2.8 Select all trips that would take 3 hours.
A. Walk at a rate of 2 miles per hour on a 5-mile trail.
B. Drive 180 miles from Raleigh to Boone going 60 miles per hour
C. Bike 14 miles per hour going from Greensboro to Winston Salem

The ratio of the amount Peter spent to that of John is 2:3, so:

(a) If Peter spent 500 dollars, then John spent 75p dollars

(b) If John spent 600 dollars, then they spend altogether 1000 dollars.

(c) If both boys spent 2000 dollars altogether, then John spent 1200 dollars and Peter spent 800 dollars.

(d) If John spent 100 dollars more than Peter, then they both spent 500 dollars as Peter will spend 200 dollars while John spends 300 dollars.

Let us represent the amount of money spent for Peter and John with P and J respectively.

Using the ratio 2:3 for the amount Peter spent to that of John;

If Peter spent 500 dollars, then;

2/3 = $500/J {cross multiply}

J = (3 × $500)/2

J = $1500/2

J = $750

If John spent 600 dollars, then;

2/3 = P/$600 {cross multiply}

P = (2 × $600)/3

P = $1200/3

P = $ 400

Peter and John spent altogether = $1000

If both boys spent 2000 dollars altogether, then;

their total ratio = 5

unit amount = $2000/5

unit amount = $400

Peter spent = 2 × $400 = $800

John spent = 3 × $400 = $1200

If John spent 100 dollars more than Peter, then;

2/3 = P/(P + $100) {cross multiply}

3P = 2(P + $100)

3P = 2P + $200 {collect like terms}

3P - 2P = $200

P = $200.

Peter spent = $200

John spent = $300.

In conclusion, using the ratio 2:3 for the amount of money spent by Peter and John respectively, we have the answers: $750, $1000, $800 for Peter and $1200 for John, and $200 for Peter and $300 for John for the questions lettered (a), (b), (c), and (d) respectively.

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3.64 x [tex]10^8[/tex] divided by 3.3 x [tex]10^4[/tex] is equal to 110.12121212121212.

The division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into a number of equal parts. The symbol for division is typically a forward slash (/) or a horizontal line. For example, if you have 10 apples and you want to divide them equally among 5 people, each person would receive 2 apples (10 ÷ 5 = 2). The result of division is called the quotient.

Here is one way to divide 3.64 x 10^8 by 3.3 x 10^4 step by step:

Write the numbers as decimal numbers: 3.64 x 10^8 is equal to 364000000 and 3.3 x 10^4 is equal to 33000.

Divide the decimal numbers: 364000000 ÷ 33000 = 11006.06

The result is 11006.06.

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The measure of ∠A is 123 degrees.

The angle made between the radius and the tangent at the point of contact on a circle is 90°.  

Therefore,

∠D = 90 degrees

∠E = 90 degrees

The diagram ACDE forms a quadrilateral. The sum of angles in a quadrilateral is 360 degrees.  Therefore, we have to equate the sum of the quadrilateral angles to 360 degrees.

Hence,

90 + 90 + 2x + 7 + 5x - 2 = 360

180 + 7x + 5 = 360

7x = 360 - 180 - 5

7x = 180 - 5

7x = 175

x = 175 / 7

x = 25

Therefore,

∠A = 5(25) - 2 = 125 - 2 = 123 degrees.

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On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

y = –1 2 x + 3 and y = 1 2 x - 1, the systems of linear equations.

from the graph , we have,

the solution set to this system of equations is,

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

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Answer: D

Step-by-step explanation:

Answer:

Yes, the tank is more than half full of gasoline after 3.5 hours.

Step-by-step explanation:

To calculate the amount of gasoline left in the tank after 3.5 hours, we need to subtract the amount used (1.45 gallons per hour) from the total capacity (11.6 gallons). So 11.6 - (1.45 x 3.5) = 9.3 gallons, which is more than half the tank's capacity of 11.6 gallons. Hope this helps!

Answer;

-2

Step-by-step explanation;

Well take the last numbers in these points and subtract them

4 - (-8)

4+8

12

You've got the upper part of the slope fraction now subtract the first two numbers.

-4-2

-6

Put this fun together, 12/-6 = -2

hence, slope=-2 .

Answer:

Step-by-step explanation:

-2

Answer:

2,506

Step-by-step explanation:

1/5/2023

7:37PM

First, we need to find the number of students that are freshmen: 3400 students x 3/8 = 1050 students

Next, we need to find the number of students that are in favor of forming a track team: 3/5 of the freshmen are in favor = 3/5 * 1050 = 630 students

To find the number of non-freshmen students: 3400 students - 1050 students = 2350 students

Now we need to find the number of non-freshmen students in favor of forming a track team: 1/5 of the non-freshmen students are in favor = 1/5 * 2350 = 470 students

Finally, to find the number of students opposed to the idea we need to subtract the number of students in favor from the total number of students: 3400 students - (630 students + 470 students) = 3400 - 1100 = 2300 students

So there are 2300 students at Central High School that are opposed to the idea of forming a track team.

The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.

Therefore, 2 quarts will be:

= 2 × 4.

= 8 cups

Therefore, the price per cup will be:

= $5.36 / 8

= $0.67

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Answer:

Step-by-step explanation:

ur mom

The description does NOT guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other

A quadrilateral is a four-sided polygon. It is a closed geometric figure with four straight sides and four angles and A rectangle is a four-sided shape with two pairs of parallel, perpendicular sides. Its opposite sides are equal in length and also opposite angles are equal in measurement.

Therefore, the correct answer is as identified. It can be concluded that the one that does not guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other

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The percentage of the cookies were gingerbread is 60%.

Given that, the total number of gingerbread cookies and sugar cookies= 55 and the number of gingerbread =22.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%"

Here, Difference =55-22

=3

Percentage =33/55 ×100

= 0.6 ×10

= 60%

Therefore, the percentage of the cookies were gingerbread is 60%.

Answer:

Step-by-step explanation:

 cccccc

Answer:

1440

Step-by-step explanation:

"Percent" means "out of 100"

5 "percent" means 5 out of 100

[tex]\frac{5}{100} =\frac{72}{x}[/tex]

We need to find the number that when multiplied by 5, equals 72.

72 / 5 = 14.4

Now, we need to multiply 100 by 14.4 to "scale" proportionately.

100 * 14.4 = 1440

We can check our work:

1440 * (0.05) = 72

Answer:

y = -8/3x + 8/3

Step-by-step explanation:

(-2, 8) and (1, 0)

m = 0-8/1+2

m = -8/3

y = -8/3x + b

0 = -8/3(1) + b

0 = -8/3 + b

b = 8/3

y = -8/3x + 8/3

The statement that "the midpoint of a line is found by subtracting two coordinates and dividing the answers by two" is false

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula midpoint involves addition two coordinates instead of subtraction, and dividing by two.

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The final answer of the corrected expression is  (-22, -26).

What is the solution to the linear equation?

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

We have given:

 y = x - 4

-2x + y = 18

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

-2x + (x - 4) = 18

-x - 4 = 18

x = 22

y = 22 - 4

y = 18

Solution: (22, 18)

The error is in lines 3, 4, and 5.

It should have,

 y = x - 4

-2x + y = 18

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

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22

x = -22

y = -22 - 4

y = -26

Solution: (-22, -26)

Hence, the final answer of the corrected expression is  (-22, -26).

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The compound inequality on the number line is shown below.

We have been given a compound inequality. We are asked to graph the given inequality on number line.    

x>8 and x≤3

The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.

We will have solid dots at  x>-8 and x≤-3 .

One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.

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On solving the provided question we can say that -  Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

On solving the provided question, we can say that the value of x = 5√3

values of x and y

Pythagorean theorem,

The trigonometric ratio: soh-cah-toa, and

According to the given question:

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]

Pythagorean Theorem

[tex]5²+x²=10²\\x²=100−25=75\\[/tex]

x=√75=√3×25=5√3

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The equation 1/2r = π/CB is true. Choose the second option

The circumference of a circle is the distance around the circle, or the length of the perimeter of the circle. It is given by the formula:

circumference = 2πr = πd

where r is the radius and d is the diameter

Note: d = 2r

Given: d2 = 2r and CB denotes the circumference of ⨀B

CB =  πd2  

CB =  2πr   (d2 = 2r)

Divide both sides by CB:

CB/CB =  2πr/CB

1 = 2πr/CB

Divide both sides by 2r:

1/2r = 2πr/2rCB

1/2r = π/CB

Thus, the second equation is true

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Answer:

The average rate of change is −10.

