Jack wants to simplify the expression below.

(6.7x -3) - (3.4x - 1) + (2x - 2)

Answer the following questions.

1) How can Jack regroup the expression by Commutative Property?

2) After regrouping in step 1, how can Jack further simplify the expression by

Distributive Property?

3) What is Jack's final simplified expression?

Answer:

61.2 cm²

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h ([tex]b_{1}[/tex] + [tex]b_{2}[/tex] )

Substitute in given values

A = [tex]\frac{1}{2}[/tex] × 4 × (13.8 + 16.8 ) = 2 × 30.6 = 61.2 cm²

The answer is 61.2cm² .

[tex]((13.8 + 16.8) \times 4) \div 2[/tex]

This equation helps you get the answer.

Final answer:

To find the empty space in the can of tennis balls, calculate the volume of one tennis ball and multiply by three (since there are typically three balls per can), then subtract from the volume of the can. There are 43.54 inches³ of empty space in the can, after rounding to the nearest hundredth.

Explanation:

To calculate the empty space inside the can of tennis balls, we first need to determine the volume of one tennis ball and then the volume of the can. Given the radius of each tennis ball is 1.5 inches, we use the formula for the volume of a sphere:

V_ball = 4/3 π r³

Substitute with r = 1.5 inches and π = 3.14:

V_ball = 4/3 × 3.14 × (1.5 inches)³

V_ball = 4/3 × 3.14 × 3.375 inches³

V_ball = 14.13 inches³ (rounded to the nearest hundredth)

Next, we calculate the volume of the can, using the formula for the volume of a cylinder:

V_can = π r² h

Substitute with r = 1.75 inches and h = 9 inches:

V_can = 3.14 × (1.75 inches)² × 9 inches

V_can = 3.14 × 3.0625 inches² × 9 inches

V_can = 85.93 inches³ (rounded to the nearest hundredth)

The empty space within the can is therefore the volume of the can minus the volume of three tennis balls (assuming the can holds three balls):

Empty space = V_can - 3 × V_ball

Empty space = 85.93 inches³ - 3 × 14.13 inches³

Empty space = 85.93 inches³ - 42.39 inches³

Empty space = 43.54 inches³ (rounded to the nearest hundredth)

Therefore, there are approximately 43.54 inches³ of empty space inside the can.

Answer:

Step-by-step explanation:

The number of ways that you can draw 2 balls without restriction is 10 * 10 = 100

Two balls will give you 2 or less (meaning 1) or 2*2 = 4

Four ways are possible

2  and 2

2 and 1

1 and 2

1 and 1

4/100 = 1/25 is the probability of making this happen.

Answer:

An approximate number is a close number that is only off by x number of places (Like a rounded number). An exact number is exactly correct. For example:

3 - 1.5 is approximately 2, but is exactly 1.5.

Mark Brainliest if this helps!

Final answer:

An exact number is one that is known with complete precision, such as the number of books on a shelf. An approximate number, or inexact number, includes uncertainty and comes with an error range, often due to measuring limitations such as estimating a length with a ruler. The level of rounding applies to approximate values determines their reliability, and significant figures are influenced by inexact numbers.

Explanation:

The difference between an exact number and an approximate number lies in their level of precision and the source of the number. Exact numbers are count numbers that are known with complete precision. An example of an exact number is the number of students in a classroom, which might be exactly 25. On the other hand, inexact numbers, also known as measured numbers, come with an error range due to the limitations of measuring instruments or methods. For instance, when using a ruler, you might measure a length as approximately 12.7 cm, but the true length might be slightly less or more.

It's important to note that the more rounding that is applied to a number, the less reliable it becomes. Approximations are common in various fields, including physics, where scientists and engineers make educated guesses, or 'guesstimates', based on available data and formulae with limited accuracy. These approximations are essential for problem-solving and can help in making quantitative decisions and realistic predictions.

Conversion factors in measurements are considered to be exact numbers because they are defined as such by the measurement systems. In calculations involving both exact and inexact numbers, the precision of the inexact numbers dictates the number of significant figures in the result.

Answer:

C

Step-by-step explanation:

The point slope form of a line is [tex]y - y_1 = m(x-x_1)[/tex]. If the point is (2,5) then the equation will be [tex]y - 5=m(x-2)[/tex]. Only option C matches this equation.

Answer:

6

Step-by-step explanation:

Area of a triangle: bh/2

4*3/2=6

Answer:

6 units²

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = DE = 3 units and

h is the distance from the vertex F to DE = 4 units, hence

A = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 units²

Answer:

the mean high temperature is 71 degrees and the mean low is 31 degrees

Step-by-step explanation:

Answer:

[tex]L=15\ m[/tex]

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

[tex]P=2L+2W[/tex]

In this problem we have

[tex]P=42\ m[/tex]

[tex]W=6\ m[/tex]

substitute in the formula and solve for L

[tex]42=2L+2(6)[/tex]

simplify

[tex]21=L+(6)[/tex]

[tex]L=21-6=15\ m[/tex]

8/32 is the answer to your problem

The equivalent fraction of given fraction is  [tex]\frac{8}{32}[/tex].

