the functions f(x) and g(x) are graphed

The 24 feet high up the ladder will reach to the wall if the ladder height is 25 feet and is placed 7 feet from the wall.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Length of the ladder = 7 feet

The distance between the wall bottom end to ladder bottom end = 7 feet

As we can see in the diagram the ladder and wall making a right angle triangle ABC in which

AC = 25 feet

BC = 7 feet

Let's suppose the length of the wall is h feet

AB = h feet

From the Pythagoras theorem:

AC² = AB² + BC²

Put the values of AC and BC, we get

25² = h² + 7²

625 = h² + 49

625 - 49 =  h²    (subtract by 49 on both sides)

576 = h²

h = 24 feet         (taking square root on both sides)

Thus, the 24 feet high up the ladder will reach to the wall.

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Given the points are A(3, 2) and B(6, 4).

If it is asking about the slope of the line AB, then we can use the slope formula as given by :-

[tex] Slope, \;m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

where (x₁, y₁) = A(3, 2) and (x₂, y₂) = B(6, 4)

[tex] m = \frac{4-2}{6-3} =\frac{2}{3} [/tex]

Hence, m = 2/3 would be slope of the line AB.

If it is asking about the y-intercept of the line AB, then we can use slope-intercept form as given by :-

y = mx + b

where m is the slope and b is the y-intercept.

we can plug the value of m = 2/3 and point A(3, 2) into the equation and solve for b.

[tex] 2=(\frac{2}{3} )(3) +b \\\\
2 = 2 + b \\\\
b = 0 [/tex]

Hence, b = 0 would be y-intercept of the line AB.

If it is asking for the equation of the line AB, then we can use slope-intercept form and put values of m = 2/3 and b = 0.

y = mx + b

[tex] y=\frac{2}{3} x+0 \\\\
y=\frac{2}{3} x \;\;
or\;\; 3y=2x [/tex]

Hence, [tex] y=\frac{2}{3} x \;\; or\;\; 3y=2x [/tex] would be equation of the line AB.

Answer:

'Sometimes' is the correct option

Step-by-step explanation:

We are given the statement,

'A kite is a rhombus'.

We know that,

Rhombus - is a parallelogram whose all four sides are equal and opposite angles are equal.

Kite - is a quadrilateral having two equal length adjacent sides and the angles where the pair of adjacent sides meet are equal.

So, we get that,

Thus, the kite is a rhombus when the all the sides of a kite are equal.

Hence, 'A kite is sometimes a rhombus'.

Answer:

Actually, it's never true.

Step-by-step explanation:

A kite is a quadrilateral defined to have no pairs of parallel sides.

A rhombus is a quadrilateral that has two pairs.

Final answer:

Lucy will need to ride around the block 3 times today to cover 3/4 of a mile, as each lap around the block is 0.25 miles long.

Explanation:

Lucy rode her bike around the block and covered a total distance of 1 mile by doing so 4 times. Each lap around the block is therefore 0.25 miles long (1 mile ÷ 4 laps = 0.25 miles per lap). To cover 3/4 of a mile, Lucy needs to complete three laps (3/4 of a mile ÷ 0.25 miles per lap = 3 laps). This is because 3/4 divided by 1/4 (which is the distance of one lap) equals 3. Hence, Lucy will need to ride around the block 3 times today to cover 3/4 of a mile.

To reach an 8-foot ceiling, you would need to stack approximately 1600 pennies. This is calculated by dividing the ceiling height in inches (96 inches) by the thickness of a penny, which is around 0.06 inches, and rounding to the nearest whole number.

To solve this problem, we need to understand that a penny is approximately 0.0598 inches thick. Since there are 12 inches in a foot, an 8-foot ceiling would be 96 inches tall. Therefore, to stack pennies from the floor to an 8-foot ceiling, you would divide 96 (the total inches of the ceiling height) by 0.0598 (the thickness of one penny).

Let's round 0.0598 inches to 0.06 inches for ease of computation. When we divide 96 by 0.06, we get approximately 1600 pennies. So, it would take roughly 1600 pennies to stack from the floor to an 8-foot ceiling.

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Answer:

All of them will double at the same time.

Step-by-step explanation:

The rule of 72 wa created to have an estimate of how long will an account that pays interests will take to double its value, in this case, as they all have the same interest rate, and the rule of 72 depends only on the interests that the account pays, there will be no difference between the doubling time of the accounts since eventhough they all have different amounts of money, having the same interest rate, will make them grow at the same rate.

