Divide 1540 by 7.

Please show working

The slope of a line that is perpendicular to the line through the points is - 25/123

The change in the y-coordinate relative to the change in the x-coordinate of a line is referred to as the slope of that line. The net change in the y-coordinate is y, while the net change in the x-coordinate is x. As a result, the change in the y-coordinate with regard to the change in the x-coordinate may be expressed as,

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

The reciprocal of the perpendicular line's slope is negative. This implies that you switch the slope's sign to its opposite.

m₁ × m₂ = -1

Where,

m₁ = Slope of the first line

m₂ = Slope of the second line

According to the question

Given

points A (4.95, 5.96) and B (8.01, 21.03)

So the equation of the line passing from these two points will be

(y - y₁) = \(\frac{y_2 - y_1}{x_2 - x_1}\) (x - x₁)

So the equation we get will be

(y - 5.96) = \(\frac{21.03 - 5.96}{8.01 - 4.95}\) (x - 4.95)

⇒ y - 5.96 = 4.92 (x - 4.95)

⇒ y - 5.96 = 4.92x - 24.55

⇒ y = 4.92x - 18.39

This is the required equation passing from the two given points with slope m = 4.92 ⇒ m = 123/25

Now

∵ m₁ × m₂ = -1

∴ (123/25) × m₂ = -1

⇒ m₂ = - (25/125)

Hence, the slope of a line that is perpendicular to the line through the points is - 25/123

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The slope of a line that is perpendicular to the line through the points is - 25/123

The change in the y-coordinate relative to the change in the x-coordinate of a line is referred to as the slope of that line. The net change in the y-coordinate is y, while the net change in the x-coordinate is x. As a result, the change in the y-coordinate with regard to the change in the x-coordinate may be expressed as,

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

The reciprocal of the perpendicular line's slope is negative. This implies that you switch the slope's sign to its opposite.

m₁ × m₂ = -1

Where,

m₁ = Slope of the first line

m₂ = Slope of the second line

According to the question

Given

points A (4.95, 5.96) and B (8.01, 21.03)

So the equation of the line passing from these two points will be

(y - y₁) = \(\frac{y_2 - y_1}{x_2 - x_1}\) (x - x₁)

So the equation we get will be

(y - 5.96) = \(\frac{21.03 - 5.96}{8.01 - 4.95}\) (x - 4.95)

⇒ y - 5.96 = 4.92 (x - 4.95)

⇒ y - 5.96 = 4.92x - 24.55

⇒ y = 4.92x - 18.39

This is the required equation passing from the two given points with slope m = 4.92 ⇒ m = 123/25

Now

∵ m₁ × m₂ = -1

∴ (123/25) × m₂ = -1

⇒ m₂ = - (25/125)

Hence, the slope of a line that is perpendicular to the line through the points is - 25/123

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Given the algebraic expression,  \(2x^2y\), the error in the analysis shown in the diagram attached is the wrong listing of terms.

The correct analysis is:

Recall:

Given an expression, say, \(2x^2 + 4x + 5\).

Thus, we are given the expression, \(2x^2y\),

The expression has only 1 term: \(2x^2y\)

1 coefficient: 2

It has no constant.

Therefore, given the algebraic expression,  \(2x^2y\), the error in the analysis shown in the diagram attached is the wrong listing of terms.

The correct analysis is:

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Answer:

I'm pretty sure its 180 !!

Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

\(\implies 6 \times 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

\(\implies (0.06) \cdot (0.154)=0.00924\)

-----------------------------------------------------------------------------------------------

Answer option A

\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)

Therefore, this is a valid answer option.

Answer option B

\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)

Multiply the numbers 6 and 154:

\(\implies 6 \times 154 = 924\)

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)

Therefore, this is a valid answer option.

Answer option C

\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

\(\implies 6 \cdot 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

\(\implies 0.924\)

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

\(\boxed{6 \cdot 154 \cdot (0.00001)}\)

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)

Therefore, this is a valid answer option.

