Evaluating functions digtal escape

The answer of given equation is = 1 { [tex]( a)^0[/tex] that means the value is 1}

An exponent and a power both refer to the same concept, which is a way to represent repeated multiplication of a number or a variable by itself. The exponent or power is usually represented as a superscript to the right of the base number or variable.There are 10 basic rule

For example, in the expression 2³, the base number is 2, and the exponent or power is 3. This means that 2 is being multiplied by itself three times. So, 2³ is equal to 2 x 2 x 2, which equals 8.

Similarly, in the expression[tex]x^4[/tex], the base is x, and the exponent or power is 4. This means that x is being multiplied by itself four times. So,[tex]x^4[/tex] is equal to x x x x, which can be written as x multiplied by itself four times.

Any number or variable raised to the power of 0 is equal to 1. Therefore,

[tex](x^36y^18z^12)^0[/tex] = 1  ( According to this rule, when the power of any integer is zero, then its value is equal to 1, such as;

[tex]a^0[/tex]= 1

where ‘a’ is any non-zero term.

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Answer:

2.5

Step-by-step explanation:

I took the test :)

There are 7 pencils measuring more than 5 1/2 inches but less than 7 2/4 inches.

An inch is a unit of length in the imperial and US customary systems of measurement. Equal to 1/12 of a foot, it is usually denoted by the symbol "in". It is also equal to 2.54 centimeters. The inch is commonly used in the construction industry, engineering, and other fields.

To answer this question, we must first convert all of the measurements into the same unit of length. We will convert 5 1/2 inches and 7 2/4 inches into decimals by dividing the fractions by their denominators. 5 1/2 inches is equal to 5.5 inches and 7 2/4 inches is equal to 7.25 inches.

Now, we can calculate how many pencils are measuring more than 5.5 inches but less than 7.25 inches. To do this, we will subtract the smaller number (5.5) from the larger number (7.25).

7.25 - 5.5 = 1.75

This means that there are 1.75 inches between the two measurements. Since each pencil takes up about 0.25 inches, we can divide 1.75 by 0.25 to determine how many pencils would fit in that space.

1.75 / 0.25 = 7

Therefore, there are 7 pencils measuring more than 5 1/2 inches but less than 7 2/4 inches.

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Complete questions as follows-

how many pencils measure more than 5 1/2 inches but less than 7 2/4 inches?

Answer:

E = 2(3x) = 6x

Step-by-step explanation:

To find the number of edges of a prism, we can use the formula E = (2n), where E is the number of edges and n is the number of vertices.

For a prism, we know that it has two identical polygonal faces (the bases), each with x sides. Each of these faces will have x vertices since each vertex is where two sides meet. The other vertices of the prism will be where the lateral faces meet the bases, which is equal to x for each base. Therefore, the total number of vertices in the prism is 2x + x = 3x.

Using the formula E = (2n), we can find the number of edges of the prism:

E = 2(3x) = 6x

Therefore, the expression for the number of edges of the prism is 6x, which is not listed as an option. The closest option is B, 3x, but that represents the number of edges of a triangular prism, not a prism with x sides.

24 cupcakes in 1 hour and 18 cupcakes in 3/4 hour (or 45 minutes) both have same rate of change.

The rate of change refers to the speed at which a variable or quantity changes over a given period of time. It is often expressed in terms of units per time, such as meters per second or dollars per year. The rate of change can be positive or negative, depending on whether the variable is increasing or decreasing.

A constant rate refers to a fixed or unchanging rate of change over time. In other words, it is a steady and consistent rate that does not fluctuate or vary. This term is commonly used in mathematics and finance to describe situations where a value or quantity changes at a constant rate over a given period of time.

Athena made 3 dozen cupcakes in 1 1/2 hours. To find the constant rate of change, we need to determine the number of cupcakes she made per hour.

1 dozen = 12 cupcakes

So, Athena made 3 dozen cupcakes = 3 x 12 = 36 cupcakes.

Constant rate of change = Cupcakes made / Time taken

Option 1: 24 cupcakes in 1 hour

Option 2: 18 cupcakes in 3/4 hour (or 45 minutes)

Both options represent the same constant rate of change as Athena's, which is 36 cupcakes per hour.

