If the area of a triangle is 72 square inches and the height is 6 inches, what is the length of the base

Answer:

When the red lines in a geometric figure are not parallel, the congruency of angles may vary. Vertical angles formed by the intersection of non-parallel lines are always congruent, while corresponding angles and alternate interior angles may or may not be congruent. The congruency of angles depends on the specific relationship between the angles and the lines in the figure, and further analysis of the figure would be necessary to determine which angles are congruent.

The square of binomial have in common is x² - 14x + 49

The first two products you have given, (x + 9)(x + 9) and (x - 7)(x - 7), are examples of the square of a binomial. To find the product of two binomials, we use what's called the FOIL method. FOIL stands for First, Outer, Inner, Last, and it's a way to remember the steps involved in multiplying two binomials.

When we multiply (x + 9)(x + 9), we first multiply the first terms in each binomial: x * x = x². Then we multiply the outer terms: x * 9 = 9x. Next, we multiply the inner terms: 9 * x = 9x. Finally, we multiply the last terms in each binomial: 9 * 9 = 81. So, putting it all together, we get:

(x + 9)(x + 9) = x² + 9x + 9x + 81

= x² + 18x + 81

Similarly, when we multiply (x - 7)(x - 7), we get:

(x - 7)(x - 7) = x² - 7x - 7x + 49

= x² - 14x + 49

To know more about binomial here

https://brainly.com/question/13870395

#SPJ4

Complete Question:

Find each product. (x + 9) (x + 9) , (x - 7)(x - 7) (2x - 1 )²

a. What do all products of the square of a binomial have in common?

The annual interest rate of the account is 3.5%

The formula for simple interest is:

I = Prt

where I is the interest earned, P is the principal (initial amount deposited), r is the annual interest rate (as a decimal), and t is the time in years.

We know that P = £13,000, t = 15 years, and I = £19,825 - £13,000 = £6,825.

Plugging in these values, we get:

£6,825 = £13,000 * r * 15

Simplifying this equation, we get:

r = £6,825 / (£13,000 * 15) = 0.035 = 3.5%

Therefore, the annual interest rate of the account is 3.5% to 1 decimal place.

To learn more about interest rate here:

https://brainly.com/question/21111038

#SPJ4

Mark Twain's quote about breaking down overwhelming tasks into manageable pieces is a valuable lesson for high school students, particularly when it comes to writing. (option d)

In the context of writing, this quote can be particularly helpful. Writing a story or essay can seem like a daunting task, but if you break it down into smaller pieces, it becomes much more manageable. This is where the process of outlining comes in. An outline is essentially a roadmap of your writing, breaking it down into smaller components that you can tackle one at a time.

In mathematical terms, you can think of this process as a series of equations. Each equation represents a small, manageable piece of the overall problem.

By breaking down the problem into smaller equations, you can solve each one individually, which ultimately leads to solving the larger problem. This is similar to how breaking down a writing project into smaller pieces can help you write a well-structured and coherent piece.

Hence the correct option is (d).

To know more about quote here

https://brainly.com/question/15703655

#SPJ4

The cost of the car with 60,000 miles would be = $13,000 approximately.

To calculate the cost of the car form the given graph above is to draw a straight line that connects most of the points of interception.

From the graph, the most appropriate point of interception would be on $13,000 since each line in y-axis represents a thousand dollars.

Therefore, the cost of the car with 60,000 miles would be = $13,000 approximately.

Learn more about graph here:

https://brainly.com/question/25184007

#SPJ1

The width of the rectangle is x + 4

Since the area of the rectangle is x^2 + 15x + 44, the product that give the value can be solved by factorization

To factorize the expression x^2 + 15x + 44, we need to find two numbers whose product is 44 and whose sum is 15. These numbers are 11 and 4, because 11 times 4 is 44 and 11 plus 4 is 15.

Now we can write the expression as:

x^2 + 11x + 4x + 44

Grouping the terms in pairs:

(x^2 + 11x) + (4x + 44)

Factoring out the greatest common factor from each pair:

x(x + 11) + 4(x + 11)

Now we can see that we have a common factor of (x + 11):

(x + 11)(x + 4)

Therefore, the factored form of x^2 + 15x + 44 is:

(x + 11)(x + 4)

the width of the rectangle is x + 4

Learn more about area of rectangle at

https://brainly.com/question/13048427

#SPJ1

Answer:

230°

Step-by-step explanation:

Because Arc RSP had three letters that means its a major arc or greater than 180°

Arc RP is the portion of the circle not intercepted by the angle so 360 minus the measure of RP is RSP

360 - 130 = 230

lines a and b are perlendicularr and the equation of line a is y=x+3.Therefore, after calculation, the equation of line b is y = -x + 3.

