3
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30

The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.

What is a rectangle?

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

The number of lines along the length is 11.

The length of the frame is 10 units.

The number of lines along the width is 8.

The width of the frame is 7 units

The dimension of an object is length × width.

The dimension of the frame is 10 units × 7 units.

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If an equilateral triangle has an altitude of 15 meters, then the perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex] meters

The altitude of the equilateral triangle = 15 meters

The equilateral triangle is the triangle with equal side. The interior angle of the equilateral triangle will be 60 degrees. Number of vertices and edges will be three . The line of symmetry is 3

The altitude of of the equilateral triangle h = [tex]\sqrt{3}[/tex]a /2

Where h is the altitude of the equilateral triangle

a is the side of the equilateral triangle

Then the equation will become

15 =  [tex]\sqrt{3}[/tex] a /2

[tex]\sqrt{3}[/tex]a = 15 × 2

Multiply the terms

[tex]\sqrt{3}[/tex]a = 30

Move  [tex]\sqrt{3}[/tex] to the right hand side of the equation

a = 30 /  [tex]\sqrt{3}[/tex]

a = 10[tex]\sqrt{3}[/tex] meters

The perimeter of the equilateral triangle = 3 × 10[tex]\sqrt{3}[/tex]

= 30[tex]\sqrt{3}[/tex] meters

Therefore, perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex]

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Answer: 8x^2 + xy - 15y^2

Step-by-step explanation:

first do the FOIL method than add 3xy to the equation after

Answer:

[tex]8x^2+xy-15y^2[/tex]

Step-by-step explanation:

[tex](4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2[/tex]

Answer:

4 : 2 = 10 : 5.

Step-by-step explanation:

Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)

Using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

The power to which a number must be increased in order to obtain another number is known as a logarithm.

For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

So, solve using a log as follows: (1/243) ^-x/3 = 4

[tex]\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}[/tex]

Therefore, using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

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Answer:

Step-by-step explanation:

(227-127)/4=x

"/" means divide.

13/16 as a decimal rounded to the nearest tenth is 0.8.

A decimal is a way to represent the same thing but in a different form. In this case, we will convert the fraction 13/16 into a decimal and round it to the nearest tenth.

To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, 13 divided by 16 is equal to 0.8125. This means that 13/16 as a decimal is 0.8125.

To round a decimal to the nearest tenth, we look at the digit in the hundredths place (the second digit after the decimal point).

If this digit is 5 or greater, we round up the tenths place (the first digit after the decimal point). If it is less than 5, we leave the tenths place as is. In this case, the digit in the hundredths place is 2, which is less than 5.

Therefore, we leave the tenths place as is, and the final answer is 0.8.

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Answer:a=3, d=common difference=3, a2=7, a3=9

Step-by-step explanation:

firstly we have given a,d  (using the arithmetic progression formula)

                                          (  an=a+(n-1) )

so we have made a sequence a2=a+d=7  

                                                   a3=a+2d=9

Answer:

C = $24 + 0.45x

Step-by-step explanation:

If we let total amount spent by a guest to the park as $C and number of tickets bought is x then the algebraic expression to represent the total amount spent by a guest is

C = $24 + 0.45x

The ordinary numbers for the expressions will be

a. 3.25*10⁴ = 32500

b. 6.04*10⁻³= 0.00604

c. 2400000 = 2.4*10⁶

d. 0.00147 = 1.47*10⁻³

What are expressions exactly?

In mathematics, expressions are mathematical assertions made up of at least two sentences that contain numbers, variables, or both and are linked by an operator. Mathematical operations include addition, subtraction, multiplication, and division. For example, x + y is an equation that uses an addition operator to separate the components x and y. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is six times the size of another number, x. This sentence is mathematically stated as x/2 + 6. Mathematical expressions are used to address complex problems.

Now,

Given expressions/Numbers are a. 3.25*10⁴  then ordinary form is

3.25*10000

=32500

b. 6.04*10⁻³ then ordinary numbers is

=6.04/1000

=0.00604

c. 2400000 then standard from is

=2.4*1000000

=2.4*10⁶

d. 0.00147  then standard form is

=1.47/1000

=1.47*10⁻3

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A residual plot that shows clear patterns or trends in the residuals suggests that the line of best fit is not a good model.

