5 Make a Plan How will you solve? Explain.
3. An athlete ran a total of 1,500 kilometers in races before retiring. The athlete finished thirty-two 15-kilometer races. The rest were 10-kilometer races. How many of the races were 10-kilometer races?

Answer:

√65

Step-by-step explanation:

Compute the Euclidean distance between the following points:

p_1 = (-2, 3) and p_2 = (5, -1)

The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:

sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)

Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):

= sqrt((-2 - 5)^2 + (--1 + 3)^2)

(-1)^2 = 1:

= sqrt((-2 - 5)^2 + (1 + 3)^2)

-2 - 5 = -(2 + 5):

= sqrt((-(2 + 5))^2 + (3 + 1)^2)

2 + 5 = 7:

= sqrt((-7)^2 + (3 + 1)^2)

Multiply each exponent in -7 by 2:

= sqrt((-1)^2×7^2 + (3 + 1)^2)

7^2 = 49:

= sqrt((-1)^2×49 + (3 + 1)^2)

(-1)^2 = 1:

= sqrt(49 + (3 + 1)^2)

3 + 1 = 4:

= sqrt(49 + 4^2)

4^2 = 16:

= sqrt(49 + 16)

| 1 |

| 4 | 9

+ | 1 | 6

| 6 | 5:

Answer: √65

The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]

Explain Pythagoras theorem.

The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.

The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.

Using Pythagoras theorem in both the triangles,

Find the hypotenuse in above triangle

[tex]h^2=P^2+B^2[/tex]

[tex]h^2=4+4=8[/tex]

h = [tex]2\sqrt{2}[/tex]

Now, using Pythagoras theorem in below triangle,

[tex]h^2=P^2+B^2[/tex]

[tex]5^2 = x^{2} + 8[/tex]

25 = [tex]x^{2}[/tex] + 8

[tex]x^{2}[/tex] = 25 - 8 = 17

x = [tex]\sqrt{17}[/tex]

Therefore, x = [tex]\sqrt{17}[/tex]

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The relation is:

(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)

Is a function, because each element in the domain is mapped to a single element in the range.

A relation maps elements from one set, called the domain, into another set, called the range.

For example, the element x mapped into element y is written as (x, y).

Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.

So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).

Here the relation is:

(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)

So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.

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Answer:

Step-by-step explanation:

Let

n--------> the number

we know that

1) the sentence" Three less than the product of seven and a number"  represent the expression------>  

2) the sentence" is four more than the number"  

represent the expression ------->  

3) the complete sentence" Three less than the product of seven and a number is four more than the number"  represent the expression

represent the expression ------->  

therefore

the answer is

(7n-3) =(n+4)

Answer:

100°

Step-by-step explanation:

180°- 80°= 100°

The angles are supplementary, meaning that they have to add up to 180.

Hope this helps!!! :)

Answer:  [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]

Given: [tex]3x + 2y = 5[/tex]

We are needed to find the slope-intercept form.

We know that the slope-intercept form of an equation is given by

[tex]y = mc + c[/tex]

[tex]3x + 2y = 5[/tex]

[tex]2y = 5 -3x[/tex]

[tex]2y = -3x + 5[/tex]

[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]

Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]

Answer:

y = 3x + 2

y = 1/2 x -1

Step-by-step explanation:

The slope intercept form of a line is

y = mx + b  You substitute in the slope for m and the y intercept for b

The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.

Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.

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Answer:

equal to area of rectangle

Step-by-step explanation:

Please mark me brainlest

Answer:

C

Step-by-step explanation:

Because it says -8 x 7, the * is negative and the 7 is positive.

Answer:

x > 24 goes to the bottom

x < 24 goes to the 3rd slot

x ≤ 24 goes to the 1st slot

x ≥ 24 goes to the 2nd slot

Step-by-step explanation:

Hope this helps.

The number of liters in the tank after 109 seconds is 60.5 liters.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

2.5 liters = 1 minute

2.5 liters = 60 seconds

Multiply 109/60 on both sides.

109/60 x 2.5 liters = 109 seconds

4.5 liters = 109 seconds

This means,

4.5 liters is drained after 109 seconds

Now,

The liters of water in the tank.

= 65 - 4.5

= 60.5 liters

Thus,

There are 60.5 liters in the tank.

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In 11.56 years the given amount of $ 900 will be double.

The interest charged on a loan or deposit is known as compound interest which depends on both the principal amount and rate of interest.

The formula  used for

where P = Principal amount

r = Rate of interest in decimal

n = Number of compounds per year  

t = Time period  

Here from the given data,

Principal amount, p = $ 900

Rate of interest, r = 6% = 6/100 = 0.06

Number of compounds, n = 12    [ ∵ compounded mothly ]

Here we need to find the time period

Assume that after 'n' years the amount will be doubled i.e $ 1800

From the given problem,

Amount, A = 900(1+0.06/12)¹²ⁿ        

= 900(1+0.06/12)¹²ⁿ

= 900(1 + 0.005)¹²ⁿ

= 900 (1.005)¹²ⁿ  

As we assumed after 'n' years the amount is $ 1800

=> 900 (1.005)¹²ⁿ = 1800  

=> (1.005)¹²ⁿ = 2    

Apply to log on both sides

=> log (1.005)¹²ⁿ = log 2

=> 12n log(1.005) = log 2

=> 12n = log 2/log(1.005)

[ use calculator for log (1.005) and log 2]

=> 12n = 0.301029996/ 0.00216606176  

=> 12n = 138.975722

=>  n =  11.5813102

=>   n = 11.56  

Therefore,

In 11.56 years the given amount of $ 900 will be double.

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By setting up the equation, we get the system of linear equations are

9x + 7y = 77

3x + 5y = 49

solving these equation Cost to rent a chair = $1.75

cost to rent a table = $8.75

A system of linear equations is a collection of one or more linear equations involving the same variables.

There are several methods for solving systems of linear equations, including:

Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.

Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.

Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.

etc.

To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.

First, solve the first equation for y:

9x + 7y = 77

7y = -9x + 77

y = (-9/7)x + 11

Now substitute this expression for y into the second equation:

3x + 5((-9/7)x + 5(11) = 49

3x - (45/7)x + 55 = 49

solving for x :

x = 1.75

Now substitute this value for x back into the first equation to find y:

y = 8.75

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Angle θ with 0∘ < θ < 360∘ that has the same: sine as 30°:∅= degrees

cosine as 30°:∅= degrees are 150 and 330 degrees.

What is trigonometric function?

Trigonometric functions are referred to as Circular Functions may be merely outlined because the functions of an angle of a triangle

Main Body:

We have to find an angle θ with 0° < θ < 360° that has the same:

(a) sin(30∘)

We know that sin(θ) is positive in 2nd quadrant and in the 2nd quadrant θ lies between 90∘ and 180∘.

sin(30∘)=sin(180∘−30∘)

[∵sin(180∘−θ)=sin(θ)]=sin(150∘)

Thus:

sin as 30∘:θ=150 degrees

(b) cos(30∘)

We know that cos(θ) is positive in the 4th quadrant and in the 4th quadrant θ lies between 270∘ and 360∘.

cos(30∘)=cos(360∘−30∘)

[∵cos(360∘−θ)=cos(θ)]=cos(330∘)

Thus:cos as 30∘

:θ=330 degrees

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The equation that can be used to find the length of the side of the original square is 4(x+5) = 60. Option A. is the answer

Given that:

When the length of a side of a square is increased by 5, the perimeter of the new square is 60.

Let x represent the length of the side of the original square

when x is increased by 5, you have (x+5)

Perimeter (P) = 4 × length of the side

Thus, 4(x+5) = 60

Therefore,  the equation to find the length of the side is  4(x+5) = 60

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Answer:

---------------------------------

Given  number is 71830.

The last part:  830 is same on both lines.

We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:

It is 11 thousands.

Answer:

11,000 (or) 11 thousands

Step-by-step explanation:

Now we have to,

→ find the missing number.

→ Let the number be x.

Forming the equation,

→ 60,000 + x + 800 + 30 = 71,830

Then the value of x will be,

→ 60,000 + x + 800 + 30 = 71,830

→ x + 60,830 = 71,830

→ x = 71,830 - 60,830

→ [ x = 11,000 ]

Hence, the value of x is 11,000.

The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:

y = A · [tex]e^{B\cdot x}[/tex]

Where:

If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:

4 / 5 = A · [tex]e^{-B}[/tex]

20 = A · [tex]e^{B}[/tex]

If we divide the latter expression by the former, then:

25 = [tex]e^{2\cdot B}[/tex]

㏑ 25 = 2 · B

B = (1 / 2) · ㏑ 25

B ≈ 1.609

And the value of A is:

A = 20 / [tex]e^{1.609}[/tex]

A ≈ 4.002

The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

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Answer:

X=100

Step-by-step explanation:

I assume you want to find the value of x.

3/5x=60

5/3*60=x

x=20*5=100

Answer:

goes from(6,0),(10,1),(14,2) in +ve

If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.

When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

We know f(x) + g(x) = (f + g)(x).

Given, f(x) = 4x - 5 and g(x) = 6 - 3x.

∴ f(x) + g(x) = (4x - 5) + (6 - 3x).

f(x) + g(x) = 4x - 3x - 5 + 6.

f(x) + g(x) = x + 1.

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The explicit formula for the geometric sequence 6, -24, 96, ... is

Every term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio

The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.

For the given sequence the first term is a = 6

The common ratio is solved as follows

a * r  = second term

6 * r = -24

r = -24/6

r = -4

check

-24 * -4 = 96 correct

The nth term of a geometric sequence

= ar^(n - 1)

= a * -4^(n - 1)

checking for the third term

= a * -4^(n - 1)

= 6 * -4^(3 - 1)

= 6 * -4^(2)

= 6 * 16

= 96

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Answer:

  see attached

Step-by-step explanation:

Given the equation for a line, y +3 = (x -6), you want to identify the slope and a point on the line, then graph it.

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Comparing this to the given equation, you can see ...

This tells you the slope is 1 and a point on the line is (6, -3).

You graph this equation by plotting point (6, -3) and drawing a line through it that goes up 1 unit for each 1 unit to the right. A graph is attached.

__

Additional comment

If you like, you can rearrange the equation to slope-intercept form by subtracting 3:

  y +3 -3 = (x -6) -3

  y = x -9

This tells you another point is -9 on the y-axis.

Answer:

Step-by-step explanation: 270

Answer: 1.49 x [tex]10^{-5}[/tex]

Step-by-step explanation:

Answer:

------------------------------

The difference of the functions is:

The difference between functions is positive, therefore it is a vertical shift up by 2 units.

The bags of chips sold are 111.

The percentage is the term use to tell the hundredth part of something.

Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,

Let the original number of bags of the chips be x,

Since, 75% is already sold, so left number of bags are = 100%-75% = 25%

Therefore,

25% of x = 37

x = 37x4

x = 148

The number of bags sold = 75% of 148

= 75x148/100

= 111

Hence, they sold 111 bags of chips.

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The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.

The correct long division is shown below.

This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.

In the following proportions:-

A. [tex]\frac{2}{8} =\frac{3}{12}[/tex]

C. [tex]\\\\\ \frac{25}{10} =\frac{5}{2}[/tex]

D. [tex]\\\\ \frac{3}{4} =\frac{15}{20}[/tex] Are Equal

What are proportion?

A part, share, or quantity that is compared to a total is referred to as a proportion. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

When two ratios are equal, they are said to be in proportion.For instance, the time it takes a train to go 50 kilometers per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours at 50 km/h.

[tex]A) \\\\\frac{2}{8} =\frac{3}{12} =\frac{1}{4}\\\\(B) \\\\\frac{3}{4} \ !=\frac{8}{10}= \frac{4}{5}\\\\\ (C)\\\\\frac{25}{10} =\frac{5}{2}\\\\(D)\\\\ \frac{3}{4} =\frac{15}{20}[/tex]

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