A student creates a scale drawing for a triangular vegetable garden. the next step to finalize the drawing is to determine the side lengths. what is the approximate length of side LA?

Answer:

<YTZ

Step-by-step explanation:

Vertical angles are congruent.

<VTW measures 40°.

<YTZ is vertical to angle VTW.

m<YTZ = m<VTW

m<YTZ = 40°

Answer: <YTZ

Answer:

The quen is as following:

ABC is a right triangle at C,

Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.

The solution is:  m∠HCL = 30°

Step-by-step explanation:

See the attached figure.

∵The triangle is right at C   ∴∠C = 90°

∴∠A + ∠B = 90° ⇒(1)

∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

∴∠A = 5 times ∠B

Substitute at (1)

∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15°  and ∠A = 75°

∵CL is an angle bisector of ∠ACB

∴ ∠ACL = 90°/2 = 45°

∵ CH is an altitude to AB ⇒ ∠CHA = 90°

At the triangle AHC:

∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°

∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°

Answer:

x = ± 2i\(\sqrt{3}\)

Step-by-step explanation:

note that \(\sqrt{-1}\) = i

x² = - 12 ( take square root of both sides )

x = ± \(\sqrt{-12}\) = ± \(\sqrt{4(3)(-1)}\) = ± 2i\(\sqrt{3}\)

Answer:

C

Step-by-step explanation:

unit rate means 1 and it says that 15 per hour which shows that c is the answer

Answer:

C. Joe rides his bike 15 miles per1 hour.

Step-by-step explanation:

Key word: PER

Any time you see the words PER, EACH, stuff like that, it is unit rate. Hope this helps!

Range = 7. IQR = 4.5. Variance: 8.67, Std Dev: 2.96 when researcher organized diet groups on weight loss weighed five clients after several weeks on the program.

The range of the weight-loss scores can be calculated by subtracting the smallest value from the largest value. In this case, the range would be

13 - 6 = 7.

The inter-quartile range (IQR) is calculated as the difference between the 75th percentile and the 25th percentile of the data.

IQR: 11.25 - 6.75 = 4.5

To calculate the variance, first find the mean weight-loss score by summing all the scores and dividing by the number of clients: (13 + 12 + 6 + 9 + 9 + 10) / 6 = 9.17. Next, subtract the mean from each score and square the result for each client:

\((13 - 9.17)^2 = 3.69\\(12 - 9.17)^2 = 1.69\\(6 - 9.17)^2 = 16.0\\(9 - 9.17)^2 = 0.02\\(9 - 9.17)^2 = 0.02\\(10 - 9.17)^2 = 0.69\)

Next, sum the squared deviations and divide by the number of clients minus one (n-1):

(3.69 + 1.69 + 16.0 + 0.02 + 0.02 + 0.69) / (6-1) = 4.83

The variance is 4.83 and the standard deviation is the square root of the variance: \(\sqrt{(4.83)} = 2.19.\)

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To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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The screenshot you sent us didn't not require it to be a fraction, so i will make it a decimal

47/100*70=

0.47*70=

4.7*7=

32.9

Answer:

32.9 = x

47% of 70 = 32.9/70

or, if rounded, = 33/70

Step-by-step explanation:

Two ways:

A. 47/100 = x/70

47 = 100x/70

3290 = 100x

32.9 = x

47% of 70 = 32.9

B. 70 * 47% = x

70 * .47 = x

32.9 = x

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer: (a)

Step-by-step explanation:

Given

The pattern is 2, 4, 16, 256...

From the pattern, we can see that the next term is square of the previous i.e.

\(\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2\)\(\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2\)

So, for the \(n^{th}\) term, the function is \(f(n)\)

For the next term, it is \(f(n+1)\)

So,

\(\Rightarrow f(n+1)=[f(n)]^2\)

Answer:

0.4636 radians

Step-by-step explanation:

To find theta in radians, we need to use the inverse tangent function, also known as arctangent. From the right triangle in the image, we have:

tangent(theta) = opposite/adjacent = 10/20 = 1/2

Taking the inverse tangent of both sides, we get:

theta = arctan(1/2)

Using a calculator or a trigonometric table, we find:

theta ≈ 0.4636 radians

Therefore, theta is approximately 0.4636 radians

Answer:

opposite

Step-by-step explanation:

it's negative

Answer:

B

Step-by-step explanation:

The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller

X X^2

95 9025

96 9216

98 9604

Sum = 289 27845

n 3

The sample mean 96.33333333 SUM/n

Population mean 96.33333333 SUM/n

Sample standard dev \(1.527525232 \sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}\)

Population standard dev \(1.247219129 \sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}\)

Population Mean(μ) = 96.33

Population standard deviation (σ) = 1.25

Option A) 95,96,98 and X bar = 96.33

Sampling distribution :

mean (μx = μ) = 96.33

standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72

Option A) Means are the same but the standard deviation of the sampling distribution is smaller

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Answer:

-3

Step-by-step explanation:

Answer: The slope whould be 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept:

(0,0)

x|y

----

0|0

1|3

The area of the trapezoid is 1.56 square units

The area of trapezoid is calculated using the formula

= 1/2 (sum of bases) * height

= 1/2 (a + b) * height

In the problem the dimensions made available are

height =

base (a) = 1

base (b) = 1 3/5

substituting the values into the formula

= 0.5 (1 + 1 3/5) * 1 1/5

= 0.5 * 13/5 * 1 1/5

= 1.56 square units

The area of the trapezoid is 1.56 square units

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Jabez is correct without calculating the product of 54 x 0.06 correctly because his estimation aligns with the mathematical principle that multiplying a number by a decimal less than 1 will result in a smaller product.