Here are some characteristics of a residual plot that suggest that the line of best fit is a poor model,

The residuals show a clear pattern or trend, such as a curve or a U-shape.

The residuals are not evenly distributed above and below zero.

There are one or more outliers or extreme values that stand out from the rest of the data.

The variability of the residuals changes across the range of the predictor variable.

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The exponential function that goes through points (0,12) and (2,300) is [tex]y = 12(5)^x[/tex].

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The coordinate points are (0,12) and (2,300).

The exponential function has form [tex]y=ab^x[/tex].

So, the x values are 0,2 and y values are 12,300.

Substitute the first x and y values in the equation -

[tex]12=ab^0[/tex]

a = 12 ...... equation (1)

Substitute the second x and y values in the equation -

300 = ab² ...... equation (2)

Substitute the value of equation (1) in equation (2) -

300 = (12)b²

b² = 300 / 12

b² = 25

b = √25

b = 5

Substitute the values of a and b in exponential function -

[tex]y = 12(5)^x[/tex]

Therefore, the exponential function is [tex]y = 12(5)^x[/tex].

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The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:

π * 0.5^2 * 25 = 19.63 cubic feet

So the cost of the utility pole would be 19.63 * $25.81 = $509.24

Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.

The probability that at most four of the M&M are yellow is  0.3357 and the probability that at least two of the four of the M & M are yellow is   0.6622

The probability that at most two of the four M&M's are yellow can be calculated using the cumulative distribution function (CDF) of the binomial distribution. The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. In this case, the number of trials is 4, and the probability of success (getting a yellow M&M) is 0.13.

The cumulative distribution function of the binomial distribution can be expressed as:

P(X <= k) = SUM[i=0 to k] (n choose i) * p^i * (1-p)^(n-i)

Where n is the number of trials, k is the value we want to find the probability for, p is the probability of success, and (n choose i) is the number of combinations of n items taken i at a time, which can be calculated as n! / (i! * (n-i)!).

For this problem, we want to find the sum of probabilities for X = 0, 1, and 2, so we have:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (4 C 0) * (0.13)^0 * (0.87)^4 + (4 C 1) * (0.13)^1 * (0.87)^3 + (4 C 2) * (0.13)^2 * (0.87)^2

= 0.3357

NB: "C" represent combination.

So the probability that at most two of the four M&M's are yellow is approximately 0.3357.

b. The probability that at least two of the four M&M's are yellow can be found by subtracting the probability of getting 0 or 1 yellow M&M's from 1. So:

P(X >= 2) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((4 C 0) * (0.13)^0 * (0.87)^4 + (4 C1) * (0.13)^1 * (0.87)^3)

= 0.6622

So the probability that at least two of the four M&M's are yellow is approximately 0.6622.

The mean of the distribution is given by n * p = 4 * 0.13 = 0.52, and the standard deviation is given by sqrt(n * p * (1-p)) = sqrt(4 * 0.13 * 0.87) = 0.9304.

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Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations

When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.

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The size of angle BCA is 45 degrees

A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.

Where the two uneven sides meet, the two angles are equal. It can be thought of as two congruent triangles sharing a base. It has two diagonals that right-angle intersect with one another.

Given:

From the Figure we can see that

AB = BC and AD = DC = AC

and, ABC = 90 degrees

Now, In triangle ABC using Angle sum Property

A + B + C = 180

So,  A + 90 + C = 180

A + C = 90

As, AB = BC

Then, 2C = 90

C = 45

Hence, the angle is 45 degrees

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The Question attached here seems to be incomplete/ inappropriate. The complete Question is:

ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle  BCA

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 7: 5 (oranges to apples) we can use this equation to solve the problem:

We multiply by 0.714285714 because we can see that 7 is being multiplied by 0.714285714 to get 5.

Therefore, if the ratio stays proportional, you will need 120 litres of apple juice for every 168 litres of orange juice.

