In rectangle ABCD, A C B D are the diagonals. A C equals 3 x plus 15 and B D equals 4 x minus 5 what is the length of AC

Answer: -4

Step-by-step explanation:

Note that the shape with with two parallel sides is called an irregular parallelogram. See the attached image.

The polygon  is an irregular quadrilateral because two sides are parallel lines and the other two sides are not.

Irregular polygons have infinitely many sides because their lengths are not equal. Shapes such as parallelograms, trapeziums, and quadrilaterals are irregular polygons because their neighboring sides and angles are not equal.

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The equivalent expression to the given expression; - √-7 as required to be written in terms of i is; -i√7.

It follows from the task content that the equivalent expression to the given; -√-7 is to be determined.

Since the given expression is; - √-7; we have;

- (√-1 × √7) where √-1 = i, so that we have;

= -i√7.

Ultimately, the expression in terms of i is; -i√7.

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Answer:

The following objects would most likely weigh 2 kilograms:

The actual weight of each object may vary, but based on typical weights, any of these objects could weigh around 2 kilograms.

Answer:

8

Step-by-step explanation:

6 + 2 = 8

Answer:8

Step-by-step explanation: 6 +2 =8

Answer:

Y + 3x = 10

Step-by-step explanation:

You need to know that Standard Form is: Ax + By = C

Y-4=-3x+6              Add 3x to both sides

Y - 4 + 3x = 6         Add 4 to both sides

Y + 3x = 10

Required equation is $125 = $82 + x and the amount of money he still has to save to buy the bicycle is $43.

What is equation?

A statement that two expressions are equal. It typically contains one or more variables is called equation which are usually represented by letters, and it may also contain numbers and mathematical operations such as addition, subtraction, multiplication, and division.

Let x be the amount of money that Desmond still needs to save to buy the bicycle.

Since he has already saved $82, the total amount of money he needs to save,

Total cost of bicycle = Cost he has saved + Amount he still needs to save

$125 = $82 + x

We can solve for x by subtracting $82 from both sides:

$125 - $82 = x

Simplifying, we get:

$x = $43

Therefore, Desmond still needs to save $43 to buy the bicycle.

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The volume of the following regular pentagonal prism rounded to the nearest tenth is: 1384.1 cm³.

To calculate the volume of a pentagonal prism, we should apply the formula:

V = 5/2 × apothem × base × height

In the given question, the height is 8 cm and the apothem is 6.9 cm. This apothem can be applied in solving for side length as follows:

2 × 6.9cm × tan 36°

= 10.03

Next, we find the area of the Pentagon as follows:

5/2 × 10.03 × 6.9 cm

= 173.02

The volume now equals:

173.02 × 10.03

= 1384.1 cm³.

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Answer:

Step-by-step explanation:

To find the equation of a line passing through a given point that is perpendicular to a given line, we need to follow these steps:

Find the slope of the given line by rearranging the equation into slope-intercept form y = mx + b, where m is the slope.

Find the slope of a line perpendicular to the given line by taking the negative reciprocal of the slope found in step 1.

Use the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope found in step 2, to write the equation of the perpendicular line.

Step 1: Find the slope of the given line 5x - 3y = 10

We can rearrange the equation into slope-intercept form by solving for y:

5x - 3y = 10

-3y = -5x + 10

y = (5/3)x - (10/3)

The slope of this line is 5/3.

Step 2: Find the slope of a line perpendicular to the given line

The slope of a line perpendicular to the given line is the negative reciprocal of 5/3:

m_perp = -3/5

Step 3: Use the point-slope form to write the equation of the perpendicular line passing through (-3, -7).

We plug in the values we found for the slope and the given point into the point-slope form:

y - y1 = m_perp(x - x1)

y - (-7) = (-3/5)(x - (-3))

Simplifying this equation, we get:

y + 7 = (-3/5)x - 9/5

Now we can rearrange this equation into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:

y = (-3/5)x - 44/5

Therefore, the equation of the line passing through the point (-3, -7) and perpendicular to the line 5x - 3y = 10 is y = (-3/5)x - 44/5.

We need 30 liters of the 35% acid solution and 40 liters of the 70% acid solution.

The volume of each solution is calculated as follows;

Let x be the number of liters of the 35% acid solution

Let y be the number of liters of the 70% acid solution

x + y = 70 ----- (1)

0.35x + 0.70y = 0.55(70) ----- (2)

The equation is simplified as;

0.35x + 0.70y = 38.5

from (1) x = 70 - y

Substitute x = 70 - y into equation 2:

0.35(70 - y) + 0.70y = 38.5

24.5 - 0.35y + 0.70y = 38.5

0.35y = 14

y = 40

Substitute y = 40 into equation 1 to solve for x:

x + 40 = 70

x = 30

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To sum up, Stanley Marks had a starting balance of $300 to establish the petty cash fund. During the month of April, he paid out a total of $160 and replenished the petty cash fund with $400.

