A ladder i reting againt a wall. The top of the ladder touche the wall at a height of 18 ft. Find the length of the ladder if the length i 6 ft more than it ditance from the wall

To find the value of h, we can use the given hint and apply the Pythagorean theorem to the right triangles formed by the line segments PQ, QR, and PR.

Let PQ = x and QR = 21 - x. Since PR is a straight line, PR = PQ + QR = x + (21 - x) = 21.

Now, we have two right triangles: ΔPQH and ΔQHR.

In ΔPQH, we have:

x^2 + h^2 = 20^2
x^2 + h^2 = 400  (1)

In ΔQHR, we have:

(21 - x)^2 + h^2 = 13^2
(441 - 42x + x^2) + h^2 = 169  (2)

Now we have a system of two equations with two unknowns (x and h). We can solve for h by subtracting equation (1) from equation (2):

(441 - 42x + x^2) - (x^2) = 169 - 400
-42x + 441 = -231
42x = 672
x = 16

Now substitute the value of x back into equation (1) to find h:

16^2 + h^2 = 400
256 + h^2 = 400
h^2 = 144
h = √144
h = 12

So the value of h is 12.

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Answer:

PR = 2*36 = 72

SU = (1/2)54 = 27

RS = 36

Step-by-step explanation:

By the Midpoint Theorem, the argent that connects midpoints of the sides of a triangle equals half the parallel side. That said,

Answer:

the answer should be -185

Answer:

0

Step-by-step explanation:

1/2 (18 + 14)- (18 - 14)^2

=1/2 (32) - 4^2

=16 - 16

=0

Answer:

2$

Step-by-step explanation:

Answer:

V=550cm^3

Step-by-step explanation:

Answer:  549.5 cm squared

Step-by-step explanation:

The graph of the line y=-2/3x-1 can be given as follows,

What is a equation of ?

The general equation of straight line is y=mx+c where m is the slope and c is the y-intercept.

every point on the line satisfies its equation.

We are given a point (6,-5) and slope -2/3.

we first need to find the equation of the line

y=mx+c

\(y=\frac{-2}{3}x+c\)

The point (6,-5) satisfies the equation.

\(-5=\frac{-2}{3}(6)+c\)

\(-5=-4+c\\c=-1\)

Substituting the value of c in the equation

we get,

\(y=\frac{-2}{3}x-1\)

Now we plot the graph of the equation,

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we can estimate that the proportion of defectives being produced by the machine is around 0.316.

What is proportion?

A comparison between the size, number, or amount of one thing or group with that of another. In our class, there are three boys for everyone lady.

If the random sample of size 2 yields 2 defects, that means both items in the sample were defective. Let p be the proportion of defectives being produced by the machine.

The probability of selecting a defective item on the first draw is p, and the probability of selecting a defective item on the second draw is also p (assuming sampling without replacement).

Since both items were defective, the probability of this happening is p * p = p².

So,

p² = (number of samples with 2 defects) / (total number of samples)

We don't know the values of these numbers, but we can use them to estimate p. For example, if we had a total of 100 samples and 10 of them had 2 defects, then:

p² = 10/100 = 0.1

p ≈ √(0.1) ≈ 0.316

Hence, we can estimate that the proportion of defectives being produced by the machine is around 0.316.

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Take the root of both sides and solve.

X = 12, -12

Answer:

A

Step-by-step explanation:

-6a+2(2a+2)

-6a+4a+4

-2a+4

Answer:

-2a+4 is the answer

we need to follow BODMAS rule

easy steps

more questions contact me

all the best and good luck

I'm from Srilanka

Answer: In 1858 twelve pairs of the European rabbit were released on a ranch in of mosquitoes only 90 per cent of the remaining population was killed

Step-by-step explanation:

Answer:

if two lines are not on the same plane, then the lines are skew.

Step-by-step explanation:

if p statement is called the hypothesis of the conditional statement.

then q statement is called the conclusion of the conditional statement.

The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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Answer:

DE = 4.24

Step-by-step explanation:

The diagram is not shown; However, the question can still be solved without the diagram.

Having said that,.

Given that

DF = EF = 3

This implies that DE is the hypothenus and will be solved using Pythagoras theorem.

DE² = EF² + DF²

Substitute 3 for EF and DF

DE² = 3² + 3²

DE² = 9 + 9

DE² = 18

Take Square Root of both sides

DE = √18

DE = 4.242640687119285

DE = 4.24 (Approximated)

The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

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The statement "F(x) > 0 over the interval (-∞, -4)" is true.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. The addition, subtraction, multiplication, and division of functions are discussed in function algebra. We just perform the same operation for individual functions at the same input for every arithmetic operation of two functions at an input.

Here,

For any value of x less than -4, substituting it into the expression f(x) = x² + 4 will result in a positive value since x² is always positive. For example, if x = -5, then f(x) = (-5)² + 4 = 9 + 4 = 13, which is positive.

So, for all values of x that are less than -4, the function f(x) will have a positive value, making the statement "F(x) > 0 over the interval (-∞, -4)" true.

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Answer:

A median of a triangle is a line segment that passes through a vertex and bisects the midpoint of the opposite that vertex .

To find the cost of each small ice cream, we need to subtract the cost of the large ice creams from the total amount earned and divide the remaining amount by the number of small ice creams sold.


