Help please!!!

A school building has a 100-foot guy wire attached to the top of the building. When pulled taut it touches level ground 42 feet from the base of the school. At approximately what angle does the wire make with the ground? Give the answer in degrees.

A) 24.83° B) 65.17° C) 22.78° D) 42° E) None of these

Answer:

[tex]67\frac{23}{28}[/tex]

Step-by-step explanation:

[tex]36-\left[100\div \:560-32\left(8\div \:4-1\right)\right]\\\\100\div \:560-32\left(8\div \:4-1\right)\\\\=100\div \:560-32\cdot \:1\\\\=\frac{100}{560}-32\cdot \:1\\\\=\frac{100}{560}-32\\\\=-\frac{891}{28}\\\\\\=36-\left(-\frac{891}{28}\right)\\\\36-\left(-\frac{891}{28}\right)\\\\=36+\frac{891}{28}\\\\\frac{36\cdot \:28}{28}+\frac{891}{28}\\\\\frac{36\cdot \:28+891}{28}\\\\=\frac{1899}{28}\\\\\\\frac{1899}{28}(1899\div28)=67\frac{23}{28}[/tex]

The distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Distance = average velocity × time

Let the time and distance of the run, respectively, be t₁ and.d₁

Let those of the bicycle race be t₂ and d₂

From the question,

t₁ + t₂ = 5

d₁ = 8t₁

d₂ = 27t₂

Total distance = 97

8t₁ + 27t₂ = 97

8 ( 5 - t₂ ) + 27t₂ = 97

40 - 8t₂ + 27t₂ = 97

40 + 19 t₂ = 97

19t₂ = 57

t₂ = 3 hours

t₁ + t ₂ = 5

t₁ = 5 - t₂

t₁ = 5 - 3 = 2 hours

Now the distances are calculated as:-

d₁ = 8t₁ = 8 x 2 = 16 miles

d₂ = 27t₂ = 27 x 3 = 81 miles

Therefore the distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.

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Answer:

5 %  

Step-by-step explanation:

3020 *  x    = 151          x is the percentage in decimal form

x = 151 / 3020 = .05    which is 5 %

Answer:

100

Step-by-step explanation:

Answer:

The rate of interest is6.4 %

Step-by-step explanation:

Given : Principal (P) = Rs12500  

         Total amount (A) = Rs16500.

         The time period (t) =5  years

To find : Rate of interest (R) = ?

Solution :

It is given that Principal (P) = Rs. 12500

        Total amount (A) = Rs.   16500

        The time period (t) =5  years  

We have to find rate of interest (R).

We know the formula for simple interest as,

       S.I. = A-P

             = 16500±12500

             = Rs. 4000

Now, to find rate of interest, use the formula for simple interest as

           S.I. =  

          ∴

          ∴ *R

             ∴  

                    ∴  

                       ∴R=6.4  %                          

∴  The rate of interest is6.4 %.

The area of the rectangle is equal to 216ft^2.

We have given that,

A flower bed is in the shape of a rectangle.

It measures 7 yards long and 3 yards wide. David wants to use a mulch to cover the flower bed.

The mulch is sold by the square foot.

A yard is equal to 3 feet.

7 yards = 7(3) = 24 feet

3 yards = 3(3) = 9 feet

Area of the rectangle=  Lw

Area of the rectangle= 24(9)

Area of the rectangle= 216 ft^2

Therefore the area of the rectangle is equal to 216ft^2.

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Answer:

30/48

Step-by-step explanation:

Answer:

Rose bought 14 packages of granola bars.

Step-by-step explanation:

Total bill = 1 bag of potatoes + x amount of packages of granola bars

Total bill = $74.25

1 bag of potatoes = $6.00

1 package of granola bar = 5.25

We set the equation to:

74.25 = 6.00 + 5.25x

Subtract 6.00 from both sides:

68.25 = 5.25x

Divide both sides by 5.25 to leave x by itself

68.25/5.25 = 5.25x/5.25

13 = x

This means Rose bought 13 packages of granola bars.

Let's recheck our work by inputting x = 13 into the equation:

74.25 = 6.00 + 5.25(13)

74.25 = 6.00 + 68.25

74.25 = 74.25

The graph of the linear equation 6x - 2y = 12 would be option C .

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Subtract both sides from 6x, leaving you with the equation:

-2y = -6x + 12

Now, you divide all of the sides by -2,

y = 3x - 6

The graph of the linear equation 6x - 2y = 12 would be option C .

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The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).

In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).

We must check if the proposition is true for every ordered pair. Let analyze each case:

Case I

[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]

Case II

[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]

Thus, the proposition is false.

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Answer:

regular pentagon. 2 irregular. 3 irregular. 4 regular octagon. 5 regular nonagon. remember that regular polygon is a polygon that

Answer:

step 2: 8x-4=2(6+x+6)

Step-by-step explanation:

[tex]4(2x - 4) = 8 + 2x + 8 \\ 8x - 16 = 16 + 2x here \\ 8x - 2x = 16 + 16 \\ 6x = 32 \\ \frac{6x}{6} = \frac{32}{6} \\ x = 5[/tex]

Answer:

4(2x-4)=8+2x+8

8x-16=16+2x

8x-2x=16+16

6xboth sides over 6

x=5.3repiting

Answer:

3.375 °C

Step-by-step explanation:

Mean temperature for first 7 days = 4 °C

⇒ Total temperature over first 7 days = 4 °C × 7 = 28 °C

Temperature on 8th day = -1 °C

[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]

Therefore, mean temperature for first 8 days:

= [28 - 1] ÷ 8

= 27 ÷ 8

= 3.375 °C

So, we know that:

[tex]A=\dfrac{1}{2}ab\\P=a+b+c\\a^2+b^2=c^2[/tex]

We also know that [tex](a+b)^2=a^2+2ab+b^2[/tex]. We will use that fact to find [tex]c[/tex] in terms of [tex]A[/tex] and [tex]P[/tex].

