A gardener uses a wheelbarrow to move soil from a truck to his garden. On the first trip from the truck to the garden, the wheelbarrow
is half-full of soil and the gardener applies a certain force to cause it to accelerate. On the second trip, the wheelbarrow is full of soil.
Although the gardener applies the same amount of force to the wheelbarrow, he cannot move it with the same rate of acceleration.
What should the gardener do to move the wheelbarrow at the same rate of acceleration for the second trip?
A. reduce the amount of soil by one-half and apply the same amount of force
B. keep the amount of soil the same and apply less force
C. reduce the amount of soil by one-quarter and apply the same amount of force
D. double the amount of soil, and apply less force
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Final answer:

The statement establishes the condition for obtaining a driver's license which is passing a road test. Since Tamara passed her test, according to the given logic, she will receive her driver's license. The subject matter is related to Law.

Explanation:

The question provided is related to the process of acquiring a driver's license and is rooted in understanding conditional statements, which are often associated with the field of logic, a branch of philosophy. However, the most practical context here is Law, as it involves legal criteria for obtaining a driver's license. The logic presented in the statement is straightforward: If you pass a road test, you will get your driver's license. Tamara passed her road test. Based on this information, we can deduce that Tamara will get her driver's license because she has fulfilled the condition set by the law or the driving authority responsible for issuing licenses.

Answer:

1/72

Step-by-step explanation:

Answer:

The answer is 4. as 2 plus 2 is equal to 4

Step-by-step explanation:

2+2=4

Answer:

the correct answer is B

"yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square."

Step-by-step explanation:

took the test, got it right. nice day folks. amos @kay_flores575

Right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.

" Area is the space occupied by any two dimensional  object on the flat surface."

"Right angled triangle is a two dimensional figure with three sides and three vertices . Any one of the interior angle should be equals to 90°."

Formula applied

Pythagoras theorem

a² = b² +c²

According to the question,,

Three square with areas 64inches , 225 inches and 289 inches.

We can write this areas as

  289 = 225 + 64

⇒(17)² = (15)² + (8)²

Applying formula we can say that a right triangle can be formed.

Hence, we conclude that Option B is correct.

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The inequality which represents the greatest amount of money, f, Maria can spend on food and drinks is f < 8.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Maria has 15 dollars that she can spend at the movies.

Total amount Maria has = $15

Cost of a movie ticket = $7

Let f be the amount that she can spend maximum on food and drinks.

f < remaining amount

f < 15 - 7

f < 8

Hence the inequality is f < 8.

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The digits of the number are 7 and 3

Step-by-step explanation:

In a two-digit number:

We need to find the digits

Assume that the unit digit is x and the ten digit is y

∵ x represents the unit digit

∵ y represents the ten digit

∵ The ten digit is four less than the unit digit

- That means subtract 4 from the unit digit to get the ten digit

∴ y = x - 4 ⇒ (1)

∵ Seven times the tens digit plus five times the units digit is

   equal to 56

- That means multiply the ten digit by 7 and the unit digit by

   5 and add the two products and equate the sum by 56

∴ 7y + 5x = 56 ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (2) by equation (1)

∵ 7(x - 4) + 5x = 56

- Simplify the left hand side

∴ 7x - 28 + 5x = 56

- Add the like terms in the left hand side

∴ 12x - 28 = 56

- Add 28 to both sides

∴ 12x = 84

- Divide both sides by 12

∴ x = 7

- Substitute the value of x in equation (1) to find y

∵ y = 7 - 4

∴ y = 3

∴ The number is 37

The digits of the number are 7 and 3

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Answer:250

Step-by-step explanation: Subtract 90 from 75 which is 15 then divide 15 by .06 which is 250

Answer:a

Step-by-step explanation:

a

Answer:

18.84 feet farther is it around the outer edge of the path than around the inner edge.

Step-by-step explanation:

Given:

A circular path 3 feet wide has an inner diameter of 350 feet.

Use 3.14 for π.

Now, to find how much farther is it around the outer edge of the path than around the inner edge.

Width of the circular path = 3 feet.

Inner diameter of circular path = 350 feet.

So, to get the inner radius we divide the inner diameter of circular path by width of circular path:

[tex]350\div 3[/tex]

[tex]=116.67\ feet.[/tex]

r = 116.67 feet.

Now,

Thus, the outer radius is:

[tex]116.67+3[/tex]

[tex]=119.67\ feet.[/tex]

R = 119.67 feet.

Now, we get the circumference of inner edge and outer edge:

Circumference of inner edge = 2πr.

[tex]Circumference\ of\ inner\ edge=2\times 3.14\times 116.67[/tex]

                                                 [tex]=732.69\ feet.[/tex]

Circumference of outer edge = 2πR.

[tex]Circumference\ of\ outer\ edge=2\times 3.14\times 119.67[/tex]

[tex]Circumference\ of\ outer\ edge=751.53\ feet.[/tex]

Now, to get how much farther is it around the outer edge of the path than around the inner edge:

Circumference of outer edge - circumference of inner edge.

[tex]751.53-732.69[/tex]

[tex]=18.84\ feet.[/tex]

Therefore, 18.84 feet farther is it around the outer edge of the path than around the inner edge.

The difference in distance around the outer edge of the path compared to the inner edge is 18.84 feet.

To find how much farther it is around the outer edge of the circular path compared to the inner edge, we need to calculate the circumferences of both the inner and outer edges and find the difference.

1.  First, calculate the inner circumference using the inner diameter of 350 feet:

Inner Circumference = π × inner diameter = 3.14 × 350 = 1099 feet.

2. Next, calculate the outer diameter by adding the width of the path to each side of the inner diameter:

Outer Diameter = inner diameter + 2 × width of the path = 350 + 2 × 3 = 356 feet.

3. Then, calculate the outer circumference using the outer diameter:

Outer Circumference = π × outer diameter = 3.14 × 356 = 1117.84 feet.

4. Finally, find the difference between the outer and inner circumferences:

Difference = Outer Circumference - Inner Circumference = 1117.84 - 1099 = 18.84 feet.

Therefore, it is 18.84 feet farther around the outer edge of the path than around the inner edge.

The cost of 2 erasers will be - $1.2

We have pencils and erasers.

We have to determine the cost of 2 erasers.

The equation modelling is a method of forming

According to the question -

Assume that the cost of a single pencil is x and that of eraser is y. Then -

5x + 4y = 7.65   ---[1]

and

4x + 5y = 7.20   ---- [2]

4x = 7.20 - 5y

Consider Equation - [1] :

5x + 4y = 7.65

4x + x + 4y = 7.65

7.20 - 5y + x + 4y = 7.65

x - y = 0.45

x = 0.45 + y    ----- [3]

Substituting x from equation 3 in [1] -

5[0.45 + y] + 4y = 7.65

2.25 + 5y + 4y = 7.65

9y = 5.4

y = 0.6

Therefore -

x = 0.45 + 0.6 = 1.05

Therefore, the cost of 2 erasers will be -  2 x 0.6 = $1.2

Hence, the cost of 2 erasers will be - $1.2

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Answer:

D. 100°

Step-by-step explanation:

m<MLN = m<MON/2

50°= m<MON/2

50×2 = m<MON

m<MON=100°

180 degrees is half of a circle, and clockwise means turning in the direction a clock does - right.

So a point would be turned right halfway around.

Answer:

x = 4

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex](x - 7) = - 2

Multiply both sides by 3 to clear the fraction

2(x - 7) = - 6 ← distribute left side

2x - 14 = - 6 ( add 14 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

Step-by-step explanation:

2/3(x - 7) = -2....distribute the 2/3 thru the parenthesis

2/3x - 14/3 = -2 ....if u want to get rid of the fractions, multiply by the common denominator of 3, and u get :

2x - 14 = -6 ....add 14 to both sides

2x = -6 + 14

2x = 8 ....divide by 2

x = 8/2....reduce

x = 4 <=====

check it..

