The graph below shows the solution for the following system.
{f(x)=2x−3
g(x)=2^x−4
Linear function passing through (0, negative 3), (1.5, 0) & about (2.7, 2.3).
Exponential function passing through (negative 3, negative 4), (0, negative 3), (2,0) & about (2.7, 2.3).


Which statements are true?

Select all that apply.

x=0 is a solution to the system.

(1.5,0) and (2,0) are solutions to the system because the graphs of f(x) and g(x) cross the x-axis at those points.

When x≈2.7, the graphs of f(x) and g(x) intersect because they are equal to each other at that value.

f(x)=g(x) when x=0.

Answer:

Option D

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle B is formed by the intersection of the lines a and c. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

b^2 = a^2 + c^2 - 2*a*c*cos(B).

The question specifies that c=71, B=123°, and a=65. Plugging in the values:

b^2 = 65^2 + 71^2 - 2(65)(71)*cos(123°).

Simplifying gives:

b^2 = 14293.0182932.

Taking square root on the both sides gives b = 119.6 (rounded to the one decimal place).

This means that the Option D is the correct choice!!!

Answer:

[tex]\large\boxed{h=\dfrac{3V}{\pi r^2}}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cone:}\ V=\dfrac{1}{3}\pi r^2h.\\\\\text{Solve for}\ h:\\\\\dfrac{1}{3}\pi r^2h=V\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}\pi r^2h=3V\qquad\text{divide both sides by}\ \pi r^2\\\\h=\dfrac{3V}{\pi r^2}[/tex]

Answer:

Option A) 121.73

Step-by-step explanation:

The given scenario can be represented by a Triangle ABC attached in the image below.

We have 3 sides of the triangle ABC, using the measure of these sides we can find the angle opposite to side c which will help us in finding the measure of bearing.

Law of cosine relates the 3 sides of the triangle and angle opposite to one side by following equation:

[tex]c^{2}=a^{2}+b^{2}-2abcos(C)[/tex]

Using the values of a,b, and c we get:

[tex]230^{2}=200^{2}+260^{2}-2(200)(260)cos(C)\\\\2(200)(260)cos(C)=200^{2}+260^{2}-230^{2}\\\\ cos(C)=\frac{200^{2}+260^{2}-230^{2}}{2(200)(260)}\\\\ cos(C)=\frac{547}{1040}\\\\ C=cos^{-1}(\frac{547}{1040})\\\\ C=58.267[/tex]

Thus, the measure of angle C comes out to be 58.267 degrees. The angle with which the boat will have to turn will be:

180 - 58.267 = 121.733 degrees.

Therefore, option A is the correct answer

Answer:

A.) 121.73

Step-by-step explanation:

I got it correct on founders edtell

Answer:

y = 2x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2, so

y = 2x + c ← is the partial equation

To find c substitute (- 2, 3 ) into the partial equation

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = 2x + 7 ← equation of line

[tex]\huge{\boxed{f(4)=\bf{-3}}}[/tex]

In this case, you are replacing all instances of [tex]x[/tex] with [tex]4[/tex]. [tex]f(4)=3(4)-15[/tex]

Multiply. [tex]f(4)=12-15[/tex]

Subtract. [tex]f(4)=-3[/tex]

For this case we must simplify the following expression:

[tex]-3 (x + 3) ^ 2-3 + 3x[/tex]

We solve the parenthesis:

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

We apply distributive property to the terms within parentheses:

[tex]-3x ^ 2-18x-27-3 + 3x =[/tex]

We add similar terms:

[tex]-3x ^ 2-18x + 3x-27-3 =\\-3x ^ 2-15x-30[/tex]

Answer:

[tex]-3x ^ 2-15x-30[/tex]

Answer: [tex]-3x^2-15x-30[/tex]

Step-by-step explanation:

We need to remember that [tex](a\±b)^2=a^2\±2ab+b^2[/tex]

Knowing this, we can simplify  the expression:

[tex]-3(x + 3)^2 - 3 + 3x=-3[x^2+2(x)(3)+3^2]-3+3x=-3[x^2+6x+9]-3+3x[/tex]

Apply Distributive property:

[tex]=-3x^2-18x-27-3+3x[/tex]

Add like like terms:

[tex]=-3x^2-15x-30[/tex]

Since it has the form [tex]ax^2+bx+c[/tex], it is already expressed in Standad form.