Given fraction is,  [tex]\frac{4}{16}[/tex]

It is observed that both numerator and denominator of given fraction is divisible by 4.

Simplest form of  [tex]\frac{4}{16}[/tex] is,

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

Equivalent fraction that has a denominator of 32 is,

                  [tex]\frac{1}{4}=\frac{1*8}{4*8}=\frac{8}{32}[/tex]

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Final answer:

Using the given information, the total travel time by airplane and bus is calculated as 4.47616 hours, which includes flying time and additional travel time by bus.

Explanation:

To calculate the total travel time by airplane including the additional travel time by bus, we must first find out the time taken by the airplane to cover the distance between the two airports. This can be done by dividing the distance by the airplane's average speed. Afterward, we add the bus travel time to get the total travel time.

The time taken by the airplane to cover 1,450 miles at an average speed of 350 mph is calculated by dividing distance by speed: 1,450 miles ÷ 350 mph = 4.142857 hours. Note that we do not round this number to maintain accuracy.

Next, we convert the bus travel time of 20 minutes into hours: 20 minutes ÷ 60 minutes per hour = 0.3333 hours.

Now, we add both the airplane and bus travel times together: 4.142857 hours + 0.3333 hours = 4.47616 hours total travel time.

I hope the answer is 7/4

Hey there!

The first thing we can do is find the number of third in 4.

We can do this by multiplying 4 by 3 since there are 3 thirds in a whole.

4 x 3 = 12

So, 4 = 12/3

If she studies for 2/3 an hour each night, then we can divide 12 by 2 to figure out how many 2/3 go into 12/3.

12 ÷ 2 = 6

So, she studied for 6 days.

Hope this helps!

Answer:

its either c or b

Step-by-step explanation:

formula: 1/2*b*h or 1/2*5*3+3/4

the answer i got was 33/4

Answer:

1.7 seconds, and

3.3 seconds

Step-by-step explanation:

We simply need to plug in 8 into h and solve for t:

[tex]h=-15Cos(\frac{2\pi}{5}t)\\8=-15Cos(\frac{2\pi}{5}t)\\-\frac{8}{15}=Cos(\frac{2\pi}{5}t)\\\frac{2\pi}{5}t=Cos^{-1}(-\frac{8}{15})\\\frac{2\pi}{5}t=2.13\\t=\frac{2.13}{\frac{2\pi}{5}}\\t=1.70[/tex]

Since cosine is negative in the 3rd quadrant as well, we need to figure out the 3rd quadrant equivalent of 2.13 radians.

First, π - 2.13 radians = 1.01 radians.

Then, we add 1.01 to π radians, so we get 4.15 radians

Solving from the last part, we have:

[tex]t=\frac{4.15}{\frac{2\pi}{5}}\\t=3.3[/tex]

also, t = 3.30 seconds

*Note: we put the calculator mode in radians when solving

So, t = 1.7 seconds & 3.30 seconds

Answer:

The graph for the following system of inequalities is attached below.

Step-by-step explanation:

The given system of inequalities is

[tex]x+y>3[/tex]                    .... (1)

[tex]x+y<-4[/tex]                  .... (2)

From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.

The related equation of first inequality is

[tex]x+y=3[/tex]

Put x=0 to find the y-intercept.

[tex]0+y=3\Rightarrow y=3[/tex]

The y-intercept is 3.

Put y=0 to find the x-intercept.

[tex]x+0=3\Rightarrow x=3[/tex]

The x-intercept is 3.

The related equation of second inequality is

[tex]x+y=-4[/tex]

Put x=0 to find the y-intercept.

[tex]0+y=-4\Rightarrow y=-4[/tex]

The y-intercept is -4.

Put y=0 to find the x-intercept.

[tex]x+0=-4\Rightarrow x=-4[/tex]

The x-intercept is -4.

The related lines are dotted line because the sign of inequalities are > and <.

Check each inequality be (0,0).

[tex]0+0>3[/tex]

[tex]0>3[/tex]

This statement is false. So the shaded region of first inequality is opposite sides of the origin.

[tex]0+0<-4[/tex]  

[tex]0<-4[/tex]  

This statement is false. So the shaded region of first inequality is opposite sides of the origin.

The graph for the following system of inequalities is attached below.

Answer:

This is the correct graph on Odyssey :)

Answer:

Hiro factored them correctly.

Step-by-step explanation:

The factors of 14 are 1, 2, 7, and 14.

7 * 2 = 14

10 and 4 make the product of 14.

10 + 4 = 14

Bilial factored 14y3 correctly.

Hiro factored 14y2 as (7y2)(2y)
Bilial factored 14y3 as (10y)(4y2)

To determine which one factored 14y3 correctly, we need to compare their factorizations to the original expression: 14y3. Hiro's factorization (7y2)(2y) does not match the original expression, as it is missing a y term. On the other hand, Bilial's factorization (10y)(4y2) matches the original expression.

Therefore, "Bilial factored 14y3 correctly."

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Answer:

Range: all real numbers greater than or equal to  2

Step-by-step explanation:

The range is the possible numbers that the output can take

Y can be any number greater than or equal to 2

Range: all real numbers greater than or equal to  2

Solve for x by simplifying both sides of the equation, then isolating the variable.

So the answer to your question is :

x = 16.

Hope this helps,

Davinia.

Answer:

x = 16

Step-by-step explanation:

distribute parenthesis on both sides and simplify

3x - 12 - 7 = 2x - 3

3x - 19 = 2x - 3 ( subtract 2x from both sides )

x - 19 = - 3 ( add 19 to both sides )

x = 16

Answer:6

Step-by-step explanation:

500/12 is 41 so therefore you do 48/12 is 6.

Answer:

1 19/125

Step-by-step explanation:

1.) 12/500 = 0.024

2.) 0.024 * 48 = 1.152

3.) 1.152 converted to a fraction is 144/125, or 1 19/125

answer X= 5 over 7 and 2 over 7y step by step explaination add 2y on both sides u cancelled -2y and positive 2y u bring down 7X u get 7X=-5+3 then u divide and u get that answer yw have a nice day mark me brainliest

Answer:

2y=-x7

Love mORgan

Step-by-step explanation:

Do you mean:

(6^5/7^3)^2?

If so, you will get

6^10/7^6 or about 513.954016

It is to be note that  (6⁵ / 7³)² simplifies to become approximately 514.64

To simplify the expression (6⁵ / 7³)², we start by evaluating the exponents first.

6⁵ means 6 raised to the power of 5, which is 6 * 6 * 6 * 6 * 6 = 7776.

7³ means 7 raised to the power of 3, which is 7 * 7 * 7 = 343.

Now, we substitute these values back into the expression  -

(7776 / 343)² = (22.6666666667)² = 514.64197531

Therefore, it is right to state that (6⁵ / 7³)² simplifies to 514.64197531 which is approximately, 514.64.

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if you're solving for x,

start by isolating x squared to get

x^2 = 16 (we added 8 to both sides)

then square root each side:

sqrt of x^2 = x; sqrt of 16 = 4.

we end up with x = 4 (positive and neg)

if you're factoring

minus 8 from both sides to get

x^2 - 16

from there we can factor to get

(x + 4)(x - 4)

Answer:

x = 149

Step-by-step explanation:

Lines m and n are parallel lines as shown by the double arrows on each line.

The angles marked x and 149 deg are corresponding angles of parallel lines cut by a transversal.

Postulate:

If parallel lines are cut by a transversal, then corresponding angles are congruent.

According to the postulate above, since the angles marked 149 and x are corresponding angles, they are congruent.

x = 149

Answer:

X=149

Step-by-step explanation:

Lines m and n are parallel. You know this because the 2 marks on both lines mean that they are the same and parallel.

Answer:

x=5

Step-by-step explanation:

-6+5=-1

start at -6 then go right units until u get -1 you got right 5 units

The value of x in the given equation is:

                              x=5

We are given a algebraic expression in terms of the variable x by:

             [tex]-6+x=-1[/tex]

Now, we are asked to find the value of x from the equation.

i.e. we have to solve for x.

i.e. by some appropriate algebraic operation we need to solve for x.

so we will add 6 on both the sides of the equation to get:

[tex]-6+x+6=-1+6\\\\i.e.\\\\-6+6+x=5\\\\i.e.\\\\0+x=5\\\\i.e.\\\\x=5[/tex]

           Hence, the value of x is: 5

Divide 4 by 25 either by hand or by calculator. Hope this helped.

Answer: [tex]\frac{4}{25}[/tex]=0.16

Step-by-step explanation:

How convert 4/25 into a decimal is :

* Hopefully this helps:)!! Mark me the brainliest:)!!!

Answer:

It is 2 1/2

Step-by-step explanation:

Move z and 24, switch signs then add numbers

Answer:

z=34

Step-by-step explanation:

Here is:

2+8-z=-24

2+8+24=z

z=34

Best regards

Answer:

Choice A

Step-by-step explanation:

We apply the law of exponents;

[tex](a^{b})^{c}=a^{bc}[/tex]

[tex]\sqrt{0.08^{12}}=(0.08^{12})^{\frac{1}{2}}[/tex]

applying the law of exponents we simply multiply 12 and 1/2 to get;

[tex]0.08^{6}[/tex]

The actual length of a lap cannot be determined without the scale of the map. The 25 cm measurement seems to be from the map, so without knowing the real-world equivalent of the map's measurements, we can't find the actual distance.

The length of a lap around the reservoir cannot be directly determined from the information given. The measurement provided (25 cm) appears to be a distance measured on a map or plan of the area, and not in real life. In order to convert that measurement into a real-world distance, we need the scale of the map. A map's scale is typically represented as a ratio that indicates the relationship between a certain distance on the map and the real-world distance it represents.

For example, if the map's scale was 1 cm : 1 km, then a measurement of 25 cm on the map would represent a real-world distance of 25 km. However, without the scale, we cannot accurately determine the actual length of a lap around the reservoir. This concept is extremely important in geography and cartography as well as in mathematical problems dealing with maps and scales.

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