Perpendicular refers to a line, ray, or segment that intersects another line or segment at a right angle, or 90-degree angle. The point of intersection is called the point of perpendicularity and is equidistant from the endpoints of the segment.

An equation of a line is a mathematical representation of a straight line. It can be written in various forms, including slope-intercept form, point-slope form, and standard form, and relates the variables x and y.

According to the given information:

If line a has the equation y = x + 3 and line a is perpendicular to line b, then the slope of line b is the negative reciprocal of the slope of line a.

The slope of line a is 1, so the slope of line b is -1/1, which simplifies to -1.

To find the equation of line b, we need to find the y-intercept (b) using the point-slope form of a linear equation. We can choose any point on line b, but since we don't have any specific point given, we can use the y-intercept of line a, which is 3.

So, the equation of line b is y = -x + 3.

To know more about equation of line, perpendicular visit:

https://brainly.com/question/25790244

#SPJ1

There were about 557 principals in attendance based on the prediction

To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.

In the exhibit room, out of 70 people, 52 were principals.

So, the proportion of principals in the exhibit room was 52/70

We can predict the number of principals in attendance at the conference as follows:

Number of principals = proportion of principals x total number of attendees

If we plug in the values, we get:

number of principals = 52/70 x 750 = 557

So, based on this prediction, we can say that there were 557 principals in attendance at the conference.

Read more about proportion at

https://brainly.com/question/1781657

#SPJ1

Answer:

44 <= x

Step-by-step explanation:

The general solution to the differential equation is y = -1/(3x³ + C)

Where C is an arbitrary constant.

The concept used to solve this differential equation is the separation of variables. Separated the variables on either side of the equation and then integrated both sides to get the general solution with a constant of integration.

Note that, the solution is valid only for y ≠ 0 as the differential equation is undefined for y = 0.

Here we have  

dy/dx = 9x²y²

Solve the differential equation using the separation of variables.

=> dy/dx = 9x² y²

Let's separate the variables by dividing both sides by y² and dx:

=> 1/(y²) dy = 9x² dx

Now we can integrate both sides:

=> ∫1/(y²) dy = ∫9x² dx

Using the power rule of integration, we get:

=> -1/y = 3x³ + C

Where C is the constant of integration.

To solve for y, we can multiply both sides by -1:

=> y = -1/(3x³ + C)

Therefore,

The general solution to the differential equation is y = -1/(3x³ + C)

Where C is an arbitrary constant.

Learn more about Differential equations at

https://brainly.com/question/31583235

#SPJ4

The costs of each treat are

To solve this, we use the followign representations

x = cookies

y = ice cream 1

z = ice cream 2

Treat 1

Using the columns to generate the system of equations, we have

x + y + z = 25.71

z + 2x = 23.21

3y = 26.94

So, we have

y = 8.98

The other equations become:

x + 8.98 + z = 25.71

z + 2x = 23.21

When solved, we have

x = 6.48

z = 10.25

Treat 2

Using the rows to generate the system of equations, we have

x + 2y = 7.17

y + 2x = 5.37

3z = 14.97

So, we have

z = 4.99

The other equations when solved, we have

x = 1.19

y = 2.99

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

The thickness of the concrete pad is 58 and 2/81 yd³. So correct option B.

Volume is the measure of the amount of space occupied by a three-dimensional object or substance. It is typically measured in units such as cubic meters, cubic feet, liters, or gallons. The formula for calculating the volume of a simple shape like a cube, rectangular prism, or cylinder involves multiplying its length, width, and height or its base area and height. More complex shapes may require more advanced formulas or techniques for determining their volume. Volume is an important concept in many fields, including physics, engineering, architecture, and chemistry, and is often used to measure quantities such as liquids, gases, and solids.

To find the volume of the concrete pad, we need to multiply the length, width, and thickness of the pad.

First, we need to convert the dimensions to yards by dividing by 3 since there are 3 feet in a yard:

Length: 31 and 1/3 yards = 94/3 yards

Width: 16 and 2/3 yards = 50/3 yards

Thickness: 1/9 yard

Now we can calculate the volume:

V = (94/3) * (50/3) * (1/9)

V = 4700/81 cubic yards

V ≈ 58.02 cubic yards

Therefore, the answer is B. 58 and 2/81 yd³.