Answer:

4p + 1 > −15 or 6p + 3 < 45

has solution any number.

The graph looks like this

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

     ---------(-4)---------(7)-------------

The shading is everywhere from left to right.

Step-by-step explanation:

Let's solve this first:

4p+1>-15

Subtract 1 on both sides:

4p>-16

Divide both sides by 4:

p>-4

or

6p+3<45

Subtract 3 on both sides:

6p<42

Divide both sides by 6:

p<7

So our solution is p>-4 or p<7

So let's graph that

~~~~~~~~~~~~~~~~~~~~~~~~~~~~O

                         O~~~~~~~~~~~~~~~~~~~~~~~~~~~~ p>-4

---------------------(-4)---------------------(7)--------------------

or is a key word! or means wherever the shading exist for either is a solution.

So this shading is everywhere.

The answer is all real numbers.

The final graph looks like this:

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

     ---------(-4)---------(7)-------------

The shading is everywhere from left to right.

Answer:

Solution is (-∞,∞)

Step-by-step explanation:

[tex]4p + 1 > -15 \ or \ 6p + 3 < 45[/tex]

Solve each inequality separately

[tex]4p + 1 > -15[/tex]

Subtract 1 from both sides

[tex]4p> -16[/tex]

Divide both sides by 4

[tex]p> -4[/tex]

Solve the second inequality

[tex]6p + 3 < 45[/tex]

Subtract 3 from both sides

[tex]6p< 42[/tex]

Divide both sides by 6

[tex]p< 7[/tex]

[tex]p> -4 \ or \p< 7[/tex]

Solution is (-∞,∞)

Answer:

JM ≈ 12.9 miles

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference × fraction of circle

     = πd × [tex]\frac{90}{360}[/tex]

JM = π × 16.4  × [tex]\frac{1}{4}[/tex]

     = [tex]\frac{16.4\pi }{4}[/tex] ≈ 12.9

The length of the arc JM will be 12.88 miles.

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/360) 2πr

The diameter is 16.4 miles. Then the radius will be

r = d / 2

r = 16.4 / 2

r = 8.2 miles.

And angle (θ) will be 90 degrees.

Then the length of the arc JM will be

Arc = (90/360) 2π x 8.2

Arc = 12.88 miles

More about the arc length of the sector link is given below.

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To find the probability of drawing certain colour of balls, we first need to find the total number of balls:

5 + 7 +5 = 17

For the number of red balls that need to be added

The original probability of drawing a red ball:

red ball/ total number of balls

= 5/17

To find the number of balls required, we can set an equation.

Let the number of red balls that need to be added be x.

5+x / 17+x = 5/6

(5+x) x 6 = (17+ x) x5

30 +  6x = 85 + 5x

6x - 5x = 85 - 30

x = 55

Therefore, 55 red balls need to be added.

For the number of black balls that need to be added

The original probability of drawing a white ball:

white ball/ total number of balls

=5/17

To find the probability required, we can set an equation.

Let the number of black balls that need to be added be y.

5/ 17 + y = 1/6

5 x 6 = 17 + y

30 = 17 + y

30 - 17 = y

y = 13

Therefore, 13 black balls need to be added.

Hope it helps!

Answer:

-3,3.1, 3 2/10

Step-by-step explanation:

When you are putting different numbers from least to greatest, you need to put them in the same form...

First things first we should put -3 wayy up front. negative numbers are worth less than positive numbers.

Then we need to turn 3 2/10 into a decimal.

3 2/10 -------> 3.2

3.2 is more than 3.1

Thus, the order is

-3,3.1, 3 2/10

Hope this helps and have a nice day.

Answer:

-3, 3.1, 3 2/10

Step-by-step explanation:

3 2/10, 3.1, -3

Negative numbers are smaller than positive numbers

-3

Then we need to compare fractions and decimals.

Lets change the fraction to a decimal

2/10 = .2

3.2 and 3.1

3.1 < 3.2

So in order from least to greatest

-3, 3.1, 3 2/10

Answer:

y=(6(x+6)(x-3))/((x-2)(x+3))

Step-by-step explanation:

The vertical asymptote should be in the denominator. The x-interceps should be in the numerator. Because we have horizontal asymptote y=6, then we have to put 6 in the numerator. the horizontal asymptote is the leading coefficient of the numerator ÷ the leading coefficient of the denominator, when the degree of the numerator and denominator are the same.