Let's start by finding the number of large ice creams sold. We know that 1/3 of the total number of ice creams sold is large. So, 1/3 * 240 = 80 ice creams are large.

Next, we can calculate the total cost of the large ice creams sold. Since each large ice cream costs £3.80, the total cost of the large ice creams is 80 * £3.80 = £304.

Now, we can find the total cost of the small ice creams by subtracting the cost of the large ice creams from the total amount earned. £640 - £304 = £336.

Finally, to find the cost of each small ice cream, we divide the total cost of the small ice creams (£336) by the number of small ice creams sold (240 - 80 = 160). £336 / 160 = £2.10.

Therefore, the cost of each small ice cream is £2.10.

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\(<body bgcolor="black">

<h2 align="left"><font color="white" face="Times New Roman">No, I'm not agree</h2><hr>

<p align="left"><font color="yellow" face="Times New Roman">2x=3y=> x/y=3/2</p><hr>

<p align="left"><font color="yellow" face="Times New Roman">•°•, x:y = 3:2</p>

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..

Answer:

I don't agree with him

Step-by-step explanation:

2x = 3y

If 2x = a , 3y has to equal a

2x = a

x = a/2

3y = a

y = a/3

Therefore,

x:y = x/y

\(\frac{x}{y} = \frac{\frac{a}{2}}{\frac{a}{3}}\)

\(\frac{\frac{a}{2}}{\frac{a}{3}} = \frac{a}{2} . \frac{3}{a}\)

\(\frac{a}{2} . \frac{3}{a} = \frac{3}{2}\)

Or; If 2x = 1 , 3y has to equal 1

2x = 1 , x=1/2

3y= 1 , y=1/3

x/y = (1/2) / (1/3) = 1/2. 3/1  = 3/2

Actually, we did same thing but maybe you can understand better

so, x/y = 3/2 , not 2/3. That's why I don't agree with him

Hope this helps ^-^

Answer: 3 inches

Step-by-step explanation: 9 divided by 3 is 3

6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

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Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

Answer:

$455.53

Step-by-step explanation:

Starting balance: $313.54

Money taken out of account: $45.78, $52.55

Money put into account: $240.32

$313.54 - $45.78 - $52.55 + $240.32 = $455.53

Answer: $455.53

Answer:

1/5 or 0.2

Step-by-step explanation:

Conversion a mixed number 1 1/ 5

to a improper fraction: 1 1/5 = 1 1/ 5

= 1 · 5 + 1/ 5

= 5 + 1/ 5

= 6/ 5

To find a new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/ 5

= 5/ 5

b) Add the answer from previous step 5 to the numerator 1. New numerator is 5 + 1 = 6

c) Write a previous answer (new numerator 6) over the denominator 5.

One and one fifth is six fifths

Subtract: 6/ 5

- 2/ 5

= 6 - 2/ 5

= 4/ 5

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 5) = 5. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 5 = 25. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - six fifths minus two fifths = four fifths.

Multiple: the result of step No. 2 * (-3/ 4

) = 4/ 5

* (-3/ 4

) = 4 · (-3)/ 5 · 4

= -12/ 20

= -3 · 4/ 5 · 4

= -3/ 5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-12, 20) = 4. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - four fifths multiplied by minus three quarters = minus three fifths.

Multiple: the result of step No. 3 * 3 = -3/ 5

* 3 = -3 · 3/ 5 · 1

= -9/ 5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-9, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - minus three fifths multiplied by three = minus nine fifths.

Divide: the result of step No. 4 : (-9) = -9/ 5

: (-9) = -9/ 5

· -1/ 9

= -9 · (-1)/ 5 · 9

= 9/ 45

= 9 · 1/ 9 · 5

= 1/ 5

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of -9/ 1

is 1/ -9

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 9 gives 1/ 5

.

In other words - minus nine fifths divided by minus nine = one fifth.

\(\huge\bold\green{Answer:-}\)

Greatest common factor (GCF) of 10 and 40 is 10.

GCF(10,40) = 10

\(\huge\bold\red{Explanation:-}\)

We will now calculate the prime factors of 10 and 40, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10 and 40.

Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 2¹ × 5¹

Prime Factorization of 40

Prime factors of 40 are 2, 5. Prime factorization of 40 in exponential form is:

40 = 2³× 5¹

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5

Factors of 40

List of positive integer factors of 40 that divides 10 without a remainder.

1, 2, 4, 5, 8, 10, 20

Greatest Common Factor

We found the factors and prime factorization of 10 and 40. The biggest common factor number is the GCF number.

So the greatest common factor 10 and 40 is 10.

The Greatest Common Factor of 10 and 40 is 5.

The greatest common factor is the largest number that is a factor of two or more numbers (GCF). The greatest number (factor) divides them, yielding a Natural number. Once all of the number's variables have been identified, there are a handful that are shared by both. The greatest common factor is the largest number found among the common factors. The GCF is often referred to as the Highest Common Factor (HCF)

For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

Given:

We have to find the greatest common factor of 10 and 40.

So factorizing each number

10 = 2 x 5

40 = 2 x 2 x 2 x 5

Here the common factor of 10 and 40 is

= 2 x 5

= 10

Thus, the Greatest Common Factor is 10.

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