[tex]A=\dfrac{1}{2}ab\Rightarrow 2ab=4A\\P=a+b+c\Rightarrow a+b=P-c[/tex]

Therefore:

[tex](P-c)^2=c^2+4A\\P^2-2cP+c^2=c^2+4a\\2cP=P^2-4A\\c=\dfrac{P^2-4A}{2P}[/tex]

Answer:

2 / 36 = 1/18

Step-by-step explanation:

there are 2 ways to get 3

1 then 2 or 2 then 1 , 2 out of a possible 36 outcomes

[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=250 \end{cases}\implies 250=2\pi r\implies \cfrac{250}{2\pi }=r\implies \stackrel{cm}{39.79}\approx r[/tex]

The perimeter and area of the square are 16√5 mm and 80 mm²

Perimeter of a square = 4L

where

Therefore,

Perimeter of a square = 4 × 4√5

Perimeter of a square = 16√5 mm

Area of a square = l²

Area of a square = (4√5)²

Area of a square = 16 × 5

Area of a square = 80 mm²

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Answer:

[tex]9\pi[/tex]

Step-by-step explanation:

[tex]\text{Arc length,}~ s = r\theta\\\\~~~~~~~~~~~~~~~~~~=12 \times \left( \dfrac{135\pi}{180} \right)\\\\~~~~~~~~~~~~~~~~~~=9\pi[/tex]

Answer:

well i mean it all depends were you live at

Step-by-step explanation:

in new york it will be $36,198. but in California it would be about $31,682 and  Your average tax rate is 16.51% and your marginal tax rate is 24%.  

The point (1,6) belongs to the solution region of the system of inequalities.

The system of inequalities is given as:

y>1.5^x + 4

y< 2/3x + 6

Next, we plot both inequalities on a graph (see attachment)

From the attached graph, the point (1,6) is on the solution region of the inequalities

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The x coordinate of point A that is shown on the graph is 3π/16.

From the information given, y = kcos(8x). Also, the axis of symmetry is given as kx.

Therefore, the x coordinate will be:

= π/8 + π/16

The LCM of 8 as 16 is 16.

= 2π/16 + π/16

= 3π/16

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A percentage is a way to describe a part of a whole. The number of people who don't have pets is 50 people.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given at the Red bridge School, 1/3 of pupils have a pet dog 2/5 have cat and 1/15 have a hamster.

A.) Number of people who don't have pets = 1 - 1/3 - 2/5 - 1/15

                                                                        = (15-5-6-1)/15

                                                                        = 3/15

                                                                        = 1/5

B.) Given there are 25 people at the school. Therefore, the number of people who don't have a pet is,

Number of people who don't have pets = (1/5) × 250 = 50

C.) The percentage increase of pupils at the Bluebell School that has no pets compared to the Red bridge School is,

Percentage increase = (23%-20%)/20% × 100% = 15%

Hence, the number of people who don't have pets is 50 people.

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The solution of the inequality are (iii) and (iv)

The solution of the equality is x = 8.

The solution of the equality is x = 0.

The solutions of the inequalities can be found as follows:

x³ + 3(5 - 2) ≥ 20 - 4

x³+ 3(3) ≥ 16

x³+ 9 ≥ 16

x³ ≥ 16 - 9

x³ ≥  7

x ≥ ∛7

x ≥ 1.9

Therefore, (iii) and (iv) are solution.

4(72 - x²) = 3.12 - 4

288 - 4x² = 36  - 4

288 - 4x²= 32

-4x² = -256

x²=  256 / 4

x²=64

x= √64

x= 8

7(x + 12) = 7.12

7x + 84 = 84

7x= 84 - 84

7x= 0

x = 0

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Answer:

C

Step-by-step explanation:

Two negatives cancel out and turn into a positive.

In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8

So the answer is C

Answer:

[tex]B)~ 3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }[/tex]

Step-by-step explanation:

[tex]3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }\\\\\\= 3\sqrt{\dfrac 75} + i\sqrt{\dfrac 95 }\\\\\text{It is now in the standard form of a complex number (a+bi).}[/tex]

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).

If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:

a · 0² + b · 0 + c = 0     (1)

a · 1² + b · 1 + c = 16      (2)

a · 3² + b · 3 + c = 0      (3)

The solution to this system is a = - 8, b = 24, c = 0.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

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Answer:

Domain:

X is all the real numbers

or

[tex] - \infty < x < \infty [/tex]

Range:

[tex]y \leqslant 0[/tex]

or

[tex] - \infty < y \leqslant 0[/tex]

Step-by-step explanation:

This is the graph.

The amount of money Conor should save each month for 5 months is £136.

Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number.

The amount of money Conor should save each month = total amount needed / number of month

£680 / 5 = £136

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[tex]\sqrt[n]{a^n}=a[/tex], therefore [tex]\sqrt[4]{5^4}=5[/tex].

Answer:

It is 5

Key solutions:

Step-by-step explanation:

Isolate the exponents and remove the square, giving you 5

[tex]\left(\sqrt[4]{5}\right)^4\\=5[/tex]