From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]

The age of your uncle is modeled by:

y = 2 + 3*x

Evaluating it, we can see that when you are 12 years old, your uncle will be 38 years old.

Let's define the variables: y as your uncle's age and x as your age.

Here we know that your uncle is 2 years older than 3 times your age, so we can write the linear equation:

y = 2 + 3*x

This is the equation we needed to find.

b) If you are 12 years old, then we can write x = 12 in the equation above, then we will get:

y = 2 + 3*12

y = 2 + 36

y = 38

That's the age of your uncle.

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The minimum value of the given quadratic equation is 31/8. Solved using graph method to find a minimum value that is c - b^2/4a.

By graphing the equation and locating the minimum point on the graph, you may visually determine the minimum value. The graph's vertex will have the lowest y-value. When you have a graphing calculator that can perform the majority of the work for you, this is very simple.

A graph makes it simple to determine the minimum value of a quadratic equation. One can use the graph to identify the minimum point of the quadratic equation and to find the minimum value in a visual way. If the quadratic equation is written as [tex]y= ax^2 + b*x + c[/tex]one can follow the equation that says the minimum value is min = c- (b^2/4a) to obtain the minimum value of the quadratic equation.

Given Quadratic equation is y = 2x^2 + 3x + 5

a = 2 , b =3 ,c = 5.

Minimum value  = c - (b^2/4a)

= 5 - 9/8

=31/8.

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Answer:29,697

Step-by-step explanation: multiply 57x521 and you get 29,697

Answer:

x = 6

Step-by-step explanation:

x:(x + 3) = 2:3

[tex] \frac{ \\ x}{x + 3} = \frac{2}{3} [/tex]

cross multiply

3x = 2(x + 3)

3x = 2x + 6

subtract (2x) from both sides

3x – 2x = 2x – 2x + 6

x = +6

x = 6

Therefore ,As a result, the answer to the provided equation is that a burrito costs $2.50 and a soft taco costs $1.50.

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.

Here,

Let the price of a soft taco be set at s.

Let b be the price for one burrito.

Therefore, we have this system.

3s + 3b = 11.25

4s + 2b = 10.00 (1) (1)

By multiplying the first equation by 3, we get that.

If s + b = 3.75, take b off of both sides.

s = 3.75 - b (2) (2)

Subtract (2) from (1) and you get

Simplify 4 (3.75 - b) + 2 b = 10.00.

15 - 4b + 2b = 10.00

Subtract 15 from both sides (-2b + 15 = 10) to get the total.

Divide both sides by -2 to get -2b = - 5.00.

b = 2.50

as well as (2)

s = 3.75 - 2.50 = 1.50

As a result, the answer to the provided equation is that a burrito costs $2.50 and a soft taco costs $1.50.

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The degree of the polynomial [tex]5x^{3} + 4x^{2} + 7x[/tex]  is 3 , that means it is a third degree polynomial called as cubic polynomial  .

What is Degree Of Polynomial ?

The degree of the polynomial is defined as  the highest power of the polynomial expression. But, if the polynomial has multiple variables, the degree of polynomial can be found by adding the powers of the different variables  in the polynomial expression.

For Example : the degree of polynomial ⇒  [tex]9x^{2} + 7x + 2[/tex] is  2 .

The polynomial is given as : [tex]5x^{3} + 4x^{2} + 7x[/tex] , we have to find the degree ,

So , we can see that the the term having the highest power of the given polynomial is [tex]5x^{3}[/tex] , and the degree is 3 .

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Answer:The Surface Area of Pyramid is 105 cm².

Step-by-step explanation:

What is Surface Area of Pyramid?

If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by (½)Pl + B Square units.

Given:

slant height, l= 8 cm

So, the base Perimeter = 4 x 5

                                     = 20 cm

Now, area of the base = 5 cm x 5 cm

                                    = 25 cm²

Then,  surface area of a square pyramid

= 1/2 x slant height x base perimeter + area of base

= 1/2 x 8 x 20 + 25

= 80 + 25

= 105 cm²

The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).

What is interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .

Given exponential function is f(x) = B^x.

A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.

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Answer:

C. ∠1 and ∠3 are vertical angles and congruent.

Answer:

a.  The total cost of fixing the drain is $198

b. The plumber spend 13 hours fixing the drain

Step-by-step explanation:

We know the equation is

C=25h+73

C = the total cost

h = the number of hours

Let's solve question a by putting 5 in for h

C=25(5)+73

C = 125 + 73

C = $198

So, the total cost of fixing the drain is $198

Let's solve question b by butting 398 in for c

398=25h+73

325 = 25h

h = 13 hours

So, the plumber spend 13 hours fixing the drain

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We can conclude from answering the above question that the first two patterns of the matrix  form a sequence in the third from top with the numbers 4-2-6.

A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.

We can conclude from answering the above question that the first two patterns of the matrix  form a sequence in the third from top with the numbers 4-2-6.

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What is the image of ( 12 , − 4 ) after a dilation by a scale factor of 1/4 centered at the origin is (3, -1)

Transformation is the movement of a point in the coordinate plane. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease of a figure by a scale factor k. If the value of k > 1, then it is an enlargement but if k < 1, it is a reduction.

The point (12, -4) is dilated by a scale factor of 1/4 using the rule (x, y) ⇒ (x/4, y/4). The new point is (4, -1)

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Answer:

y=2x+3

Step-by-step explanation:

y=mx+b

y=2x+3

Therefore , the solution of the given problem of algorithm comes out to be solution of the non solvable and solvable problems cannot be solved.

A method for performing calculations or solving problems is known as an algorithm. Algorithms act as a thorough set of instructions that step-by-step direct hardware- or software-based processes through a series of planned activities. In every aspect of IT area, algorithms are utilized regularly.

Here,

Two different kinds of issues arise in TOC: - Problems that can be and can't be computed When something is "computable" (or "solvable"),

it means that it can be solved using an algorithm or a set of steps.

No method exists that can produce an output that is either "true" or "false," hence this problem is non-computable (or unsolvable).

Therefore , the solution of the given problem of algorithm comes out to be solution of the non solvable and solvable problems cannot be solved.

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Answer: #18 is (1/2,0)

#19 (0,-1)

#20 5

#21 8√2 or 11.313708498985

Step-by-step explanation:

If her monthly payment is P3,000 and interest is compounded semi-annually at 9%, the cost of the TV set comes to P17,545.08.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.

In finance and economics, compound interest is common.

In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.

The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.

According to our question-

9% = 0.09 / 2

=0.045 + 1 =1.045^(1/6)

=1.00736312 - 1 x 12 x 100

=8.836%

PV=0;

PMT=3000;

R=0.08836/12; N=6; PV

=PMT*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)

PV==17,545.08

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In order to calculate how many postcards he sold, multiply €0.30 by (45.9 + 42) to get €97.20.

Multiplication, division, addition, and subtraction are all possible in mathematics. Expression, number, and mathematical operator are the components of a mathematical expression (such as addition, subtraction, multiplication, or division, etc.). Expressions and phrases can be contrasted. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For instance, the phrase 4m + 5 consists of the terms 4m and 5, as well as the provided expression's variable m, all of which are separated by the arithmetic sign +.

given

A stationer sells 17 magazines for €2.70 each, for a total of €45.9; 28 newspapers cost €1.50 each,

for a total of €42; and

x postcards, for a total of €0.30x,

for a total of €97.20.

In order to calculate how many postcards he sold, multiply €0.30 by (45.9 + 42) to get €97.20.

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Answer:

R = 144400000/59 [this is a fraction]

The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.

In this question we find a linear function in slope-intercept form:

y = m · x + b

Where:

From which we must obtain the linear function in standard form:

a · x + b · y = c

Where:

We can derive the standard form of the linear equation by algebra properties:

y = m · x + b

(1 / b) · y = (m / b) · x + 1

- (m / b) · x + (1 / b) · y = 1

If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:

- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1

(1 / 12) · x + (1 / 6) · y = 1

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The total number of pizzas consumed by the 10 members of the club is 2.5 and 3.5 pizzas remain, as Mr. Cam bought 6 pizzas and each of the 10 members ate 1/4 of a pizza.

Mr. Cam bought 6 pizzas for the club and each of the 10 members ate 1/4 of the pizza. To find out how many pizzas were eaten, we can use the formula:

Number of members x Pizza per member = Total Pizzas Consumed

In this case, we can substitute the given values in the formula:

10 members x 1/4 pizza/member = 10/4 = 2.5 pizzas

This means 2.5 pizzas were consumed by the members. Since Mr. Cam bought 6 pizzas and 2.5 pizzas were eaten, the total number of pizzas remaining is 6 - 2.5 = 3.5 pizzas.

This equation works because it uses the concept of the unitary method, where we find the total number of pizzas consumed by multiplying the number of members by the number of pizzas each member ate. This way we can find the total amount of pizza consumed.

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Altogether, the recipe uses 1/2 cup of flour and 1/8 cup of sugar.

Altogether in math refers to the sum of two or more numbers or values. It is a way of combining two or more items to obtain a total. In math, the term "altogether" is used to denote the sum of all the individual items, as opposed to all of them considered as one. For example, the sum of the numbers 2, 4, and 6 is 12, which is the "altogether" in math.

To calculate this, we must convert the fractions into decimals and then add them together.

The 1/3 cup of flour can be converted to 0.33 cup, and the 1/8 cup of sugar can be converted to 0.125 cup.

When added together, they equal 0.455 cup, or 1/2 cup. Therefore, the recipe uses a total of 1/2 cup of flour and 1/8 cup of sugar.

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Answer:1) 43 2)53 3)22 4)23

Step-by-step explanation:

The value of Isabel's account after three years can be calculated using the future value of the annuity formula.

Isabelle's budget car is:

Reason:

Monthly savings, PMT = $200

Account compound interest, r = 1.7%

t = Account value after 3 years is displayed as increase.

We know that:

[tex]FV =PMT * \frac{[(1+i)^n -1]}{i}[/tex]      --------------------- (1)

Where;

    i = r/12

⇒ n = 12 × t

From the above equation(1), we get:

[tex]FV =200 * \frac{[(1+\frac{1.7}{2} )^{12*3} -1]}{\frac{1.7}{12} }[/tex]

    ≈ 7381.4

Therefore,

The budget cars she can buy, those that require a down payment of less than $7,381.4, which  are:

The required down payment of choice 02 is $6200.

The required down payment of choice 03 is $5100.

The required down payment of choice 04 is $7250.

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C). The highest amount their liability coverage will provide is  $400,000

This is because most standard liability policies will provide up to $300,000 for bodily injury and $100,000 for property damage, but the policyholder may be able to purchase additional coverage for higher limits if they need it. The exact amount of coverage will depend on the policy the policyholder purchased.

Liability insurance is a component of the general insurance system of risk financing that protects the purchaser from the risks of liabilities imposed by lawsuits and similar claims, as well as the insured if the purchaser is sued for claims covered by the insurance policy.

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The range and the IQR of the weights are 3.3 pounds and 0.95 pounds respectivly.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.

The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

a) the range is the difference between the highest and lowest value:

range =7.5-4.15 =3.3 pounds

the IQR is the difference between the third and first quartile

IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds

b) Skewed because the mean and median are not the same value.

c) All values will be multiplied by 16

Mean: 96 ounce

Standard deviation: 10.4 ounce

Quartiles: 89.6 ounce and 104.8 ounce

Median:99.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

d) The mean,quartiles and median increase by 30,the result remain unchanged:

Mean: 126 ounce

Standard deviation: 10.4 ounce

Quartiles: 119.6 ounce and 134.8 ounce

Median:129.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

e)  The median, quartiles and IQR might not changed,because they are unaffected by an outlier.

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Answer:

Y-intercept: 15

Slope: 1.3

Equation: y = 1.3x + 15

Step-by-step explanation:

Base on the table:

# of haircuts = x

Cost ($) = y

Knowing that;

y-intercept = The starting point (y)

Thus, based on the table the y-intercept is 15.

Y-intercept: 15.

To find the slope.

We first have to pick two points on the line & determine their coordinates.

Then subtract y-coordinates of these two points and also subtract x-coordinates for these two points.

After that divide the y by the x.

Shown below:

I'm going to use;

(0,15) and (1,20.5)

0 = x₁

15 = x₂

1 = y₁

20.5 = y₂

Now we do;

20.5 - 1 = 19.5

15 - 0 = 15

19.5 / 15 = 1.3

Hence, Slope = 1.3

Slope: 1.3

The equation - y = mx + b

Knowing that;

b = y-intercept

m = Slope

Substitute it in we have;

y = 1.3x + 15

Equation: y = 1.3x + 15

RevyBreeze

Rafael claims it's easiest to score points when a scatterplot has a linear association. Sahana says it's easiest when a scatterplot has a strong association. Both Rafael and Sahana are correct, in their own way.

A scatterplot with a linear association means that there is a straight line relationship between the two variables being plotted. In such a scatterplot, it is relatively easy to make predictions based on the line of best fit, as well as to calculate the correlation coefficient(r), which can indicate the strength and direction of the linear relationship.

On the other hand, a scatterplot with a strong association means that the points in the plot are closely grouped together, indicating a high degree of correlation between the variables. It is relatively easy to make predictions based on the overall pattern of the points in the scatterplot, even if there is no clear linear relationship.

So, Rafael is correct that scoring points is easiest when a scatterplot has a linear association because it is relatively easy to make predictions based on the line of best fit and correlation coefficient. And Sahana is correct that scoring points is easiest when a scatterplot has a strong association because it is relatively easy to make predictions based on the overall pattern of the points in the scatterplot.

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The solution of the expression 3x² - 4 = 0 is x = ±2/√3.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation

Here we have the expression 3x² - 4 = 0.

Now, we have to solve this one by using the following steps:

First we have to add 4 to both sides of the equation, then we get the expression as,

=> 3x² = 4

Now, we have to Divide each term by 3 and simplify, then we get

=> x² = 4/3

Then we have to take the specified root of both sides of the equation to eliminate the exponent on the left side,

=> x = √4/3

When we simplify this one further, then we get

=> x = ±2/√3.

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The difference between the two polynomials (9x²+8x) - (2x²+3x) is:

7x² + 5x.

Polynomial:

A polynomial is a type of algebraic expression where the exponents of all variables must be integers. The exponent of each polynomial variable must be a non-negative integer. A polynomial consists of a constant and a variable, but you cannot divide a polynomial by a variable.

Example: Express the polynomial 5 + 2x + x2 in standard form.

To express the above polynomial in standard form, first check the degree of the polynomial.

The degree of the given polynomial is two. Write an expression involving the degree of the polynomial.

There is a term with variable exponent less than 2, i.e.1, then write it down.

Finally, we write a term with the variable exponent 0 as the constant term.

According to the Question:

Given polynomials is:

(9x²+8x) - (2x²+3x)

First, multiply the negative sign in the second polynomial

i.e., (9x²+8x) - (2x²+3x)

= 9x²+8x - 2x²-3x

Now, evaluate those terms who have same variables

=  9x²  - 2x² +8x-3x

= 7x² + 5x

Hence, the difference between polynomials are: 7x² + 5x.

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