Geometry Help about triangles!!

Answer:

Width = 10 feet, Length = 25 feet

Step-by-step explanation:

the width is x

the length is 3x-5

so, 2(x+(3x-5))=70 is the equation

2(x+3x-5)=70

2x+6x-10=70

8x-10=70

8x=10

x=10.

Width = 10 feet

Length = 25 feet

Answer:

x=9

Step-by-step explanation:

<B = <E  from the concurrency statement

5x = 45

Divide by 5

5x/5 = 45/5

x = 9

Answer:

Hey there!

These are similar triangles, and similar triangles have congruent angles.

Thus, we have 5x=45

Simplifying, we have x=9

Let me know if this helps :)

Answer:

PT = 17

Step-by-step explanation:

Since T is the midpoint of PQ, then

PT = TQ , substitute values

4x + 5 = 8x - 7 ( subtract 4x from both sides )

5 = 4x - 7 ( add 7 to both sides )

12 = 4x ( divide both sides by 4 )

3 = x

Thus

PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

17

Step-by-step explanation:

since T is mid point of PQ

PT=TQ

\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)

so

\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)

To estimate the rate of jaundice among newborns to within plus or minus 3% with 92% confidence, at least 1068 babies must be randomly selected and tested.

To calculate the minimum sample size required to estimate the rate of jaundice among newborns to within plus or minus 3% with 92% confidence, we can use the following formula:

n = [ (z-score)² × p × (1-p) ] / E²

where:

n is the sample size we want to calculate

z-score is the critical value of the standard normal distribution corresponding to the desired confidence level. For 92% confidence, the z-score is 1.75.

p is the estimated proportion of newborns with jaundice. Since we do not have any prior information about this, we can use 0.5 as a conservative estimate.

E is the maximum margin of error, which is 3% or 0.03 in this case.

Substituting these values, we get

n = [ (1.75)² × 0.5 × (1-0.5) ] / (0.03)²

n = 1067.

Rounding up, we get a minimum sample size of 1068

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he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040

If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.

(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.

(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.

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The simplified expression is 2(x-2)(x-1) / (x+1).

To simplify the expression (2x-4)(x-1)/(x-3)(x+1)(x-3), we can cancel out common factors and simplify further.

First, let's cancel out common factors between the numerator and the denominator:

(2x-4)(x-1) / (x-3)(x+1)(x-3)

The numerator (2x-4) can be factored out to 2(x-2), and the denominator (x-3)(x-3) can be written as (x-3)^2:

2(x-2)(x-1) / (x-3)^2(x+1)

Now, we can check for any additional common factors that can be canceled out. The (x-3) term appears in both the numerator and the denominator, so we can cancel it out:

2(x-2)(x-1) / (x-3)(x+1)

After canceling out the common factor (x-3), we are left with:

2(x-2)(x-1) / (x+1)

Therefore, the simplified expression is 2(x-2)(x-1) / (x+1).

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Jennifer paid $2.27 for the bag of apples after using the coupon.

Jennifer bought a bag of apples and had to consider the tax and coupon discount in her final payment. Here's a breakdown of the calculation:

1. Jennifer initially bought the bag of apples for $2.50.
2. The tax on her purchase was 19 cents ($0.19).
3. She used a coupon to receive a 42-cent ($0.42) discount.

To calculate her final payment, we first need to add the tax to the initial price of the apples:

$2.50 (initial price) + $0.19 (tax) = $2.69 (price with tax)

Next, we subtract the coupon discount from the price with tax:

$2.69 (price with tax) - $0.42 (coupon discount) = $2.27

Therefore, Jennifer paid a total of $2.27 for the bag of apples after including the tax and applying her coupon discount.

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The percentage of students at the college have a gpa below 2.4 is 15.87%.

Given,

The gpa's are normally distributed with given mean and SD.

mean \(\bar{x}\)= 2.8

SD σ=0.4

raw score=2.4

The z score can be calculated by using the formula

z=\(\frac{x-\bar{x}}{\sigma}\)

z=\(\frac{2.4-2.8}{0.4}\)

\(z=\frac{-0.4}{0.4}\)

z=-1

Using the z table we get the value P(z<-1), it is 0.8413, as it is less than we subtract it from 1 and we get 0.1587. As the value we got is negative, we used left tail z table to get the value of the z.

To get the percentage, we have to multiply by 100,

0.1587 x100

=15.87%

Therefore, the percentage of students at the college with gpa below 2.4 is 15.87%.

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Answer:

An apple and a pear weigh less than an orange and a peach together, and a pear and an orange weigh less than an apple and a peach together. Which of the pieces of fruit is the heaviest? Step 1: Weigh an apple, a pear, and an orange. Step 2: The apple weighs more than the pear and the orange

The expected instantaneous rate of change, denoted as r, for a geometric Brownian motion stock price (St) represents the average rate at which the stock price is expected to change at any given point in time. It is typically expressed as a constant or a deterministic function.

On the other hand, the expected return, denoted as r - 0.5σ^2, on the stock ln(St) over an interval of time [0,t] represents the average rate of growth or change in the logarithm of the stock price over that time period. It takes into account the volatility of the stock, represented by σ, and adjusts the expected rate of return accordingly.

The key difference between the two is that the expected instantaneous rate of change (r) for the stock price represents the average rate of change at any given moment, while the expected return (r - 0.5σ^2)t on the stock ln(St) over an interval of time considers the cumulative effect of volatility on the rate of return over that specific time period.

In other words, the expected instantaneous rate of change focuses on the average rate of change at a specific point in time, disregarding the impact of volatility. On the other hand, the expected return over a given interval of time accounts for the volatility in the stock price and adjusts the expected rate of return to reflect the effect of that volatility.

The expected instantaneous rate of change (r) for a geometric Brownian motion stock price represents the average rate of change at any given moment, while the expected return (r - 0.5σ^2)t on the stock ln(St) over an interval of time considers the cumulative effect of volatility on the rate of return over that specific time period.

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If Builtrite is in the 21% tax bracket and had $50,000 in interest expense, the after-tax cost of this interest expense would be $39,500.

To calculate the after-tax cost of the interest expense, we need to apply the tax rate to the expense.

Taxable Interest Expense = Interest Expense - Tax Deduction

Tax Deduction = Interest Expense x Tax Rate

Given that Builtrite is in the 21% tax bracket, the tax deduction would be:

Tax Deduction = $50,000 x 0.21 = $10,500

Subtracting the tax deduction from the interest expense gives us the after-tax cost:

After-Tax Cost = Interest Expense - Tax Deduction

After-Tax Cost = $50,000 - $10,500

After-Tax Cost = $39,500

Therefore, the interest expense would cost Builtrite $39,500 after taxes. This means that after accounting for the tax deduction, Builtrite effectively pays $39,500 for the interest expense of $50,000.

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The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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Answer:

we conclude that the given system of equations is consistent and independent.

Hence, option B is true.

Step-by-step explanation:

From the figure it is clear that the two lines intersect at one point.

In other words, there is only one point of intersection of the given system of equations.

It means the system of equations contains exactly one solution.

We know that If a consistent system contains exactly one solution, it is termed as an independent.

Therefore, we conclude that the given system of equations is consistent and independent.

Hence, option B is true.

The correct option is option a) One standard deviation.

According to the empirical rule, the bell or mound shaped distribution will have approximately 68% of the data within one standard deviations of the mean.

According to the empirical rule, the bell or mound-shaped distribution will have approximately 68% of the data within one standard deviation of the mean. This means that if the data is normally distributed, then about 68% of the data points will fall within one standard deviation above or below the mean.

Similarly, the empirical rule states that approximately 95% of the data will fall within two standard deviations of the mean, and about 99.7% of the data will fall within three standard deviations of the mean.

This means that if the data is normally distributed, then 95% of the data points will fall within two standard deviations above or below the mean, and 99.7% of the data points will fall within three standard deviations above or below the mean.

It is important to note that the empirical rule is based on the assumption that the data is normally distributed. If the data does not follow a normal distribution, then the empirical rule may not apply.

Therefore, the answer to the question is (a) One standard deviation, (b) Two standard deviations, and (c) Three standard deviations. Option (d) Four standard deviations and (e) Four standard deviations are not correct, and option (f) None of the above is partially correct as it excludes options (a), (b), and (c), but option (g) All of the above is not correct as options (d) and (e) are incorrect.

