K Rick's dad used a ladder to hang up their Christmas lights on the roof. When he leaned the ladder against the house, it created a triangle. If the height of the wall measures 12 feet, the ladder measures 15 feet, and Rick's dad put the base of the ladder 9 feet from the wall, what is the area of the triangle that is created? A 36 feet2 B) 54 feet 67.5 feet? D 90 feet​

Answer:

HM = 11

CD = 12.5

Step-by-step explanation:

[tex]A)[/tex]

[tex]1)\ NH*HM = JH * HK[/tex]

[tex]2)\ 33 * HM = 363[/tex]

[tex]3)\ HM = 11[/tex]

[tex]B)[/tex]

[tex]1)\ GV^2 = VC * (DC + AC)[/tex]

[tex]2)\ 15^2 = 10 * (CD + 10)\\[/tex]

[tex]3)\ 225 = 10CD + 100\\[/tex]

[tex]4)\ 125 = 10CD\\[/tex]

[tex]5)\ CD = 12.5[/tex]

The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints of the segment and the ratio of the desired point from the first endpoint.

The formula is:

Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))

Where x1 and y1 are the coordinates of the first endpoint, x2 and y2 are the coordinates of the second endpoint, and r is the ratio of the desired point from the first endpoint.

The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints and the ratio of the desired point from the first endpoint. The formula is given in the form of Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1)).

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The given equation gives two solution. We can find solution by using quadratic formula or discriminant.

A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R. So a and b ≠ 0. When we consider a system of linear equations we can find the number of solutions by comparing the coefficients of the variables of the equations.

How do you find how many solutions are in a quadratic equation?

if the discriminant is positive. Then the quadratic equation has two solutions.

if the discriminant is equal. Then the quadratic equation has one solution.

if the discriminant is negative. Then the quadratic equation has no solution.

Here we have

a=5    b=-7   c=4

Disc= [tex]b^2[/tex]-4ac

Disc= [tex](-7)^2[/tex]-4(5)(4)

Disc= 49+80

      =129

Disc >0    it has two solutions.

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Complete question is: How many solutions are there for 5x^2+7x-4=0?

a) 0

b) 1

c) 2

d) 3

Answer:

What shape is it?

Please write the full question

==========================================================

Explanation:

Pick any two points on the line to apply the slope formula.

I'll select (-5,1) and (5,-1)

[tex](x_1,y_1) = (-5,1) \text{ and } (x_2,y_2) = (5,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - 1}{5 - (-5)}\\\\m = \frac{-1 - 1}{5 + 5}\\\\m = \frac{-2}{10}\\\\m = -\frac{1}{5}\\\\[/tex]

The slope as a fraction is -1/5

A slope of -1/5 means " go down 1, then to the right 5 units".

An example of this motion is when going from (-5,1) to (0,0)

Another example would be going from (0,0) to (5,-1)

----------

The "down 1, right 5" motion is because

Answer:

hope this helps

Step-by-step explanation:

Strawberry = 14

blueberry = 14

cherry = 7

chocolate = 7

apple = 14

The relationship between the natural logarithm (ln) and the natural exponential (e) is given by the equation ln(x) = e^x. This equation is known as the exponential form of the natural logarithm.

To explain this relationship, let's start with a simple example. Suppose we have a number x, and we want to find its natural logarithm. To do this, we can use the following equation:

ln(x) = e^x

This equation states that the natural logarithm of x is equal to the natural exponential of x. In other words, we can calculate the natural logarithm of x by raising e to the power of x. To illustrate this with an example, suppose we want to calculate the natural logarithm of 10. We can do this using the equation above as follows:

ln(10) = e^10

Now, we can use a calculator to calculate e^10. If we do this, we get the result of 22,366.48. Therefore, the natural logarithm of 10 is equal to 22,366.48.

The relationship between the natural logarithm and the natural exponential is important because it allows us to easily calculate the natural logarithm of any number. All we have to do is raise e to the power of that number, and the result will be the natural logarithm of that number. This is a very useful tool in mathematics and can be used to solve many problems involving logarithms.

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The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).

The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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a. E(B) = 9.5

b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

c. Standard variable shows how much deviation from mean variable.

In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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Answer:

x < -20

Step-by-step explanation:

To solve x/5 + 6 < 2,

First subtract 6 from both sides of the equation.

This makes x/5 < -4.

Then multiply both sides of the equation by 5.

This makes x < -20.

Therefore, the solution to the equation is x < -20.

Answer:

y < (3/4)x

Step-by-step explanation:

Answer:

$200

Step-by-step explanation:

The y-intercept is where the line meets the y-axis (vertical).  The line on the graph appears to go through the point (0, 200).

Answer:

Step-by-step explanation:

Hope this helps u!!

There will be 800 people who did not like either show.

To find out how many people did not like either show, we need to subtract the number of people who liked both shows from the total number of people surveyed.

Let A be the number of people who liked Nepal Idol, B be the number of people who liked Comedy Champion, and C be the number of people who liked both shows.

According to the problem, we have:

A = 775

B = 975

C = 450

To find the number of people who did not like either show, we can use the formula:

Total number surveyed - (A + B - C)

Substituting the values given in the problem, we get:

1500 - (775 + 975 - 450) = 800

Therefore, 800 people did not like either show.

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Answer:

The value is 195 When x = 4 in 3x³ + 3.

Step-by-step explanation:

3x³ + 3

Insert 4 for x.

3(4)³ + 3

Cube the 4.

3(64) + 3

Multiply 3 by 64.

192 + 3

Add.