Given the horizontal asymptote, vertical asymptotes and x intercepts, the equation of the rational function is y = 6((x+6)(x-3))/((x-2)(x+3)). The vertical asymptotes are found by setting the function's denominator equal to zero, while the x-intercepts come from setting the numerator to zero.

In this question, we are asked to write the equation of a rational function based on given conditions. The function's vertical asymptotes are located at x = 2 and x = -3, and has x-intercepts at (-6,0) and (3,0), with a horizontal asymptote at y = 6.

The general form of a rational function is y = (ax+b)/(cx+d). Asymptotes help define the behavior and boundaries of the function. In this situation, we can set the denominator of our function equal to zero to find our vertical asymptotes, giving us (x-2)(x+3). To achieve our stated x-intercepts, we set the numerator equal to zero, providing (x+6)(x-3). Combining these, the function becomes y = ((x+6)(x-3))/((x-2)(x+3)). The output of the function approaches the horizontal asymptote as x approaches infinity. Thus to have y = 6 as our horizontal asymptote, we adjust our function to maintain this behaviour, settling on y = 6((x+6)(x-3))/((x-2)(x+3)).

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Answer:

a) increases b) decreases

Step-by-step explanation:

Typically, descriptions of trends are indicated as the change of the dependent (y) variable with respect to the increase of the independent (x) variable. In this case, age is the x variable and hours of sleep is the y variable.

Answer:

The data shown on the scatter plot below demonstrates the relationship between a young boy’s age (in months) and the average number of hours that he sleeps each night.

Step-by-step explanation:

The slope of the best fit line shows that as the boy’s age  

increases

the average number of hours that he sleeps each night  

decreases

.

Answer:

9

Step-by-step explanation:

70% of 30 is 21, so to find the number of boys, take the original 30, and subtract 21, leaving you with 9, hope this helps and good luck bud :)

There are 9 boys in the class.

To determine the number of boys in a class where 70% are girls, multiply the total number of students by the percentage of boys in the class.

Given:

Answer: There are 9 boys in the class.

Answer:

27/20

Step-by-step explanation:

7+1=8

5*4=20

5*1=5

8/20+5/20+14/20

Add numbers from left to right to find the answer.

8+5=13+14=27

27/20 is the correct answer.

Answer:

C) Lateral Area

Step-by-step explanation:

A) Base Area

The formula for base area of of a cylinder is pir^2.

B) Aread

The formula for surface area or area of a cylinder is 2pirh x 2pir^2 = 2pir (h + r)

C) Lateral Area

The formula for lateral area of a cylinder is 2pirh

D) Volume

The formula for volume of a cylinder is base area x h or pir^2h

!!

Answer:

C. Lateral area.

Step-by-step explanation:

We have been given that a right cylinder where h is the height and r is the radius. We are asked to determine the meaning of our given expression [tex]2\pi rh[/tex].

We know that lateral surface area of cylinder is equal to the circumference of base of cylinder times the height of the cylinder.

We know that base of cylinder is circular and circumference of circle is [tex]2\pi r[/tex], therefore, the expression [tex]2\pi rh[/tex] represents lateral area of cylinder.

Answer:

The correct option is 3.

Step-by-step explanation:

The given equation is

[tex]2x^2+12x-14=0[/tex]

It can be written as

[tex](2x^2+12x)-14=0[/tex]

Taking out the common factor form the parenthesis.

[tex]2(x^2+6x)-14=0[/tex]

If an expression is defined as [tex]x^2+bx[/tex] then we add [tex](\frac{b}{2})^2[/tex] to make it perfect square.

In the above equation b=6.

Add and subtract 3^2 in the parenthesis.

[tex]2(x^2+6x+3^2-3^2)-14=0[/tex]