To know more about dimensions visit:

https://brainly.com/question/19902331

#SPJ1

The complete question is:

Answer:

A

Step-by-step explanation:

it cant be 9 per hour cuz it is a smaller amount and A is the only one that makes sens

Answer:

true

Step-by-step explanation:

The kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

The kite's vertical distance from the ground is the sum of its vertical height from Jennifer's hand and the distance from the ground to the hand

we shall represent the vertical height of the kite from Jennifer's hand with the letter x so that;

x = 36 inches × sin 39°

x = 3 feet × sin 39° {36 inches = 3 feet}

x = 1.8880 feet

kite's vertical distance from the ground = 1.9 ft + 5.5 ft = 7.4 feet

Therefore, the kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.

Read more about angle of elevation here:https://brainly.com/question/2096694

#SPJ1

Answer:

To find the value of Clare's home in 2006 after an 18% increase, we can use the following formula:

Value in 2006 = Value in 2001 x (1 + Percent Increase)

Plugging in the values given in the problem, we get:

Value in 2006 = $135,000 x (1 + 0.18)

Simplifying this expression, we get:

Value in 2006 = $135,000 x 1.18

Value in 2006 = $159,300

Therefore, Clare's home was worth $159,300 in 2006 after an 18% increase in value from its original price of $135,000 in 2001.

Answer: 50 * 1,967 = 98,350

50 * 1,000 = 50,000

Step-by-step explanation: 50 * 1,967 = 50 * 1,000 + 50 * 967 = 50,000 + 48,350 = 98,350.

The incorrect measurements of the right triangle is 36² + 60² = 48²

Given data ,

Let the triangle be represented as ABC

Now , let the height of the triangle be AB = 36 miles north

Let the base of the triangle be BC = 48 miles east

Now , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , 36² + 48² = 60²

So , the incorrect option from the data is 36² + 60² = 48²

Hence , the triangle is formed

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

Mass of water vapor (g) / volume of air (m^3) is the humidity measure of absolute humidity

The humidity measure of "mass of water vapor (g) / volume of air (m^3)" is called absolute humidity. Absolute humidity is a measure of the total amount of moisture in the air, expressed as the mass of water vapor per unit volume of air. It is different from relative humidity, which is a measure of the amount of moisture in the air relative to the maximum amount of moisture that the air can hold at a particular temperature.

Mixing ratio is also a measure of the amount of moisture in the air, but it is expressed as the mass of water vapor per mass of dry air, not per unit volume of air. Vapor pressure is a measure of the pressure exerted by water vapor in the air, expressed in units of pressure (such as millibars or pascals), not as a ratio.

Learn more about absolute humidity here

brainly.com/question/15658805

#SPJ4

Answer:

Answers down below!

Step-by-step explanation:

Mean: 58.75

Median: 63

Range: 70

Mode: 63

Hope this helps!

The z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.

The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the data value, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (80 - 52) / 9 = 3.11 (rounded to two decimal places)

Therefore, the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.

Learn more about z-score ,

https://brainly.com/question/15016913
#SPJ4

The z-score for a data value of 80 in this data set is approximately 3.1.

Calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9.

To find the z-score, follow these steps:

Identify the data value (x), mean (µ), and standard deviation (σ).

In this case, x = 80, µ = 52, and σ = 9.

Use the z-score formula:

z = (x - µ) / σ

Plug in the values:

z = (80 - 52) / 9

Perform the calculations:

z = 28 / 9

Round the answer to the nearest tenth: z ≈ 3.1

So, the z-score for a data value of 80 in this data set is approximately 3.1.

for such more question on z-score

https://brainly.com/question/28000192

#SPJ11

Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

Learn more about Salaries payable:

https://brainly.com/question/28238827

#SPJ4

The total area of the four offices in the building is 1296 square feet.

When we talk about the area of a shape, we are referring to the amount of space that it occupies. In this case, since the offices are squares, we can find the area of each office by multiplying the length of one side by itself. This is represented by the formula A = s², where A is the area and s is the length of one side.

So, if each office has a side length of 18 feet, we can find the area of one office by plugging that value into the formula: A = 18² = 324 square feet.

Since there are four offices, we can find the total area of all four offices by multiplying the area of one office by 4: 324 square feet x 4 = 1296 square feet.

