Find the exact lengths of the given special right trangle

Answer:

Option A

Step-by-step explanation:

7x - y = 7

x + 2y = 6

Subtract 2y from both sides;

x = -2y + 6

Lets substitute x;

7(-2y + 6) - y = 7

Distribute;

-14y + 42 - y = 7

-15y + 42 = 7

Subtract 42 from both sides;

-15y  = -35

Divide both sides by -15

y = \(\frac{35}{15}=\frac{7}{3} = 2\frac{1}{3}\)

Lets substitute y;

x + 2(\(\frac{7}{3}\)) = 6

x + \(\frac{14}{3}\) = 6

Subtract \(\frac{14}{3}\) from both sides;

x = \(-\frac{14}{3} +6=-\frac{14}{3}+\frac{6}{1}=\frac{-14+18}{3} =\frac{4}{3}=1\frac{1}{3}\)

Answer:

x = 150

Step-by-step explanation:

What we need to do is first use the sum of interior angles theorem to find the total sum of this odd hexagon.

n = sides of the shape.

(n-2)*180° = Sum of interior angles

For us this would be 720° total. Now make an equation

121 + 96 + 101 +162 + 90 + x = 720

Then we simplify

570 + x = 720

-570         -570

And then subtract 570 on both sides and we get our answer.

x = 150

Answer:

Step-by-step explanation:

Move 6a to the other side

Subtract 7a and 6a

use inverse operations. So add 3 on both sides

Answer:

a = 6

Step-by-step explanation:

The given equation is,

→ 7a - 3 = 3 + 6a

Now the value of a will be,

→ 7a - 3 = 3 + 6a

→ 7a - 6a = 3 + 3

→ a = 3 + 3

→ [ a = 6 ]

Hence, the value of a is 6.

Answer: 37 degrees

Hope this helps :)

Step-by-step explanation:

(The box in the corner tells you this is a right angle)

A right angle is 90 degrees

90 - 53 = 37

Answer:

37 degrees

Step-by-step explanation:

Angle a is equivalent to 37 degrees because the picture signifies a right angle; all right angles are equal to 90 degrees. The equation to solve this would be: 53+x=90, you would solve this by subtracting 90-53=x; x=37

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Answer:

3821.9 [cm³].

Step-by-step explanation:

1) the required volume can be calculated as:

V=V(prism)-V(cylinder);

2) V(prism)=32*12*11=4224 [cm³];

3) V(cylinder)=π*r²*32=3.1415*4*32≈402.1 [cm³];

4) finally, V=4224-402.1=3821.9 [cm³].

For more info see the picture in the attachment.

Answer:

3,822.08 cm2

Step-by-step explanation:

You would start off by finding the volume of the who post which is 4,224. You then would find the volume of the hole cut out which is 401.92. Then you would subtract 401.92 from 4,224 giving you 3,822.08.

Hope this helps!

Based on the average daily balance, the finance charge for this credit card that charges 10.5% APR is $2.10.

The finance charge consists of the interest and other fees that lenders charge borrowers.

One of the methods for computing the finance charge is the average daily balance, which takes the sum of the daily balances and divides by the number of days in the billing cycle.

APR interest rate = 10.5%

Monthly period days = 30

Days 1-3: $200 (initial balance)        3 days      $600 ($200 x 3)

Days 4-20: $300 ($100 purchase)  17 days   $5,100 ($300 x 17)

Days 21-30: $150 ($150 payment)  10 days   $1,500 ($150 x 10)

Total balances = $7,200

Average daily balance = $240 ($7,200 ÷ 30)

Finance charge = $2.10 ($240 x 10.5% x 30/360)

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Answer:

Step-by-step explanation:

\((sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\)

we take the LHS so here goes,

\((sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\\(\frac{1}{cosA} -\frac{1}{sinA})(1+\frac{sinA}{cosA}+\frac{cosA}{sinA})\\\\(\frac{sinA-cosA}{sinAcosA})(\frac{sinAcosA+sin^2A+cos^2A}{sinAcosA})\\\)

since , \(sin^2A+cos^2A=1\)

the identity becomes,

\((\frac{sinA-cosA}{sinAcosA})(\frac{1+sinAcosA}{sinAcosA})\\\\(\frac{sinA+sin^2AcosA-cosA-cos^2AsinA}{sin^2Acos^2A})\\\\\)

now, we know,

\(sin^2A=1-cos^2A\) and \(cos^2A=1-sin^2A\)

the identity becomes,

\((\frac{sinA+(1-cos^2A)cosA-cosA-(1-sin^2A)sinA}{sin^2Acos^2A} )\\\\\)

\((\frac{sinA+cosA-cos^3A-cosA-sinA+sin^3A}{sin^2Acos^2A})\)

sin A and cos A cancel out it becomes zero

\(\frac{sin^3A-cos^3A}{sin^2Acos^2A} \\\\\)

Splitting the denominator the identity becomes

\(\frac{sin^3A}{sin^2Acos^2A}-\frac{cos^3A}{sin^2Acos^2A} \\\\\frac{sinA}{cos^2A} - \frac{cosA}{sin^2A} \\\\\frac{sinA}{cosA}(\frac{1}{cosA})-\frac{cosA}{sinA}(\frac{1}{sinA})\\\\\)

Hence,

\(tanAsecA-cotAcosecA\)

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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The infinite sum of the given series is -8/5.

The given series is (-2) + (0.5) + (-0.125) + ...

We can see that the series is a geometric progression with first term 'a' = -2 and common ratio 'r' = 1/(-4).

For a geometric progression to have a sum, the absolute value of the common ratio must be less than 1.

|r| = |1/(-4)| = 1/4 < 1

So, the given series has a sum and we can use the formula for the sum of an infinite geometric series:

sum = a / (1 - r)

Substituting the values of 'a' and 'r', we get:

sum = (-2) / (1 - (-1/4)) = (-2) / (5/4) = -8/5

Therefore, the infinite sum of the given series is -8/5.

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Answer:

D. All real numbers

Step-by-step explanation:

7 gallons are needed to cover 1241 square feet.

In this question,

Each gallon of porch and deck paint covers 200 square feet.

To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.

We use the unitary method to find out how many gallons of paint needs.

Using unitary method,

1241 / 200 = 6.205

However, we cannot buy a fraction of a gallon of paint.

So, the amount of gallons of paint needed is approximately equal to 7 gallons.

Therefore, 7 gallons are needed to cover 1241 square feet.

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Part a

This represents a translation of 2 units to the right. So, the points are \((6, -3), (0,0), (8, -15)\).

Part b

This represents a translation of 9 units up. So, the points are \((4,6), (-2,9), (-10,-6)\).

Part c

This represents a translation of 3 units left and 1 unit down. So, the points are \((1, -4), (-5, -1), (-13, -16)\).

Answer:

-18c + 17

x = 32

Answer:

66.5%

Step-by-step explanation:

Explanation:

No matter how many times you roll the die, the probability of landing on 6 is 1/6 each time. This is of course assuming the die is fair, i.e. each of the 6 sides are equally likely.

The probability is 1/6 each time because the previous events do not affect the current roll. Each roll is independent of one another. So in effect, the info of getting 6 to show up 24 times is unneeded filler info set up as a distraction. The same can be said about the value 60 as well.

Answer:

We get the approximate value of [n] as 5.

What is logarithm? What is a mathematical equation and expression?

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -

$$$\log_{b}({b^x})=x$$

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.

A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.

We can write -

We can write -10ⁿ = 31100

We can write -10ⁿ = 3110010ⁿ = 311 x 10²

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)Therefore, we get the approximate value of [n] as 5.

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Since the events are not mutually exclusive, there is a possibility that they occur simultaneously. Therefore, we need to consider this possibility in calculating the probability of event a occurring before event b.

Answer:

Let P(a) and P(b) be the probabilities of event a and event b, respectively. Then, the probability that event a occurs before event b is given by the formula:

P(a before b) = P(a) + P(a and b)/[1 - P(b)]

Here, P(a and b) represents the probability that events a and b occur simultaneously. Since the events are independent, we can calculate this probability as:

P(a and b) = P(a) x P(b)

Substituting this value in the formula, we get:

P(a before b) = P(a) + P(a) x P(b)/[1 - P(b)]

Simplifying this expression, we get:

P(a before b) = P(a) / [1 - P(b)]

This formula gives us the probability that event a occurs before event b, given that a and b are independent events (and not mutually exclusive). We can use this formula to calculate the probability of event a occurring before event b for any given values of P(a) and P(b).

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Answer:

side length of cube=4inch

Step-by-step explanation:

volume of cube(V)=64sqinch

length of side(l)=?

Now,

volume of cube(V)=l^3

64=l^3

∛64=l

4=l

l=4inch

Answer:

32

Step-by-step explanation:

I mutiplied 2 to the 5th power and it equals 32

Answer: (6, -1)

Step-by-step explanation:

<3

Answer: B. . Wealthy individuals who mostly invest in startups with good potential in exchange for stocks in the business

Step-by-step explanation:

Angel investors are wealthy individuals who mostly invest in startups with good potential in exchange for stocks in the business.

It should be noted that when new businesses are been established or wants to start up, they usually have little capital and often times, need someone to help them with funds.

Am angel investor invests in such companies in exchange for ownership equity and also gives them the.nweded support.

The dimensions of the poster with the smallest area are as follows: The width is 20 cm, and the height is 16 cm.

To determine these dimensions, we need to consider the area of the printed material on the poster, which is fixed at 388 square centimeters. Let's assume the width of the printed material is x cm.

Since the side margins are each 2 cm, the total width of the poster (including the margins) becomes x + 2 cm + 2 cm = x + 4 cm.

Similarly, the total height of the poster is x + 4 cm as well because the top and bottom margins are both 4 cm.

To calculate the area of the entire poster, we multiply the width by the height: (x + 4 cm) * (x + 4 cm) = (x + 4)^2 cm^2.

According to the problem, the area of the printed material is 388 square centimeters. Therefore, we have the equation (x + 4)^2 cm^2 = 388 cm^2.

Solving this equation, we find x + 4 = 19 cm, which means x = 15 cm.

Hence, the dimensions of the poster, width is 15 cm + 4 cm = 19 cm, and the height is also 15 cm + 4 cm = 19 cm.

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Answer: 27

Step-by-step explanation:

If 2 scoops of ice cream cost $6, then 1 scoop of ice cream costs $6/2 = $3.

So, 9 scoops of ice cream would cost 9 x $3 = $27.

Answer:

27$

Step-by-step explanation:

If two wcoops of ice crewm cost 6$ them one scoop would cost 3$ because 6/2 =3. If one scoop costs 3$ then 9 scoops would cost 9x3 so 27$

The symmetrical interval that includes 93% of the sample means is (3.2455 gallons per month, 3.5545 gallons per month) assuming the population follows a normal distribution.

To calculate the probabilities and identify the symmetrical interval, we'll use the provided information:

Given:

Population mean (μ) = 3.4 gallons per month

Population standard deviation (σ) = 0.85 gallons per month

Sample size (n) = 100

a. Probability that the sample mean will be less than 3.3 gallons per month: To calculate this probability, we need to use the sampling distribution of the sample mean, assuming the population follows a normal distribution. Since the sample size (n) is large (n > 30), we can approximate the sampling distribution as a normal distribution using the Central Limit Theorem. The mean of the sampling distribution is equal to the population mean (μ), which is 3.4 gallons per month. The standard deviation of the sampling distribution, also known as the standard error (SE), can be calculated as σ / √n:

SE = σ / √n

= 0.85 / √100

= 0.085 gallons per month

Now, we can calculate the z-score using the formula:

z = (x - μ) / SE

Substituting the values:

z = (3.3 - 3.4) / 0.085

= -0.1 / 0.085

= -1.1765

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -1.1765. The probability that the sample mean will be less than 3.3 gallons per month is approximately 0.1190. Therefore, the probability is 0.1190.

b. Probability that the sample mean will be more than 3.6 gallons per month:

Similarly, we can calculate the z-score for this case:

z = (x - μ) / SE

= (3.6 - 3.4) / 0.085

= 0.2 / 0.085

= 2.3529

Using a standard normal distribution table or calculator, we find the probability corresponding to a z-score of 2.3529. The probability that the sample mean will be more than 3.6 gallons per month is approximately 0.0096.

Therefore, the probability is 0.0096.

c. Identifying the symmetrical interval that includes 93% of the sample means:

To find the symmetrical interval, we need to determine the z-scores corresponding to the tails of 93% of the sample means.

Since the distribution is symmetrical, we can divide the remaining probability (100% - 93% = 7%) equally between the two tails.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a tail probability of 0.035 on each side. The z-score is approximately 1.8125.

The symmetrical interval is then given by:

=μ ± z * SE

=3.4 ± 1.8125 * 0.085

=(3.4 - 1.8125 * 0.085, 3.4 + 1.8125 * 0.085)

=(3.4 - 0.1545, 3.4 + 0.1545)

=(3.2455, 3.5545)

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Answer: x=2.500

Step-by-step explanation:

5=2x

Divide by two on both sides

2.500=x

The correct statement are:

Based on the given information, we can make the following conclusions:

A. The interquartile range for high school students is smaller than college students.

The statement is False

B. The mean for high school students is smaller than college students.

The statement is False because the mean of College is 25.28 and mean for High school is 30.4.

C. The range for high school students is larger than college students.

The statement is True .

D. The college median is equal to the high school median.

The statement is True because the median for both is 24..

E. The mean absolute deviation is larger for college students than high school students.

The statement is False.

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The coordinates of point A after the dilation are (-19, 39)

From the question, we have the following parameters that can be used in our computation:

A = (1, 4)

The scale factor and the center are given as

k = 6

(a, b) = (5, -3)

The coordinate of point A after the dilation is then calculated as

A' = (k(x - a) + a, k(y - b) + b)

substitute the known values in the above equation, so, we have the following representation

A' = (6(1 - 5) + 5, 6(4 + 3) - 3)

Evaluate

A' = (-19, 39)

Hence, the coordinates of point A after the dilation are (-19, 39)

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Answer:

f(4)=5

Step-by-step explanation:

f(x)=x^2-6x+13

f(4)=4^2-6(4)+13

f(4)=16-24+13

f(4)=5