Erin and her friends are taking a road trip. She has agreed to drive between hours 3 and 6 of the trip. If h represents the hours of the trip Erin will be driving, then h ≥ 3 and h≤ 6 represents her portion of the driving. While she is driving, her distance and time are modeled by the inequality d < 70h. What are the possible hours and distances Erin could be driving? When graphing this scenario, let h be the horizontal variable and d be the vertical variable.

Answer: y = 3x - 2

Step-by-step explanation:

Equation of a straight line is

y=mx + c

m is the slope and c is the intercept

comparing it with the equation

y=3x - 2

m = slope =3

and c= intercept= -2

To find the amount of material needed for a certain number of uniforms, we can use a proportion and multiply the amount of material needed for 1 uniform by the desired number of uniforms.

To find out how many yards are needed for 8 uniforms, we can set up a proportional relationship between the number of uniforms and the amount of material needed. We can do this by dividing the amount of material needed for 1 uniform by the number of uniforms, and then multiplying by the desired number of uniforms. The formula for this is (Amount of material needed for 1 uniform / Number of uniforms) * Desired number of uniforms. Using this formula, we can determine that 8 uniforms would require (12 yards / 1 uniform) * 8 uniforms = 96 yards of material.

To find out how many yards are needed for 15 uniforms, we can use the same formula. (12 yards / 1 uniform) * 15 uniforms = 180 yards of material.

Therefore, 8 uniforms require 96 yards of material, and 15 uniforms require 180 yards of material.

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The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is determined in the following steps given below.

[tex]\rm Probability=\dfrac{10}{3}\times \left (\dfrac{1}{3} \right ) ^3\times \left (\dfrac{5}{6} \right ) ^7\\\\Probability= \dfrac{10}{3}\times \dfrac{1}{27} \times \dfrac{78125}{279936}\\\\Probability=0.034[/tex]

Hence, the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.

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28 chores he now has left to do.

An arithmetic intelligence operation minus simulates the process of deleting items from either a collection. To subtract is to take something or something from a particular group. The group's total number of items decreased and became lower when people eliminated it. The components of a subtraction issue are the issues dealing with, forces at play, and differences. The negative symbol, or, denotes subtraction.

35 tasks have been assigned to Tom for today.

He accomplished 7 of them this morning.

The remaining days are:

= 35-7

= 28 chores

The remaing chores are 28.

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Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

A line passes through the origin and has a slope of 4

y=4x is the equation of the line.

We have to find the equation of the line that is parallel to the first line and passes through the point (1, –2)

Slope is 4 as it is parallel.

We have to find the y intercept

-2=4(1)+b

b=-6

So equation is y=4x-6

Hence, Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)

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Final answer:

To find the remainder of 314162 divided by 7, we use modular arithmetic and find that the powers of 314 mod 7 repeat every 3 powers. Since 162 is a multiple of 3, 314162 mod 7 equals 1.

Explanation:

The question asks for the remainder when 314162 is divided by 7. To solve this problem, we can use a concept known as modular arithmetic, which deals with the remainder upon division. The key here is to find a pattern in the powers of 314 modulo 7, because large numbers can be cumbersome to work with directly. A helpful property is that (a×b) mod n = [(a mod n)×(b mod n)] mod n.

Let's consider the powers of 314 mod 7:

3141 mod 7 = 2

3142 mod 7 = (314 × 314) mod 7 = (2 × 2) mod 7 = 4

3143 mod 7 = (3142 × 314) mod 7 = (4 × 2) mod 7 = 1
Since we reached 1 again, the sequence will repeat every 3 powers. Now, 162 is divisible by 3 (162 = 3 × 54). Therefore, we can conclude that 314162 mod 7 will have the same remainder as 3143 mod 7, which is 1.

Answer:

B

Step-by-step explanation:

edge

Answer:

0.34 miles per minute

Step-by-step explanation:

We have to convert 30 feet per second to miles per minute.

1 minute = 60 seconds

Therefore, in one minute = 60 × 30 = 1800 feet

5280 feet = 1 mile

180 feet =  [tex]\frac{1800}{5280}[/tex]

              = 0.3409 ≈ 0.34 mile

Therefore, 0.34 mile per minute.

A quotient is a quantity that is obtained by dividing two integers. The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).

A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.

The quotient of the division (2x²+3x-9) ÷ (x+3) can be found as shown below,

[tex]\dfrac{2x^2+3x-9}{(x+3)}\\\\=\dfrac{2x^2+6x - 3x -9}{(x+3)}\\\\=\dfrac{2x(x+3)-3(x+3)}{(x+3)}\\\\=\dfrac{(2x-3)(x+3)}{(x+3)}\\\\[/tex]

= (2x - 3)

Hence, The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).

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5 +3 = 8

3^2 = 9

5^2 = 25

25 +9 = 34

smaller number is 3

To make m the subject of the equation x-2m=p, add 2m to both sides, subtract p, and divide by 2. The result is m as the subject of the equation, represented as the fraction (x - p)/2.

To solve the equation x-2m=p for m as the subject, we want to isolate m on one side of the equation. Here is the step-by-step process:

Now m is the subject of the equation, and it is represented as a fraction as requested.

Answer:

Two times the difference of x and seven plus ten

Step-by-step explanation:

The equivalent decimal number will be 15.25.

What is Decimal number?

A decimal number is a number that consists of a whole and a fractional part.

Given that;

The number is,

⇒ 15 1/4

⇒ 61 / 4

Now,

Solve the number in decimal form as;

The number is,

⇒ 15 1/4

⇒ 61 / 4

⇒ 61 ÷ 4

After divide we get;

⇒ 61 ÷ 4 = 15.25

Thus, The equivalent decimal number will be 15.25.

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Answer:

it's 9 grams for apex

The sum of the expression in scientific notation is given by option D) 6.548 × 10⁻².

Given expression is,

0.00348 + (6.2 x 10⁻²)

We have to first find the sum.

For that, rewrite the number in the scientific form in the normal form.

Since the exponent of 10 is -2, the decimal point is shifted 2 units to the left.

6.2 x 10⁻² = 0.062

0.00348 + (6.2 x 10⁻²) = 0.00348 + (0.062)

                                     = 0.06548

Now, we have to write this in scientific notation as the power of 10.

After shifting the decimal point to the right up to 2 units, 0.06548 becomes = 6.548.

So, 0.06548 = 6.548 × 10⁻²

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The velocity function of an object moving along the {x} - axis would be -

v{t} = sin(t) + t³ + 2.

The acceleration at any instant of time is called instantaneous acceleration. Mathematically -

a = dv/dt

dv = a dt

∫dv = ∫a dt

Given is the acceleration function as -

a(t) = 3t² + cos(t)

We know that -

a = dv/dt

dv = a dt

∫dv = ∫a dt

v{t} = ∫{3t² + cos(t)} dt

v(t) = sin(t) + t³ + C

Now -

v(0) = 2

sin(0) + 0 + C = 2

C = 2

So, we can write the velocity function as -

v{t} = sin(t) + t³ + 2

Therefore, the velocity function of an object moving along the {x} - axis would be -

v{t} = sin(t) + t³ + 2.

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It increases the amount by 700,000

Answer:

A is the mofluffin answer

Step-by-step explanation:

(1) the area of a rectangle with vertices at ​ (−6, 3) ​, ​ (−3, 6) ​ , (1, 2) , and (−2, −1)

To find area of rectangle we need to find the length and width

Length = distance between (−6, 3)  and (−2, −1)

Distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

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

=  [tex]\sqrt{(4)^2 + (-4)^2}[/tex]=[tex]\sqrt{(16) + 16}[/tex] =[tex]\sqrt{32}[/tex]

width = Distance between (−6, 3) ​, ​ (−3, 6)

Distance = [tex]\sqrt{(-3-(-6))^2 + (6-3)^2}[/tex]

=[tex]\sqrt{3^2+3^2}= \sqrt{18}[/tex]

Area = Length * width = [tex]\sqrt{32} *\sqrt{18} = \sqrt{576}= 24[/tex]

(2)  the area of a triangle with vertices at (0, −2) , ​ (8, −2) ​ , and ​ (9, 1) ​

Area of triangle = [tex]\frac{1}{2} * base * height[/tex]

base  is the distance between (0,-2) and (8,-2)

Distance =  [tex]\sqrt{(8-0)^2 + (-2-(-2))^2}[/tex] = 8

To find out height we take two vertices (8,-2) and (9,1)

Height is the change in y values = 1- (-2) = 3

base = 8  and height = 3

So area of triangle = [tex]\frac{1}{2} * 8 * 3 = 12[/tex]

(3) the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​

To find perimeter we add  the length of all the sides

Distance between (−2, 1)  and (−2, 4) = [tex]\sqrt{(-2+2)^2 + (4-1)^2}[/tex]= 3

Distance between(−2, 4) ​and (2, 7) = [tex]\sqrt{(2+2)^2 + (7-4)^2}[/tex]= 5

Distance between (2, 7)  and (6, 4) = [tex]\sqrt{(6 - 2)^2 + (4-7)^2}[/tex]= 5

Distance between (6, 4) ​ and (6, 1) ​= [tex]\sqrt{(6 - 6)^2 + (1-4)^2}[/tex]= 3

Distance between  (6, 1) and (−2, 1) ​= [tex]\sqrt{(-2-6)^2 + (1-1)^2}[/tex]= 8

Perimeter = 3 + 5 + 5 + 3 + 8 = 24

(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)

Length = Distance between  (3,-3) and (4,2) ​= [tex]\sqrt{(4-3)^2 + (2+3)^2}[/tex]= [tex]\sqrt{26}[/tex]

Width = Distance between (-6,4) and (4,2) ​= [tex]\sqrt{(4+6)^2 + (2-4)^2}[/tex]= [tex]\sqrt{104}[/tex]

Perimeter = 2(lenght + width) = 2*( [tex]\sqrt{26}[/tex]+[tex]\sqrt{104}[/tex] )

= 30.6 units

The area of the rectangle is [tex]24\;square\;units[/tex].

1. According to the question, the vertices of the rectagle are at ​ [tex](-6, 3) ;(-3, 6) ;(1, 2)[/tex] , and [tex](-2, -1)[/tex].

The distance between two vertices on the coordinate plane is

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So,

[tex]Length=D_1\\D_1=\sqrt{(6-3)^2+(-3+6)^2}\\D_1=\sqrt{9+9}\\D_1=3\sqrt 2 units[/tex]

Similarly,

[tex]Width=D_2\\D_2=\sqrt{(-2+6)^2+(-1-3)^2}\\D_2=\sqrt{16+16}\\D_2=16\sqrt 2\;units[/tex]

The area of the rectangle is equals to product of length and width of the rectabgle.

So,

[tex]Area=length\times width\\Area=3\sqrt{2}\times 4\sqrt{2}\\Area=24\;square\;units[/tex]

Hence, the area of the rectangle is [tex]24\;square\;units[/tex].

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The measure of the vertex angle is 72 degrees

The sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;

54 + 54 + x = 180

where

x is the vertex angles

Simplify

108 + x = 180

x = 180 - 108

x = 72 degrees

Hence the measure of the vertex angle is 72 degrees

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