Step-by-step explanation:

The average rate of change of f(x) on the interval [a,b] is f(b) − f(a) / b−a.

We have, a=3, b=5, f(x) = -1x^2 − 2x + 2.

Thus, f(b) − f(a) = −(5)^2 −2(5) + 2 − [−(3)^2 −2(3) + 2]

= -25 - 10 + 2 - ( -9 - 6 + 2 )

= -33 - 13

= - 20

Then, b−a = 5 - 3 = 2

f(b) − f(a) / b−a = - 20 / 2 = −10

Answer: the average rate of change is −10.

Answer:

Below

Step-by-step explanation:

(25380 - 18000) / 18000     * 100% =

7380/18000 * 100 = 41 % increase

Answer: 5

Step-by-step explanation:

A triangle's area is half of a squares, so we can treat this as a square for now. It says the area is 20 units squared, and if we convert this to the area of the square, it is 40 units. 40/8 is 5, and so 5 is the length of x

1. The length of the sides of the two smaller squares are 3 and 4

2. Area of 4 triangles and middles square = 25

3. Area of the big square = 5

The dimensions of the the triangle and the square are

length of square = 1

base = 3

height = 4

Area of the triangle

= 1/2 base * height

= 0.5 * 3 * 4

= 6

For four triangles

= 4 * 6

= 24

Area of small square

= 1 * 1

= 1

summation of the areas

= 24 + 1

= 25

Solving for side of the big square from the area

= √25

= 5

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Answer:

$25,900 initially

$8,128 after 11 years

Step-by-step explanation:

One thing to note, is I'm assuming you meant: [tex]v(t)=25,900(0.90)^t[/tex] and not  [tex]v(t)=25,900(0.90)^2[/tex], otherwise that would just be a constant function and not an exponential function.

There are a couple key features of exponential functions we can derive from simply analyzing the equation.

For now I will be using the form: [tex]y=a(b)^x\text{ where b} > 0, \text{b}\ne 1[/tex]

The y-intercept, is just the "a" value, which is because the y-intercept is simply when x=0, and if we raise a number to the power of zero, we get one (excluding zero as a base), so we get the form: [tex]y=a[/tex], so "a" is our y-intercept.

there's actually two type of exponential functions: exponential growth and exponential decay.

Exponential Decay:

Exponential decay, as the name implies, is when a function is decaying or decreasing. This occurs when [tex]0 < b < 1[/tex].

The decay rate can be represented as "r" in decimal form, where: [tex]b=1-r[/tex].

The reason for this is because "1" can be thought of as 100% and "r" is r%, so you're taking away r% or decaying the value by r%, also known as a decay rate.

Exponential Growth:

Exponential growth as the name implies, is when a function is growing or increasing. This occurs when b > 1

The growth rate can be represented as "r" in decimal form where: [tex]b=1+r[/tex]

The reason for this is similar to decay rate except instead of taking away r% or decaying, it's "giving r%" or growing.

The question doesn't actually require finding exponential growth or decay, but it's still an important key feature.

In this case, we really just need to find the y-intercept and plug in t=11.

The y-intercept in many graphs, not just exponential graphs, represents some sort of initial value, which in this case, is the initial value of the car. As stated above, this y-intercept is just the value in front, which is 25,900.

As for the value after 11 years, we simply need to plug in t=11 to get the following: [tex]v(11)=25,900(0.90)^{11}[/tex], from here we can use a calculator to simplify this: [tex]v(11)\approx25,900(0.31381059609)\approx 8,127.694438731[/tex], which rounds to 8,128

Answer:

8296/17 = 488

4590/34 = 135

4550/26 = 175

8132/38 = 214

5265/15 = 351

8760/24 = 365

5643/33 = 171

4403/37 = 119

2400/48 = 50

Answer:

No solution

Step-by-step explanation:

When you solve it, it ends up as 0=-7 which isn't true.

Answer:

No solution!

Step-by-step explanation:

Answer: If 2 melons cost Php190.50, then 4 melons cost 381 .

If 1 kg of Bangus costs Php167.35, then 3.5 kgs of Bangus cost 585.725

Step-by-step explanation:

2x2=4

190.50x2=381

1x3.5=3.5

167.35x3.5=585.725

Answer: