A 4,800-pound wrecking ball is held in static equilibrium by two cables, one horizontal and one at an angle of 40° from vertical (see the figure below). Find the magnitudes of the tension vectors T and H. (Round your answers to the nearest whole number.)

The tables that shows a proportional relationship include the following:

x 1 2 3 4 5

y 4 5 6 7 8

p 1 3 5 7 9

q 3 7 11 15 19

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.

In Mathematics, the graph of any proportional relationship is characterized by a straight line because as the values on the x-axis (x-coordinate) increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously as shown in tables B and C.

In conclusion, tables B and C comprises data values that shows proportional relationship in a graph.

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Answer:

1

Step-by-step explanation:

Flip 10/25 to become 25/10 and times it by 2/5

In order to calculate the composite function (gow)(x), that is, g(w(x)), we need to use w(x) as the input (value of x) in the function g(x).

So we have:

Now, calculating (wog)(x), we have:

The number of students in Señora Clara  is 300 students

20% of Señora Clara's students are going to Spain for a semester

60 students are going to spain

The number of students in  Señora Clara can by first calculating the percent of 20

20/100

= 0.2

Next is to divide 0.2 by 60

60/0.2

= 300

Hence there are 300 students in Señora Clara

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The value of x is 26° and y is 9°.

A pair of neighboring angles created by the intersection of two lines is known as a linear pair of angles. When two angles share a vertex and an arm but do not overlap, they are said to be adjacent angles. Due to their formation on a straight line, the linear pair of angles are always complementary. So, the total of two angles in a pair of lines is always 180 degrees.

The value of x and y are : x= 26° and y= 9°.

As a linear pair, (5x - 17)° + (3x - 11)° = 180°.

or, 8x - 28°= 180°

8x = 180° + 28°

Therefore, the value of x is 26°.

Now,

3x - 11°= 3×26°-11° = 67°

Again,

67°+90°+(2y+5)° = 180° { being linear pair}.

157°+2y+5° = 180°

or, 2y + 162° = 180°

or, 2y = 180° - 162°

y =

Therefore, the value of y is 9°.

The value of x is 26° and y is 9°.

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The ways that you can maximize a tax-sheltered retirement program include:

1. when the contributions made by the employer are not taxable

2. when the employee has started making contributions early in life,

A tax-sheltered is a retirement savings plan that enables self-employed individuals and workers of tax-exempt organizations to invest pretax money to create retirement income. A dependable source of income in retirement, tax-sheltered annuities are made to pay out consistently throughout time.

The fact that employer contributions are tax-free is one of the best features of retirement programs. Only when an employee takes money out of their retirement accounts do taxes need to be paid. If the employee starts making contributions early in life, the plans also allow the employee the chance to maximize returns, which is another benefit that the employee can get from them.

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The number of fiction and non fiction books are 10 and 2 respectively.

There are 5 times as many fiction books in the class library as there are nonfiction books.

Therefore,

let

x = number of non fiction book.

number of fiction book = 5x

The number of information books is 7 more than the sum of the number of fiction and nonfiction books.

Therefore,

number of information book = 7 + x + 5x

number of information book = 7 + 6x

There are 19 information books in the library.

Hence,

19 = 7 + 6x

19 - 7 = 6x

6x = 12

x = 12 / 6

x = 2

Therefore,

The number of non fiction book = 2

The number of non fiction book = 5(2)  = 10

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Answer:

[tex]a_5 = \frac{17}{20}[/tex]

Step-by-step explanation:

Use the general progression formula where

[tex]d=\frac{3}{20}\\a_n=\frac{1}{4}+\frac{3n-3}{20}[/tex]

Solving this for the 5th term returns the answer

[tex]a_5=\frac{17}{20}[/tex]

Part (a)

We can add the total number of males and the total number of students who take biology, and then subtract the intersection.

[tex]42+34-14=62[/tex]

Part (b)

There are 90 people in all, so the probability is [tex]\frac{62}{90}=\frac{31}{45}[/tex]

Answer:

see below

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 . In the given triangle ΔNBA BO is a median.
By applying the property of median it divides the opposite side into two equal parts.
Therefore,
NO = OA ...(a)
We have,
NO = x+3 and OA = 2x-9

from (a)
NO = OA
x+3 = 2x-9
∴ 3+9 = 2x-x
∴ x = 12
∴ The Value of x is 12.

Que 2 - In ΔMTV
Given - TP is an angle bisector
             m∠MTP = 12 , m∠MTV = 3x - 3.
Ans - TP is an angle bisector which means it divides the angle into two equal parts. (By angle bisector theorem)
∴ m∠MTP = m∠VTP ..... (a)
m∠MTV = m∠MTP + m∠VTP
∴m∠MTV = 2(m∠MTP)
∴3x-3 = 2(12)
∴3x-3 = 24
∴3x = 24 + 3
∴3x = 27
∴ x = 27/3
∴ x = 9
∴ The Value of x is 9.

The transformation is:

g(x) = -f(x) - 4

So is a reflection across the x-axis followed by a translation of 4 units downwards.

Here we have the two functions:

f(x) = 3x + 1

g(x) = -3x - 5

So we start at f(x), first we apply a reflection across the x-axis so we change the sign to get:

g(x) = -f(x) = -3x - 1

Now we can apply a translation of 4 units downwards so we get:

g(x) = -f(x) - 4 = -3x - 1 - 4 = -3x - 5

And in this way we transformed f(x) into g(x).

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52x - 100y + 490 = 0 , is the required linear function.

What does the term "linear function" mean?

A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.

Given, the monthaly cost = y

   the number of minute used = x

Hence,  

           the monthly cost of the phone = (4.90 + 0.52 × the number of minute used)

Given the monthly cost = y

          the number of minute used = x

Hence      y = 4.90 + 0.52 * x

    or    y = [tex]\frac{490}{100} + \frac{52}{100 } * x[/tex]

     or 100y = 455 + 52x

       or 52x - 100y + 490 = 0 , is the required linear function.

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Answer:

If I assume that I can use x to mean "all real numbers that are less than -3 or greater than or equal to 5",

Then I can write this as follows: x<-3 and x>=5

This includes all whole numbers (or integers), all fractions (or rational numbers), and all numbers that cannot be expressed as fractions such as pi, or the square root of 29 (or irrational numbers).

Answer:

75deg

Step-by-step explanation:

the angle for the entire thing is 131 degrees. Since you are given angle 1 you can subtract that value from the whole to find the remaining degrees. So 131-56=75

Based on the number of equal parts that Lester divided the cake into such that each family member got 1/6 of the whole pie, the proportion of the part of the leftover pie that Lester brought home was 2 / 3

Lester brought back part of some pie from the Sweet Slice pie shop, and then divided it into 4 equal parts for his family. This led to the family getting 1/6 of the pie each.

To find out how much of the total pie that Lester brought back from Sweet Slice pie shop, you need to add the proportions received by his family:

= 1 / 6 + 1 / 6 + 1/ 6  + 1/6

=  4 / 6

At the simplest form this is:

= 4 / 6

= 2 / 3

Rest of the question is:

How much of the pie had Lester brought back from the pie shop?

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Answer: 1.662E-7 square kilometers

Step-by-step explanation:

A circle of radius = 23 or diameter = 46 or circumference = 144.5 cm has an area of: 1.662E-7 square kilometers (km²) 0.1662 square meters (m²)

Answer:

No, he can only make 48 sliders with 7 pounds of ground beef.

He would need about 12 pounds to make 78 sliders

Step-by-step explanation:

The value of m + n from getting the values of m and n from the constant polynomial P(x) = (2m - 4)x² + (5 - n)x + 13 is; 7

A constant Polynomial is defined as a polynomial is a function of the form f(x) = a

where a is a real number, whose highest degree is zero.

Thus, examples of constant Polynomials are f(x) = 5, g(x) = -11 , h(y) = 7/4

Now, we are given the polynomial expression;

P(x) = (2m - 4)x² + (5 - n)x + 13

From the definition of constant Polynomials, we can say that;

2m - 4 = 0 and 5 - n = 0

Thus;

m = 2 and n = 5

Then, m + n = 2 + 5 = 7

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Answer:

A

Step-by-step explanation:

C means the number of miles into the city, while H means the miles on the highway. If (c,h) becomes (138,200), this means that c=138 and h=200. So, 138 miles can be traveled into the city while 200 can be traveled on the highway. hope this helps!

Assuming they work until their cost become the same, obviously.

The difference between the first charge of painter A and painter B = 376 - 280 = 96.

The hourly cost difference between painter B and painter A = 15 - 12 = 3.

So, painter A in the first hour has 96 more dollars than painter B, and as every hour pass, the difference goes down by 3 (as painter B gets 3 more dollars every hour)

Therefore, it would take 96 : 3 = 32 hours for the cost to be the same

Recheck : After 32 hours, painter A has 376 + 32 x 12 = 760 (dollars)
painter B has : 280 + 15 x 32 = 760 (dollars)

Answer:

-6(y+3)

Step-by-step explanation:

Answer:

If p(x) = ax²

-3x+10

p(-2) =

f(g(-2))

Possible values for the actual distance that the toy cart rolled before stopping with 30% error in the calculation conducted earlier is equal to 10.92centimeters.

As given in the question,

Distance covered by toy cart before stopping =15.6

Percentage of error found in calculation= 30%

30% of 15.6

= (30/100) × 15.6

= 4.68cm

Possible value for the actual distance that toy cart rolled before stopping

= Calculated distance - error distance

= 15.6 -4.68

=10.92centimeters

Therefore, possible values for the actual distance that the toy cart rolled before stopping with 30% error in the calculation conducted earlier is equal to 10.92centimeters.

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The slope of the given line is m =25.

The two points of the given line is (3,75) and (4,100).

The slope of the given line can be found using the formula point-slope equation.

y₂-y₁ = m(x₂-x₁)

We need to find the slope, so let us rearrange the equation,

m =  y₂-y₁ / x₂-x₁

where (x,₁y₁) and (x₂,y₂) is (3,75) and (4,100) respectively

So let us substitute these values in the above equation, we get

m = 100 - 75 / 4 -3

m = 25/1

m = 25

Therefore, the slope of the line passing through the point (3,75) and (4,100) is 25

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value of a2+a4+a6+……+a98 IS EQUAL TO 93.

Given, the common difference (d) =1

Let a1=a Given, a1+a2+……+a98=137

⇒(98/2)(2a+97)=137    [Sn=n/2[2a+(n−1)d]

⇒2a+97=137/49…eq.(1)

a2+a4+…+a98    (n=49 terms)

a2+a4+…+a98=49/2(a2+a98)

a2+a4+…+a98=49/2[(a+1)+a+97]

a2+a4+…+a98=49/2[2a+97+1]

a2+a4+…+a98=49/2[(137/49)+1] [using eq. 1]

a2+a4+…+a98=137/2+49/2

a2+a4+…+a98=186/2 =93

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The Value of X = 7.16 ( approximate value)

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The difference between the expressions (2n -9) - (2.4n +4) is -0.4n-13

An algebraic expression can be defined as an arithmetic expression made up of variables, coefficients, terms, factors and constants.

They are also known to be composed of mathematical operations which may include;

Given the expressions;

Let's determine their difference

(2n -9) - (2.4n +4)

expand the bracket

2n - 9 - 2.4n - 4

collect like term

2n - 2.4n -4 -9

Subtract like terms

-0.4n - 13

Hence, the difference is -0.4n - 13

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