

Hence, the radius of convergence is 8.

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Answer:The two true statements are:

A. The reflection point across the y-axis is (2, 6).

D. The reflection point across the x-axis is (¯2, ¯6).

Step-by-step explanation:

Answer:

The two true statements are:

A. The reflection point across the y-axis is (2, 6).

D. The reflection point across the x-axis is (¯2, ¯6).

Step-by-step explanation:

Answer:

11.855762

Step-by-step explanation:

Answer:

11.856 miles

Step-by-step explanation:

I just know

Using the data of interquartile range and median given, only option C is correct because approximately 50% of the days had a high temperature greater than 62°F.

We are given that the median high temperature is 62°F and the interquartile range is 32. The interquartile range is the difference between the first and third quartiles, which means that the first quartile is at 62 - 16 = 46°F and the third quartile is at 62 + 16 = 78°F.

Option A: approximately 25% of the days had a high temperature less than 30°F.

Since 30°F is much lower than the first quartile (46°F), it is unlikely that 25% of the days had a high temperature less than 30°F. Therefore, option A is not true.

Option B: approximately 25% of the days had a high temperature greater than 62°F.

This statement cannot be true because the median is already at 62°F, which means that 50% of the days had a high temperature greater than or equal to 62°F. Therefore, option B is not true.

Option C: approximately 50% of the days had a high temperature greater than 62°F.

This statement is true because the median high temperature is 62°F, which means that 50% of the days had a high temperature greater than or equal to 62°F, and the interquartile range is 32, which means that the third quartile is at 78°F. Since the third quartile is above 62°F, approximately 50% of the days had a high temperature greater than 62°F. Therefore, option C is most likely true.

Option D: approximately 57% of the days had a high temperature less than 94°F.

The maximum temperature that can be associated with the interquartile range of 32°F is the third quartile, which is at 78°F. Therefore, we cannot say that approximately 57% of the days had a high temperature less than 94°F. Therefore, option D is not true.

Hence, the most likely true statement is option C: approximately 50% of the days had a high temperature greater than 62°F.

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Answer: (0, 9) or x = 0, y = 9

Step-by-step explanation:

     The solution is the point of intersection.

Here, the lines intersect at the point (0, 9) in the format of (x, y) so we can pull out the answers x = 0 and y = 9.

Answer:

(0, 9)

Step-by-step explanation:

Doing the exact same steps for the other line...

There ought to be infinitely many solutions.

How many solutions can a system of 3 linear equations with 5 variables have?

There are infinitely many solutions. Assuming the 3 linear equations are linearly independent you have 2 free variables that can be chosen freely and depending on those two values you can find the 3 remaining variables as function of those two so for any choice of those two variables you can find a solution. If the equations are not linearly independent you have effectively only 1 or two equations so you can pick 4 or 3 variables freely and then the remaining variable or variables are function of these.

How do you solve a system of equations with 3 variables?
Simultaneous equations. Easy, if they are all linear. Possibly difficult otherwise. Basically pick 1 variable and 1 equation to rearrange so that variable is expressed in terms if the other 2. Then simplify. Now you have 2 equations in 2 variables. Repeat with the remaining 2 variables. When you have solved for the last variable, you can then substitute to solve for the second last. Then backtrack to the original substitution and solve that. General advice that works even for nonlinear equations.

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Answer:

its 13 or B

Step-by-step explanation:

Based on the information of an equilateral triangle △STU and the congruence of angles ∠TXU and ∠TVS, it can be concluded that UX is congruent (≅) to SV. The proof involves establishing the congruence of corresponding angles and applying the angle-angle (AA) congruence criterion.

To prove that UX is congruent (≅) to SV using the information, we will utilize the fact that △STU is an equilateral triangle and the congruence of angles ∠TXU and ∠TVS.

We have:

△STU is an equilateral triangle (∠STU = ∠TUS = ∠UST = 60 degrees)

∠TXU ≅ ∠TVS

Proof:

1. Draw a diagram of equilateral triangle △STU.

2. Draw a line segment UX and SV originating from U and S, respectively, towards the interior of the triangle.

3. ∠TXU and ∠TVS are congruent (given).

4. ∠STU = ∠TUS = ∠UST = 60 degrees (equilateral triangle property).

5. Since ∠STU and ∠TUS are both equal to 60 degrees and ∠TXU ≅ ∠TVS, we can conclude that ∠UTX ≅ ∠VTS (angle sum property of triangles).

6. By Angle-Angle (AA) congruence, ∆UTX ≅ ∆VTS.

7. Since corresponding parts of congruent triangles are congruent, we have UX ≅ SV (side UT ≅ side VT).

Therefore, we have proved that UX is congruent (≅) to SV using the information.

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The rate of change of the volume at that particular instant is - 62.8 m^3/h.

How to get the rate of change of the volume?

First, we can write the dimensions as:

radius = R = (5m + 1m/h*t)

height = H = (8m - 4 m/h*t)

Where t is the time in hours.

Then the volume of the cylinder will be:

V = pi*R^2*H = 3.14*(5m + 1m/h*t)^2*(8m - 4 m/h*t)

To get the rate of change, we need to differentiate it with respect to t, we will get:

V' = 3.14*(2*(5m + 1m/h*t)*(1m/h)*(8m - 4 m/h*t) + (5m + 1m/h*t)^2*(-4m/h))

V' = 3.14*( (2 m/h)*(5m + 1m/h*t)*(8m - 4 m/h*t) - (4m/h)*(5m + 1m/h*t)^2)

V' = 3.14*(2m/h)*( (5m + 1m/h*t)*(8m - 4 m/h*t) - 2*(5m + 1m/h*t)^2)

As you can see the rate of change depends on t, but we want the rate of change at this instant, then we use t = 0, replacing that on the above equation we get:

V'(0) = 3.14*(2m/h)*( (5m + 1m/h*0)*(8m - 4 m/h*0) - 2*(5m + 1m/h*0)^2)

V'(0) = 3.14*(2m/h)*( (5m)*(8m ) - 2*(5m)^2)=  -62.8 m^3/h

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The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

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Answer: 6

Step-by-step explanation: 10-4=6

Answer:

\(y = 2\)

Step-by-step explanation:

1) Simplify 5y/9 - y/9 to 4y/9.

\( \frac{4y}{9} = \frac{8}{9} \)

2) Multiply both sides by 9.

\(4y = \frac{8}{9} \times 9\)

3) Cancle 9.

\(4y = 8\)

4) Divide both sides by 4.

\(y = \frac{8}{4} \)

4) Simplify 8/4 to 2.

\(y = 2\)

Hence, the answer is y = 2.

Answer:

Explain the question again

Step-by-step explanation:

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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