7.1 7.2 homework help

Answer:

3/8 gallons left

Step-by-step explanation:

she has 0.75 of a gallon

she eats 0.5(0.75) while watching TV

multiply 0.5 by 0.75 to get half of 3/4 of a gallon

0.375 of a gallon is what she has left

or 3/8 of a gallon

Answer:

The hula hoop rolls 879 \text{ cm}879 cm.

Step-by-step explanation:

Statement 1: AM is the midpoint of AB

Reason 1: Given

=====================================

Statement 2: AM+MB = AB

Reason 2: Segment Addition Postulate

Further explanation: Basically this idea is where you can break up the line segment into smaller pieces, or glue smaller segments to form a larger segment.

=====================================

Statement 3: AM = MB

Reason 3: Definition of midpoint

Further explanation: The midpoint cuts a line segment in half. The two smaller pieces AM and MB are congruent (ie equal in length)

=====================================

Statement 4: AM + AM = AB

Reason 4: Substitution

Further explanation: We replace the MB in statement 2 with AM. This replacement is possible because of the equation AM = MB in statement 3.

This concludes the proof.

Answer:

line (3)

Step-by-step explanation:

note that [tex]\frac{x}{4}[/tex] + 3 - 3 = - 12 - 3

should then be [tex]\frac{x}{4}[/tex] = - 14 Not - 9

first error occurs in line (3)

Answer:

b

Step-by-step explanation:

add 3 and 8 = 11

Answer:

The answer is A

Hoped it helped <3 tell me if I am wrong

Step-by-step explanation:

Answer:

the awnser is c

Step-by-step explanation:

the c

Answer:

Its C

Step-by-step explanation:

I got a 100% on the test

Answer:

Length of rectangle ≥ 2 yd.

Step-by-step explanation:

Suppose the length of rectangle = X yd.

Given the width of rectangle = 2 yd.

Area ≥ 4 yd²

Length * width ≥ 4 yd²

2X ≥ 4 yd²

X ≥ 2 yd

So, length of rectangle must be at least 2 yd.

****************************************************************************************

Answer:

length = 1 feet and width = 3 feet.

Step-by-step explanation:

Suppose the width of rectangle = X feet.

then length of rectangle = (2X - 5) feet.

Given the perimeter of rectangle = 8 feet.

The formula is Perimeter = 2 * (length + width)

8 = 2 * (2X - 5 + X)

8 = 2 * (3X - 5)

8 = 6X - 10

6X = 8 + 10 = 18

X = 18/6 = 3.

so 2X - 5 = 2(3) - 5 = 6 - 5 = 1.

Hence, length = 1 feet and width = 3 feet.

Answer:

Service a charges $30 per mow plus an additional $20 flat fee each month, however, Service b only charges $30 per mow, so Service b would be cheaper.

Step-by-step explanation:

This question is asking you to compare costs using linear equations.  In a linear equation, 'x' represents the independent variable, in this case the number of times the yard is mowed, and 'y' represents the dependent variable, or the monthly cost.  30 is the slope, or rate of change, which in this problem is the cost per time the yard is mowed.  In the equation for Service a, we can see that it is a charge of $30 per time, however, there is also an additional fee of $20 - which is our y-intercept.  However, Service b has two points (0,0) and (5,150).  Using these two points, we can find the slope, or rate, by subtracting the 'y' values over the 'x' values, or (150-0)/(5-0), to get 30.  Since Service b has the starting point of (0,0), or cost is $0 when there are 0 lawns mowed, then they do not have a flat fee.  

Answer:

b = sqrt(11)

Step-by-step explanation:

Using the Pythagorean theorem

a^2 + b^2 = c^2

and substituting what we know

5^2 + b^2= 6^2

25 + b^2 = 36

Subtract 25 from each side

25-25 + b^2 = 36-25

b^2 = 11

Take the square root of each side.

sqrt(b^2) = sqrt(11)

b = sqrt(11)

We only take the positive because length must be positive.

Use the Pythagorean theorem

[tex]a^2+b^2=c^2[/tex]

a,b - legs

c - hypotenuse

We have c = 6 and a = 5. Substitute:

[tex]5^2+b^2=6^2[/tex]

[tex]25+b^2=36[/tex]     subtract 25 from both sides

[tex]b^2=11\to \boxed{b=\sqrt{11}}[/tex]

Answer:

91 boxes

hope it helps

Step-by-step explanation:

you will divide $500.00 by $5.50 to find you how many cookies need to be sold

500 ÷ 5.50 = 90.9

so they need to sell about 91 boxes in order meet their goal

To check your work you can multiply

5.50 x 91 = $500.50

Using the divison operation, the number of cookies that must be sold in other to meet their target is 91

The Number of cookies that must be sold to meet their target can be obtained using the divison operation thus :

Hence,

Number of cookies to be sold = $500 ÷ 5.50 = 90.90 = 91(nearest whole number)

Therefore, the Number of cookies that must be sold to meet their target is 91.

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Answer:

h=4=30

c=2=60

Hope that help

Answer:

a ) 400 percent

b )  n = 25

c)  n= 36

Step-by-step explanation:

Is means equals, of means multiply and percents need to be changed to decimals.

a) 120 is what percentage of 30

120 = P * 30

Divide each side by 30

120/30 =P* 30/30

4 = P

Multiply by 100 to give the percentage

4 * 100

400 percent

b) 30 is 120% of what number

30 = 1.2 * n

Divide each side by 1.2

30/1.2 = 1.2n/1.2

25  = n

c) what number is 30%of 120

n = .3 * 120

n =36

Answer:

52+38

Step-by-step explanation:

An even number plus another even number results in an even sum. Examples such as 44 + 46 equaling 90 show this arithmetic principle.

The question pertains to the addition of two even numbers that equal 90. An even number is any integer that can be exactly divided by 2, which means its last digit will be 0, 2, 4, 6, or 8. When adding two even numbers, the result is always an even number.

For instance, if we consider the numbers 44 and 46, both are even:

This is just one example of even numbers adding up to 90. There are multiple pairs of even numbers that can sum up to 90, demonstrating the fundamental arithmetic principle that the sum of two even numbers is always even.

Answer:

Option c is correct option

it  will be about 5.6 weeks until 50 percent of the campus is watching the show

Step-by-step explanation:

we are given

w(x)=[tex]x+125^{\frac{1}{3} }[/tex]

w(50)=[tex]50+125^{\frac{1}{3} }[/tex]

w(50)=[tex]175^{\frac{1}{3} }[/tex]

w(50)=[tex]\sqrt[3]{175}[/tex]

w(50)=5.59

we have to convert it  into one decimal form

5.59=5.6

hence option c is correct option.

Computing w(50) using the provided function yields a value of approximately 5.6, which means it will take about 5.6 weeks for 50 percent of the campus to start watching the student-produced reality show. Thus, the correct answer to the student's question is option (C).

To compute w(50) based on the given function [tex]w(x)=(x+125)^{(1/3)}[/tex], we substitute x with 50:

[tex]w(50) = (50+125)^{(1/3)}[/tex]

Calculate the value inside the parenthesis:

[tex]175^{(1/3)}[/tex]

Taking the cube root of 175 gives us approximately:

5.6

Thus, w(50) ≈ 5.6, and we can interpret this in context by stating:

It will be about 5.6 weeks until 50 percent of the campus is watching the show.

This means the correct answer from the provided options is C. It takes approximately 5.6 weeks for the reality television show produced by the students to reach a viewership of 50 percent of the campus.

Answer:

The total area of the two triangles is 100 inches²

Step-by-step explanation:

To solve for the area of a triangle we use the formula [tex]\frac{1}{2} bh[/tex]

(or base*height divided by 2)

First I solved for the area of the blue triangle.

The base is 12 inches and the height is 10 inches.

[tex]\frac{1}{2}[/tex] * 12 * 10 equals 60 inches².

For the orange triangle the base is 8 inches and the height is 10 inches.

[tex]\frac{1}{2}[/tex] * 8 * 10 equals 40 inches².

60in² + 40in² = 100in²

Answer:

Let t represents for ticket and l represents for lunch.

As per the given statement: Dan bought 3 ticket refills and a lunch for $10.35

then, we have

[tex]3t + l = \$10.35[/tex]

Also, it is given that Bob bought 2 ticket refills and the lunch for $8.35.

⇒[tex]2t + l = \$8.35[/tex]

(a)

System of an equations are:

[tex]3t + l = \$10.35[/tex]

[tex]2t + l = \$8.35[/tex]

(b)

Let x-coordinate represents ticket refills and y-coordinates represents lunch

You can see the graph of the given equation as shown below in the attachment.

(c)

To find the cost of each items;

Using graph to estimate the cost of each items;

then;

Cost of ticket refills(t) = $2

and

Cost of lunch(l) = $4.35

Answer:

Step-by-step explanation:

Answer:

(x, y ) = (5, 4 )

Step-by-step explanation:

given the 2 equations

3x - 2y = 7 → (1)

- 3x + 5y = 5 → (2)

adding the 2 equations term by term will eliminate x

(3x - 3x) + (- 2y + 5y ) = (7 + 5 )

0 + 3y = 12

3y = 12 ( divide both sides by 3 )

y = 4

substitute y = 4 in either of the 2 equations and solve for x

(1 ) : 3x - 8 = 7 ( add 8 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

solution is (5 , 4 )

Answer:

Formula:

The general formula for the surface area (SA) of a prism is:

SA = 2B + Ph

Step-by-step explanation:

where:

B is the area of one base (since there are two identical bases, we multiply by 2).

P is the perimeter of the base (the total length of all sides of the base polygon).

h is the height of the prism (the distance between the two bases).

Steps to Find the Surface Area:

Identify the base shape and calculate its area:

Depending on the type of prism (triangular, rectangular, etc.), use the appropriate formula to find the area of one base.

Find the perimeter of the base:

Add up the lengths of all the sides of the base polygon.

Calculate the lateral surface area:

Multiply the perimeter of the base (P) by the height of the prism (h). This gives you the total area of all the lateral faces.

Sum the areas:

Add the area of two bases (2B) you calculated in step 1 and the lateral surface area from step 3. This will be the total surface area of the prism.

Tips:

Make sure you identify the correct height of the prism. It's the perpendicular distance between the two bases, not the length of a slanted lateral face.

If the lateral faces are not all the same shape (e.g., a truncated prism), you might need to calculate the area of each lateral face separately and add them all up.

By following these steps and using the formula, you can find the surface area of any prism!

Answer:

D YEET

Step-by-step explanation:

Answer:

Its C. 25

Step-by-step explanation:

I just divided 100 by 4

4x = 100      divide both sides by 4

x = 25 → c.

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

5x = 25     divide both sides by 5

x = 5 → c.

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

3x + 5 = 17       subtract 5 from both sides

3x = 12      divide both sides by 3

x = 4 → a.

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

3x + 14 = 11      subtract 14 from both sides

3x = -3     divide both sides by 3

x = -1 → b.

Answer:

Multiply the output value by 2 for  each input value increases by 1

Step-by-step explanation:

Function f is an exponential function

Since it is an exponential function , we find out common ratio of output first

WE divide second term by first term to get common ratio

[tex]\frac{\frac{1}{16}}{\frac{1}{64}}[/tex]

[tex]\frac{1}{16} * \frac{64}{1}= 4[/tex]

Change in output = 4

Now we find change in input

Input increases by 2 so change in input = 2

Factor that increase the output is  [tex]\frac{4}{2} = 2[/tex]

Answer:

Step-by-step explanation:

The given table represents an exponential function, that means that variables show a sequence which have an increasing factor that we can find by division.

If we divide the second values by the first value, we could find the factor of the exponential function.

[tex]\frac{1}{16}\div \frac{1}{64} =\frac{1}{16} \times \frac{64}{1}=4[/tex]

So, [tex]f(x)[/tex] increases by a factor of 2.

Now, using the table we see that [tex]x[/tex] values increases by a difference of [tex]+2[/tex], not a factor.

At the moment, while the input value increases by 2, the output value increases by 4.

This means that if the input value increases by 1, the output value increases by 2.

Therefore, the answer is 2.

Answers:

Gabe needs 30 liters of the 50% solution

Gabe needs 30 liters of the 70% solution

Both answers are 30

==================================

Explanation:

We have two beakers, each of which we don't know how much is inside. Let's call this x and y

x = amount of liquid in the first beaker (water+acid)

y = amount of liquid in the second beaker (water+acid)

We're told that the beakers have a 50% solution and a 70% solution of acid. This means that the first beaker has 0.5*x liters of pure acid, and the second beaker has 0.7*y liters of pure acid. In total, there is 0.5x+0.7y liters of pure acid when we combine the two beakers. This is out of x+y = 60 liters total, which we can solve for y to get y = 60-x. We will use y = 60-x later on when it comes to the substitution step

We can divide the total amount of pure acid (0.5x+0.7y liters) over the total amount of solution (x+y = 60) to get the following

(0.5x+0.7y)/(x+y) = (0.5x+0.7y)/60

We want this to be equal to 0.6 because Gabe wants a 60% solution when everything is said and done, so

(0.5x+0.7y)/60 = 0.60

0.5x+0.7y = 0.60*60 .... multiply both sides by 60

0.5x+0.7y = 36

0.5x+0.7( y ) = 36

0.5x+0.7(60-x) = 36 ........ replace y with 60-x (substitution step)

0.5x+0.7(60)+0.7(-x) = 36 .... distribute

0.5x+42-0.7x = 36

-0.2x+42 = 36

-0.2x = 36-42 .... subtract 42 from both sides

-0.2x = -6

x = -6/(-0.2) .... divide both sides by -0.2

x = 30

He needs 30 liters of the 50% solution

Use this x value to find y

y = 60-x

y = 60-30

y = 30

So he needs 30 liters of the 70% solution

3c(c+3)-4(c+3)=3c^2+9c-4c-12=3c^2+5c-12

The expression in complete factored form is (3c - 4)(c + 3)

A complete factored form is a form of expressing a complex polynomial expression as the products of factors of the polynomial. If we equate the complete factored expression with zero, we get the solutions of the polynomial expression.

The expression given is [tex]3c(c + 3) - 4(c + 3)[/tex]

Expanding the given expression  [tex]3c^{2} + 9c - 4c - 12[/tex]

= [tex]3c^{2} + 5c - 12[/tex]

= [tex]3c^{2} + 9c - 4c - 12[/tex]

= [tex]3c(c + 3) - 4(c + 3)[/tex]

= [tex](3c - 4)(c + 3)[/tex]

Thus the expression in complete factored form is (3c - 4)(c + 3)

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Answer:

Point slope form of the line is  [tex]y-10=2(x-3)[/tex]

Step-by-step explanation:

The point-slope form of a line is given as:

[tex]y-y_1=m(x-x_1)[/tex]

Where,

The question tells us the slope is 2, hence [tex]m=2[/tex] and the point given is (3,10) which means [tex]x_1=3[/tex] and [tex]y_1=10[/tex]. Substituting these values into the point slope form of a line gives us:

[tex]y-(10)=2(x-(3))\\y-10=2(x-3)[/tex]

Hence, point slope form of the line is  [tex]y-10=2(x-3)[/tex]

Answer: 15.065 grams

Step-by-step explanation:

Given: Jose and Alexia needed to weigh three samples of rock to the nearest thousandth.The weight of the first sample = 3.346 grams

The weight of the second sample = 2.479 grams

The weight of the third sample = 9.240 grams

Add all together such that the total weight=[tex]3.346+2.479+9.240[/tex]

⇒The total weight of the samples = 15.065 grams.

Therefore, the samples weigh 15.065 grams altogether.

Answer:

1:26.25

Step-by-step explanation:

Scale = 16 in:35 ft

Convert 35 ft to inches

1 ft = 12 in

35 × 12/1 = 420 in

Scale = 16 in:420 in     Divide each term by 16

Scale =      1:26.25

The scale used to create the blueprint for Mr. Willis's dock is 1:26.25, meaning that each inch on the blueprint represents 26.25 inches of the actual dock.

The actual dock is 35 feet long, and there are 12 inches in a foot, so the dock is 35 feet × 12 inches/foot = 420 inches long. The blueprint shows the dock as 16 inches long. Therefore, we use the scale factor formula:

scale factor = blueprint length / actual length

The scale factor is 16 inches / 420 inches, which simplifies to 1/26.25. Thus, the blueprint is drawn at a scale of 1:26.25, meaning that 1 inch on the blueprint represents 26.25 inches in the actual size.

Answer:

8/9 of a song per minute

Step-by-step explanation:

We want to find the rate, which is songs per minutes

songs/ minute

2/3 /  3/4

We can use copy dot flip

2/3 * 4/3

8/9  songs per minute

Answer:

I is the √-1 so it would be √-2 as your answer

Step-by-step explanation:

If the value of i = [tex]\sqrt{1}[/tex] then value of i² = 1.

When we raise numbers to powers they  are either called surds when we raise powers which are greater than zero but less than 1 in fraction from.

We call indices when we raise powers to which are greater than 1.

Indices make the base larger after simplification and surds make the bases smaller after simplification.

According to the given question i = [tex]\sqrt{1}[/tex].

∴ The value of i² is i×i = [tex]\sqrt{1}[/tex] × [tex]\sqrt{1}[/tex] = [tex]1^\frac{1}{2}[/tex] × [tex]1^\frac{1}{2}[/tex] = [tex]1^[\frac{1}{2}+\frac{1}{2}][/tex] = 1¹ = 1.

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