Problem 2: A storm causes a 14m hydro pole to lean over. The pole leans at an angle of 72° to
the ground. How high is the top of the pole from the ground?

Step-by-step explanation:

This is a simple system of equations problem, with our equation being:

[tex]\frac{4}{7}x+9=x[/tex]

We know this as her dogs (x) is equal to 4/7 of her dogs (x) plus 9. Now all we must do is solve for x:

[tex]\frac{4}{7}x+9=x\\\\\frac{4}{7}x=x-9\\\\\frac{4}{7}x=\frac{7}{7}x-9\\\\\frac{-3}{7}x=-9\\\\x=21[/tex]

Answer:

this makes no sense but I think the answer is 38 inches

Step-by-step explanation:

Answer:

7. After testing for COVID-19 at Mulago Hospital, the ratio of positive to negative to asymptomatic cases was 4:5:7

Step-by-step explanation:

ve and positive cases was 63, (a) find the number of negative cases tested at the hospital. (03 Marks)​

The balance in dollars and cents in Yolanda's account at the end of 4 years is $5,355.29

What is the future value of an ordinary?

An ordinary annuity is the one where the monthly deposit occurs at the end of each month rather than at the beginning of the months such its future value based on 5.5% annual interest rate can be determined thus:

FV=PMT*(1+r)^N-1/r

FV=balance in dollars and cents in Yolanda's account at the end of 4 years=unknown

PMT=monthly deposit=$100

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly deposits in 4 years=4*12=48

FV=$100*(1+0.00458333333333333)^48-1/0.00458333333333333

FV=$5,355.29

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Missing question:

What was the balance in dollars and cents in Yolanda's account at the end of 4 years?

For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.

Hence, the domain is [-4,4] for the given function.

The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.

For this problem, the function does not cross the x-axis, hence it has no zeros.

Looking at the graph of the function, we have that:

Hence, for the function in the given graph:

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Answer: (83 + 91 + 82 + 95) / 4

Step-by-step explanation:

        The information given tells us how to complete the question. We will be finding the average.

       Add all the scores together, and divide by the number of tests.

(83 + 91 + 82 + 95) / 4

       Since this question asks for an expression, we will end here. If it asked us to solve, we would do the following;

(83 + 91 + 82 + 95) / 4

(351) / 4

87.75

Based on the fact that both workers received the same number of hours, the minimum number of hours that each employee will be assigned is 60 hours.

One worker gets 15 hours shifts and the other gets 6 hour shifts.

If they will have the same number of working hours, the minimum number of hours for these workers will be the lowest common multiple of 6 and 15.

Multiples of 15:

Multiples of 6:

The minimum number of hours is therefore 60 hours.

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Answer: 60

Step-by-step explanation:

LCM of 6 & 15

15

-------------

15

30

45

60

75

90

105

6

---------

6

12

18

24

30

36

42

48

54

60

LCM of 6 & 15 is 60

Answer: 5578

Step-by-step explanation:

1058 + 4520 = 5578

Answer: 7(x-2(112/8))= 7(x-28)= 7x - 28*7

7x = 28*7

x=28

Joe worked for 14 hours at Job A and for 16 hours at Job B.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Now it is given that,

Joe works two part-time jobs for a total of 30 hours a week.

Let x be the number hours that Joe worked at job A in a week.

and y be the number hours that Joe worked at job B in a week.

⇒ x + y = 30        ...(i)

Now Job A pays $5.90 per hour,

Therefore,

Amount receive from Job A = 5.9x

And Job B pays $7.20 per hour

Therefore,

Amount receive from Job B = 7.20y

Also it is given that, he work at each job the week that he made $197.80

Therefore,

5.90x + 7.20y = 197.8   ....(ii)

Now multiplying equation (i) by 5.9 we get,

5.90x + 5.90y = 177      ....(iii)

Subtracting equation (ii) and equation (iii) we get,

1.3y = 20.8

Dividing both the side by 1.3 we get,

1.3y/1.3 = 20.8/1.3

Solving we get,

y = 16

Putting the value of y in equation (i) we get,

x + 16 = 30

Subtracting both the side by 16 we get,

x + 16 - 16 = 30 - 16

Solving we get,

x = 14

Thus, we get

x = 14

y = 16

Hence,

Number hours that Joe worked at job A in a week = 14 hours

and,

Number hours that Joe worked at job B in a week = 16 hours

Thus, Joe worked for 14 hours at Job A and for 16 hours at Job B.

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The equation of the linear function in slope intercept form is given as y = -2x + 1

An equation is an expression that shows the relationship between two or more numbers and variables.

From the table, the linear function contains the points (0, 1) and (2, -3), hence:

y - 1 = [(-3 - 1)/(2 - 0)](x - 0)

y = -2x + 1

The equation of the linear function in slope intercept form is given as y = -2x + 1

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Based on the linear pair postulate, the value of x is proven to be 11.

See proof below.

A linear pair is formed by two adjacent angles that lie on a straight line, thus, they have a sum that is equal to 180 degrees.

We know that angle 1 and angle 2 are a linear pair, the complete proof would be stated as follows:

Statement                                                        Reason

1. Angle 1 and angle 2 are a linear pair         1. Given

2. Angle 1 and angle 2 are supplementary   2. Linear pair postulate

3. m<1 + m<2 = 180°                                          3. Supplementary angles

4. 11x - 6 + 4x + 21 = 180                                   4. substitution

5. 15x + 15 = 180                                               5. Combine like terms

6. 15x = 165                                                      6. Subtraction property

7. x = 11                                                             7. Division property

Thus, based on the linear pair postulate, the value of x is proven to be 11.

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The number of teaspoons of key lime zest to make 30 cupcakes is

35/8 or 4 3/8

Given,

Margaret uses 1 3/4 teaspoon of key lime zest to make 12 cupcakes.

She wants to make 30 cupcakes.

We need to find how much key lime zest will Margaret use.

Example:

1 bag = N mango

Then to find the number of mangoes in 5 bags we need to multiply 5 on both sides.

5 bags = 5 x N mangoes.

We have,

1 3/4 teaspoons of key lime zest = 12 cupcakes

7/4 teaspoons of key lime zest = 12 cupcakes

7/4 = 12 cupcakes

Multiply 30 on both sides.

7/4 x 30 = 30 x 12 cupcakes

Divide both sides by 12.

7/4 x 30/12 = 30 cupcakes

35 / 8 = 30 cupcakes

or

4 3/8 = 30 cupcakes

This means,

35/8 or 4 3/8 teaspoons of key lime zest to make 30 cupcakes.

Thus the number of teaspoons of key lime zest to make 30 cupcakes is

35/8 or 4 3/8.

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Using simple linear equations, we can calculate that Andy has 3 quarters.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Let the number of quarters Andy has = x

number of dollars Andy has = 20 - x

value of quarter = 0.25x

value of dollars = 0.5(20 - x)

Total value = $9.25

⇒ 0.25x + 0.5(20 - x) = 9.25

⇒ 0.25x + 10 - 0.5x = 9.25

⇒ - 0.25x = 9.25 - 10

⇒ - 0.25x = - 0.75

⇒   x = 3

Andy has quarter = 3

He has dollars = 20 - 3 = 17

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Answer:

14

Step-by-step explanation:

PEMDAS

parathesis first

3-5=-2

2+3*5-1-2

next multiply

3*5=15

2+15-1-2

go in order of subtracting and adding

2+15=17

17-1-2

17-1=16

16-2

14

Mars is half as big as Earth and that they each have an equal amount of dry land surface to determine by how much the circumference of the Earth is larger than that of Mars.

we need D(Earth) / D(Mars).

D(Earth) / D(Mars) = 1.2763 x 10⁴km/6.8  x 10³ km ≈ 1.9

D(Earth) / D(Mars) ≈ 1.9

The fifth-largest planet in our solar system by radius, the Earth has a circumference of 3,959 miles.

The other seven planets are joined by Earth and Mars. These two planets in our solar system share some geological characteristics, such as the fact that  Mars, the seventh-largest planet in our solar system, has a radius of 2,106 miles. There are a few distinctions between Mars and Earth, though.

Hence, these planets differ in terms of their sizes, atmospheres, and temperatures.

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Answer:

b

Step-by-step explanation:

Solving the first equation we can find that the value of x is x = 5, then we can replace that in the other expression and we can see that the value of the expression is 1/4.

First, we need to find the value of x.

We know that:

x/(x + 3) = 0.625

Solving that equation we will get:

x = 0.625*(x + 3)

x - 0.625*x = 3*0.625

x*(1 - 0.625) = 3*0.625

x = 3*0.625/(1 - 0.625)  = 5

So the value of x is 5 (and it will be in both expressions)

Now we can replace that value in the given expression (just replace the variable x by the number 5)

(x - 4)/(x - 1) = (5 - 4)/(5 - 1) = 1/4

The value of the expression is 1/4.

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The value of y in the given equation is 19/20

From the question, we are to determine the value of y in the given equation

The given equation is

3 1/3(y + 1 1/8) = 6 11/12

First, convert the the fractions into improper fractions

10/3(y + 9/8) = 83/12

Multiply both sides of the equation by 3/10

3/10× 10/3(y + 9/8) = 3/10× 83/12

y + 9/8 = 3/10× 83/12

y + 9/8 = 83/40

y = 83/40 - 9/8

y = (83 - 45)/40

y = 38/40

y = 19/20

Hence, the value of y in the given equation is 19/20

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Answer:

41:60

Step-by-step explanation:

Time taken by Gavin takes = 41 minutes

Time taken by Jim takes = 1 hour

We know that   1 hour = 60 minutes

So, the ratio of times that Gavin and Jim take as a ratio would be

Gavin:Jim

41:60

Answer:

give the amount of tax please

Answer: 160

Step-by-step explanation:

20 per hour 8h a day

160 per day

20x8

The quadratic equation that contains (0, 7), (2, 15) and (3, 10) is y = - 3 · x² + 10 · x + 7.

Quadratic functions are polynomials of the form y = a · x² + b · x + c, where a, b, c are real coefficients. To determine the coefficients, we need at least three distinct points on Cartesian plane. A solution that is algebraic exact only need three points, then we must resolve this system of linear equations:

c = 7                                      (1)

4 · a + 2 · b + c = 15              (2)

9 · a + 3 · b + c = 10              (3)

The solution to this system of linear equations is (a, b, c) = (- 3, 10, 7).

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Answer:

The weight of gold in the alloy is 32 g.

Answer:

The weight is 32 grams

Step-by-step explanation:

Answer: 6.2

Step-by-step explanation:

2.9/1.3 +4.0=

2.23 + 4.0=

2.2 + 4.0=6.2

The given information is,

→ (2.9/1.3) + 4.0

Let's solve the problem,

→ (2.9/1.3) + 4.0

→ 2.23 + 4 = 6.23

Thus, the answer is 6.23.

Answer: 13 goats and 21 geese

Step-by-step explanation:

     Since we know some are goats, which have four feet, and some are geese, which have two feet, we will set up an equation.

           Let x be goats and y be geese.

4x + 2y = 94

     Next, we know both animals [usually] only have one head.

x + y = 34

     Lastly, we will solve this as a system of equations.

➜ I graphed the equations, see attached, but you can also solve by substitution or other methods.

➜ When graphing, the point of intersection is the solution. This means there are 13 goats and 21 geese.

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The value of y when x= 2 and z= 1/4 is y = 4

In this question, we have been given y varies jointly with x and z.

This means y is directly proportional to x and z.

y = 16 when x = 4 and z = 1/2

We need to find the value of y when  x= 2 and z= 1/4

From y = 16 when x = 4 and z = 1/2 we can compute the equation as,

y = 8xz

16 = 8(4)(1/2)

16 = 8 × 2

16 = 16

So, the equation is y = 8xz

Now for x= 2 and z= 1/4,

y = 8xz

y = 8 × 2 × (1/4)

y = 2 × 2

y = 4

Therefore, the value of y when x= 2 and z= 1/4 is y = 4

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The current assets total for Reese Corp. on December 31, 2014, is B. $5,555,000.

The current assets are Cash and Cash Equivalents (Marketable Securities), Accounts Receivable, Inventory, and Prepaid Liabilities (Expenses).

The current assets are the short-term portion of the total assets.

The current assets show Reese Corp.'s short-term liquidity and the company's ability to meet its short-term obligations (current liabilities), especially to suppliers, vendors, and other short-term creditors.

Reese Corp.

Trial Balance

December 31, 2014

                                                                     Dr.             Cr.

Cash                                                       $ 775,000

Accounts receivable (net)                    2,695,000

Inventory                                               2,085,000

Property, plant, and equipment (net)  7,566,000

Accounts payable and accrued liabilities                  $ 1,701,000

Income taxes payable                                                     654,000

Deferred income tax liability                                             85,000

Common stock                                                             2,350,000

Additional paid-in capital                                            3,680,000

Retained earnings, 1/1/14                                             3,450,000

Net sales and other revenues                                  13,560,000

Costs and expenses                           11,180,000

Income tax expenses                           1,179,000

                                                       $25,480,000 $25,480,000

Cash                                          $ 775,000

Accounts receivable (net)       2,695,000

Inventory                                  2,085,000

Total current assets =          $5,555,000

Thus, the current assets total for Reese Corp. on December 31, 2014, is B. $5,555,000.

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Answer:

Average salary 13.16 120 + 18 + 20/12