To determine who is correct without calculating the product of 54 x 0.06, we can use estimation.
Jabez estimated that the answer will be less than 54 but greater than 5.4. Let's analyze his estimation. When multiplying a number by a decimal less than 1, the product will always be smaller than the original number. In this case, 54 is the original number. Since 0.06 is less than 1, the product of 54 x 0.06 will definitely be smaller than 54.
On the other hand, Christina thinks the answer will be less than 5.4. Let's analyze her estimation. The original number, 54, is already greater than 5.4. When multiplying it by a decimal less than 1, the product will be even smaller. Therefore, Jabez's estimation is incorrect.
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Answer:

(a)\(x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\)

(b) 12

(c)\(2\frac{3}{4}\)

Step-by-step explanation:

\(G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\)

We are to compute the quadratic form \(x^TAx\) for A.

Part A

\(x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\)

\(x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\)

\(= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right]\)

\(= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)\)

\(= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\)

Part B

\(x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12\)

Part C

\(x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}\)

Answer:

\(24.7 \div 5.2 \\ \frac{19}{4} \: \: or \: \: 4.75\)

Answer:

\( \\ \sf24.7 \div 5.2\)

\( \\ \sf = \frac{247}{10} \div \frac{52}{10} \)

\( \\ \sf = \frac{247}{10} \times \frac{10}{52} \)

\( \\ \sf = \frac{247}{52} \)

\( \\ \sf = \frac{19}{4}\)

\( \\ \sf = 4.75\)

Answer:

  x ≥ 5

Step-by-step explanation:

You want the domain of the equation y = √(x -5) -1.

The domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...

  x -5 ≥ 0

  x ≥ 5 . . . . . . the domain of this function

__

Additional comment

The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.

<95141404393>

Answer:

stacy 30 and naomi 18

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

STEP 1= bring all the unknown factors together and the known factors toghether

-2+8=9r-10r

STEP2= SOLVE IT

+6=-1R

thus r= -6

John's account balance after considering the withdrawal and the overdrawn fee is -$35

What does it mean for an account to be overdrawn?

An account is overdrawn if the money withdrawn from it is more than the account balance, in this scenario, the check presented whose value is $110 is more than the account balance, which was the account by which the account was opened initially, hence, John's account can be said to be overdrawn.

Account balance=initial balance-amount withdrawn-overdrawn fee

Note overdrawn fee and amount withdrawn would be shown as negative values because they are obligations against the account balance

initial balance=$100

amount withdrawn=$110

overdrawn fee=$25

Account balance=$100-$110-$25

Account balance=-$35

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The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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The slope of a Line

If we represent the distance y in terms of the time x, the slope of the line represents the speed of the object.

Concretely, if

y = mx

is the equation of the line, then m is the speed of the train.

Train A's motion is represented by:

y = 76x

This means that the speed of train A is 76 miles per hour.

We now need to find the speed of train B. That will be calculated from the graph of its motion. Select two points from it, for example, (0,0) and (1,74).

Calculate the slope with the formula:

Substituting:

The speed of train B is 74 miles per hour.

This means that Train A is faster than Train B

The producer's surplus is 258.84.

Producer's surplus is a measure of the profit earned by a producer in a market. It is calculated as the difference between the price at which a producer is willing to supply a good and the actual market price. The formula for producer's surplus is PS = (P_e - MC) × Q_e, where P_e is the equilibrium price, MC is the marginal cost, and Q_e is the equilibrium quantity.

In this problem, the supply function is given by S(x) = √x+5, where x is the quantity of the item produced. The equilibrium point (x_e, P_e) is given as (40, 6.71). To find the producer's surplus, we need to first find the marginal cost.

The marginal cost is the additional cost incurred by producing one more unit of the good. In this case, it is the derivative of the supply function with respect to x, which is MC = S'(x) = 1/(2√x+5). Substituting x = 40, we get MC = 0.0905.

Now, substituting the values of P_e, Q_e, and MC in the formula for producer's surplus, we get PS = (6.71 - 0.0905 × 40) × 40 = 258.84. Therefore, the producer's surplus is 258.84.

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The function type of the graph with asymptotes, x = 2, and y = 0  is a rational polynomial, where the degree of the numerator is less than the degree of the denominator, and (x - 2) is a factor of the denominator, which is a function of the form;

\(f(x) = \frac{1}{(x - 2)}\)

An asymptote is a line to which the output value of a function approaches as the input value becomes very large approaches infinity.

The function type represented by the graph is a polynomial function that has an horizontal asymptote of y = 0, and a vertical asymptote of x = 2

A function has a vertical asymptote at the location at which the denominator approaches zero.

The vertical asymptote of x = 2 , indicates that the denominator approaches zero when x = 2, therefore, (x - 2) is a factor of the denominator

A function has an horizontal asymptote which is the value the function approaches as the input value approaches infinity.

Therefore, the horizontal asymptote of y = 0, indicates that the the degree of the numerator is less than the degree of the denominator

The function type in the question is therefore;

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Answer:

Step-by-step explanation:

That should be right :) I tried

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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