180 - 90 -18 = 72

Answer is D 72 degrees

Answer:

the answer is -1/4

Step-by-step explanation:

Final answer:

The actual root of the polynomial f(x) = 60x²– 57x – 18 among the given options is -6/5.

Explanation:

According to the Rational Root Theorem, possible roots of the polynomial equation f(x) = 60x² − 57x − 18 are the factors of the constant term (−18) divided by the factors of the leading coefficient (60). The roots could be ±1/60, ±1/30, ±1/20, ±1/15, ±1/12, ±1/10, ±1/6, ±1/5, ±1/4, ±1/3, ±1/2, ±1, ±2/5, ±3/5, ±6/5, ±9/5, ±18/5, ±2, ±3, ±6, ±9, ±18.

To determine which of the given options are actual roots of the polynomial, we substitute each value into the polynomial and check if it returns a value of zero:

Substituting x = 3 into f(x) gives 60(3)² − 57(3) − 18 = 540 − 171 − 18 = 351, which is not zero.

Substituting x = 6 into f(x) gives 60(6)² − 57(6) − 18 = 2160 − 342 − 18 = 1800, which is not zero.

Substituting x = −1/4 into f(x) gives 60(−1/4)² − 57(−1/4) − 18 = 15 − −14.25 − 18 = 11.25, which is not zero.

Substituting x = −6/5 into f(x) gives 60(−6/5)² − 57(−6/5) − 18 = 86.4 − −68.4 − 18 = 0, which is zero. Therefore, −6/5 is an actual root of the equation.

Thus, the actual root among the given options is −6/5.

The angle θ = 133π/72 radians is equivalent to  332.5° degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To convert radians to degrees, use the following formula:

Angle in degrees = angle in radians × 180°/π

Here's how to apply this formula to the given angle:

θ= 133π/72 radians

θ in degrees = (133π/72) × 180°/π

θ in degrees = (133/72) × 180

θ in degrees = 332.5°

Therefore, the angle θ = 133π/72 radians is equivalent to  332.5° degrees.

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To raise the average height by 1 inch, the 22nd person would have to be 88 inches tall.

To find how tall the 22nd person would have to be in order to raise the average height by 1 inch, we can use the concept of average. Currently, there are 21 people with an average height of 5 feet 6 inches. This means that the total height of all 21 people combined is 5 feet 6 inches multiplied by 21.

If we want to raise the average height by 1 inch, we need to add a certain amount of height to the total height of all the people in the room. Let's call this additional height 'x'. So the new total height would be the previous total height plus 'x'.

Since the total number of people in the room will become 22, the new average height will be the new total height divided by 22. We can set up an equation to solve for 'x':

5 feet 6 inches multiplied by 21 plus 'x' divided by 22 equals 5 feet 6 inches plus 1 inch.

To solve this equation, we can first convert the heights to inches: 5 feet 6 inches is equivalent to 66 inches. Now we can solve the equation:

66 multiplied by 21 plus 'x' divided by 22 equals 67.

Now we can simplify and solve for 'x':

1386 plus 'x' divided by 22 equals 67.

1386 plus 'x' equals 67 multiplied by 22.

1386 plus 'x' equals 1474.

Subtracting 1386 from both sides, we get 'x' equals 1474 minus 1386, which is 88 inches. Therefore, the 22nd person would have to be 88 inches tall to raise the average height by 1 inch.

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Answer:

For scientific notation, we write one number to the left of the decimal point and the other numbers are written as a power of ten.

2.)1,220,000,000

[tex]1.22\times10^{9}[/tex]

3.)0.0287

We can write this in fraction form as:

[tex]\frac{287}{10000}[/tex]

So, when 10000 will go up that is in numerator it will hold a negative power.

So, in scientific notation it will be [tex]2.87\times10^{-2}[/tex]

Answer:

A.X+4

Step-by-step explanation:

3x2 + 18x + 24

A. x + 4

B. x - 4

C. x - 3

D. x + 3

Apex Answers

The length of midsegment DE is going to be 38.

The correct answer is option C.

For a better understanding let us name the triangle as ABC and DE is the midpoint on side AB and Ac respectively.

We need to find the value of DE.

We are given that AD = 45 DB = 45 , AE = 55 EC = 55 DE = 6x + 2 and BC = 2x + 64

We need to find the value of midsegment which means we need to find the value of DE.

In order to find the value of DE we would first need to find the value of x.

So , for finding the value of x we would first use the concept of similarity of triangles.

In triangle ADE and triangle ABC

angleA = angleA ( common)

angleD = angleB ( as DE || BC, so the angles formed by parallel lines are going to be equal)

By AA similarity we can say that triangle ADE similar to triangle ABC.

So , now after proving that both of the triangles are similar we can say that all of the sides of the triangles are going to be equal.

AD/ AB = DE/BC = AE/AC

AD/AB = DE / BC

Substituting the required values in expression above.

45/ AB = 6x + 2/ 2x + 64

45/ 90 = 6x + 2 / 2x +64 (AB = AD + DB = 45 + 45 = 90)

Cross-multiplying :

90x + 2880 = 540x + 180

-450x = -2700

x = 6

So , the value of x is going to be 6.

As we have found the value of x now we can easily find the value of DE by substituing the value of x in expression :

DE = 6x + 2

DE= 6(6) + 2

DE = 36 + 2

DE = 38

So , the length of DE is going to be 38.

Therefore , from the given options the correct one is C.

The question probable may be:

9. Find the length of the midsegment The diagram is not to scale:

A. 18

B. 15.5

C. 38

D. 76

Answer: 8.62 meters

Step-by-step explanation:

Given: The height of the rock, in meters, is given by the function [tex]f(x)=-4.9x^2+17[/tex] , where x is the number of seconds after Noelle releases her rock.

The height of Cesar’s rock, in meters, is given by the function [tex]g(x)=-4.9x^2+13x[/tex] , where x is the number of seconds after he releases his rock.

The moment when the rocks are at the same height  then f(x)= g(x)

[tex]\Rightarrow-4.9x^2+17=-4.9x^2+13x\\\\\text{Add }-4.9x^2\text{ ion both sides, we get}\\\\\Rightarrow\ 17=13x\\\\\Rightarrow\ x=\frac{17}{13}\\\\\Rightarrow\ x=1.3076[/tex]

To calculate height put x in first equation, we get

[tex]-4.9(1.3076)^2+17=8.62189\approx8.62[/tex]

Hence, the height = 8.62 meters

6/4=b/24

1.5=b/24

24(1.5)=b

36=b

Building is 36 ft tall

Answer:

36 feet

Step-by-step explanation:

Let x be the height of the building,

Given,

Length of the building's shadow = 24 ft,

Height of the person = 6 feet,

Length of person's shadow = 4 feet.

Since, at the same time,

[tex]\frac{\text{Height of the building}}{\text{Length of building's shadow}}=\frac{\text{Height of the person}}{\text{Length of person's shadow}}[/tex]

[tex]\frac{x}{24}=\frac{6}{4}[/tex]

[tex]4x=144[/tex]   ( By cross multiplication )

[tex]\implies x = 36[/tex]

Hence, the height of the building is 36 ft.

The required solution is 8.

It is required to find the least common denominator.

The smallest common multiple of two or more numbers and the common multiple of lowest degree of two or more polynomials.

Given:

Multiply 4 times 2 to get 8, then multiply 1 times 4 for the numerator of the first fraction .

1/4=1*2/4*2=4/8

5/8=5*1/8*1=5/8

The least common denominator of 1/4 and 5/8 is 8.

Therefore, the required solution is 8.

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To solve this problem, you can use the principle of addition of rates since the work done (filling the tank) would be equal when the pipes are working together or separately. Therefore, adding the rate of pipe A and B should equal to the rate of them working together.

To solve this problem, we'll use the principle that work done is equal to rate multiplied by time. In this case, the 'work' is filling the tank, and the 'rate' is how quickly each pipe can fill it.

Pipe A, we know, takes 18 hours to fill the tank. Therefore, its rate of work is 1/18 tanks per hour. For both pipes working together, it takes 9.9 hours, so their combined rate is 1/9.9 tanks per hour.

Assuming that the pipes work independently, we can add their rates together to get the combined rate. Let the rate of pipe B be 1/b, then:

(1/18) + (1/b) = 1/9.9

Solving this equation for b, which is the time taken by pipe B alone to fill the tank will give you the answer.

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