need help with geometry (number 23)

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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If RS = ST point S is called midpoint of RT. The given statement is true.

Given that, RS = ST.

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

Here, RS = ST point S is called midpoint of RT.

The line segment RT and its midpoint S is shown on the figure below.

Therefore, the given statement is true.

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Answer:

Step-by-step explanation:

Next time please include the answer choices.

128x^5*y^8 is equivalent to (2^7)*x^5*y^8

Answer:

x=2

y=2

Step-by-step explanation:

x+3y=8

- x-4y=-6

7y=14

y=14/7

y=2

x+3(2)=8

x+6=8

x=8-6

x=2

y=2

x=2

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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Answer:

The correct answer is 61

Owen forgot to subtract the student who both belonged to a club and had a job, so he double counted them.

Explanation:

I did the test and got it right!

The X-Cordinate is 4

Answer:

I think the answer will be the infinity sign=1 whole, 1/9

Given:

Angle BAC is 15x-2 degree.

Angle DAC is 7x+4 degree.

The objective is to find the measure of each angle.

Since the given triangle is a right angled triangle.

So the sum of the angles in a right angle is a complementary angle 90 degree.

Then, the value of x can be calculated as,

Substitute the value of x in each angle.

The measure of angle BAC is,

The measure of angle DAC is,

Hence, measure of anlge BAC is 58 degree and the measure of angle CAD is 32 degree.

It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.

Monthly Cash Flow Statement for Gable Supplies Ltd for the three months ending on 30th September 2018:

Month: July August September

Opening Cash: £0 £3,550 £16,700

Cash Inflows:

Share Capital: £55,000

Loan: £110,000

Cash Sales: £45,600 £49,400 £57,000

Credit Sales: £0 £72,000 £78,000

Total Inflows: £160,600 £125,950 £135,000

Cash Outflows:

Loan Repayment: -£2,450 -£2,450 -£2,450

Equipment: -£80,000

Inventory: -£50,000 -£54,000 -£67,500

Wages: -£12,000 -£12,000 -£12,000

Overheads: -£15,000 -£15,000 -£15,000

Rent: -£36,000

Total Outflows: -£157,050 -£109,250 -£118,450

Closing Cash: £3,550 £16,700 £33,250

It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.

Additionally, credit sales to be accrued in the subsequent month from when the product was sold.

Inventory acquisition constitutes approximately 45% of revenue each month, whereas payments to suppliers get delayed by one month.

Rent, on the other hand, needs to be paid annually but paid beforehand instead of scheduled billing periods.

To note, the non-cash category of expenditures does not encompass depreciation according to the cash flow statement rules.

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The area of the top of the second mattress , 3/2x²

The equation to model the problem is y= 1.22x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let the side of mattress one be x

and, the side of Mattress 2 be y.

So, area of Mattress 2 / Area of Mattress 1 = 1 1/2

area of Mattress 2 / Area of Mattress 1 = 3/2

y²/ x² = 3/2

(y/ x)² = 3/2

y/x = √3/2

y /x = 1.22

Hence, the equation is y= 1.22 x .

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Answer:

Option (3)

Step-by-step explanation:

There are two parallel lines 'p' and 'q' and a transversal line is intersecting these lines at two distinct points.

Each pair of angles formed on the inner side of the parallel lines but opposite sides of the transversal line are the alternate interior angles.

Pair of angles (∠2 and ∠6) and (∠3 and ∠7) are the alternate interior angles.

Since, alternate interior angles are equal in measure,

∠2 ≅ ∠6

∠3 ≅ ∠7

Option (3) will be the answer.

Answer:

square or rectangle

Step-by-step explanation:

Answer:

a) For an unsubsidized loan of $15,000 at 6.8% interest for 4 years, the simple interest accumulated while you are still in school is **$4,080**.

b) If you capitalized the loan, the balance when you graduate would be **$20,322.68**.

c) After you graduate, you will begin making payments on your loan at 6.8% compounded monthly for 10 years. The monthly payment for this loan is **$174.30**.

d) The total amount of interest paid for this loan is **$10,118.00**.

e) If the loan is not capitalized, it means that the interest accrued during the in-school period is not added to the principal balance of the loan. Instead, it is paid off separately after graduation.

f) For a subsidized loan of $15,000 at 6.8% compounded monthly for 10 years, the monthly payment for this loan is **$163.19**.

g) The total amount of interest paid for this subsidized loan is **$9,782.80**.

h) The difference in savings for the subsidized loan is **$335.20**.

Answer:

B. Zero

Explanation:

The solutions of a system of equations are the points where the graphs intersect. If the lines are parallel, the lines will not intersect, so there will be no solutions to the system.

Therefore, the solutions to the system of two parallel lines are

B. Zero

The solution of the polynomial equation 2x⁵ - 14x³ = 0 will be 0, √7, and negative √7.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The polynomial equation is given below.

2x⁵ - 14x³ = 0

Simplify the equation, then we have

2x³(x² - 7) = 0

(2x³)(x - √7)(x + √7) = 0

x = 0, ±√7

x = 0, √7, -√7

The solution of the polynomial equation 2x⁵ - 14x³ = 0 will be 0, √7, and negative √7.

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Answer:

Step-by-step explanation:

First Image:

\(cos49=\frac{14}{x}\\\)

\(x=\frac{14}{cos49} =\frac{14}{0.656} =21.34 =21\)

Second Image

\(tan52=\frac{x}{20} \\x=20*tan52\\x=20*1.28=25.59\\x=26\)

Third Image

\(cos15=\frac{x}{33}\\x=33*cos15\\x=33*0.966\\x=31.87\\x=32\)

Fourth Image

\(cos16=\frac{x}{37}\\x=37*cos16\\x=37*0.96\\x=35.56\\x=35\)

Fifth Image

\(tan51 =JL/14\\\)

First, we must calculate the length of JL, the common side of both triangles before calculating KL

So;

\(JL=14*tan51\\JL=14*1.23=17.28\\JL=17\\\\Knowing JL now we can calculate KL\\\\Cos72=\frac{KL}{JL}\\\\Isolating KL\\\\KL=JL*cos72\\KL=17*cos72 = 17*0.31=5.25\\KL=5\)

Answer: a is correct

Step-by-step explanation:

At 25 years

Step-by-step explanation:

123,000 x 2.375% = 2,921.25.  This gives you the rate that the population is decreasing.  How long will it take to get to 50,000. Do reverse operations to find this answer: 123,000 - 50,000 = 73,000,  the population need to decrease by 73,000 to get to 50,000.  So let's multiply our rate of 2,921.25 x 25 = 73,031  and our final step..  123,000 - 73,031 = 49,969 below 50,000

The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

\(x=\dfrac{8}{\sqrt3}\)

Step-by-step explanation:

Given that,

\(\sin(30)=\dfrac{\dfrac{4}{\sqrt3}}{x}\) ...(1)

We need to find the value of x.

We know that,

sin30 = 1/2

Use it in equation (1).

\(\dfrac{1}{2}=\dfrac{\dfrac{4}{\sqrt3}}{x}\\\\x=\dfrac{4}{\sqrt3}\times 2\\\\x=\dfrac{8}{\sqrt3}\)

So, the value of x is equal to \(\dfrac{8}{\sqrt3}\).

Answer:

(a) 44%

(b) 32%

Step-by-step explanation:

(a) In order to find the percentage of students that prefer comedies, we can add up divide the sum of the total number of students who prefer comedies (Twice/month or less + Thrice/month or more) by the total number of students.  

Then, we can multiply this number by 100 to find the percentage:

\((\frac{45+21}{150})*100\\ (\frac{66}{150})*100\\ 44\)

(b) To find the percentage of students who visit the movies three times a month or more, we can divide the sum of the total number of students who visit the movies three times a month or more by the total number of students.

Like before, we can multiply this number by 100 to find the percentage:

\((\frac{21+27}{150})*100 \\(\frac{48}{150})*100\\ 32\)

The sample mean of the random sample is 50

The margin of error (E) is the amount of error allowed in the random sample.

The confidence interval (CI) is given by:

CI = μ ± E = (μ - E, μ + E)

Given a confidence interval of (38.02, 61.98), hence:

μ - E = 38.02     (1)

μ + E = 61.98     (2)

Hence solving equations 1 and 2 simultaneously gives:

μ = 50, E = 11.98

Hence the sample mean of the random sample is 50

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Answer: $20000

Step-by-step explanation:

The amount of cash drawings for the year will be calculated thus:

Net loss = $18,800

Beginning owner's equity = $378,800

Ending owner's equity = $330,000

Goods withdrazwn by owner = $10,000

The Ending owner's equity is calculated as:

= Beginning owner's equity - Net loss - Goods withdrazwn by owner - Cash withdrawn by owner

We'll then slot in the values given and this will be:

330,000 = 378,800 - 18,800 - 10,000 - Cash withdrawn by owner

330,000 = 350,000 - Cash withdrawn by owner

Cash withdrawn by owner will the be:

= $350000 - $330000

= $20,000

Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

Answer:

if its 8 am it stays 8 if its pm it would be 20:00

Step-by-step explanation: