Two shopping carts are pushed with the same force. One cart has a larger mass than the other. How does the mass of the shopping carts affect their acceleration?



The cart with the smaller mass will accelerate faster.


The cart with the larger mass will accelerate faster.


The cart with the smaller mass will not accelerate as fast as that with the larger mass.


Both shopping carts will accelerate at the same rate since they are the same size.

f(x) = mx + b m = slope = -5 f(2) = 10 = (-5)(2) + b b = 10 + 10 = 20 Ans. m=-5, b = 20

The two possible pairs of numbers that fit the given equations are (√7, 2) and (-√7, -2). We find these by setting up two equations based on the provided conditions and solving them simultaneously.

Let's denote the first number as 'x' and the second number as 'y'. We have two equations from the given information:

1. x² - y² = 5

2. 3x² - 2y² = 19

We can solve these equations simultaneously to find the values of 'x' and 'y'. The first step in solving a system of linear equations is to multiply the equations by what's needed to get the coefficients of one of the variables to match, so it can be eliminated when the equations are added or subtracted. Let's multiply the first equation by 3 and the second equation by 1. We then have:

3x² - 3y² = 15

3x² - 2y² = 19

If we subtract the second equation from the first, we get:

-y² = -4

which leads to y = 2 or y = -2 (squared numbers are always positive). Substituting '2' for 'y' in the first original equation, we find that x = √7 or x = -√7. Therefore, the possible pairs of numbers are (√7, 2) and (-√7, -2).

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The result of the division is:

[tex]\[\boxed{4x^2 - 10x + 11 + \frac{6}{2x + 5}}\][/tex]

To find [tex]\( \frac{f(x)}{g(x)} \)[/tex] where [tex]\( f(x) = 8x^3 - 28x + 61 \)[/tex] and [tex]\( g(x) = 2x + 5 \)[/tex], we need to perform polynomial division.

Polynomial Division

1. Divide the leading term of the dividend by the leading term of the divisor:

 [tex]\[ \frac{8x^3}{2x} = 4x^2 \][/tex]

2. Multiply the entire divisor by this result and subtract from the dividend:

[tex]\[ 8x^3 - 28x + 61 - (4x^2 \cdot (2x + 5)) = 8x^3 - 28x + 61 - (8x^3 + 20x^2) \][/tex]

  Simplifying, we get:

[tex]\[ -20x^2 - 28x + 61 \][/tex]

3. Repeat the process with the new polynomial:

 [tex]\[ \frac{-20x^2}{2x} = -10x \][/tex]

4. Multiply the entire divisor by this result and subtract:

[tex]\[ -20x^2 - 28x + 61 - (-10x \cdot (2x + 5)) = -20x^2 - 28x + 61 - (-20x^2 - 50x) \][/tex]

  Simplifying, we get:

[tex]\[ 22x + 61 \][/tex]

5. Repeat the process again:

  [tex]\[ \frac{22x}{2x} = 11 \][/tex]

6. Multiply the entire divisor by this result and subtract:

[tex]\[ 22x + 61 - (11 \cdot (2x + 5)) = 22x + 61 - (22x + 55) \][/tex]

  Simplifying, we get:

 [tex]\[ 6 \][/tex]

Putting it all together, we have:

[tex]\[\frac{f(x)}{g(x)} = 4x^2 - 10x + 11 + \frac{6}{2x+5}\][/tex]

So, the result of the division is:

[tex]\[\boxed{4x^2 - 10x + 11 + \frac{6}{2x + 5}}\][/tex]

Answer: $110

Step-by-step explanation: $110 is the correct approximation. The easiest way is to divide the total by 4, since 25% represents  1 /4 .

The ordered pairs lie on the graph of the exponential function is (3, 16).

The formula f(x) = [tex]a^x[/tex]defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x.

We have,

f(x) = 180 (0.5[tex])^x[/tex]

Now, for x = 0,

So, f(x) = 128(0.5[tex])^0[/tex]

= 128(1)

= 128

Now, for x = 1,

f(x) = 128(0.5[tex])^1[/tex]

= 128(0.5)

= 256

Now, for x = 3,

f(x) = 128(0.5[tex])^3[/tex]

= 128(1/8)

= 16

So, the correct ordered pair is (3, 16).

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Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Amount of Kevin's gross income = $45942

Amount he contribute to his retirement plan = $3435

Amount he lost in business losses = $3393

Amount he incurred in business expenses = $1128

So, His adjusted gross income will be

[tex]45942-(3435+3393+1128)\\\\=45942-(7956)\\\\=\$37986[/tex]

Hence, his adjusted gross income is $37,986.

Hence, Option 'D' is correct.

Answer:

Step-by-step explanation:

Use proportions to figure this out.  On the top you'll have miles and on the bottom you'll have minutes.  I am going to change 3/4 to .75 and 1/8 to .125:

[tex]\frac{miles}{minute}:\frac{.75}{.125}[/tex]

We want to know how many miles per 1 minute that is.  So we have the unknown on top in a new ratio, with 1 on the bottom:

[tex]\frac{miles}{minute}:\frac{.75}{.125}=\frac{x}{1}[/tex]

This second ratio is allowing us to calculate what the decimal ratio is in miles per 1 minute.  Cross multiply to get

.125x = .75 so

x = 6 miles

That tells us that the decimal ratio is equivalent to 6 miles per minute

Final answer:

To find how far Jace walked to school each day, divide the total distance (5/6 of a mile) by the number of days (5), resulting in 1/6 of a mile walked each day.

Explanation:

The question involves calculating the distance Jace walked to school each day if he walked a total of 5/6 of a mile over 5 days. To find out how far he walked each day, we need to divide the total distance by the number of days.

Here's the step-by-step calculation:

Total distance walked: 5/6 of a mile.

Number of days: 5 days.

To find the distance walked each day, divide the total distance by the number of days: (5/6) ÷ 5 = 5/6 ÷ 1/5 = 5/30 = 1/6.

So, Jace walked 1/6 of a mile to school each day.

Answer:

The answer is 48

Step-by-step explanation:

At the time of 0 there are 25 views are exist for a reader board. If the growing rate is %18 than;

[tex]25*1,18=29,5[/tex]

There is no 0,5 view is exist than we need to round up to 30. 30 views for a reader board are exist. Than we need to repeat it for future three weeks.

[tex]30*1,18=35,4[/tex]

Second week its 35

[tex]35*1,18=41,3[/tex]

Third week its 41

[tex]41*1,18=48,38[/tex]

Forth week it goes up to 48 views.

Answer:

27 blue balloons

Step-by-step explanation:

Salina was at a party and she noticed that the room had 54 balloons.

For every red balloon there were 2 yellow and 3 blue balloons.

This is written in the form of ratio as = 1 : 2 : 3

First we calculate the number of red balloon.

54 / (1 + 2 + 3)

= 54 / 6 = 9 red balloons

For every red balloons there were 3 blue balloons.

Therefore, Blue balloons = 9 × 3 = 27 blue balloons

27 blue balloons were in the room.

Talia took approximately 0.8 hours, or 48 minutes, to walk home.

To determine the time it took Talia to walk home, we can solve the equation

40(0.9 – x) = 5x.

First, distribute the 40 to get 36 - 40x = 5x.

Combine like terms to get 36 = 45x.

Divide both sides by 45 to solve for x.

Therefore, Talia took approximately 0.8 hours, or 48 minutes, to walk home.

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To solve the equation 40(0.9 – x) = 5x, distribute 40, combine like terms, and solve for x. Talia took 0.8 hours or 48 minutes to walk home.

The subject of this question is Mathematics and the grade level is High School.

To solve the equation 40(0.9 – x) = 5x, we can start by distributing 40 to the terms inside the parentheses: 36 – 40x = 5x.

Then, we combine like terms by adding 40x to both sides: 36 = 45x.

Finally, we divide both sides by 45 to find that x = 36/45 = 0.8.

Therefore, it took Talia 0.8 hours, or 48 minutes, to walk home.

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To find the width of the track, add up the lengths of all the inside and outside arcs and subtract the total length of the inside arcs from the total length of the outside arcs.

To find the width of the track, we first need to determine the difference between the inside and outside arcs of each piece. Let's assume the outside arc has a length of A inches. According to the question, the inside arc is 3.4 inches shorter than the outside arc. Therefore, the inside arc has a length of A - 3.4 inches.

Since there are ten identical pieces forming the circular track, we can add up the lengths of all the inside arcs and all the outside arcs to find the total distance covered by the track. The width of the track is then the difference between the total length of the outside arcs and the total length of the inside arcs.

Let's express the width of the track as a function of A. The total length of the outside arcs is 10A inches, and the total length of the inside arcs is 10(A - 3.4) inches. Therefore, the width of the track is:

Width = 10A - 10(A - 3.4) inches.

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Answer: [tex]\overline{EF}=\overline{HI}[/tex]

Step-by-step explanation:

Given: In the image, point A is the center of the circle.

Therefore every straight line segments passing from one to another point of circle through the center of circle A is the diameter of the circle.

Since, [tex]\overline{EF}[/tex] and  [tex]\overline{HI}[/tex] are the line segments passing from side to side of circle through the center of circle A is the diameter of the circle, then both are representing diameter of the given circle.

Since, all the diameter of a circle has a unique length .

Hence, the  line segments must be equal in length :

[tex]\overline{EF}=\overline{HI}[/tex]

Answer:

B) it includes points in quadrant ii

The graph of f(x) must include points in quadrants II and IV. Therefore, option B is the correct answer.

A function is such that f(−x) =−f (x) where the sign is reversed but the absolute value remains the same if the sign of the independent variable is reversed.

So,

The points in quadrants II are in IV.

The points in quadrants I are in III.

From the question, we understand that graph includes the points in IV.

This means that these points are also in quadrant II.

Hence, the graph of f(x) must include points in quadrants II and IV.

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In an arithmetic sequence, the common difference is constant. In a geometric sequence, the terms are obtained by multiplying the previous term by a constant ratio. In this case, the value of y in the sequence is 3 for an arithmetic sequence and 9 for a geometric sequence.

In an arithmetic sequence, the difference between consecutive terms is constant. To find the value of y in the sequence 2, 8, 3y + 5, we observe that the common difference is 8 - 2 = 6. Therefore, we can set up the equation 8 - 2 = 3y + 5 - 8 to solve for y. Simplifying, we get 6 = 3y - 3. Solving for y, we have y = 3.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. To find the value of y in the sequence 2, 8, 3y + 5, we need to determine the common ratio. We can see that the ratio between 8 and 2 is 8/2 = 4. Therefore, we can set up the equation 8/2 = (3y + 5)/8 to solve for y. Simplifying, we get 4 = (3y + 5)/8. Multiplying both sides by 8, we have 32 = 3y + 5. Solving for y, we get y = 9.

Final answer:

To find the total height of Stephan's sculpture with the base, we add the heights represented by fractions with a common denominator to get an overall height of 11/12 feet.

Explanation:

To determine the overall height of Stephan's sculpture with the base, we simply need to add the height of the sculpture to the height of the base. The sculpture is 7/12 foot tall and the base is 1/3 foot tall. To add these two fractions together, we need to find a common denominator, which is 12 in this case. So, we convert 1/3 foot into 4/12 foot. Now we can add the two fractions:

7/12 + 4/12 = 11/12 feet

Therefore, the combined height of the sculpture and the base is 11/12 feet.