195

Answer:

quadrant 1

Step-by-step explanation:

b/c quadrant(+,+)

From the origin,

she is 22 units to the right and 1 unit upwards.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

Thalia is in the room located at (22,1).

From the origin to this point  (22,1).

In the first quadrant,

From the origin,

she is 22 units to the right and 1 unit upwards.

Therefore, she is 22 units to the right and 1 unit upwards.

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answer:

b+24

step-by-step explanation:

it’s just asking for the sum so add the two values. there are no other integers given other than 24 so the answer is in expression form. hope that helps!

Answer:

$35.97

Step-by-step explanation:

33 × .09 = 2.97

33 + 2.97 = $ 35.97

Three true statements about the angles of the given figure are,

1. angle 1 and the 55 degree angle are adjacent.

5. angle 1 = 180 degree - 55 degree

6. angle 2 = 180 degree - 55 degree - 45 degree.

Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.

Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.

Analysing all the statements given in the question,the corrrect options are

Option 1, since angle 1 and 55 degree share the same vertex.

Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.

Option 6, since the sum of all the interior angles of a triangle is 180 degrees.

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The 95% confidence interval for the true mean number of reproductions per hour for the bacteria is given as follows:

(3.78, 4.22)

The bounds of the confidence interval are calculated according to the equation presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 4, \sigma = 1.9, n = 283[/tex]

Hence the lower bound of the confidence interval is of:

[tex]4 - 1.96\frac{1.9}{\sqrt{283}} = 3.78[/tex]

The upper bound of the confidence interval is of:

[tex]4 + 1.96\frac{1.9}{\sqrt{283}} = 4.22[/tex]

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Answer:

A

Step-by-step explanation:

Given

- 5x - 10 < 20 ( add 10 to both sides )

- 5x < 30

Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity

x > - 6 → A

Answer:

  B.  (see attached)

Step-by-step explanation:

You want the solution and graph of the inequality |x+3| > 2.

The inequality resolves to two inequalities with different domain definitions:

  |x +3| > 2

When the argument is negative, (x+3) < 0, this is ...

  -(x +3) > 2

  -x -3 > 2 . . . . . . eliminate parentheses

  x +3 < -2 . . . . . . multiply by -1

  x < -5 . . . . . . . . . subtract 3; consistent with the domain definition

When the argument is positive, (x+3) > 0, this is ...

  x +3 > 2

  x > -1 . . . . . . . . subtract 3

  -1 < x . . . . . . . . same thing using the < symbol

These differing solution sets do not overlap, but elements of either set are solutions to the inequality. The appropriate conjunction is "OR":

  solution: x < -5 or -1 < x

The graph is attached.

__

Additional comment

We like to use the < or ≤ symbols when expressing the solution to an inequality. That way, the relation of the variable to the boundary value is the same as its relation on a number line. Solution values are left of -5 or right of -1:

  x < -5  or  -1 < x

It helps provide a check that the graph is properly drawn.

The inequality can be rewritten as ...

  |x -(-3)| > 2

which can be interpreted as saying the positive distance from x to -3 is more than 2. This tells you the graph will have two disjoint branches, and the appropriate conjunction is OR.

If the problem were different, and the inequality were ...

  |x -(-3)| < 2

it would be telling you the solution values have a distance less than 2 from -3. They will be in one continuous band from -5 to -1, so the appropriate conjunction is AND. The solution in this case is usually written as a compound inequality with no conjunction: -5 < x < -1. (Note the use of < symbols puts the variable value in the middle, between the boundary values, as in graph D.)

Answer:

[tex]AP = \frac{1}{2} AB \\ AB = 2AP[/tex]

Let H be the number of hamburgers sold and C be the number of cheeseburgers sold.

The total number of hamburgers and cheeseburgers sold is given by the equation: H + C = 429

The number of cheeseburgers sold is given by the equation: C = 2H

Substituting the second equation into the first equation, we get: H + 2H = 429

Combining like terms, we get: 3H = 429

Dividing both sides by 3, we get: H = 143

On Thursday, 143 hamburgers were sold.

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = (x+2)(x+6) is defined for all real numbers, so the domain is all real numbers.

What do a function example's range and domain mean?

A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

The range of a function is the set of all possible output values (y-values) produced by the function. The function f(x) = (x+2)(x+6) is a polynomial, and all polynomials of the form (ax^2 + bx + c) with real coefficients (a,b,c) have range is all real numbers. The range of the function f(x) = (x+2)(x+6) is also all real numbers.

So the answer is

The domain is all real numbers, and the range is all

real numbers.

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Answer:

the answer is 6:45pm brain list me

Answer:

this is from my math teacher's notecards! :)

Step-by-step explanation:

The simplified form of the algebraic expression [tex]2c-7c[/tex] is [tex]-15[/tex]

The given algebraic expression is [tex]2c-7c[/tex] and we need to use [tex]c=3[/tex]

Let's substitute the value of [tex]c[/tex] in the given algebraic expression, that is

                      [tex]=2(3)-7(3)\\=6-21\\=-15[/tex]

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Answer:

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

Given expression

Simplify it:

Find its value by plugging in the value of c:

Answer:

-73

Step-by-step explanation:

So to begin you must find where you start on a graph. To do this you can go backwards from your first number and in this situation it would be 14.5 because the slope is -2.5x. I will use y as the answer.

y=-2.5x+14.5

From here you plug in how many terms are neeeded for the correct answer. In this situation there is 35 terms needed.

y=-2.5(35)+14.5

Solve this equation to get your answer.

y=-73

Answer:

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

Given sequence:

This is an AP with the common difference of:

The first term is a = 12.

Use the nth term equation to find the 35th term: