Marcus is 30 years younger than his mother. In 5 years, Marcus' age will be 1/4 of his mother's age. Find Marcus' mother's current age

The sector area is equal to: B. 54π yd².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θr²/2

Where:

Substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θr²/2

Area of sector = 240(π/180) × (9)²/2

Area of sector = 120(π/180) × 81

Area of sector = 54π yd².

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The area of a trapezoid with the given parallel sides and height is 4x+8 square units. Therefore, option B is the correct answer.

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (b₁+b₂)×h.

where (A) is the area of a trapezoid, 'b₁' and 'b₂' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between b₁ and b₂).

1) Given that, b₁=x-3, b₂=x+7 and the height=4

Now, area of a trapezoid = 1/2 (x-3+x+7)×4

= 2×(2x+4)

= 4x+8 square units

Hence, option B is the correct answer.

2) The given polynomials are -3x²-7x+9 and -5x²+6x-4.

Here, sum = -3x²-7x+9+(-5x²+6x-4)

= -3x²-7x+9-5x²+6x-4

= -8x²-x+5

Hence, option 1 is the correct answer.

Therefore, the area of a trapezoid is 4x+8 square units.

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Answer:

Rounding to the nearest cent implies approximating a money amount to two decimals (which represent the number of cents), applying the following rules: If the third decimal digit is lower than 5, we leave the second decimal digit as it is. E.g., $4.563 ≈ $4.56.

An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35. Thus, option 3 is correct.

It represents a relationship between variables and constants and is used to describe the behavior of a function or system. Equations can be linear or nonlinear and can have one or multiple variables. They can be used to solve real-world problems, such as finding the slope of a line, calculating distances, or determining the minimum or maximum value of a function. Equations are also used in advanced mathematical disciplines, such as calculus, algebra, and geometry.

When x = 0, y-intercept = 35.4 ≈ 35

And when x increases, the value of y decreases, so slope is negative

From the given options

There is only two negative slope equation but only one with y-intercept = 35. i.e.

y = -0.3x + 35

Thus, An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35.

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It will take Thomas 40 months to empty the account if he continues to take out $400 each month of $16,000.

To find out how many months it will take for Thomas to empty the account, we need to set M to 0 and solve for t. This will give us the number of months it will take for Thomas to spend all of the $16,000 he won on the game show. The equation we need to solve is:
0 = 16000 - 400t

First, we'll isolate the variable t on one side of the equation by adding 400t to both sides:
400t = 1600

Next, we'll divide both sides of the equation by 400 to get the value of t:
t = 16000/400

Simplifying the right side of the equation gives us:
t = 40

So, it will take Thomas 40 months to empty the account if he continues to take out $400 each month for spending money.

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The value of AB in the triangle is 2.5 cm and the value of x in the triangle is 10 units

From the question, we have the following parameters that can be used in our computation:

The triangle

On the triangle, we have the following equivalent ratio

AB : 4 = 10 : 16

Express as fraction

So, we have

AB/4 = 10/16

This gives

AB = 4 * 10/16

Evaluate

AB = 2.5

Here, we understand that the line bisects the angle BAC

This means that

x = 20 - x

So, we have

2x = 20

Divide

x = 10

Hence, the value is 10

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The intervals on which the function is increasing is (0, 1). Option D

A polynomial is a type of mathematical expression that has variables that are raised to whole number powers.

Since the factors of 5 are 1 and 5, we'll try to factor the polynomial by assuming that (x-1) and (x-5) are factors.

The product of (x-1) and (x-5) is (x² - 6x + 5), which is the polynomial we're given.

⇒ (x² - 6x + 5) is the factored form of the polynomial.

A polynomial is increasing on the intervals where it's greater than zero. So we just need to look at the sign of (x² - 6x + 5) for values between 1 and 5.

For values between 1 and 5, the function is always positive, so it's increasing on the interval (1, 5). Therefore, the increasing interval is (1, 5).

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Answer:

Below

Step-by-step explanation:

     Since :   .35 x = 28       Given    ( where x = total sweets)

x = 80 sweets total

28 are red ( given )   then  02.  * 80 = green = 16

80 - 28 - 16 = 36 remaining

                                     and are divided between  pink : white in ratio of 2:1

                                   pink are 2 out of (2+1) = 2/3

                                             2/3 * 36 remaining = 24 pink

                                                    then 12 are white

The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.

To find the percentage of 322 out of 450, we can use the following formula:

percentage = (part/whole) x 100

where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".

Using the formula mentioned above, we get:

percentage = (322/450) x 100

percentage = 0.7156 x 100

percentage = 71.56%

Therefore, percentage of 322 out of 450 is approximately 71.56%.

A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.

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The item reached its highest point at 78.4 meters by quadratic form of equation.

Suppose a quadratic form of equation has the following form

y=a[tex](x-h)^2[/tex] + k

Once in vertex form, it is said to be. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)

Using the data shown above, we can determine that

-4.9[tex]t^2[/tex] + 19.6 t + 58.8 = 0

The equation will naturally be converted to vertex form after the square is finished:

where h is the amount of time needed to reach a height of k.

Next, square the half of the linear term and add it to both sides.

-4.9([tex]t^2[/tex]-4t)=-58.8

-4.9([tex]t^2[/tex]-4t+4)=-58.8-19.6

-4.9([tex](t-2)^2[/tex])=-78.4

s(t)=-4.9([tex](t-2)^2[/tex])+78.4

As can be seen, the vertex is (2,78.4).

The maximum height is 78.4m.

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Question: An object is launched at 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t)=−4.9[tex]t^2[/tex]+19.6t+58.8. What is the maximum height of the object?

Answer: step 1:

wickets 2 and 9, (16,18) and (15,43) = 25.02ft

wickets 9 and 8, (15, 43) and (37,65) = 31.11 ft

wickets 8 and 5, (37, 65) and (63,39) = 36.7 ft

wickets 5 and 3, (63, 39) and (41, 17) = 31.11 ft

wickets 3 and 2, (41, 17) and (16, 18) = 25.02 ft

Answer:z=4663/586

Step-by-step explanation:

The weight of the bear after hibernation is 673.2 pounds

percentage, a relative value indicating hundredth parts of any quantity.

Given that Before hibernation, a bear weighs 990 pounds.

Its weight decreases by 32% during hibernation.

We need to find how much the bear weigh when it comes out of hibernation.

Lets find what is 32% of 990

32/100×990

0.32×990

316.8

Now let us subtract 316.8 from 990 pounds, to find the weight after hibernation.

990-316.8

673.2

Hence, 673.2 pounds is the weight of the bear after hibernation.

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The prime factorization of P is given as follows:

C. 2³ x 3² x 7.

The number P in this problem is defined as follows:

P = 14 x 36.

Hence we must obtain the prime factorization of each number in this problem, as follows:

Then the prime factorization of the multiplication is given as follows:

14 x 36 = 2 x 7 x 2² x 3² = 2³ x 3² x 7.

Meaning that the correct option is given by option C.

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Answer:51. 2%

Step-by-step explanation:

24+32+(16×4)+7(2+16)=24+32+64+126=246

26g of Epsom salt contains 126g of water of crystallisation.Hence, 100g of Epsom salt contains 100×126/246The % of H2​O in MgSO4​.7H2​O=

Answer: D, 9.4

Step-by-step explanation:

(pi*2*12) *45/360 = 9.4

Answer:

9.4 is correct

Step-by-step explanation:

C=2πr = 2x3.14x12=75.36

arc AB=(45/360)x75.36=9.42

The number of penguins at the zoo is 48.

Percentage is a measure of frequency that determines the value of a number as an amount out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply by 100.

Number of penguins = percentage of penguins x number of birds

50% x 96

(50/100) x 96 =

0.5 x 96 = 48

Here is the complete question:

There are 96 birds at the Parkdale Zoo. 50% of the birds are penguins. How many penguins are at Parkdale Zoo?​

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The amount of money you'll have at the end of 5 years is $4,060.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 3,500 × 3.2/100 × 5

S.I = 3,500 × 0.03.2 × 5

S.I = $560.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = $560 + $3,500

Future value, A = $4,060.

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She have 1 hour 17 minutes remaining for the second section.

what is total time ?

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.

Given:

Total time : two hours

Time taken to complete the first section =  forty-three minutes

Now , minutes she have remaining on the second section

= Total time - Time taken to complete the first section

= 2 hours - 43 minutes

= 1 hour 17 minutes

Hence , she have 1 hour 17 minutes remaining for the second section.

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Python formats all floating point numbers to two decimal places when outputting using the print statement. (FALSE)

The if statement causes one or more statements to execute only when a Boolean expression is true. ( TRUE)

Floating point  is a number format that can be used to represent a large or small value.

In writing this number is done by writing it in exponential form, so that the number has a base number, the exponential number and the base number.

The following is writing scientific notation in floating point. example in decimal numbers

261,000,000,000 written 2.61 x 10¹¹

0.000000000261 is written 2.61 x 10^-10

The Floating point representation itself has two parts, namely the mantissa part and the exponent part. The mantissa determines the digits, while the exponent determines the value of how many powers the mantissa is, as follows:

±S * B±E

S = Significant also called mantissa

E = Exponent

B  = Base

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Answer:

(4,4)

By using a graphing we can see that the lines intersect at (4,4).

therefore, 4 is the solution

don't forget to say thanks

Answer:

A

I believe because p→q

q→p

1. Adjacent angles and  1 degree is missing angle.

3. Complementary angles are  missing angle is 177 degrees.

4. Adjacent angles and missing angle is 10 degrees.

5. Adjacent angles and missing angle is 104 degrees.

6. Adjacent angles and missing angle is 10 degrees.

6. Vertical angles and missing angle is 57 degrees.

an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

1. The angles are Adjacent

54+10x+16=180

10x=180-70

x=1

So the unknown angle is 10+16=26 degrees.

3. The angles are complementary

22+4x=90

4x=68

Divide both sides by 4

x=17

So, the angle is 4(17)=68 degrees

4. The angles are Adjacent

110+7x=180

7x=70

x=10,  the other angle is 7(10)=70 degrees

5. The angles are Adjacent

72+x+4=180

x=104

The other angle is 104+4=108 degrees.

6.  92+x+78=180

x=10

The unknown angle is 10 degrees.

7. The angles are vertical.

72=x+15

x=57 degrees.

Hence,  

1. The angles are Adjacent and missing angle is 1 degrees.

3. The angles are complementary and missing angle is 177 degrees.

4. The angles are Adjacent and missing angle is 10 degrees.

5. The angles are Adjacent and missing angle is 104 degrees.

6. The angles are Adjacent and missing angle is 10 degrees.

6. The angles are Vertical and missing angle is 57 degrees.

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Answer:

l is parallel to m and u is parallel to t

Step-by-step explanation:

Parallel line means that never meet each other

Points of discontinuity for the rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4) are x = -1 and x = -4.

A rational function is a function that can be expressed as the ratio of two polynomial functions. In the case of the given rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4), the numerator is a polynomial of degree 3, and the denominator is a polynomial of degree 2.

To find any points of discontinuity for a rational function, we need to determine where the denominator is equal to zero. Division by zero is undefined, so any value of x that makes the denominator equal to zero will be a point of discontinuity for the function.

In this case, we set the denominator (x+1)(x+4) equal to zero and solve for x:

(x+1)(x+4) = 0

This equation is true if either (x+1) = 0 or (x+4) = 0. So we have two solutions:

x+1 = 0 or x+4 = 0

x = -1 or x = -4

These values of x make the denominator of the function equal to zero, which means that the function is undefined at these points. These points are known as vertical asymptotes of the function, since the function approaches infinity as x approaches these points from either side.

It's important to note that the numerator of the function does not affect the points of discontinuity, since it is always defined for any value of x. Therefore, the points of discontinuity only depend on the denominator of the function.

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The number of workers in the company is given as follows:

3900 workers.

The number of workers in the company is obtained applying the proportions in the context of the problem.

From the problem, we have that:

Hence 30% of the workers is equivalent to 1170, hence the number of workers in the company is obtained as follows:

0.3x = 1170

x = 1170/0.3

x = 3900 workers.

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Answer:

= 6 years old.

Step-by-step explanation:

Let your age 2 year ago be = x

= 2x

again

Let your age 2 years from now be x

= 2x

therefore

= 2x +2x = 24

= 4x = 24

= 4x/4 = 24/4

= x = 6

therefore you're 6 years old.

Step-by-step explanation:

I want to say Marisella. Here's my argument.

5 seats in the front row, so 5/20. Before the first person enters, 5 seats are open making it 5/20.

Once the first person sits.. now there are 4 spots in the front and only 19 total seats left, making it 4/19

Minda must view 76 movies to make Movie Prime the better deal

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, The number of movies be 'x' and from the given information the two equations can be formed as,

5.95x and 150 + 3.95x.

And  to make Movie Prime the better deal,

150 + 3.95x < 5.95x.

2x > 150.

x > 75.

So, Minda must watch greater than 75 movies.

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