Answer option E

\(\boxed{0.00924}\)

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

Answer:

A= (-4,7)

B= (-4,-3)

C= (9,-3)

length of AB= 10

length of BC= 13

length of CA= 16.4 (this is the hypotenuse)

so the two shortest sides squared and added together should equal to the longest side squared, according to the equation

10^2+13^2=16.4^2

100+169=269

since this equation is true and follows the Pythagorean Theorem, it proves that this is a right triangle

Step-by-step explanation:

Answer:

sqrt(A/pi)= r

Step-by-step explanation:

A= pi r^2

Divide each side by pi

A/pi= pi r^2/pi

A/pi=  r^2

Take the square root of each side

sqrt(A/pi)= sqrt( r^2)

sqrt(A/pi)= r

The value of r after solving A=pi\(r^{2}\) is \(\sqrt{A/Pi}\).

A mathematical relationship or rule expressed in symbols.

We have been giving the following formula and we have to solve it for r means we have to find the value of r.

A=pi\(r^{2}\)

A/pi=\(r^{2}\)

r=\(\sqrt{A/Pi}\)

Hence the value after solving the formula A=Pi\(r^{2}\) is \(\sqrt{A/Pi}\)

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Answer:

Diego

Step-by-step explanation:

In math, congruent means two figures that have the same shape and size.

Answer:

27

Step-by-step explanation:

5×6-(6/2)

=30-3

=27

Answer:

\( 27\)

Step-by-step explanation:

\(5w - \frac{w}{x} = \frac{5w}{1} - \frac{w}{x} = \frac{5(6)}{1} - \frac{6}{2} = 30 - 3 = 27\)

or

\( \frac{5(6) }{1} - \frac{6}{2} = \frac{30}{1} - \frac{6}{2} = \frac{60 - 6}{2} = \frac{54}{2} \)

Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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Let b be the price of the bath towels and h be price of the hand towels. For Helen, we can write the following equation

And for Althea, we have

Then, we have 2 equations in 2 unknowns. By multipliying the first equation by -2, we have the following equivalent system of equation

By adding both equations, we have

Then, b is given by

Therefore, 1 bath towel cost $12, which corresponds to option 3

In the given scenario, angle DBC is 51 degrees, and line segment BD is a diameter of circle E. Circle E is inscribed within triangle BCD, where BD is also a diameter.

Line segments DC and CB are secants. We need to determine the measure of arc BC.

Since line segment BD is a diameter, angle BDC is a right angle, measuring 90 degrees. We are given that angle DBC is 51 degrees. In a circle, an inscribed angle is equal to half the measure of its intercepted arc.

Therefore, the measure of arc BC can be calculated as follows:

Arc BC = 2 * angle DBC = 2 * 51 degrees = 102 degrees.

Hence, the measure of arc BC is 102 degrees.

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Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are: x² + (y - 3)²=36 and x² + (y + 8)²=36.

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign (=). The expression on the left side of the equals sign is called the left-hand side (LHS), and the expression on the right side of the equals sign is called the right-hand side (RHS). Solving an equation means finding the value of the variable that makes the equation true. I

Here,

A circle with diameter 12 units and center on the y-axis has its center at (0, c), where c is a constant. The radius of the circle is half the diameter, which is 6 units.

The equation of a circle with center (0, c) and radius r is given by:

x² + (y - c)² = r²

Substituting r = 6 and simplifying, we get:

x² + (y - c)² = 36

The only two equations among the options given that match this form are:

x² + (y - 3)² = 36 (center at (0,3))

x² + (y + 8)² = 36 (center at (0,-8))

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Answer:

6 : A

8: B

Step-by-step explanation:

The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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The angles get added.

Let z = r exp(i θ) and w = s exp(i φ). Then

zw = rs exp(i θ) exp(i φ) = rs exp(i (θ + φ))

See the attached picture:

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

261.06 (Approx)

Step-by-step explanation:

Given:

Two number = 0.678,9.01/0.0234

Find:

Multiply

Computation:

⇒ 0.678,9.01/0.0234

⇒ 0.678 x [9.01/0.0234]

⇒ 6.10878 / 0.0234

⇒ 261.058874

261.06 (Approx)

The solution for given inequality is - 30 and 18. So the answer is option c. x < −30 and x < 18.