To know more about area here

https://brainly.com/question/14994710

#SPJ4

An equation which shows how to find p, the price Mrs. Merson paid for the car include the following: B) 5500/p = 55/100.

In Mathematics and Science, a price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about the amount of money that Mersin paid for the car, an equation which shows how to find the price (p) is given by;

55% of p = 5500

55/100 × p = 5500

5500/p = 55/100

Read more on price here: https://brainly.com/question/14463202

#SPJ1

Complete Question:

Mrs. Merson is selling her car. Her research shows that the car has a current value of $5,500,

which is 55% of the amount Mrs. Merson paid for the car. A buyer wants to know the price

Mrs. Merson paid for the car.

• Which equation shows how to find p, the price Mrs. Merson paid for the car?

A) 55/p = 5500/100

B) 5500/p = 55/100

C) p/5500 = 55/100

D) p/5 = 5500/100

Answer:

The mean is 8.6 minutes.

Step-by-step explanation:

"mean" is the average, the way people might talk about it in common language (not necessarily math class language.)

To calculate the mean, you ADD and DIVIDE. You add up all the numbers in your list and divide by however many numbers there are.

ADD:

5+5+15+12+14+6+3

= 60

Then DIVIDE by 7 (bc there are 7 items in the list)

60/7

= 8.5714285714

They said to round to the nearest tenth.

8.5714285714 rounds to 8.6

The mean is 8.6 minutes.

Roehr Corporation Additional Paid-in Capital--Common account will increase by $110,000 by issuing 20,000 shares of $0.50 par common stock for $6 per share.

When a corporation issues common stock, the par value of the stock is recorded in the Common Stock account, and any amount received above the par value is recorded in the Additional Paid-in Capital--Common account. In this case, Roehr Corporation The par value of the common stock is

Total par value = Par value per share x Number of shares

= $0.50 x 20,000

= $10,000

The total amount received from issuing the stock is $6 per share x 20,000 shares = $120,000.

The additional paid-in capital is calculated as the difference between the total amount received and the total par value:

Additional paid-in capital = Total amount received - Total par value

= $120,000 - $10,000

= $110,000

Therefore, the answer is (B) $110,000.

Learn more about Paid-in Capital:

https://brainly.com/question/22556463

#SPJ4

The solution for the equation -x² + 2x + x - 3x = -9 + 2 + 6 is derived to be x = 1

We shall solve for x by simplifying the equation and making x the subject as follows:

-x² + 2x + x - 3x = -9 + 2 + 6

-x² + 3x - 3x = 8 - 9

-x² = -1

multiply both sides by -1 we have;

x² = 1

take square root of both sides

x = √1

x = 1

Therefore, the equation -x² + 2x + x - 3x = -9 + 2 + 6 will have a solution for the value of x = 1

Read more about equation here:https://brainly.com/question/1214333

#SPJ1

The linear function going through the points (0,2) and (6,0) is given as follows:

y = -x/3 + 2.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

When x = 0, y = 2, hence the intercept b is given as follows:

b = 2.

When x increases by 6, y decays by 2, hence the slope m is given as follows:

m = -2/6

m = -1/3.

Thus the equation of the line is given as follows:

y = -x/3 + 2.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The total amount paid to the finance company if the loan is repaid in 40 years is $317,376.00 (option c).

First, we need to find out how much money the couple borrowed. Since they got financing for 80% of the $150,000 purchase price, they borrowed $120,000 ($150,000 x 0.8 = $120,000).

Next, we need to find the monthly interest rate. Since the interest rate is 6% per year, the monthly interest rate is 0.06/12 = 0.005.

Now we can use the table to find the monthly payment per $1000 of mortgage for a 40-year loan with a 6% interest rate. Looking at the fifth column of the table, we find the entry that corresponds to a 6% interest rate and a 40-year loan, which is 5.86. This means that for each $1000 borrowed, the monthly payment is $5.86.

To find the monthly payment for the couple's $120,000 loan, we multiply the monthly payment per $1000 by 120 (since they borrowed $120,000). So the monthly payment is 5.86 x 120 = $703.20.

Finally, we need to calculate the total amount paid to the finance company over the 40-year period. Since the couple will make 12 payments per year for 40 years, the total number of payments will be 12 x 40 = 480. So the total amount paid will be the monthly payment ($703.20) multiplied by the total number of payments (480). This gives us a total of $317,376.

Therefore, the correct option is (c).

To know more about total here

https://brainly.com/question/14286201

#SPJ4