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The contractor will not be able to reach them with this ladder alone.

What is Trigonometric ratio?

Trigonometric ratios are mathematical tools used to relate the angles and sides of a right triangle. These ratios are defined as the ratios of the lengths of two sides of a right triangle to a given angle. There are six basic trigonometric ratios, which are sine, cosine, tangent, cosecant, secant, and cotangent.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

To solve this problem, we need to use trigonometry. Let's call the height the ladder reaches up the wall "h".

We know the length of the ladder is 19 feet and the angle it makes with the ground is 65°.

Using trigonometry, we can find the height the ladder reaches up the wall as follows:

sin(65°) = h/19

Multiplying both sides by 19, we get:

h = 19 × sin(65°)

h ≈ 16.37 feet

So the ladder reaches a height of about 16.37 feet up the wall. Since the repairs are 17 feet up the wall, the contractor will not be able to reach them with this ladder alone.

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If a survey is taken at a movie theater in Winterville. The first 225 people who entered the theater were asked about their favorite type of movie. The  true about this situation is: C. The population is the total number of people who go to the movie theater, and the sample is the first 225 people at the theater.

In this situation, the survey was taken of the first 225 people who entered the movie theater. Therefore, the sample is the group of 225 people who were surveyed. The population of interest is the total number of people who go to the movie theater, as these are the individuals who could potentially have a favorite type of movie.

However, it is not practical to survey every person who goes to the movie theater, so a sample of 225 people was taken from the population.

Therefore, option C is the correct answer.

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Answer:

Step-by-step explanation:

Median: C) 13

First Quartile: A) 8.5

Third Quartile: B) 17.5

Explanation:

To find the median, we need to arrange the numbers in ascending order:

{3, 5, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(10 + 11)/2 = 10.5.

To find the first quartile, we need to find the median of the lower half of the data set.

The lower half is {3, 5, 5, 8, 9, 10, 11, 12}.

Since there are an even number of values, we take the average of the middle two numbers:

(8 + 9)/2 = 8.5.

To find the third quartile, we need to find the median of the upper half of the data set.

The upper half is {14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(17 + 18)/2 = 17.5.

Answer: 106°

Step-by-step explanation:

First add the two angles together: 51+23=74

Then subtract it from 180 because the sum of all angles in a triangle is 180°: 180-74=106

Therefore, the answer the 106°

Applying the triangle proportionality theorem, the measure of side FD in the image is calculated as: FD = 13.6.

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Use the triangle proportionality theorem to find AB:

AB/BC = AE/ED

Substitute:

AB/12 = 6/9

AB = (12 * 6) / 9

AB = 8

Find CD using the Pythagorean theorem:

CD = √(AC² - AD²)

Substitute:

CD = √(20² - 15²)

CD = 13.2

Since ΔACD ~ ΔDFC, therefore their sides are proportional:

AC/FD= CD/FC

Substitute:

20/FD= 13.2/9

FD= (20 * 9) / 13.2

FD = 13.6

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The events are Not Mutually Exclusive (Inclusive)

The concept of mutually exclusive events is based on the idea that two events cannot occur at the same time. In other words, the occurrence of one event means that the other event cannot happen.

In the case of the jersey example, the events "picking a purple jersey" and "picking a jersey with a number greater than five" are not mutually exclusive because it is possible to pick a jersey that satisfies both conditions (i.e., a purple jersey with a number greater than five).

On the other hand, if the events were mutually exclusive, it would mean that it is impossible for them to happen at the same time. For example, if we modified the scenario to have only yellow jerseys numbered one to five and purple jerseys numbered six to ten, then the events "picking a purple jersey" and "picking a jersey with a number greater than five" would be mutually exclusive, as no jersey can satisfy both conditions.

Therefore, in the original scenario where the bag contains six yellow jerseys numbered one to six and four purple jerseys numbered one to four, the events are not mutually exclusive (inclusive).

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Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Solving our equation:

A = 1500(1 + (0.04 × 5)) = 1800

A = $1,800.00

The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 4% per year for 5 years is $1,800.00.

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be Spοrts & Sοrts must sell abοut 607,385 vοlleyballs.