2/3(x - 7) = -2

2/3(4 - 7) = -2

2/3 (-3) = -2

-6/3 = -2

-2 = -2 (correct)....it checks out :)

Answer: length = 11cm , width = 5cm

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle is given by :

P = 2 ( L + w )

The length is 1 cm more than twice the width implies:

L = 1 + 2w

substituting into the formula , we have

32 = 2 ( 1 + 2w + w )

32 = 2 ( 1 + 3w)

32 = 2 + 6w

32 - 2 = 6w

30 = 6w

Therefore :

w = 5

then

L = 1 + 2w

L = 1 + 2 ( 5 )

L = 1 + 10

L = 11

Therefore , the length is 11 cm and the width is 5cm

Answer:

Step-by-step explanation:

c/9≤-4

multiply both sides of the inequality by 9(c/9×9≤4×9) to isolate the 9 being divided by c(inverse operation):

c≤-36

that is the inequality.

to graph it, draw a number line with a closed circle on -36. then, draw an arrow on the line going toward the negative numbers, or the left side to demonstrate that c is less than or equal to -36.

The solution to the inequality is C ≤ -36, and the graph shows all values to the left of -36 on a number line.

To solve the inequality "C divided by 9 is less than or equal to -4," you can follow these steps:

- Start with the inequality: C/9 ≤ -4.

- To isolate C, you can multiply both sides of the inequality by 9 (since dividing by 9 is the opposite of multiplying by 9). Be sure to do the same operation to both sides to maintain the inequality's balance.

C/9 * 9 ≤ -4 * 9

This simplifies to:

C ≤ -36

So, the solution to the inequality is C ≤ -36.

To graph this solution on a number line, you can:

Draw a number line.

Mark a point at -36 (you can label it as C ≤ -36).

Shade the part of the number line to the left of -36 to indicate that C is less than or equal to -36.

This graph visually represents the solution to the inequality: C is any number less than or equal to -36.

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Answer:

The image would just be upside down. C would stay where it is, A would be at the point (2, -3), D would be at the point (0, -1), and B would be at the point (4, -1)

Step-by-step explanation:

Answer:

The equation which is equivalent to [tex]t^2-8t+15=0[/tex] is

[tex](t-3)(t-5)=0[/tex]

Step-by-step explanation:

Given that the time a projectile spends in the air can be modeled by the equation [tex]t^2-8t+15=0[/tex], where t represents the amount of time traveled in seconds.

To find the equation is equivalent to  [tex]t^2-8t+15=0[/tex] :

[tex]t^2-8t+15=0[/tex]

[tex]t^2-3t-5t+15=0[/tex]

[tex]t(t-3)-5(t-3)=0[/tex]

[tex](t-3)(t-5)=0[/tex]

Therefore the equation which is equivalent to  [tex]t^2-8t+15=0[/tex] is

[tex](t-3)(t-5)=0[/tex]

Final answer:

The equivalent equation to the quadratic equation representing the time a projectile spends in the air, t² -8t + 15 = 0, is (t - 3)(t - 5) = 0, which results from correctly factoring the original equation.

Explanation:

The time a projectile spends in the air is represented by the quadratic equation t² -8t + 15 = 0. To find an equivalent equation, we must factor the quadratic equation correctly. The correct factored form that corresponds to the original equation is (t - 3)(t - 5) = 0, based on the rules of factoring quadratics and finding roots that sum up to -8 (the coefficient of t) and multiply to 15 (the constant term).

The process of factoring involves finding two numbers that add up to the coefficient of the linear term (-8 in this case) and multiply to the constant term (15 here). The numbers -3 and -5 satisfy both these conditions as (-3) + (-5) = -8 and (-3) × (-5) = 15. Therefore, the equivalent equation is (t - 3)(t - 5) = 0.

Answer:

= x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18

Step-by-step explanation:

x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18 - 0

Since all the exponents have different bases, the only thing we can do is subtract 18 from 0, which gives us an answer of:

= x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18

Answer:

The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]

Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]

Step-by-step explanation:

Given expression is [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]

To simplify the given expression as below :

[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]

[tex]=\frac{12x^5y^9z^{-8}}{5x^{-3}y^4z^{-4}}[/tex]

[tex]=\frac{12x^5y^9z^{-8}x^3y^{-4}z^4}{5}[/tex]  ( by using the property [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )

[tex]=\frac{12x^5.x^3.y^9.y^{-4}z^{-8}z^4}{5}[/tex]

[tex]=\frac{12}{5}x^{5+3}.y^{9-4}.z^{-8+4}[/tex] ( by using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\frac{12}{5}x^8y^5z^{-4}[/tex]

[tex]=\frac{12x^8y^5}{5z^4}[/tex]  ( by using the property [tex]a^{-m}=\frac{1}{a^m}[/tex] )

[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]

The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]

Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]

Answer:

Therefore,

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]

Step-by-step explanation:

Simplify

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}[/tex]

Solution:

Using the Identities

[tex]1.\ x^{-a}=\dfrac{1}{x^{a}}[/tex]

[tex]2.\ \dfrac{1}{x^{-a}}=x^{a}[/tex]

[tex]3.\ \dfrac{x^{a}}{x^{b}}=x^{(a-b)}[/tex]

Therefore,

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{24x^{(5+3)}y^{(9-4)}z^{(-8+4)}}{10}[/tex]

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{2\times 12x^{8}y^{5}z^{-4}}{2\times 5}[/tex]

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]

Therefore,

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]

Answer:

I wanna say B. not 100% sure

sorry if wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer is B

Answer:

We assume, that the number 180 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 180, so we can write it down as 100%=180.

4. We know, that x% equals 483.6 of the output value, so we can write it down as x%=483.6.

5. Now we have two simple equations:

1) 100%=180

2) x%=483.6

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=180/483.6

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 483.6 is what percent of 180

100%/x%=180/483.6

(100/x)*x=(180/483.6)*x       - we multiply both sides of the equation by x

100=0.37220843672457*x       - we divide both sides of the equation by (0.37220843672457) to get x

100/0.37220843672457=x

268.66666666667=x

x=268.66666666667

now we have:

483.6 is 268.66666666667% of 180

Answer:

(-1,5), (0,3), (2,-1)

Step-by-step explanation:

We can just test out each of the answers as follows:

Let's start with (-2,-1). We see that f(-2) = 3 - 2x(-2) = 3+4 = 7, so this is not a solution.

Now let's work out the rest:

f(-1) = 3 - 2x(-1) = 3 + 2 = 5. So yes (-1,5) is a solution

f(0) = 3-2x0 = 3 so yes, (0,3) is a solution

f(1) = 3 - 2x1 = 1 so (1,0) is not a solution

f(2) = 3 -2x2 = -1, so yes (2,-1) is a solution

Answer:

The approximate value is [tex]56.63^o[/tex]

Step-by-step explanation:

Let

[tex]\theta[/tex] ----> the measure of angle in degrees

we have that

[tex]cos(\theta)=0.55[/tex]

Using a calculator

Find the measure of angle  [tex]\theta[/tex]

[tex]\theta=cos^{-1}(0.55)[/tex]

[tex]\theta=56.63^o[/tex]

Answer:

x = 14,4

Step-by-step explanation:

x = 3,6 * 4

x = 14,4

Answer:

33cm^2

Step-by-step explanation:

Rectangle:

5 x 6 = 30

Triangle:

1 side 6 - 3 = 3

2 side 7- 5 = 2

area of right triangle:

A = (ab) / 2

A = (3 * 2) / 2

A = 3

sum:

30 + 3 = 33

Answer:

swallla swalla swalla swalla drake swalla drake swalla swalla swalla freaky freaky gurlll

Step-by-step explanation:

The lot costs 5000 dollars.

Step-by-step explanation:

The cost of a House and the lot = $40,000.

Let us assume the cost of lot as 'x'

Given that, The cost of the house is 7 times as much as the lot.

Therefore, The cost of the house= 7x

The cost of both the house and the lot= x + 7x

$40,000 = x + 7x

40,000 = 8x

x = 40,000/8

x = 5,000

The lot costs $5000.

The cost of the lot is determined by setting up an equation using the information given in which the house costs seven times as much as the lot and they total $40,000. This equation, when solved, shows the cost of the lot as $5,000.

To solve this problem, we need to set up an equation using the information given. Let's use x to represent the cost of the lot. According to the question, the house costs seven times as much as the lot, so the house costs 7x. Together, they cost $40,000. So we have the equation:

x + 7x = $40,000

We simplify this to 8x = $40,000. Then, when we solve for x by dividing both sides of the equation by 8, we find that x, or the cost of the lot, is $5,000.

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Answer:

-14x+6

Step-by-step explanation:

-3(4x-2)-2x

-12x+6-2x

-12x-2x+6

-14x+6