[tex]2(x^2+6x+3^2)-2(3^2)-14=0[/tex]

[tex]2(x+3)^2-18-14=0[/tex]

[tex]2(x+3)^2-32=0[/tex]             .... (1)

Add 32 on both sides.

[tex]2(x+3)^2=32[/tex]

The vertex from of a parabola is

[tex]p(x)=a(x-h)^2+k[/tex]        .... (2)

If a>0, then k is minimum value at x=h.

From (1) and (2) in is clear that a=2, h=-3 and k=-32. It means the minimum value is -32 at x=-3.

The equation [tex]2(x+3)^2=32[/tex] reveals the minimum value for the given equation.

Therefore the correct option is 3.

The correct answer is option 3. [tex]2(x + 3)^2 = 32[/tex].

To find the minimum value of the quadratic equation [tex]2x^2 + 12x - 14[/tex] = 0, we can rewrite it in vertex form, which reveals the minimum or maximum value of a quadratic function.

The given options are attempts at rewriting the quadratic equation in vertex form. Let’s rewrite the equation:

First, complete the square:

1. Start with the equation: [tex]2x^2 + 12x - 14[/tex]

2. Factor out the coefficient of x² from the first two terms: [tex]2(x^2 + 6x) - 14[/tex]

3. Complete the square inside the parentheses:
- Take [tex](\frac{6}{2})^2 =9[/tex] - Add and subtract 9 inside the parentheses: [tex]2(x^2 + 6x + 9 - 9) - 14[/tex]
- Simplify inside the square: [tex]2((x + 3)^2 - 9) - 14[/tex]

4. Distribute and simplify: [tex]2(x + 3)^2 - 18 - 14 = 2(x + 3)^2 - 32[/tex]

Comparing this with the options, we have [tex]2(x + 3)^2 = 32[/tex].

The correct answer is: [tex]2(x + 3)^2 = 32[/tex].

Answer:

I believe the answer is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle. The correct option is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

To find the measure of angle A, we need to use the tangent trigonometric function this is because except for the hypotenuse of the triangle the other two sides of the equation are known.

Therefore, the equation of the tangent function of trigonometry for angle A can be written as,

tan(A) = Perpendicular /Base

tan(A) = 9.4 / 6.7

Hence, the equations below that can be used to find the measure of ∠A is tanA=9.4/6.7.

Learn more about Trigonometric functions:

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flooring a value, simply means, dropping it to the closest integer, so for the floor function or ⌊x⌋, that means

⌊ 2.5 ⌋ = 2

⌊ 2.00000001 ⌋ = 2

⌊ 2.999999999999⌋ = 2

⌊ -2.0000000001⌋ = -3

⌊ -2.999999999999⌋ = -3

let's recall that on the negative side of the number line, the farther from 0, the smaller, so -1,000,000 is a tiny number compared to the much larger -1.

⌊ -5.2 ⌋ = -6.

The notation [[x]] is not standard in typical mathematics; however, it seems that you are looking for a function that represents the floor of x. The floor function, often denoted as ⌊x⌋, is defined as the greatest integer that is less than or equal to x.
To find the floor of -5.2:
1. Identify the integer part of -5.2 without rounding. The integer part is -5 since this is the whole number component of -5.2.
2. Determine if the decimal part (.2 in this case) would cause the number to round up or down. Since the floor function requires us to find the greatest integer less than or equal to the number, we ignore the positive decimal part because it doesn't change the floor for negative numbers.
3. For positive numbers, the floor is the same as stripping away the decimal part without rounding. However, for negative numbers, if the number is not already an integer, the floor is actually one less than the integer part.
4. In the case of -5.2, because the number is negative and not an integer (due to the decimal part), the floor value is -6.
So, f(-5.2) = ⌊-5.2⌋ = -6.

Answer:

Second option:

[tex]d = 15.6\ mm,\ C = 49.01\ mm[/tex]

Step-by-step explanation:

We can observe that the radius of the circle is given. This is:

[tex]r = 7.8\ mm[/tex]

And the missing measures are the diameter of the circle and the circumference.

Since the diameter of a circle is twice the radius, we get that this is:

[tex]d=2r\\\\d=2(7.8\ mm)\\\\d=15.6\ mm[/tex]

To find the circumference of the circle, we can use this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle.

Substituting the radius into the formula, we get:

[tex]C=2\pi r\\\\C=2\pi (7.8\ mm)\\\\C=49.01\ mm[/tex]

Answer:

The cost of each candy bar is $3....

Step-by-step explanation:

Let:

x= $4 (soft drink)

z= price of each candy bar

y=5z(Total price of 5 candy bars)

C= $19(spent money)

The equation is:

C= x+y

$19=$4+5z

Subtract 4 from both sides:

$15=5z

Divide both sides by 5

z=$3

Hence the cost of each candy bar is $3....

Answer:

[tex]18\sqrt{2}[/tex]

Step-by-step explanation:

We need to simplify the following expression: [tex]2\sqrt{18} + 3\sqrt{2} + \sqrt{162}[/tex]

Then:

[tex]6\sqrt{2} + 3\sqrt{2} + 9\sqrt{2}[/tex]

[tex]18\sqrt{2}[/tex]

Therefore, the result is: [tex]18\sqrt{2}[/tex]

Step-by-step explanation:

Triangles can be solved if you know either of three pieces of information:

You can solve for the remaining sides and angles using law of sine and law of cosine.

Law of sine:

(sin A) / a = (sin B) / b = (sin C) / c

Law of cosine:

c² = a² + b² − 2ab cos C

Here, A is the angle opposite side a, B is the angle opposite side b, and C is the angle opposite side c.

Law of cosine can also be written as:

b² = a² + c² − 2ac cos B

a² = b² + c² − 2bc cos A

And law of sine can also be written as:

a / (sin A) = b / (sin B) = c / (sin C)

(Notice that when C = 90°, law of cosine becomes Pythagorean theorem.)

Triangle theorems, like the Pythagorean theorem, are used to establish relationships between the sides of triangles and solve problems. These theorems are used to find unknown sides of triangles when other sides are known. Understanding and applying these theorems can enhance your problem-solving skills in several disciplines.

Theorems about triangles, such as the Pythagorean Theorem, can be used to solve various types of mathematical and real-life problems. The Pythagorean Theorem establishes a relationship between the sides of a right-angled triangle. It states that the square of the hypotenuse (side opposite the right angle, labeled 'c') is equal to the sum of the squares of the other two sides (labeled 'a' and 'b'). This relationship is represented by the equation: a² + b² = c².

To use this theorem in solving problems, usually, two sides of a right triangle are known, and the other side is what we need to find out. For example, if the lengths of a and b are known, then c can be found using the formula c = √a² + b². Similarly, if c and one of the other sides are known, the unknown side can be found by rearranging the Pythagorean theorem equation.

Equipped with the understanding of the Pythagorean theorem and other triangle theorems, you can combine various problem-solving strategies to tackle a vast array of problems. This reasoning skill is useful not only in mathematics but also in science disciplines and in everyday life.

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For this case we must find the domain of the following function:

[tex]f (x) = \frac {x + 2} {x-3}[/tex]

By definition, the domain of a function is given by all the values for which the function is defined. The given function is not defined when the denominator is equal to zero, that is:

[tex]x-3 = 0\\x = 3[/tex]

Thus, the domain of the function is given by all real numbers except 3.

Answer:

x other than 3

Answer:

Her income increase by 27.5% from 2004 to 2007

Step-by-step explanation:

Step 1 : Kieya's income in 2004 was $40,000

Step 2 : Kieya's income in 2007 was $51,000

Step 3 : Calculate difference in $

Income in 2007 - Income in 2004 = Increase (+ve) or decrease (-ve) in income

51000 - 40000 = 11000 increase in income

Step 4 : Calculate difference in terms of percentage

Income of 2007-Income of 2004  x 100

          Income of 2004

51000-40000 x 100

    40000

= 0.275 x 100

= 27.5 %

!!

Option A. 11,000 :)

hope this helps!

Answer:

C. She paid $30 for the table.

Step-by-step explanation:

y = 35x+ 30

This is in slope intercept form

y =mx+b

where m is the slope, which tells us the change

and b is the y intercept, which tells us how much the initial value was (when x=0)

Since x is the number of chairs, and letting x=0

y= 0 chairs +30

Since y= cost of the chairs and the table

y= 30, which is the cost of the table since we bought 0 chairs

Answer:

Statement 1, 2 and 4 are true where as statement 3 is not true.

Step-by-step explanation:

Statement 1: The y-intercept is -1

Point (3/8, 1/2)

Slope = m = 4

y = mx + c

1/2 = 4(3/8) + c

1/2 = 3/2 + c

1/2 = 3/2 + 2c/2

-2 = 2c

c = -1

This statement is true as the y-intercept is -1.

Statement 2: The slope intercept equation is y= 4x - 1

slope = m = 4

y-intercept = c = -1

y = mx + c

y = 4x - 1

This statement is true as the slope intercept equation is y= 4x -1

Statement 3: The point slope equation is y - 3/8 = 4 (x - 1/2)

Point slope equation: y - y1 = m (x - x1)

Points: (x, y) (3/8, 1/2)

y1 = 1/2

x1 = 3/8

Slope = m = 4

y - 1/2 = 4 (x - 3/8)

This statement is not true as the slope intercept equation is y - 1/2 = 4 (x - 3/8) instead of y - 3/8 = 4 (x - 1/2).

Statement 4: The point (3/8, 1/2) corresponds to (x1, y1) in the point slope form of the equation

This statement is true as shown in statement 3's explanation where x1 = 3/8 and y1 = 1/2

!!

Answer:

748 mm^2.

Step-by-step explanation:

We can split it up into 2 congruent triangles whose common base is 44 mm. and who have the same height 17 mm.

Area of a triangle= 1/2 * base * height.

So the area of the whole figure = 2 * 1/2 * 44 * 17.

=  44 *17

= 748 mm^2.

Answer:

It's 78 when you round it to nearest 10

To calculate the mileage, you divide the total miles driven (973.50 miles in this case) by the total gallons used (29.5 gallons in this case). Doing so would give you how far the motorcyclist can travel on a single gallon of gasoline, which is the mileage in miles per gallon.

To calculate the mileage in miles per gallon (mpg) of a motorcyclist, we need to divide the total amount of miles driven by the total amount of gallons used. In this case, the motorcyclist has ridden 973.50 miles and used 29.5 gallons.

So, the formula would be: Mileage = Total Miles / Total Gallons

Applying the values from the question to the formula gives: Mileage = 973.50 miles / 29.5 gallons

This would provide you with your miles per gallon, indicating how far the motorcyclist can travel on a single gallon of gasoline.

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the motorcyclist got an average of 33 miles per gallon on their trip.

To calculate the mileage in miles per gallon for the motorcyclist who rode 973.50 miles using 29.5 gallons of gasoline, you divide the total miles traveled by the gallons of gas used:

Therefore, the motorcyclist got an average of 33 miles per gallon on their trip.

Answer:

280

Step-by-step explanation:

If a square has sides of length 70 meters, the perimeter is 280.

Formula: P=4a

P = 4a = 4·70 = 280

Answer:

17/25

Step-by-step explanation:

First, convert the decimal into a fraction. To do so, move the decimal point to the right two place values and place over 100.

0.68 = 68/100

Next, simplify. Divide common factors. Remember, what you do to one side, you do to the other. Divide 4 from both sides:

(68/100)/4 = (17/25)

17/25 is your answer.

~

0.68 can be expressed as the fraction 17/25 in the lowest terms.

Step 1: Let x be the decimal representation of the fraction.

x = 0.68

Step 2: Since there are two digits after the decimal point, we can multiply both sides of the equation by 100 to eliminate the decimal.

100x = 68

Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 4.

100 ÷ 4 = 25

68 ÷ 4 = 17

The simplified fraction is:

0.68 = 17/25

Therefore, 0.68 can be expressed as the fraction 17/25 in the lowest terms.

More on lowest-term fractions can be found here: https://brainly.com/question/29156749

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