In mathematics, an inequality is an unequal comparison between 2 algebraic terms or algebraic expressions. The signs we used in inequality are Lessthan (<), greater than (>) or Less than or equal to(≤), greater than or equal to (≥).  

To solve an inequality we can add or subtract the same integer on both sides or we can multiply or divide the same integer on both sides. which doesn't change the condition of inequality.

Here we have an inequality that is

The inequality is three-fourths times the absolute value of the quantity third times x plus 2 end quantity is less than 6.  

The above statement can be converted as follows

=> \(\frac{3}{4} | \frac{x}{3} +2| < 6\)    

The equation can be solved as follows

=> \(3 | \frac{x}{3} +2| < 24\)    [  Multiplied by 4 on both sides ]

=> \(3 | \frac{x+6}{3} | < 24\)    

=> \(| x+6 | < 24\)    

=> \(x+6 < \pm24\)    

Take \(x+6 < 24\)  

=> x + 6 - 6 < 24 - 6     [ Subtract - 6 on both sides ]

=> x < 18

Take x + 6 < - 24

=> x + 6 - 6 < - 24 - 6   [ Subtract - 6 on both sides ]

=> x < - 30  

Therefore,

The solution for given inequality is - 30 and 18. So the answer is option c. x < −30 and x < 18.

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To find the average quarterly loads for the rest of the years, you can use the formula below:

Average Quarterly Load = Total Annual Load  4 For example, let's say the total annual load for Year 1 is 800.

To find the average quarterly loads for Year 1, we would divide 800 by 4 to get an average quarterly load of 200. Then, you can use this average quarterly load to find the seasonal indices for each quarter of each year.To find the seasonal index for a given quarter and year, you would divide the actual quarterly load by the average quarterly load for that year.

For example, let's say the actual load for Quarter 1, Year 1 is 240. To find the seasonal index for this quarter and year, we would divide 240 by 200 to get a seasonal index of 1.2. You would repeat this process for each quarter and year to find the seasonal indices for all quarters and years.

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Answer:

Step-by-step explanation:

B

The factor of the given expression 2x²+13x+15 will be (2x+3)(x+5).

To express equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to factor the expression into an equivalent form 2x²+13x+15

This expression could also be given by;

2x²+13x+15

We know that if D≥0, then trinomial 'ax²+bx+c' can be written in form a(x-x1)(x-x2),

where x1 and x2 - roots of ax²+bx+c=0.

Then D=b²-4ac=13²-15*2*4=49,

2x²+13x+15

Factor =2(x+5)(x+1.5)

The answer is: (2x+3)(x+5).

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The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer:

1809.56 \(cm^3\)

Step-by-step explanation:

The volume of any shape can be found by multiplying the area of the cross-section by the length of the object.  Since the object in this problem is a cylinder, the cross-section would be a circle with a radius of 8 cm.  The area of the cross-section can be found with

\(A=\pi r^2\\A=\pi(8cm)^2\\A=201.06cm^2\)

To find the volume, multiply the area by the height (9cm):

\(V=A*h\\V=201.06cm^2(9cm)\\V=1809.56cm^3\)

Answer:

  58.4°

Step-by-step explanation:

You have ∆FGH with f = 12 cm, g = 6 cm, and h = 14 cm, and you want to know the measure of angle F.

The law of cosines tells you ...

  f² = g² +h² -2gh·cos(F)

Solving for angle F gives ...

  F = arccos((g² +h² -f²)/(2gh))

  F = arccos(88/168) ≈ 58.412°

Angle HFG is about 58.4°.

Answer:

F = 9/5C + 32

Step-by-step explanation:

F = 9/5C + 32

Since F means Fahrenheit and C means Celsius

Therefore the answer is already written

Answer: F = 9/5C + 32

Answer: C = 5/9 ( F - 32 )

Step-by-step explanation:

i dont know to do the 5 over 9 on the computer but thats the answer

Edmentum Answer

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

No

Step-by-step explanation:

Angle measures of a triangle must add up to 180 and this only adds up to 87