The well-knοwn straightfοrward apprοach, actual variables, and any relevant infοrmatiοn frοm the initial and specialist questiοns can all be used tο finish the assignment. Custοmers may be given anοther chance tο try the gοοds in respοnse. If nοt, significant expressiοn in οur understanding οf prοgrams will be lοst.

Here,

We must figure οut hοw many vοlleyballs must be sοld tο cοver the fixed and variable cοsts in οrder tο estimate the break-even pοint.

The quantity οf vοlleyballs needed tο break even is X.

Fixed cοst plus variable cοst equals tοtal cοst.

Selling price x Number οf units sοld equals tοtal revenue.

The tοtal revenue and entire expense are equal at the break-even pοint.

Thus, we can cοnstruct the equatiοn:

Fixed cοst plus variable cοst multiplied by the selling price equals the quantity sοld.

=> $25.12 X = $3,709,246.60 + $19.01 X

=> $25.12 X - $19.01 X = $3,709,246.60

=> $6.11 X = $3,709,246.60

=> X = $3,709,246.60 / $6.11

=>  X ≈ 607,385

In οrder tο break even, Spοrts & Sοrts must sell abοut 607,385 vοlleyballs.

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Answer:

A.

Step-by-step explanation:

I had this question before but instead of finding the equation, it gave me THE equation to solve.

The area οf family game rοοm is 152 square yards.

The tοtal space οccupied by a flat (2-D) surface οr the shape οf an οbject is defined as its area. The area οf a plane figure is the space enclοsed by its bοundary. The number οf unit squares that cοver the surface οf a clοsed fοrm is the figure's area.

Tο find the area let's divide the figure in 3 parts: twο rectangles and οne triangle.

1. Fοr area οf first rectangle:

Length = 12 yards and width = 8 yards

Area οf rectangle = L x B

Area οf rectangle = 12 x 8

Area οf first rectangle = 96 square yards

2. Area οf secοnd rectangle:

Length = 8 yards and width = 4 yards

Area οf secοnd rectangle = L x B

Area οf secοnd rectangle = 8 x 4

Area οf secοnd rectangle = 32 square yards

3. Area οf triangle:

Base = 6 yards and height = 8 yards

Area οf triangle = 1/2 x base x height

Area οf triangle = 1/2 x 6 x 8

Area οf triangle = 24 square yards

Area οf the family game rοοm = Area οf first rectangle + Area οf secοnd rectangle + Area οf triangle

Area οf the family game rοοm = 96 + 32 + 24

Area οf the family game rοοm = 152 square yards

Therefοre, the area οf family game rοοm is 152 square yards.

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A. He earned GH¢12035.77 in interest over 7 years.

B. He received a total of GH¢26135.77 at the end of 7 years.

Compound interest is a type of interest where the interest earned is added to the principal amount and then the interest is calculated on the new total. In other words, it is interest earned on both the initial principal and the interest accumulated on that principal over time.

A man deposited GH¢14100.00 at 8% per annum compound interest. If at the end of 4

years he transfers the total amount to another bank offering 12% compound interest per

annum.

a. How much interest did he get at the end of 7 years?

b. Calculate the total amount he received at the end of seven years.

To solve this problem, we can use the compound interest formula:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = final amount

P = principal amount (initial deposit)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

Using this formula, we can solve the problem as follows:

a. First, we need to find the amount of money he will have after 4 years of compound interest at 8% per annum:

P = GH¢14100.00

r = 8% = 0.08

n = 1 (compounded annually)

t = 4 years

A =  P[tex](1 + r/n)^{(nt)}[/tex]

A = GH¢14100.00(1 + 0.08/1)^(1*4)

A = GH¢18285.12

So after 4 years, he will have GH¢18285.12. Now we need to find out how much interest he will earn over the next 3 years, when he transfers the money to another bank offering 12% compound interest per annum:

P = GH¢18285.12

r = 12% = 0.12

n = 1 (compounded annually)

t = 3 years

A =  P[tex](1 + r/n)^{(nt)}[/tex]

A = GH¢18285.12(1 + 0.12/1)^(1*3)

A = GH¢26135.77

So after 7 years, he will have GH¢26135.77. To find out how much interest he earned, we can subtract the initial deposit:

Interest = A - P

Interest = GH¢26135.77 - GH¢14100.00

Interest = GH¢12035.77

Therefore, he earned GH¢12035.77 in interest over 7 years.

b. Calculate the total amount he received at the end of seven years.

To calculate the total amount he received at the end of 7 years, we simply add the initial deposit to the interest earned:

Total amount = P + Interest

Total amount = GH¢14100.00 + GH¢12035.77

Total amount = GH¢26135.77

Therefore, he received a total of GH¢26135.77 at the end of 7 years.

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The volume of water that flowed through the pipe in 3 minutes is 29100 cm³

First, we need to find the area of the shaded area. This given by:

Area of shaded area = Area of sector - area of triangle AOC

Area of shaded area = (72/360 * π * 4.8²) - (1/2 * 4.8 * 4.8 * sin 72)

Area of shaded area = (72/360 * 22/7 * 4.8²) - (1/2 * 4.8 * 4.8 * sin 72)

Area of shaded area = 11.56 cm²

Volume of water  = area * rate * time

Volume of water in 3 minutes = 11.56  * 14 * 180    (3 minutes = 180 sec.)

Volume of water in 3 minutes = 29131.2 cm³

Volume of water in 3 minutes = 29100 cm³ (to 3 significant figures)

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The probability that the flight will be no more than 5 minutes late is 0.02 (to 2 decimals).

The probability that the flight will be more than 10 minutes late is 1 - 0.0083 = 0.9917 (to 2 decimals).

The expected flight time is 126 minutes.

The probability density function for flight time in minutes would be a horizontal line that starts at 0 and ends at a height of 5/12 (since the flight time is uniformly distributed between 2 hours and 2 hours, 12 minutes, which is a range of 12 minutes, and the total area under the curve must equal 1).

To find the probability that the flight will be no more than 5 minutes late, we need to find the area under the probability density function from 0 to 5 minutes late. This area is equal to:

(5/12) * (5/60) = 0.0208

So the probability that the flight will be no more than 5 minutes late is 0.02 (to 2 decimals).

To find the probability that the flight will be more than 10 minutes late, we need to find the area under the probability density function from 10 to 12 minutes late, and then subtract that from 1 (since we want the probability that the flight is more than 10 minutes late). This area is equal to:

(5/12) * (2/60) = 0.0083

So the probability that the flight will be more than 10 minutes late is 1 - 0.0083 = 0.9917 (to 2 decimals).

To find the expected flight time, we need to find the mean of the uniform distribution, which is equal to the average of the minimum and maximum values:

(mean) = (2 hours + 2 hours, 12 minutes) / 2 = 2 hours, 6 minutes = 126 minutes

Therefore, the expected flight time is 126 minutes.

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Answer: B

Step-by-step explanation: I took the test.

According to the information, the combined total profit TechWiz made from selling both MP3 and DVD players would be: 35x + 18(128 - x)

Let x be the number of MP3 players sold. Then the number of DVD players sold would be 128 - x (since the total number of players sold is 128).

The profit made from selling x MP3 players would be $35 times x, which is 35x.

Similarly, the profit made from selling (128 - x) DVD players would be $18 times (128 - x), which is 18(128 - x).

Therefore, the combined total profit TechWiz made from selling both MP3 and DVD players would be:

35x + 18(128 - x)

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We may infer after addressing the stated question that As a result, the vertices of triangle A'B'C' are as follows: A'(-2, -4) (-2, -4); B'(-7, -6) (-7, -6); C'(-1, -13) (-1, -13)

A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.

To reflect a point (x,y) over the line y=-x, we first swap its x and y coordinates, then negate both:

The inverse of point (x,y) is (-y, -x).

