ΔABC is a right triangle in which ∠B is a right angle, AB = 1, AC = 2, and BC = sqrt(3).

cos C × sin A =

I think the answer is 3/4, because cos(c) = adj / hypot and sin(a) = opposite / hypot

cos(c) = sqrt(3) / 2
sin(a) = sqrt(3) / 2
which is 3/4 when multiplied.

Answer:

The actual price is 13.6 % lower than the expected price....

Step-by-step explanation:

Lets suppose the expected price = x

CPI = ( expected price ) : ( price in 1983 ) *100

219  =  ( x  : 12.95 ) *100

Divide both sides by 100.

x : 12.95 = 2.19

x =2.19*12.95

= $28.36  ( expected price )

p = ( 24.50*100 ) / 28.36

p= 2450/28.36

= 86.4 %

100 % - 86.4 % = 13.6 %

The actual price is 13.6 % lower than the expected price....

Answer:

c

Step-by-step explanation:

because i said so brudda

[tex]|\Omega|=50\cdot49=2450\\|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{2450}=\dfrac{3}{35}\approx8.6\%[/tex]

The probability of randomly selecting two jelly beans in succession without replacement is;

0.0857

The jar contains 50 jellybeans.

Thus; N = 50

The individual berries include;

5 lemon

10 watermelon

15 blueberry

20 grape

Probability of first being a jelly bean = 15/50

Probability of second being jelly bean = 14/49

Thus,probability of selecting 2 jelly beans in succession without replacement is =

15/50 × 14/49 = 0.0857

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Answer:

GLH is congruent to JLK as the quadrilateral is a parallelogram,

KJ = GH OR HJ = GK

GL = LJ OR. HL = LK

triangle JKG = GHJ

triangle HGK = KJH

Answer:

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

          Statement                                     Reason

1.   GH ║ KJ                                      Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ     Alternate interior angle theorem

3. GH ≅ KJ                                        Definition of parallelogram

4.  Δ GLH ≅ Δ JLK                            ASA postulate of congruence

Hence, proved...

Check the picture below.

1. (3 + xz)(–3 + xz)

2. (y² – xy)(y² + xy)

3. (64y2 + x2)(–x2 + 64y2)

Explanation

The difference of 2 squares is in the form (a+b)(a-c).

(3 + xz)(–3 + xz) = (3 + xz)(xz -3)

                           = (xz + 3)(xz - 3)

                          = x²y²-3xy+3xy-9

                          =x²y² - 3²

(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²

                          = y⁴ - x²y²

(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)

                                      = 4096y⁴-64y²x²+64y²x²-x⁴

                                      = 4096y⁴ - x⁴

Answer:

  18°

Step-by-step explanation:

The law of cosines tells you ...

  a² = b² + c² -2bc·cos(A)

Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.

  cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140

  A = arccos(133/140) ≈ 18.2° ≈ 18°

Answer:

25 years

Step-by-step explanation:

Solution:-

- Data for the average daily temperature on January 1 from 1900 to 1934 for city A.

- The distribution X has the following parameters:

                    Mean u = 24°C

                    standard deviation σ = 4°C

- We will first construct an interval about mean of 1 standard deviation as follows:

  Interval for 1 standard deviation ( σ ):                                    

                    [ u - σ , u + σ ]

                    [ 24 - 4 , 24 + 4 ]

                    [ 20 , 28 ] °C

- Now we will use the graph given to determine the number of years the temperature T lied in the above calculated range: [ 20 , 28 ].

