Please find the missing side length using trig!

The length of the third side of the triangle will be 2 feet. Then the correct option is F.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Any two parts of a triangle can be added together to have a length larger than the third side.

A triangle has two side lengths of 3 feet. Let 'x' be the third side.

By the theorem, the inequality is given as,

x < 3

The length of the third side of the triangle will be 2 feet. Then the correct option is F.

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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)

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 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 m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:

m ∈ (-∞, -4) ∪ (4, ∞).

The quadratic formula tells us that the quadratic equation's roots

[tex]x^2 + mx + 4 = 0[/tex]

are provided by:

[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]

The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:

Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.

Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.

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The probability for the sample space of a fair die rolled out {1, 2, 3, 4, 5, 6} with different conditions are :

a. Probability of getting 6 = 1/6

b. Probability of an even number on a die = 1/2

c. Probability of number more than 2 = 2/3.

Sample space is equal to {1, 2, 3, 4, 5, 6}

Number of times die rolled out = only once.

Total number of outcomes = 6

Probability = ( Number of favourable outcomes ) / ( Total outcomes )

Required probability in fraction form with lowest terms:

a. Probability of getting 6

Favourable outcomes ={ 6 }

Number of favourable outcomes = 1

Probability of getting 6  = 1 / 6

b. Probability of getting an even number

Favourable outcomes = { 2, 4, 6 }

Number of favourable outcomes = 3

Probability = 3 / 6

                  = 1 / 2

c. Probability of getting number greater than 2

Favourable outcomes = { 3, 4, 5, 6 }

Number of favourable outcomes = 4

Probability = 4 / 6

                  = 2 / 3

Therefore, the required probability as per the mentioned conditions are:

a. Probability of getting 6 = 1/6

b. Probability of even number = 1/2

c. Probability of number greater than 2 = 2/3.

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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 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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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

Answer:

Step-by-step explanation:

3400/170 = 20 minutes.

Answer:

20 minutes

Step-by-step explanation:

3400 words / 170 wpm

20 minutes

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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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]

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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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: In a right-angled triangle, we can use the Pythagorean Theorem to find the length of the remaining side. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the length of side BC can be found using the Pythagorean Theorem:

BC^2 = AB^2 + AC^2

BC^2 = 10.5^2 + 5.2^2

BC^2 = 110.25 + 27.04

BC^2 = 137.29

BC = √137.29

BC ≈ 11.68 m

Now that we have the length of side BC, we can use the inverse cosine function (cos^-1) to find the angle ∠CBA:

∠CBA = cos^-1 (BC / AB)

∠CBA = cos^-1 (11.68 / 10.5)

∠CBA ≈ 68.194°

Rounding to 3 significant figures, the answer is ∠CBA = 68.2°.

Step-by-step explanation:

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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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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The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.

Let us consider the present age of Earl to be x years.

According to the given question, the present age of Robin is twice that of Earl = 2x

And since it is given that Adam is 8 years younger than Earl, then his age

= x - 8

After 6 years, the age of Earl will be x + 6

Robin's age  will be = 2x + 6

Adam's age will be = x - 8 + 6 = x - 2

According to the given question, Robin's age will be thrice the age of Adam.

Hence, 2x + 6 = 3 (x - 2)

⇒ 2x + 6 = 3x - 6     ⇒ 6 + 6 = 3x - 2x     ⇒ 12 = x

Thus, the present age of Earl is 12 years,

Robin's age = 2x = 2 x 12 = 24 years

Adam's age = x - 8 = 12 - 8 = 4 years

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a) The function would be A(t) = 6000(1 + 0.09)ᵗ

b) The amount in the account in 2012 was approximately $11,737.51.

What is the function model?

In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.

a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:

A(t) = 6000(1 + 0.09)ᵗ

where A(t) is the amount in the account after t years.

b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:

A(8) = 6000(1 + 0.09)⁸

= 6000(1.09)⁸

≈ $11,737.51

Therefore, the amount in the account in 2012 was approximately $11,737.51.

Hence,

a) The function would be A(t) = 6000(1 + 0.09)ᵗ

b) The amount in the account in 2012 was approximately $11,737.51.

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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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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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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.

Answer: (2, -1)

Step-by-step explanation:

Answer:

S∞ = 96

Step-by-step explanation:

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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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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On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8

In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.

When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.

the line is y = -2/3x+1

so the slope, m = -2/3

since it parallel , new slope = 3/2

the slope intercept of line is

y +1 = 3/2(x+6)

y + 1= (3/2)x + 9

y = (3/2)x + 9 - 1

y = (3/2)x + 8

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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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