Math

A 6. 0 kg bowling ball traveling at 2 m/s strikes a 1. 5 kg bowling pin. Describe and compare the forces that act on the bowling ball and the bowling pin

during the collision.

Answer:

30.8% increase.

Step-by-step explanation:

17 - 13 |13| * 100% = 4 13 * 100 = 30.8%

I hope this helped you!

The estimated value of the multiplication is equivalent to 480.81.

Given is the expression as -

102.3 x 4.7

480.81

Therefore, the estimated value of the multiplication is equivalent to 480.81.

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A basis for the eigenspace corresponding to a = 11 is (1, -2, 0) and a basis for the eigenspace corresponding to a = 2 is (0,1,1).

An eigenspace is the set of all vectors that are multiplied by a matrix and remain unchanged. In this case, the eigenspace is the set of all vectors that when multiplied by the matrix A will result in a vector with a scalar multiple of the eigenvalue. The eigenvalue is found by solving the characteristic equation, which is the determinant of the matrix minus the eigenvalue multiplied by the identity matrix.

For the matrix A, the eigenvalues are 11 and 2. The corresponding eigenspace for each eigenvalue is then found by solving the homogeneous system of equations. For a = 11, the solution to the system is (1, -2, 0) and for a = 2, the solution is (0,1,1). Both of these vectors form a basis for the corresponding eigenspaces.

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The effective annual rate of interest if you do not make any payments for a year is 35%.

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.

We can write -

A = 500(1 + 0.3/12)¹²⁽¹⁾

A = 500(1 + 0.025)¹²

A = 500 x (1.025)¹²

A = 675

Effective annual interest rate for a year is as follows -

A = 500(1 + r/1)⁽¹⁾⁽¹⁾

675 = 500(1 + r)

1 + r = 675/500

1 + r = 1.35

r = 0.35

r = 35%

Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.

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The missing angles and their reasons are as follows;

a) x = 65°; Opposite angles

b)  y = 71°; Alternate angles

c) z = 44°; sum of angles in a triangle

a) In triangles or line geometry, we know that the angles that are directly opposite to each other are known as opposite angles. They are also referred to as as vertical angles or even vertically opposite angles in some cases and are always congruent to each other.

We see that x is an opposite angle to 65 and so;

x = 65°

b) Alternate angles are gotten on the opposite sides of a transversal line they always have the same size. In this problem, we see that y is an alternate angle to 71° and as such;

y = 71°

c) The sum of angles in a triangle is 180° and as such;

x + y + z = 180°

Thus;

65 + 71 + z = 180

z = 180 - 136

z = 44°

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The two types of Angles of the triangle are  Acute Angle ( angle that are less than 90 degree) and Obtuse Angle ( angle between 90 and 180 degree ).

What are Angles ?

The Angle is defined as the geometrical shape that is constructed by joining two rays to each other at their end points.

The two types of angles of the triangle are Acute Angle and Obtuse Angle :

(i) Acute Angle :

An angle can be called as Acute if the measure of the angle is less than 90 degree .

(ii) Obtuse Angle :

an angle can be called as Obtuse if the measurement of the angle is greater than 90 degree and less than 180 degree .

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The area of the figure is 51.63 m²

A composite figure is figure that is made up of two or more different shapes.

The composite figure in the given image is made up of a rectangle, semicircle and a triangle. Therefore, the area of the composite figure will be the sum of the areas of the shape it is made of. Thus:

Area of figure = area if rectangle + area of semicircle + area of triangle

Area of figure = LW + 1/2πr² + 1/2bh

Area of figure = (6 × 5) + (1/2 × 3.14 × 3²) + (1/2 × 3 × 5)

Area of figure = 30 + 14.13 + 7.5

Area of figure = 51.63 m²

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Answer:

65%

Step-by-step explanation:

39/60 X 100

(39 being the number of movies he rated very good, divided by the total number of movies he watched which is 60)

Two tiny parallel horizontal lines serve as the "equality sign" connecting 1 kilogramme of NaCl to 27 ml of a solvent.

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If Jupiter is about 5.2 Astronomical Units (AU) from the Sun and Neptune is about 30.1 AU from the Sun, Neptune is about 5.79 times far from the Sun as Jupiter.

Therefore the answer is 5.79.

To find how many times as far from the Sun Neptune is as Jupiter, we need to divide the distance from the Sun to Neptune by the distance from the Sun to Jupiter.

Neptune is about 30.1 AU from the Sun and Jupiter is about 5.2 AU from the Sun, so:

= Distance from the Sun to Neptune / Distance from the Sun to Jupiter

= 30.1 / 5.2

= 5.79

So, Neptune is about 5.78 times as far from the Sun as Jupiter.

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Answer:

a=7b/11

Step-by-step explanation:

11a=7b

11a/11=7b/11

a=7b/11

Answer: 11a=7b

-divide 11 from both sides

you'll end up with this result:

a=7b/11

Answer:

$899.54

Step-by-step explanation:

To find the cost of sod for a trapezoid shaped yard, we need to first find the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (1/2) * h * (b1 + b2)

where h is the height of the trapezoid and b1 and b2 are the lengths of the bases.