           T1 = 20 , n1 = 2 years

           T2 = 21 , n2 = 3 years  

           T3 = 22 , n3 = 2 years

           T4 = 23 , n4 = 4 years  

           T5 = 24 , n5 = 3 years

           T6 = 25 , n6 = 3 years  

           T7 = 26 , n7 = 5 years

           T8 = 27 , n8 = 2 years

           T5 = 28 , n9 = 1 years

- The total number of years:

               ∑ni = n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9

                     =  2 + 3 + 2 + 4 + 3 + 3 + 5 + 2 + 1

                     = 25 years          

Answer:

22,25,27 there are multiple questions that have the same question but different answers on Edge

Step-by-step explanation:

I hope this helped :)

Note that,

[tex]9x^2+24x+20=4\Longrightarrow9x^2+24x+16[/tex]

Which factors to,

[tex](3x+4)^2=0\Longrightarrow3x+4=0[/tex]

And simplifies to solution C,

[tex]\boxed{x=-\dfrac{4}{3}}[/tex]

Hope this helps.

Any additional questions please feel free to ask.

r3t40

Answer:

[tex]\large\boxed{C.\ x=-\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]9x^2+24x+20=4\qquad\text{subtract 4 from both sides}\\\\9x^2+12x+12x+16=0\\\\3x(3x+4)+4(3x+4)=0\\\\(3x+4)(3x+4)=0\\\\(3x+4)^2=0\iff3x+4=0\qquad\text{subtract 4 from both sides}\\\\3x=-4\qquad\text{divide both sides by 3}\\\\x=-\dfrac{4}{3}[/tex]

Answer:

  x = 5

Step-by-step explanation:

You want to find x such that ...

  x^2 +(x +1)^2 = 61

  2x^2 +2x -60 = 0 . . . . . simplify, subtract 61

  x^2 +x -30 = 0 . . . . . . . divide by 2

  (x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.

The relevant solution is x = 5.

Answer:

A. The CV is a relative measure of risk/return.

Step-by-step explanation:

The coefficient of variation of any investment, is used to measure and calculate the total risk of that investment with respect to its per unit expected return rate.

We can also define the coefficient of variation as a ratio of standard deviation to the expected value of an investment.

The answer is - A. The CV is a relative measure of risk/return.

The coefficient of variation (CV) is a relative measure of risk/return; thus, statement A is correct, and statement D is correct as it relates to the preferences of risk-averse investors. This measure is useful for assessing the consistency of investment returns, especially when comparing different investment options.

The coefficient of variation (CV) is a statistical measure that is used to assess the relative variability of data. It is calculated by dividing the standard deviation by the mean and multiplying by 100. This ratio provides a standardized measure of the dispersion of data points in a data set around the mean, which is particularly useful when comparing the variability between datasets with different units or scales.

Now let's examine the given statements:

A. The CV is a relative measure of risk/return.

B. The CV is an absolute measure of risk/return.

C. The higher the CV value the more acceptable the risk/return profile for a risk-averse investor.

D. The lower the CV value the more acceptable the risk/return profile for a risk-averse investor.

Statement A is correct: the CV is indeed a relative measure because it expresses the standard deviation as a percentage of the mean, making it unitless and thus comparable across different data sets and scales.

Statement D is also correct: a lower CV indicates that the returns are less volatile relative to the mean return, which is generally preferred by risk-averse investors. Risk-averse investors prefer investments with more predictable and stable returns, as such investments are associated with lower levels of relative risk.

Answer:

1/2

Step-by-step explanation:

Given:

sinx=-1/2

cosy=√3/2

finding x

x=sin^-1(-1/2)

x=-π/6

x=-30°

finding y

cosy=√3/2

y=cos^-1(√3/2)

y=π/6

y=30°

Now finding cos(x-y)

cos(-π/6-π/6)

=cos(-π/3)

=1/2!

Answer:

Step-by-step explanation:

(a) For a depth of x, the two sides of the rain gutter are length x, and the bottom is length (12-2x). The cross sectional area is the product of these dimensions:

  A = x(12 -2x)

This equation describes a parabola that opens downward. It has zeros at ...

  x = 0

  12 -2x = 0 . . . . x = 6

The maximum area is halfway between these zeros, at x=3.

The maximum area is obtained when the depth is 3 inches.