Amount is a term used to refer to the size or quantity of something. It can refer to a physical quantity, such as the amount of water in a container, or to a more abstract concept, such as the amount of money owed. Amounts can be measured in physical units, such as liters or kilograms, or in monetary units, such as dollars or euros. Amounts can also be expressed in terms of other units, such as the number of hours worked or the number of miles driven.

Apr 6 Paid $40 to a supplier for office supplies

Apr 10 Paid $60 to a delivery person

Apr 15 Paid $25 to a vendor

Apr 20 Paid $15 to a cab driver

Apr 25 Paid $20 to a repair person

Apr 30 Paid $400 to replenish the petty cash fund

At the end of April, Stanley Marks had to reconcile the petty cash fund. In order to do so, he had to calculate the total amount of money that he had paid out during the month and the total amount of money that he had replenished the petty cash fund with. Stanley Marks needed to make sure that the total amount of money paid out matched the total amount of money replenished, so that he could properly balance the petty cash fund.

Stanley Marks reconciled the petty cash fund by totaling the amount of money that had been paid out during the month of April. He totaled the amounts of $40, $60, $25, $15, and $20, which amounted to $160. He then totaled the amount of money that had been replenished in the petty cash fund, which was $400. The total amount of money that was paid out was equal to the total amount of money that was replenished, so the petty cash fund was properly balanced.

Stanley Marks had a starting balance of $300, which was the amount of money he wrote a check for to establish the petty cash fund. He then had a total of $160 that he paid out during April. Finally, he had a total of $400 that he replenished the petty cash fund with. This brought the total balance of the petty cash fund to $340, which was $40 more than the starting balance of $300. This is the amount of money that Stanley Marks had at the end of April.

To sum up, Stanley Marks had a starting balance of $300 to establish the petty cash fund. During the month of April, he paid out a total of $160 and replenished the petty cash fund with $400. This brought the total balance of the petty cash fund to $340 at the end of April. By properly reconciling the petty cash fund, Stanley Marks was able to ensure that the total amount of money paid out matched the total amount of money replenished. This is how Stanley Marks was able to properly balance the petty cash fund.

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The Savings budget is $150 per month

Utility budget is $225,000

Auto budget is $823 per month

Saving behavior, they want to save 15% of their income, so their savings budget would be:

a. Savings budget = 15% of $1,000 = $150 per month

b. Tri-County Supply budgets 5% of the previous year's total revenue for utilities, so their utility budget would be:

Utility budget = 5% of $4,500,000 = $225,000

c. Mr. Jones needs to increase his auto budget to 15% of his monthly income, which is $5,488 per month. So his monthly auto budget would be:

Auto budget = 15% of $5,488 ≈ $823 per month

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Answer:

To rewrite the mixed number 9 2/5 as an improper fraction, we can multiply the whole number (9) by the denominator of the fraction (5) and add the numerator of the fraction (2), then write the result over the denominator:

9 2/5 = (9 × 5 + 2)/5 = 47/5

Therefore, 9 2/5 can be written as the improper fraction 47/5.

Answer:

3 = equal

5 = equal

Step-by-step explanation:

3. both angles are alternate angles

5. both triangles are equal

Where the above conditions are given, the IQR for X is from 156 acres to 192 acres.

To find the interquartile range (IQR), we need to first find the first and third quartiles of the sample.

Given:

Sample size (n) = 38

Sample mean (μ) = 174

Sample standard deviation (σ) = 55

We know that the first quartile (Q1) is the 25th percentile and the third quartile (Q3) is the 75th percentile.

Using the standard normal distribution table, we can find the z-scores for Q1 and Q3:

z-score for Q1 = invNorm(0.25) = -0.6745

z-score for Q3 = invNorm(0.75) = 0.6745

Now, we can use the following formulas to find Q1 and Q3:

Q1 = μ + z-score for Q1 * (σ / sqrt(n))

Q3 = μ + z-score for Q3 * (σ / sqrt(n))

Substituting the given values, we get:

Q1 = 174 - 0.6745 * (55 / sqrt(38)) ≈ 155.52

Q3 = 174 + 0.6745 * (55 / sqrt(38)) ≈ 192.48

Therefore, the IQR for X is from 156 acres to 192 acres.

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Answer:

no

Step-by-step explanation:

The value of the side x is 4. 36

To determine the value, we need to know that there are six different trigonometric identities. They are;

From the information given, we have that;

the acute angle is 28 degrees and the obtuse angle is 126 degrees. The adjacent side of 28-degree angle is 8.2 and the opposite side is x.

Opposite side = x

Adjacent side = 8.2

Now, using the tangent identity;

tan 28 = x/8.2

multiply the values

x = 0. 5317(8.2)

multiply

x = 4. 36

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Answer:

y =27/39x + 7

Step-by-step explanation:

Step 1: Calculating Slope (m).

m = y2-y1/x2-x1

m = (25)-(-2)/(26)-(-13)

m = 25+2/26+13

m = 27/39

m = 0.692

Now putting value of m in equation (i)

y = 0.692x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (-13,-2) for calculating y-intercept:

y = mx + b

-2 = 0.692(-13) + b

-2 = -9.00 + b

7 = b

b = 7

Now putting value of b in equation (ii)

y = 0.692x + 7

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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Let's call the number of minutes of calls "x".

For the first plan, the cost will be:

Cost = $18 + $0.15x

For the second plan, the cost will be:

Cost = $12 + $0.20x

To find the point at which the costs of the two plans are equal, we can set the two equations equal to each other and solve for x:

$18 + $0.15x = $12 + $0.20x

Subtracting $12 from both sides, we get:

$6 + $0.15x = $0.20x

Subtracting $0.15x from both sides, we get:

$6 = $0.05x

Dividing both sides by $0.05, we get:

x = 120

Therefore, if a customer makes more than 120 minutes of calls per month, the first plan with the $18 monthly fee and $0.15 per minute charge will be more cost-effective. If a customer makes less than 120 minutes of calls per month, the second plan with the $12 monthly fee and $0.20 per minute charge will be more cost-effective.

Answer:

120 minutes

Step-by-step explanation:

Let x be the number of minutes of calls made in a month.

For the first plan, the monthly cost is $18 + $0.15x.

For the second plan, the monthly cost is $12 + $0.20x.

To find the point where the costs are equal, we need to solve the equation:

18 + 0.15x = 12 + 0.20x

Subtracting 0.15x from both sides gives:

18 = 12 + 0.05x

Subtracting 12 from both sides gives:

6 = 0.05xDividing both sides by 0.05 gives:

x = 120

Therefore, the costs of the two plans will be equal for 120 minutes of calls.

the value of the side c is √3 and h is 7.

What is Trigonometric Functions?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used in various fields such as engineering, physics, and navigation. The six fundamental trigonometric functions are sine, cosine, tangent, secant, cosecant, and cotangent. These functions are based on the ratios of the sides of a right-angled triangle. By using trigonometric formulas and identities, we can calculate the values of these functions for the perpendicular side, hypotenuse, and base of a right triangle.

tan(60)= 3/c

c = 3/tan(60)

c = 3/√3

c = √3

for 2nd

tan(45)= h/7

h = 7*1

h=7

Hence the value of the side c is √3 and h is 7.

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a)she need 3.68 negative point , The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.and the breakeven time for Moira's loan is 10 months

Breakeven time refers to the amount of time it takes for the savings from a particular action to equal the costs associated with that action. It is the point at which the benefits and costs are equal, and after which the benefits will begin to exceed the costs.

a. Moira has to buy 14,000/380,000 = 0.0368 or 3.68% in negative points to offset $14,000 in closing fees. The closing expenses are reduced by 1% of the principle for every negative point, therefore Moira has to buy 3.68/1 = 3.68 negative points.

b. The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.

c.When the savings from buying the negative points equal the additional interest paid because of the higher APR, that is the breakeven point for Moira's loan. 3.68 x 380,000 x 1% = $14,040 is the savings from buying 3.68 negative points. The difference between the interest paid at the original APR of 3.25% and the interest paid at the new APR of 3.7452% represents the additional interest paid as a result of the higher APR. A 10-year, $380,000 mortgage at 3.25% would have a monthly payment of $3,680.97 according to an online mortgage calculator. During a period of ten years, interest payments total $73,276.23. A 10-year, $380,000 mortgage at 3.7452% has a $3,918.23 monthly payment. Throughout a ten-year period, interest was paid a total of $88,668.83. The additional interest paid as a result of the higher APR equals $15,392.60 ($88,668.83 x $73,276.23). The breakeven point is therefore $14,040/$15,392.60 = 0.910 or roughly 10 months.

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Answer:

The height of the block is two-thirds of its width, so we have h = (2/3)x.

The length of the block is 4 times its height, so we have l = 4h = 4(2/3)x = (8/3)x.

The volume of the block is given by V = lwh, so substituting the values we have:

V = (8/3)x * x * (2/3)x = (16/81)x³

Therefore, the volume of the block is (16/81)x³ cubic cm.

228 in base 10 to base three is determined as 22110₃.

Converting a number from one base to another involves representing the same value in a different positional numeral system.

To convert the number 228 from base 10 to base 3, we can follow these steps:

3 | 228

   = 76 R 0 (so the remainder here 0)

   = 25 R 1 (the remainder here 1)

   = 8 R  1 (the remainder here 1)

   = 2 R 2 (the remainder here 2)

   = 0 R 2 (the remainder here 2)

write the remainders from bottom to top = 22110₃

228 in base 10 to base 3 = 22110₃

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let's firstly convert the mixed fraction to improper fraction and then divide.

[tex]\stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}\div \cfrac{3}{5}\implies \cfrac{7}{3}\cdot \cfrac{5}{3}\implies \cfrac{35}{9}\implies {\Large \begin{array}{llll} 3\frac{8}{9} \end{array}}[/tex]

Answer: 24 i am a expect