Substituting the given values, we get:

Area = (1/2) * 46 ft * (78 ft + 111 ft)

= (1/2) * 46 ft * 189 ft

= 4274 ft^2

To find the cost of sod for this area, we need to multiply the area by the cost per square foot of sod. The cost will be:

Cost = 4274 ft^2 * $0.21/ft^2

= $899.54

So the cost of sod for this yard will be $899.54.

Answer:

Approximately - 9.7%

Step-by-step explanation:

By using the percent change formula, you will be able to calculate the percent decrease.

(b-a)/a times 100 <-- (percent change formula)

(120-133)/133 times 100

-13/133 times 100

-9.7744%

Answer:

  9.8% decrease

Step-by-step explanation:

You want the percent decrease from 133 to 120.

The amount of change as a percent can be found using the formula ...

  percent change = ((new value)/(old value) -1) × 100%

Here, the new value is 120, and the old value was 133. The change is ...

  percent change = (120/133 -1) × 100% ≈ (0.90226 -1) × 100%

  = -0.09774 × 100% ≈ -9.8%

The change from 133 to 120 is a 9.8% decrease.

__

Additional comment

When the sign of the change is negative, as here, the change is a decrease. If the sign is positive, the change is an increase. That is, a change of -9.8% is a 9.8% decrease. (You can use either the minus sign or the word "decrease" to indicate the direction of the change. The acceptable form of the answer will depend on your grader.)

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The equation in option e) is not correct because it would not give correct height of the trees in this problem

Since the Magnolia trees are 3 feet tall and grow at an average of 3/4 foot per year.

If x is the number of years and y is the height. we can write:

y = 3/4(x) + 3

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

y-y1 = m(x−x1)

y = 3/4(x) + 3 in slope-point  form is:

y = 3/4(x) + 3

y-3 =  3/4(x-0)

This means option a) is correct

Yes, this equation is okay to use for the height of the trees in this problem

b) y - 6 = 3/4(x-4)

y - 6 = 3/4(x-4)

y - 6 = 3/4(x)- 3

y - 6 + 3 = 3/4(x)

y - 3 = 3/4(x)

This is correct

c) y - 4.5 = 3/4(x-2)

y - 4.5 = 3/4(x-2)

y - 4.5 = 3/4(x)- 1.5

y - 4.5 + 1.5 = 3/4(x)

y - 3 = 3/4(x)

This is correct

d) y - 12 = 3/4(x-12)

y - 12 = 3/4(x-12)

y - 12 = 3/4(x) - 9

y - 12 + 9 = 3/4(x)

y - 3 = 3/4(x)

This is correct

(e) y - 15= 3/4(x-15)

y - 15= 3/4(x-15)

y - 15= 3/4(x)-11.25

y - 15 + 11.25= 3/4(x)

y - 3.75 = 3/4(x)

This is not correct because it does not reflect the given information

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Answer:

The function that correctly depicts the scenario is:

cost(n) = 18.50 * 1.06^n

This function takes the number of years n as input and returns the cost of eating at the all-you-can-eat buffet after n years.

The cost of eating at the all-you-can-eat buffet 10 years from now can be calculated as follows:

cost(10) = 18.50 * 1.06^10 ≈ $30.59

The cost of eating at the all-you-can-eat buffet 15 years ago can be calculated as follows:

cost(-15) = 18.50 * 1.06^(-15) ≈ $8.01

Step-by-step explanation:

So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.

The factorial of a non-negative integer n, represented by n! is the product of all positive integers less than or equal to n. It is the mathematical operation that is applied to a non-negative integer.It is also used in many areas of mathematics, including calculus and number theory, as well as in many areas of science, including physics, chemistry, and computer science.

A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.

To factor a trinomial of the form "ax² + bx + c," we can use the following steps:

First, we need to determine two numbers that multiply to give us "c" and add to give us "b." In this case, the two numbers are 4 and 5 because 4 x 5 = 20 and 4 + 5 = 9, which is equal to "13m".

Next, we can factor the trinomial into the form (ax + b)(cx + d) by grouping the middle term and the constant term together.

So, the factored form of the trinomial is (2m + 4)(m + 5)

So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.

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Answer:

d which implies m/3 + 5 = 9

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{13}-\underset{x_1}{1}}} \implies \cfrac{ -4 }{ 12 } \implies {\Large \begin{array}{llll} - \cfrac{1 }{ 3 } \end{array}}[/tex]

Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.

3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.

Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.

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For the given complementary angles, the measure of angle  A is found to be 45°.

For the stated question-

Angle A is complementary to Angles B.

So,

Angle A  + Angles B = 90°

Angle A  + 55° = 90°

Angle A = 90° - 55°

Angle A = 45°

Thus, the measure of angle  A is found to be 45°.

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Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards

Multiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.

In this problem, we may require the use of some mathematical operators to find the solution to the problem.

1.

He currently has 216 cards, but he needs 15 sets of cards.

1 set of card = 72 cards

Let's calculate the number of sets he currently has.

1 set of card = 72 cards

x set = 216 cards

cross multiply both sides and solve for x.

x * 72 = 216 * 1

x = 216 / 72

x = 3 sets

He currently has 3 sets of cards.

Since he wants 15 sets of cards, we will need 12 more set of cards.

The number of cards can be calculated by multiplying 12 by 72

Number of cards = 12 * 72 = 864

He needs 864 more cards.

2.

1 set of card = $27

1 set = 72 cards

But she's bringing $9 to join, we can calculate the ratio of cards she will get.

1 / 27 = x / 9

x = 9 / 27

x = 1/3

She will get 1/3 of the cards bought which will be

72 * 1/3 = 24 cards

She will get 24 cards

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Therefore , the solution to the given problem of inequality comes out to be 120d + 1,500 = 110d + 2,500.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right

Here,

Given : $1,500 a week to a wage

$55 per hour

Thus ,

Taking all the information in concern

We get,

where d is the is he number of hour

120d + 1,500 = 110d + 2,500

Therefore , the solution to the given problem of inequality comes out to br

120d + 1,500 = 110d + 2,500.

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x=12

L||M means L will be parallel to M.

Two lines are parallel if their corresponding angles are the same.

Corresponding angles are shown below.

As the two angles given are corresponding, L||M when x+5 = 2x-7.

x+5 = 2x-7

x = 12

Therefore, the value of x which makes L||M is 12.

Answer:

x = 12

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + 5 = 2x - 7

Then the value of x will be,

→ x + 5 = 2x - 7

→ x - 2x = -7 - 5

→ -x = -12

→ [ x = 12 ]

Hence, the value of x is 12.

When these equations are solved, the value of x is 4 and the value of y is 3. Therefore, the value of x + y = 7.

To solve the system of equations, we will use the elimination method.

First, we multiply the first equation by 3 and the second equation by 5.

3(3x + 5y = 9)

5(5x + 3y = 7)

Then, we add the equations together:

9x + 15y = 27

25x + 15y = 35

Now, we subtract the second equation from the first to eliminate the x terms:

-16y = -8

y = 0.5

Next, we plug this value for y into one of the original equations and solve for x:

3x + 5(0.5) = 9

3x = 8.5

x = 2.83

Finally, we plug the values of x and y into the original equation to verify that they are correct:

3(2.83) + 5(0.5) = 9

So, the value of x is 2.83 and the value of y is 0.5. Therefore, the value of x + y = 2.83 + 0.5 = 3.33.

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well, maybe Pam has been eating the wrong chips or something, but if she's correct, that can only happen if both equations are exactly equal, are they?

[tex]\boxed{\cfrac{x}{16}=4}\implies x=(16)(4)\implies \cfrac{x}{4}=16 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{4}=16\implies x=(4)(16)\implies \boxed{\cfrac{x}{16}=4}\qquad \begin{array}{llll} \textit{yeap, Pam is correct}\\ \textit{she's Da Bomb} \end{array}[/tex]

Answer:

To form a right triangle, one of the sides of the triangle must be the hypotenuse and the other two sides must be the legs. The hypotenuse is the longest side of a right triangle and the side opposite the right angle. In this case, the side with length 5x is the hypotenuse. Therefore, the sides with lengths 3x and 24 must be the legs.

We can use the Pythagorean Theorem to determine the value of x that will make this a right triangle. The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:

5x^2 = 3x^2 + 24^2

Solving for x, we get:

x = sqrt(24^2/(5^2 - 3^2)) = sqrt(576/16) = 6

Therefore, a value of x = 6 will make this a right triangle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x ÷ 48 = 4

Multiplying both sides by 48 we get:

x ÷ 48 x 48 = 4 x 48

x =  192

Answer:

Step-by-step explanation:

12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12

Answer:

The answer is 18

Step-by-step explanation:

22½ = [(22 × 2) + 1] ÷ 2 = 45/2

1 ¼ = [(1 × 4) + 1] ÷ 4 = 5/4

Now,

45/2 ÷ 5/4

45/2 × 4/5

(45 × 4) ÷ (2 × 5)

180/10 = 18

Thus, 18 people are at Chrissy's birthday party.

Answer: 25cm²

Step-by-step explanation:

Ok, so I haven't actually learnt this in school so I'm going to give it my best shot. (Don't be surprised if I get this wrong though.)

So, Quadrilaterals A and B are similar. They have the same angles. Therefore, (I'm thinking that) Quadrilateral B is just a scaled-up version of Quadrilateral A.

Here comes my theoretical part:

If one side of Quadrilateral B is 5 times longer than the same side of Quadrilateral A...

(Quadrilateral A is 3cm, and Quadrilateral B is 15cm).

... then the area of the entire Quadrilateral B should just be 5 times bigger than Quadrilateral A.

Therefore, (I'm guessing), Quadrilateral B has an area of 25cm²