The distance is decreasing with time meaning that the object is going back to the starting point.

When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.

Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.

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If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.

Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:

Area = length x width = 75 meters x 50 meters = 3750 square meters

Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:

Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter

Multiplying the area by the cost per square meter gives us:

Total cost = AED 45,000

Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

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Answer: 2x + 12

Step-by-step explanation:

Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex]  is 5.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex].

Part C: The factoring from Part B is correct, as multiplying the two binomials in the parentheses yields [tex]2x2 + 5x − 3[/tex].

Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex] is 5. The greatest common factor (GCF) of a set of numbers is the largest number that is a factor of all numbers in the set. To find the GCF, first list all the factors of each number. The common factors among the numbers are the ones that are found in each list of factors. The largest number in the list of common factors is the GCF.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex]. To factor this expression, first identify the GCF, which is 5. Then divide the expression by 5 and factor the result. Since the result is a binomial, use the difference of squares formula, (x + a)(x − a). The resulting expression is then[tex]5(2x2 + 5x − 3[/tex]).

Part C: To check the factoring from Part B, multiply the two binomials in the parentheses. The result is [tex]2x2 + 5x − 3[/tex], which is the same as the original expression. To multiply, use the FOIL method. Multiply the First terms [tex](2x2 and 2x2)[/tex], the Outer terms[tex](2x2 and -3)[/tex], the Inner terms (5x and 2x), and the Last terms [tex](5x and -3)[/tex]. The resulting expression is [tex]2x2 + 5x − 3.[/tex]

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Let's call the original number of students in the group "n". Each student contributed $2.50, so the total amount the original group of students collected is $2.50 * n.

When 5 more students join the group, the new total number of students is n + 5, and each student contributes $2.50 - $0.50 = $2.00. So the total amount the new group collects is $2.00 * (n + 5) = $2.00n + $10.

Since the total amount collected remains the same, we can set the two expressions for the total amount equal to each other:

$2.50n = $2.00n + $10

Solving for n, we have:

$0.50n = $10

n = 20

So, there were originally 20 students in the group. To find out how much they plan to spend on the gift, we can multiply the original number of students by the original contribution amount:

$2.50 * 20 = $50.00

Therefore, the students plan to spend $50.00 on the gift.

100% of the number is: the number x ÷ 0.8 × 1 = the number If 80% of a number is x, then the number can be found by dividing x by the percentage as a decimal.

To convert a percentage to a decimal, divide the percentage by 100.

So, if 80% of the number is x, then:

x ÷ 0.8 = the number

In other words, to find the whole number, we need to divide the part (x) by the percentage as a decimal (0.8).

Once we have the whole number, we can find 100% of it by simply multiplying the whole number by 1.

So, 100% of the number is:

the number x ÷ 0.8 × 1 = the number

In conclusion, if 80% of a number is known, the whole number can be found by dividing the part by the percentage as a decimal, and 100% of the number can be found by simply multiplying the whole number by 1. Understanding the concept of percentage and the ability to convert between percentages, decimals, and whole numbers is an important skill in various areas of life and work.

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The expression for the amount of money Eric has after he pays his brother back is x- 17.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given:

Eric owes his brother $17.

let x be the amount of money Eric got for his birthday.

If Eric gave the money back to his brother then he left with

= x - 17

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The price of gasoline and oil will be equal in price after 4 years when the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months.

To find out when the price of gasoline and oil will be equal, we have to set the two prices equal to each other and solve for time. The price of gasoline decreases at the rate of $0.03 every two months and the price of oil increases at a rate of $0.05 every six months.

We can start with the initial prices and solve for the time when they are equal:

$2.27 - 0.03t = 0.45 + 0.05t

where t represents the time in years.

Solving for t, we get:

$2.27 - 0.03t = 0.45 + 0.05t

$1.82 = 0.08t

t = 22.5

Since t is in months, we have to divide by 12 to convert it to years:

t = 22.5 / 12 = 1.875

So the price of gasoline and oil will be equal in price after approximately 4 years.

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Answer:

S∞ = 96

Step-by-step explanation: