Samuel was preparing for the triathlon. He did 3 activities every morning: ran for 30 minutes, covering 4.5 miles swam for 20 minutes, covering 2 3 mi biked for 45 minutes, covering 9 miles What was Samuel's average speed during his morning training?

Answer:

B' (2,3)

Step-by-step explanation:

See the pictures below.  B was two units below y = 1 so B' needs to be 2 units above y = 1.  That places the point at (2,3)

we are given m=6 and a point MEANING WE CAN SUBSTITUTE THE KNOWNS TO GET C IN THE EQUATION Y=MX+C

[tex]2 = 6( \frac{1}{2} ) + c \\ 2 = 3 + c \\ c = 2 - 3 \\ c = - 1[/tex]

THEREFORE

[tex]y = 6x - 1[/tex]

IS THE ANSWER.

HOPE THIS HELPS

The equation of the line passing through P(0, 0) perpendicular to y = -9x - 1 will be  [tex]y = \frac{1}{9}x[/tex]

The given question states that the line passes through the point P(0, 0) perpendicular to the line y = -9x - 1. We have to find out the equation of the line. We have to find the equation in slope-intercept form.

We know the slope intercept is: y = mx + b

Also, given the perpendicular line has slope m₂ = -9 according to slope-intercept form. And we know that perpendicular lines have a slope that is equal to the negative reciprocal.

So, the Slope of the line m₁ = Negative reciprocal of the slope of the perpendicular line.

=>  [tex]m_{1} = -\frac{1}{m_{2} }[/tex]

=> [tex]m_{1} = -\frac{1}{(-9)}[/tex]

=> [tex]m_{1} = \frac{1}{9 }[/tex]

We get the slope [tex]m_{1} = \frac{1}{9 }[/tex]. Also, it is given that the line passes through (0, 0) so the y-intercept b = 0. Putting these values in slope-intercept form, we get:

=> y = mx + b

=> [tex]y = \frac{1}{9} x[/tex]

Hence, the equation of the line is [tex]y = \frac{1}{9} x[/tex]

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Answer:

x = 36

Step-by-step explanation:

  To find the value of 'x', isolate 'x'.

[tex]\sf \dfrac{5}{6}x = 30\\\\ \text{Multiply both sides by 6,}\\\\ 5x = 30*6\\\\\text{Divide both sides by 5,}\\\\ x = \dfrac{30*6}{5}\\[/tex]

x = 6 * 6

x = 36

always substitute the function

(for example here we have) h(x) with its value

goodluck :)

Hello!

Since h(x) = -3x + 2  and h(x) = -4

 [tex]\hookrightarrow \text{Thus: } -3x + 2 = -4[/tex]

Let's solve:

 [tex]-3x + 2 = -4\\-3x = -4-2\\-3x=-6\\x = 2[/tex]

Hope that helps!

Volume of the sphere = 17157.28 cubic centimeters

How to calculate the volume of a sphere?

Given:

Diameter (d) = 32

r = d/2 = 16

We know that the  volume of a sphere is,

[tex]V=\frac{4}{3} \pi r^{3} \\\\ = \frac{4}{3} (3.14) (16)^{3}\\\\=17157.28 cm^{3}[/tex]

What is the volume of a sphere?

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[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ d\ to\ r\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Calculating\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]

Answer:

70.6% decrease

Step-by-step explanation:

4250-1250 = 3000

4250x = 3000

x=70.6%

70.6% decrease

:]

Answer:

-6/5

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (14 - 8)/(-3 - 2)

slope = 6/(-5)

slope = -6/5

The solution is -6/5

The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the first point be A

Now , the value of A is A ( 2 , 8 )

Let the second point be B

The value of B is B ( -3 , 14 )

And , the slope of the line between 2 points is given by the formula,

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 14 - 8 ) / ( -3 - 2 )

On simplifying the equation , we get

Slope m = 6 / ( -5 )

Slope m = -6/5

Therefore , the slope of the line is m = -6/5

Hence , The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5

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The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up

The equations of the functions are given as

f(x) = 3x + 9

g(x) = 3x - 10

Let the translations from f(x) to g(x) be h and k

So, we have

g(x) = f(x + h) + k

This gives

f(x + h) = 3(x + h) + 9 + k

Open the brackets

f(x + h) = 3x + 3h + 9 + k

Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k

g(x) = 3x + 3h + 9 + k

This means that

3x + 3h + 9 + k = 3x - 10

Evaluate the like terms

3h + 9 + k = - 10

This gives

3h + k = - 19

Express -19 as -21 + 2

3h + k = -21 + 2

Express 21 as 3 * 7

3h + k = -3 * 7 + 2

By comparison, we have

h = -7 and k = 2

This means that the transformation is 7 units right and 2 units up

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The total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.

The total monthly earnings for salespeople can be calculated as follows:

Monthly salary = base salary + sales commission

Given that what a local salesman generates a base salary of $875 and a 10% sales commission on any and all sales above $1,800, the salesman must make the following sales in order to earn $1500 in a given month:

Let the sales done by 'x'.

Then,

875 + 7% (x - 1800) = 1500

875 + (7/100) (x - 1800) = 1500

7(x - 1800) = 62500

x - 1800 = 8928.7

x = 894657.14

Thus, the total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.

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The number of the people did we survey = 12/19

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers.

The set of whole numbers is 0 through 9 (inclusive). Every value in this set is an example of a whole number. Examples are 0, 15, 53, and so forth.

To convey a thorough grasp of more complicated number identifiers like real, rational, and irrational numbers, whole numbers are employed as building blocks. Calculations can be made simpler and issues can be resolved more quickly by rounding decimal numbers to the next whole number.

According to question,

the exact percentage of the people is between 24% and 38%

24%÷ 38%

=0.24/0.38

=12/19

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The representation of the linear model shows that the height of the balloon after 15 seconds is 0 feet.

In statistics, the term "linear model" has several meanings depending on the situation.

The water balloon is hurled from a height of 40 feet above, as can be seen from the linear model.

The balloon now ascends to a height of 70 feet before returning to ground due to gravity.

The balloon drops to the earth and makes a splash after about ten seconds.

Therefore, the balloon will remain at the ground for some more time.

As a result, according to the linear model, the balloon's height at time 15 seconds is always 0 feet.

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××1=× 123 =×/1= the value of x is one

Check the picture below.

Answer:6.1 ounces

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{5} x - 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 8x - 20y = 40[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 20y = 40 - 8x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 20y = 8x - 40[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{8}{20} x - \frac{40}{20} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{5} x - 2[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The linear equation perpendicular to 5x-4y=4 is:

y = (-4/5)*x + 42/5

We want to find a line perpendicular to:

5x - 4y = 4

Solving this for y, we get:

y = 4 - 5x

y = (4 - 5x)/-4 = -1 + (5/4)*x

We can see that the slope of this line is 5/4, the slope of a perpendicular line will be the inverse of the opposite, so we get:

slope = -4/5.

Then the line is something like:

y = (-4/5)*x + b

To find the value of b, we use the fact that the line passes through (-8, 2)

2 = (-4/5)*-8 + b

2 = (-32/5) + b

2 + 32/5 = b

10/5 + 32/5 = b

42/5 = b

The linear equation is:

y = (-4/5)*x + 42/5

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i hope that this helps :)

1. The slope is -2.

2. The slope is 1.

3. cost of 1 yards fabric is $6.49.

4. The average speed is 65 miles/ h.            

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

The slope of line is the measure of steepness or the direction of line the coordinate plane.

m = Δy/Δx

where, m is the slope

1. The co- ordinates of the graph is (0, 0) and (-1, 2)

slope = (2-0) / (-1 - 0) = 2/ (-1) = -2

Thus, the slope is -2.

2. The co-ordinates of the graph is (0, 0) and (4, 4)

slope = (4 - 0) / (4- 0) = 4/4  = 1

Thus, the slope is 1.

3. cost of 7 yards fabric = $45. 43

cost of 1 yards fabric = 45. 43/7

                                  = $6.49

4. Distance = 325 miles

Time = 5 hours

So, average speed = 325 / 5

                                = 65 miles/ h

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We already know that Jackson biked k kilometers.

Maria biked 8 more kilometers than Jackson, which means that she biked

Peter biked 2 fewer kilometers than Jackson, which means that he biked

To get the total all of them biked, we add those expressions together.

The question wants us to represent your the equation y - 4 = 6()

Answer:

v = -1.5

Step-by-step explanation:

[tex]v = 2 + ( -7 \times .5) = - 1.5[/tex]

Answer:

44, -60, 4

Step-by-step explanation:

8(5) + 4 ---- 40 + 4 ---- 44

8(-8) + 4 ---- -64 + 4 ---- -60

8(0) + 4 ---- 0 + 4 ---- 4

The difference between distance around Earth's equator and distance around the Moon's equator is 284.4.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.

Given Data

The distance around Earth's equator is

4.00 x 104 km

= 416 km

The distance around the Moon's equator is

6.8 x 103 km

= 700.4

Difference = Distance around Earth's equator -  Distance around the Moon's equator

Difference = 700.4 - 416

Difference = 284.4

The difference between distance around Earth's equator and distance around the Moon's equator is 284.4.

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The perimeter and area of the given trapezoid are 92.4 cm and 420.525 cm².

So, the area and perimeter of the trapezoid:

The perimeter of the trapezoid formula: P = a + b + c + d

The area of the trapezoid formula: a+b/2 × h

Therefore, the perimeter and area of the given trapezoid are 92.4 cm and 420.525 cm².

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