Hence, by reflecting each of A, B, and C over the line y=-x, we can obtain the vertices of triangle A'B'C':

Vertex A' is the mirrored image of A. (-2, -4)

Vertex B' is a mirror of Vertex B. (-7, -6)

Vertex C' is the mirrored image of C. (-1, -13)

As a result, the vertices of triangle A'B'C' are as follows:

A'(-2, -4) (-2, -4)

B'(-7, -6) (-7, -6)

C'(-1, -13) (-1, -13)

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Answer:

The mean of the sample distribution of sample means will be equal to the population mean, which is 317 grams. The standard deviation of the sample distribution (also called the standard error) will be equal to the population standard deviation divided by the square root of the sample size:

standard error = 29 / sqrt(25) = 5.8

To find the weight at which the mean weight of 25 fruits will be greater than 5% of the time, we need to find the z-score that corresponds to the 95th percentile (since 5% of the time we want the mean weight to be greater than some value). Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 95th percentile is approximately 1.645.

Now we can use the formula for z-scores to find the weight at which the mean weight of 25 fruits will be greater than 5% of the time:

z = (x - mu) / se

where x is the weight we want to find, mu is the population mean (317 grams), and se is the standard error (5.8 grams).

Substituting the values we have:

1.645 = (x - 317) / 5.8

Solving for x, we get:

x = 317 + 1.645 * 5.8 = 326.5

Rounding to the nearest gram, we get that the mean weight of 25 fruits will be greater than 326 grams 5% of the time.

The inequality that represents c, the number of candles she needs to sell to pay for a visit to Knotts costing $100 when each candle is sold for $5, is expressed as: c ≥ 20.

The inequality c * 5 ≥ 100 is derived from the fact that each candle is sold for $5, so the total amount of money she earns from selling c candles is given by 5c. This amount must be greater than or equal to the cost of the visit, which is $100.

By multiplying both sides of the inequality by 1/5, we get c ≥ 20, which means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Therefore, the answer is: c ≥ 20.

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Answer:

Already rounded?

Step-by-step explanation:

I mean 15.700 is a decimal. So thousandths place would be what you put. Sorry but you already have the answer.

If the manager of a home economics stores considering the pricing a new model of digital cameras. The maximum revenue is $78,000.

To find the price that will maximize monthly value, we need to determine the price that will give us the highest revenue. Revenue is given by the formula:

Revenue = Price x Quantity

Let's let x be the number of times the price is decreased by $20 from $900. Then the price of the camera would be:

Price = 900 - 20x

And the quantity sold would be:

Quantity = 70 + 5x

So the revenue would be:

Revenue = (900 - 20x)(70 + 5x)

Expanding this expression gives:

Revenue = 63000 + 1300x - 100x^2

To maximize this quadratic function, we need to find the x-value that corresponds to the vertex of the parabola. The x-value of the vertex is given by:

x = -b/2a

where a = -100, b = 1300, and c = 63000. Substituting these values gives:

x = -1300/(2(-100)) = 6.5

Since we can't decrease the price by a fractional amount, we'll round this down to 6, which means we'll decrease the price by $120. So the price of the camera that maximizes monthly revenue is:

Price = 900 - 20(6) = $780

And the quantity sold at this price is:

Quantity = 70 + 5(6) = 100

So the maximum revenue is:

Revenue = 780(100) = $78,000.

Therefore the revenue is $78,000.

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Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

If Lorna uses 7.2 cups of flour in 3 different baking recipes, and uses an equal amount of flour in each recipe, we can find the amount of flour she uses in each recipe by dividing the total amount of flour by the number of recipes:

Flour per recipe = Total flour / Number of recipes

Flour per recipe = 7.2 cups / 3 recipes

Flour per recipe = 2.4 cups per recipe

Therefore, Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

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Answer:

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.Converting to a mixed number, they had 16 2/3 marbles altogether.

The distance across the lot, or the altitude of the trapezoid, is 60 feet.

Let's denote the length of the shorter base by x, and the length of the longer base by y. Then, we can use the formula for the area of a trapezoid:

Area = (x + y) * h / 2,

where h is the altitude (distance across the lot) and Area is given as 8,400 square feet.

We also know that the sum of the bases is 280 feet, so x + y = 280.

Now we can solve for h:

h = 2 x  Area / (x + y)

Substituting the given values, we get:

h = 2 x  8,400 / 280 = 60 feet.

Therefore, the distance across the lot, or the altitude of the trapezoid, is 60 feet.

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Answer:

D. 10 (6y-9-2x)

Step-by-step explanation:

10×6y 10× -9 10×-2x

60y -90 -20x

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).