__

(b) For an area of at least 16 square inches, we want ...

  x(12 -2x) ≥ 16

  x(6 -x) ≥ 8 . . . . . divide by 2

  0 ≥ x² -6x +8 . . . . subtract the left side

  (x -4)(x -2) ≤ 0 . . . factor

The expression on the left will be negative for values of x between 2 and 4 (making only the x-4 factor be negative). Hence the the depths of interest are in that range.

At least 16 square inches of water will flow for depths between 2 and 4 inches, inclusive.

The maximum cross-sectional area of the gutter which allows the most water flow is achieved at a depth of 4 inches. For a flow rate of 16 square inches, we need to solve the equation for the cross-sectional area equal to 16 to find the corresponding depth.

Your question pertains to maximizing the cross-sectional area of a rain gutter made from 12-inch wide aluminum sheets. This involves the use of calculus, specifically optimization, and basic geometry.

Let's denote 'x' as half the width of the base. When the sides are turned up 90 degrees, the sides will be of length 'x'. Since the gutter is 12 inches wide, the equation for the width is 2x+x=12. So, x=4.

To maximize the cross-sectional area, you need to set the derivative of the area function equals to zero.

For your second question, to find the depths that will allow at least 16 square inches of water to flow, equate the cross-sectional area equals to 16, and solve for 'x'.

In conclusion,

The depth that would allow maximum cross-sectional area and the most water flow is when x = 4 inches,. To allow 16 square inches of water to flow, solve for 'x' when the cross-sectional area equals to 16.

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Answer:

a. 8.4 km  b. 20 km/hr or 20,000 m/hr

Step-by-step explanation:

This is your polynomial:

[tex]d(v)=.004v^2+.2v+6[/tex]

The important thing to realize is that d(v) is the distance it takes for the boat to stop.  That will come later, in part b. Besides that, we also need to remember that v is velocity, which is speed, in km/hr.

For part a. we are looking for d(v), the stopping distance, when v = 10.  That means that we will sub in a 10 for each v in the function and solve for d(v):

[tex]d(10)=.004(10)^2+.2(10)+6[/tex] so

d(10) = 8.4 km

Now comes the part I was referring to above.  Part b is asking us the speed of the boat if it takes 11.6 meters to stop.  If d(v) is the stopping distance, we sub 11.6 in for d(v) in the function:

[tex]11.6=.004v^2+.2v+6[/tex]

The only way w can solve this for velocity is to get everything on one side of the equals sign, set the polynomial equal to 0, then plug the values into the quadratic formula.  

[tex]0=.004v^2+.2v-5.6[/tex]

Plugging that into the quadratic formula gives you 2 values of velocity:

v = 20 km/hr and -70 km/hr

We all know that neither time nor distance in math will EVER be negative so we can discount the negative number.  However, I believe that you asked for the distance in meters, so 20 km/hr is the same as 20,000 m/hr.

Answer:

V = $3.50t + $90.5....

Step-by-step explanation:

V(t) is a function of t that expresses the value in year 2000+t.  

We know that the increase is $3.50 times t.

So,

V(t) = $3.50t + c  

where c is the constant.

V(15) =  $3.50 (15) + c = $143     [t=15 as mentioned in the question]

and therefore  

c = $143 - $3.50 (15)

c= $143 - $52.50

c= $90.5  

Now we got the value of c. We can write the equation as  

V = $3.50t + $90.5....

The subject of this question is linear equation. The dollar value of a product expected to change over several years can be calculated using the future value formula V = P(1 + r)^(t-15), where P is the present value, r is the rate of change per year, and t represents the year.

To develop a linear equation that represents the dollar value V of a product in a certain year t, you can use the formula for future value received years in the future: V = P(1 + r)^(t-15), where P is the present value in 2015, r is the rate of change per year, and t represents the year.

For example, if a firm's payment was $20 million in 2015 and was expected to increase by 10% per year, then the value in 2020 (t = 20) would be calculated as: V = $20 million * (1 + 0.10)^(20-15).

