From the top of a vertical pole the angle of depression to Ian standing at the foot of the pole is 43°. Liam is on the other side of the pole, and the angle of depression from the top of the pole to Liam is 52°. The boys are standing 58 m apart. Find the height of the pole, to the nearest meter

Answer:

[tex](4x-9)^2*(2x^2+2x+1)^2[/tex]

Step-by-step explanation:

(((4x-9)•(((2•(x2))+2x)+1))•(4x-9))•((2x2+2x)+1)

]  (((4x-9)•((2x2+2x)+1))•(4x-9))•(2x2+2x+1)

Trying to factor by splitting the middle term

Factoring  2x2+2x+1

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  +1

Step-1 : Multiply the coefficient of the first term by the constant   2 • 1 = 2

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   2 .

     -2    +    -1    =    -3

     -1    +    -2    =    -3

     1    +    2    =    3

     2    +    1    =    3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

 ((4x-9)•(2x2+2x+1)•(4x-9))•(2x2+2x+1)

Multiplying Exponential Expressions:

4.1    Multiply  (4x-9)  by  (4x-9)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (4x-9)  and the exponents are :

         1 , as  (4x-9)  is the same number as  (4x-9)1

and   1 , as  (4x-9)  is the same number as  (4x-9)1

The product is therefore,  (4x-9)(1+1) = (4x-9)2

Trying to factor by splitting the middle term

5.1     Factoring  2x2+2x+1

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  +1

Step-1 : Multiply the coefficient of the first term by the constant   2 • 1 = 2

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   2 .

     -2    +    -1    =    -3

     -1    +    -2    =    -3

     1    +    2    =    3

     2    +    1    =    3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Multiplying Exponential Expressions:

5.2    Multiply  (2x2+2x+1)  by  (2x2+2x+1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (2x2+2x+1)  and the exponents are :

      1 , as  (2x2+2x+1)  is the same number as  (2x2+2x+1)1

and   1 , as  (2x2+2x+1)  is the same number as  (2x2+2x+1)1

The product is therefore,  (2x2+2x+1)(1+1) = (2x2+2x+1)2

Final result :

 (4x - 9)2 • (2x2 + 2x + 1)2

Answer:

Step-by-step explanation:

1/4+9/? =1

1/4 + 9/12 = 1

9/12 = 3/4

1/4 + 3/4 = 1

Answer: 1093.5

Step-by-step explanation:

The area of the bottom and top faces are each (26)(7.5)=195, so their combined area is 195(2)=390.

The area of each of the rectangular faces lying on the 7.5-inch side is (7.5)(10.5)=78.75, so their combined area is (78.75)(2)=157.5.

The area of each of the rectangular faces lying on the 26-inch side is (26)(10.5)=273, so their combined area is 546.

So, the total surface area is 546+157.5+390=1093.5

The maximum is at (9,9) and the maximum value is 126 after plotting all the inequalities on the coordinate plane option (B) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

We have a system of inequalities:

8x + 2y > 36

-3x+ 6y < 27

-7x + 5y > -18

After plotting all the inequalities in the coordinate plane, we get:

Intersection points:

(4, 2)

(3, 6)

(9, 9)

Checking for the minimum values at all the points:

f(x, y) = 9x + 5y

f(4, 2) = 9(4) + 5(2) = 46

f(3, 6) = 9(3) + 5(6) = 57

f(9, 9) = 9(9) + 5(9) = 126

The maximum value is 126

Thus, the maximum is at (9,9) and the maximum value is 126 after plotting all the inequalities on the coordinate plane option (B) is correct.

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Answer:

A

Step-by-step explanation:

Find the distance of adjecent and opposite by forming new triangle that has (x1 and y1); (x2 and y2) distance... Using Pythagorean theorem, you can get the distance which is sqrt(x1²+y1²) and sqrt(x2²+y2²)

So you can use 1/2×base×height formula..

1/2×sqrt(x1²+y1²)×sqrt(x2²+y2²)

Simplify and you got A.

Using it's concept, it is found that the probability that the probability that the slip of paper shows a number that is a multiple of 5 or a multiple of 6 is given by:

p = 8/25 = 0.32 = 32%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 25 numbers, and the ones that are multiples of 5, 6 or both are given as follows:

5,6,10,12,15,18,20,24

8 numbers, hence the probability is:

p = 8/25 = 0.32 = 32%.

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Answer:

r≥−2 is the answer.

The total number of the outcomes will be 12. The table is shown below with all the outcomes.

A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.

Julie went to visit her aunt and uncle for the weekend.

She took the following clothes:

two pairs of slacks – one brown, one black;

three sweaters – one tan, one red and one white;

two shirts – one white and one gray.

Then the total number of the outcomes will be

Total outcomes = 2 x 3 x 2

Total outcomes = 12

The table is shown below with all the outcomes.

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In the figure attached, the graph of the function is shown.

1. f(9) ≈ 6 means that at t = 9 (year 1977 + 9 = 1986) the cost to produce 1 watt of solar energy was $6

2. f(4) ≈ 25, which means in the year 1981 (=1977 + 4) the cost was $25 per watt  

f(3.5) ≈ 28, which means at half of the year 1980 (=1977 + 3.5) the cost was $28 per watt  

3. When f(t) = 45, t is equal to 2, which means that the year was 1979 (= 1977 + 2)

4. From the graph we can compute the following table:

x  |  y

0  |  80

1   |  60

f(x) = a*b^x

where a is the initial value and b is the decay factor.

Replacing with data from the table:

f(0) = a*b^0

80  = a

f(1) = a*b^1

60/80 = b

0.75 = b

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The value for y is 17.5°

The equation is

Sin (3y - 30°) = Cos (7y +50°)​

Trigonometry is the branch oh Mathematics which involve the study of right angles , its sides and trigonometric ratios.

the equation given in the question is

Sin (3y - 30°) = Cos (7y +50°)​

cos(90 - [tex]\rm \theta\\[/tex] ) = sin  [tex]\rm \theta\\[/tex]

Therefore

sin(3y-30°) = sin( 90-(7y+50°)

Equating the terms

3y - 30 = 90-7y -50

4y = 90-50+30

4y = 120-50

4y = 70

y = 17.5

The value for y is 17.5°

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A system of equations to have no real solution, the lines of the equations must be parallel to each other. There were 10 multiple choice question, while 15 descriptive type questions.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

Let the number of multiple choice questions be represented by x, while the number of descriptive questions be represented by y. Therefore, the total questions can be written as,

x + y = 25

Solving for x,

y = 25 - x

The total score of Ronald can be written as,

3x + 8y = 150

3x + 200 - 8x = 150

-5x = -50

x = 10

Substitute the value of x in any one of the equation,

x + y = 25

10 + y = 25

y = 15

Hence, there were 10 multiple choice question, while 15 descriptive type questions.

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Answer: The last option, 28 minutes

Step-by-step explanation:

    See attached for my work. If you are color blind let me know, I color-coded where I "pulled" numbers from.

    To answer this problem, we can look at the graph. We need to see for how long the black line is above the blue.

Answer:

28 minutes

Step-by-step explanation:

Hello!

The black line represents Lynn's speed throughout the course of the run, while the blue line represents Kael's run throughout the run.

The y-values of the graph represent the speed of each person, while the x-values represent the time.

To find out how long Lynn was running faster than Kael, we can find the range of the x-values when the black line is ABOVE the blue line.

The first point when it was above the blue line is when x is at 12. The final point is when x is at 40.

Since the units are minutes, Lynn was faster than Kael for 28 minutes.

In a right angle triangle, one angle is of 90 degrees. Then the measure of the angle 3 will be ∠3 = 90° – ∠2.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

We know that in a right angle triangle, one angle is of 90 degrees.

And the angle sum of the triangle is 180 degrees. Then we have

90° + ∠2 + ∠3 = 180°

                  ∠3 = 90° – ∠2

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Answer:

total = 96 sweets

Step-by-step explanation:

sweets shared in the ratio 4 : 5 : 7 = 4x : 5x : 7x ( x is a multiplier )

Seth got 18 more sweets than Frank , that is

7x = 4x + 18 ( subtract 4x from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Then

total = 4x + 5x + 7x = 16x = 16 × 6 = 96 sweets

Answer:

See below  ----pick the one that you need

Step-by-step explanation:

Total cost = 21   +   21 * .06    +   21 * .15  

               =  21 ( 1 + .06 + .15)

                            = 21(1.21)

Step-by-step explanation:

The domain is the possible x values of a function.

Since our function is a reciprocal function, our denominator can't equal 0. Note x=0, is a vertical asymptote.

So our domain is

All Reals except 0,

or (-oo,0) U (0, oo).

The statements that are true based on the diagram are:

From the image attached one can see that  points A and B are seen on the line v and that can also be seen on the plane T.

Still on the diagram, the line z, is known to be made up of points C and D, as it intercept or passes through the plane Z at point C.

The intersection of the planes R and T is known to be line y  because, the intersection of two planes  is known to appear as a line that is seen in the area of their intersection.

Therefore, The statements that are true based on the diagram are:

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Answer:

  3x^3 +14x^2 +2x +35

Step-by-step explanation:

The distributive property is used to find the product of polynomials. Terms can be collected to express the result with terms in order of decreasing degree.

__

  (3x^2 -x +7)(x +5)

  = x(3x^2 -x +7) +5(3x^2 -x +7) . . . . apply the distributive property

  = (3x^3 -x^2 +7x) +(15x^2 -5x +35) . . . . show the products

  = 3x^3 +(-1 +15)x^2 +(7 -5)x +35 . . . . . collect like terms

  = 3x^3 +14x^2 +2x +35 . . . . . . . . write in standard form

Answer:

3/10 and 0.3

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

-1/2

Step-by-step explanation:

use a graphing calculator or use slope formula.

was -3/6 but I reduced it

Answer:

the customer pays 4500 for the gas cooker

Answer:

C.  Add 15 to both sides

Step-by-step explanation:

Given equation:

99x – 15 = 45

To solve:

Step 1:  Add 15 to both sides:

⇒ 99x – 15 + 15 = 45 + 15

⇒ 99x = 60

Step 2:  Divide both sides by 99:

⇒ 99x ÷ 99 = 60 ÷ 99

⇒ x = 60/99

⇒ x = 20/33

Answer:

Choice C: Add 15 to both sides.

Step-by-step explanation:

Given:

99x – 15 = 45

Aim:

To Find the first step.

Solution:

The first step will be Add 15 to both sides:

Choice C is accurate.

[tex] \rule{225pt}2pt[/tex]

EXTRA:

Let's solve the equation further.

Then transpose 99 to the RHS:

The number of pounds of cashews used in the mixture is 18 pounds

let

x = pounds of cashew

Total weight = peanuts + cashew

= 12 + x

Total cost = cost of peanut + cost of cashew

= 30 + 5(x)

= 30 + 5x

Cost per pound = Total cost / Total weight

4 = (30 + 5x) / (12 + x)

4(12 + x) = 30 + 5x

48 + 4x = 30 + 5x

48 - 30 = 5x - 4x

18 = x

x = 18 pounds

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Answer:

2893

Step-by-step explanation:

Answer: conflict means to clash with someone or something conflict is to disagree with someone

Addition of money spens=$274.56

Divided by 8=$274.56/8

=$34.32

Answer:

length is 12 width is 8

Step-by-step explanation:

The phrasing was a bit weird but I think you meant the length is 4 cm greater. for the area L*W=area so just go through your time tables till you find the right combination