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Answer:

75

Step-by-step explanation:

40 - 5 = 35 years till the son will be 40, his fathers age

40+35 = 75, the dad's age 35 years in the future when the son is 40

Answer:

76

Step-by-step explanation:

Well just substitute 22 in for w. Multiply 4 time 22 that equals 88. Then just subtract 12 from 88, and you end up with your final answer of 76

Answer:

A=1.20

B=1.10

B is better value

Step-by-step explanation:

4.80 divided by 40=1.20

5.50 divided by 50=1.10

Answer:

A. £0.12

B. £0.11

C. Pencils from shop B

Step-by-step explanation:

A. 4.80÷40= 0.12

B. 5.50÷50= 0.11

C. £0.11 is cheaper than £0.12, therefore pencils from shop B is better value for money.

Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line

m = \(\frac{4-0}{0-(-2)}\) = \(\frac{4}{0+2}\) = \(\frac{4}{2}\) = 2

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line

Answer:

140 inches

Step-by-step explanation:

Find the area of the square.

4 + 10 = 14 (Length)

11 + 4 = 15 (Breadth/Width)

Area = 14 x 15 = 210 inches

Find the area of the 2 unshaded squares in the square.

Area of square at the top = 4 x 4 = 16 inches

Area of square at the bottom = 6 x 9 = 54 inches

Add the 2 squares of the area together.

16 + 54 = 70 inches

Now deduct the area of the huge box by the area of the 2 unshaded squares.

210 - 70 = 140 inches

No, this correspondence is not a function because a function is a relation between two sets of values in which each value of the first set corresponds to exactly one value in the second set.

In this case, there is no information given about the correspondence, so it is impossible to determine if it is a function or not.

A function is a special type of relation in which each value of the first set, sometimes referred to as the domain, is associated with exactly one value in the second set, called the range. A function must satisfy the property of functional uniqueness, meaning that each element of the domain is associated with exactly one element in the range. If a correspondence fails to meet this requirement, then it is not a function. Without knowing any more information about the correspondence, it is impossible to determine if it is a function or not.

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Answer:

the triangle consists 180 degree

so , açording to me the must be like this

Step-by-step explanation:

hope it becomes helpful to you ☺️☺️

good luck

Answer:

Step-by-step explanation:

10 days

Answer: It will take 103 minutes and 9 seconds to dig 40 sq.m. of land.

Explanation:

To determine how long it will take to dig 40 sq.m. of land, we need to first convert the time it took to dig 200 sq.m. of land to a common unit of time, such as seconds. We can do this by multiplying the number of hours by the number of seconds in an hour, the number of minutes by the number of seconds in a minute, and adding these values together with the number of seconds.

8 hours * 3600 seconds/hour = 28800 seconds

35 minutes * 60 seconds/minute = 2100 seconds

45 seconds

Total time = 28800 seconds + 2100 seconds + 45 seconds = 30945 seconds

Next, we need to calculate the time it takes to dig one square meter of land. We can do this by dividing the total time it took to dig 200 sq.m. of land by the number of square meters dug.

Time per sq.m. = 30945 seconds / 200 sq.m. = 154.725 seconds/sq.m.

Finally, we can multiply the time it takes to dig one square meter of land by the number of square meters we want to dig to determine the total time it will take to dig 40 sq.m. of land.

Time to dig 40 sq.m. = 154.725 seconds/sq.m. * 40 sq.m. = 6189 seconds

This is equivalent to approximately 103 minutes and 9 seconds.

Therefore it will take 103 minutes and 9 seconds to dig 40 sq.m. of land.

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Answer:

0.25

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.

So we first simplify the expression by dividing 1/2 by 6:

1/2 ÷ 6 = 1/2 × 1/6

Next, we multiply the two fractions by multiplying their numerators and denominators:

1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12

Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.

Answer:

TQ=14

Step-by-step explanation:

Given:

QV=15

Since the figure is a kite because SR=QR and TV is perpendicular to SQ:

SV=QV and ST=TQ

so:

4x-1=15

x=4

ST=3x+2=14

TQ=14

Given: X-3(x+2)=4X-3(x+2)=4

Find: the solution of the given equation

Explanation:

on solving equation (1) and (2) , we get

Answer:

x = -5

Step-by-step explanation:

    x - 3(x + 2)= 4

    x - 3x - 3*2 = 4     {Distributive property}

   x - 3x  - 6    = 4

Combine like terms in LHS,

         -2x - 6  = 4

Add 6 to both sides,

               -2x = 4 + 6

               -2x = 10

Divide both sides by (-2)

                   x = 10 ÷ (-2)

                   \(\sf \boxed{x= -5}\)

To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

25

Step-by-step explanation:

because 5^6=78125

Step-by-step explanation:

Answer:

0001 0000

this is the answer and i had to make it longer so i could post it