From this equation, you can predict the future value of the product in terms of the year and rate of inflation.

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Answer: Price of a discount amision= Full Admission Price - discount Amount

Step-by-step explanation:

We have two variables "X" and "Y", where X= Full Admision Price and  Y= Discount Price of Admision  and we have to get the price of a discount admision or "Z" so the expresion will be Z= X-Y or Price of a discount admision = Full admision Price- discount Amount.

Answer:

Product B

Step-by-step explanation:

Divide the number of ounces i the bottle by the price of the bottle. Product A has a unit price of $0.17 and Product B has a unit price of $0.20. Therefore Product B has a lower unit price :))

Answer:

  (2.31079, 6.83083)

Step-by-step explanation:

The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

Here, that means the new coordinates are ...

  (4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)

To rotate the point (4,6) counterclockwise about the origin by 15 degrees, we can use the rotation formulas. The new coordinates are approximately (2.833, 6.669).

To rotate a point counterclockwise about the origin, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Using the given point (4,6) and an angle of 15 degrees, we can substitute the values into the formulas to find the new coordinates:

x' = 4 * cos(15) - 6 * sin(15) = 4 * 0.9659258263 - 6 * 0.2588190451 ≈ 2.833166271

y' = 4 * sin(15) + 6 * cos(15) = 4 * 0.2588190451 + 6 * 0.9659258263 ≈ 6.669442572

Therefore, the new coordinates of the point after rotation are approximately (2.833, 6.669).

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Answer:

  $240

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

[tex]m=\dfrac{12,000+12,000rt}{12t}=\dfrac{12,000+12,000\cdot 0.04\cdot 5}{12\cdot 5}\\\\m=\dfrac{14,400}{60}=240[/tex]

Keri's monthly loan payment is $240 per month.

Answer: 300 per month

Step-by-step explanation:

Answer:

60060 different ways that teams can be chosen

Step-by-step explanation:

Given data

employees n  = 14

team = 3

each project employees

n(1) =  8

n(2) = 3

n(3) = 3

to find out

how many different ways can the teams be chosen

solution

we know according to question all employees work on a team so

select ways are = n! / n(1) ! × n(2) ! × n(3)     ....................1

here  n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1

and n(1)! = 8! =  8 ×7 ×6 ×5 ×4 × 3× 2× 1

n(2)! = 3! =  3× 2× 1

n(3)! = 3! =  3× 2× 1

so now put all these in equation 1 and we get

select ways are = (14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) / (8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) × ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  (14 × 13 ×12 ×11 ×10 ×9 ) / ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  2162160 / 36

select ways are = 60060

60060 different ways that teams can be chosen

Answer:

60060

Step-by-step explanation:

#copyright

Answer:

The next two terms after a1 is

-6 and then 18

Step-by-step explanation:

Geometric sequence means your pattern for the terms is multiplication by the same number.

So a1 is the first term and r is your common ratio.

The common ratio is what you are multiplying by each time to figure out the next term.

So the geometric sequence goes like this:

a1 ,  a1*r , (a1*r)*r or a1*r^2 , a1*r^3 ,....

So anyways you have

first term a1=2

second term a2=2(-3)=-6

third term a3=-6(-3)=18

And so on...

Answer:

[tex]m(RS)=17[/tex] inches  (answer rounded to nearest tenths)

Step-by-step explanation:

Central angle there is 150 degrees.

The radius is 6.48 inches.

The formula for finding the arc length, RS, is

[tex]m(RS)=\theta \cdot r[/tex]

where [tex]r[/tex] is the radius and [tex]\theta[/tex] ( in radians ) is the central angle.

I had to convert 150 degrees to radians which is [tex]\frac{150\pi}{180}[/tex] since [tex]\pi \text{rad}=180^o[/tex].

[tex]m(RS)=\frac{150\pi}{180} \cdot 6.48[/tex]

[tex]m(RS)=16.96[/tex] inches

Answer: [tex]17\ in[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Arc Lenght:

[tex]Arc\ Length=2(3.14)(r)(\frac{C}{360})[/tex]

Where "r" is the radius and  "C" is the central angle of the arc in degrees.

You can identify in the figure that:

[tex]r=6.48\ in\\C=150\°[/tex]

Then, you can substitute values into the formula:

[tex]Arc\ Length=Arc\ RS=2(3.14)(6.48\ in)(\frac{150\°}{360})\\\\Arc\ RS=16.95\ in[/tex]

Rounded to the nearest tenth, you get:

[tex]Arc\ RS=17\ in[/tex]  

Answer:

  -3

Step-by-step explanation:

The average rate of change is the y-difference divided by the x-difference:

  (2 -14)/(6 -2) = -12/4 = -3

The average rate of change for the sequence is -3.

Answer:

-3

Step-by-step explanation:

The quadratic equation 4x^2 - 4x - 7 = 0 is solved using the Quadratic Formula with coefficients a = 4, b = -4, c = -7. The correct solutions obtained are x = 1/2 + √2 and x = 1/2 - √2, corresponding to option (c).

To solve the quadratic equation 4x^2 - 4x - 7 = 0 using the Quadratic Formula, we first identify the coefficients: a = 4, b = -4, and c = -7.

The Quadratic Formula is given by:

x = √((-b ± √(b^2 - 4ac)) / (2a)).

Substitute the identified coefficients into the formula:

x = √(((-(-4) ± √((-4)^2 - 4(4)(-7))) / (2(4))).

Simplify the expression:

x = √(((4 ± √(16 + 112)) / 8),

x = √(((4 ± √(128)) / 8),

x = √((4 ± 8√2) / 8).

Simplify further:

x = 1/2 ± √2.

Therefore, the correct answers are:

x = 1/2 + √2 and x = 1/2 - √2,

which corresponds to option (c).

Answer:

9 bottles of water

Step-by-step explanation:

Marginal benefit is a microeconomic concept that explains how much the consumer adds satisfaction to each unit consumed of a given product. Usually, the marginal benefit is decreasing, which makes logical sense, the more a customer consumes a particular good, the smaller the benefit of the next unit.

At first, the first bottle of water has a high benefit as mentioned in the exercise:  9

In the second, you are a little less thirsty, so the benefit will be 10 - 1x2 = $8

In the ninth bottle, you will have very little thirst and the benefit will be 10 - 1x9 = $1

In the tenth bottle there is no benefit, the consumer is indifferent. As a rational consumer, you will buy until the bottle is still usable, even if minimal, for 9 bottles when your benefit is $1.

As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, you will buy a total of 10 bottles of water.

As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, the price of water is $1 per bottle.

The marginal benefit equation is given as MB = $10 - $x, where x represents the number of bottles of water you have had. So, for each bottle of water you consume, the marginal benefit decreases by $1.

To determine the number of bottles of water you will buy, you need to compare the marginal benefit to the price of water:

Therefore, you will buy a total of 10 bottles of water.

Step-by-step explanation:

10 is the value of A ......

Answer:

Value of A = 10

Step-by-step explanation:

Here Isoke is solving the quadratic equation by completing the square

        10x² + 40x – 13 = 0

         10x² + 40x – 13 + 13 = 0 + 13

         10x² + 40x + 0 = 13

         10x² + 40x = 13

          10 ( x² + 4x) = 13

   Here it is given as

           A(x² + 4x) = 13  

Comparing both

           We will get A = 10

Value of A = 10

For this case we have that by definition, the arc length of a circle is given by:

[tex]AL = \frac {x * 2 \pi * r} {360}[/tex]

Where:

x: Represents the angle between JM. According to the figure we have that x = 90 degrees.

[tex]r = \frac {16.4} {2} = 8.2[/tex]

So:

[tex]AL = \frac {90 * 2 \pi * 8.2} {360}\\AL = \frac {90 * 2 * 3.14 * 8.2} {360}\\AL = 12.874[/tex]

Rounding:

[tex]AL = 12.9[/tex] miles

Answer:

12.9 miles

Answer: 12.9

Step-by-step explanation:

Answer:4

Step-by-step explanation:16/4 = 4

if 75% of equipment is iron then do the math

So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods in the golf club is equal [tex]4[/tex].

" Number is defined as the count of any given quantity."

According to the question,

[tex]'x'[/tex] represents the number of irons

[tex]'y'[/tex] represents the number of woods

As per given condition we have,

[tex]x= 2y +4[/tex]                                  [tex](1)[/tex]

[tex]x = 75\%(x+ y)\\\\\implies x = \frac{75}{100}(x + y)\\ \\\implies x = \frac{3}{4} (x+y)\\\\\implies 4x= 3x + 3y\\\\\implies x = 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]

Substitute the value of [tex](2)[/tex] in [tex](1)[/tex] to get the number of woods,

[tex]3y = 2y +4\\\\\implies y =4[/tex]

Therefore,

[tex]x= 3\times 4\\\\\implies x=12[/tex]

Hence, the  number of woods in the golf club is equal [tex]4[/tex].

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Answer:

C: [tex]V=4840 (2 s.f.)[/tex]

Step-by-step explanation:

The formula for the volume of a cone is:

[tex]V= \frac{1}{3} \pi r^2h[/tex]

Therefore,

[tex]V=\frac{1}{3}\times 3.14\times(\frac{34}{2})^2\times 16\\\\V=4840 (2 s.f.)[/tex]

The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

Volume can be defined as a three-dimensional space enclosed by an object or thing.

It is given that:

A pile of tailings from a gold dredge is in the shape of a cone.

The diameter of the base is 34 feet and the height is 16 feet.

As we know,

The volume of the cone is given by:

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

r = 34/2 = 17 ft

h = 16 feet

Plug the above values in the formula:

[tex]\rm V=\pi (17)^2\dfrac{16}{3}[/tex]

After solving:

V = 1541.33π cubic feet

Take π = 3.14

V = 1541.33(3.14) cubic feet

V = 4839.78 ≈ 4840 cubic ft

Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

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Answer:

The answer is  

√3/2

Step-by-step explanation:

The value of sin 30°=1/2.

The special right triangle is the triangle used to know the side ratio without using Pythagoras theorem every time.

There are some types of special right triangles present like 30-60-90 triangle, 45-45-90 triangles, and the Pythagorean triple triangles.

Here for deriving the value for sin 30°, we will use the 30-60-90 triangle.

The 30-60-90 triangle is given below.

the value sine is calculated by the ratio of the opposite side and the hypotenuse of the right-angled triangle.

In 30-60-90 triangle the side opposite to 30° angle is x and the hypotenuse is 2x then the side opposite to 60° angle is x√3.

In 30-60-90 triangle,

sin 30°=opposite side/hypotenus

= x/2x

⇒sin 30°=1/2

Therefore, the value of sin 30°=1/2.

Learn more about the special right triangle

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Answer:

The height of the house is between 9 and 10 feet.

Step-by-step explanation:

The shaped formed with the ground, the ladder, and the house is a right triangle.

I'm going to apply Pythagorean Theorem here.

The length of the hypotenuse is given as 24 feet.

The length from the base of the ladder and the house is 22 feet.

So to find the height the ladder reaches on the house, we need to solve

[tex]a^2+22^2=24^2[/tex]

[tex]a^2+484=576[/tex]

Subtract 484 on both sides:

[tex]a^2=576-484[/tex]

Simplify:

[tex]a^2=92[/tex]

Square root both sides:

[tex]a=\sqrt{92}[/tex]

[tex]a \approx 9.59166[/tex] feet