What is the value of x?

Answer:

55.8

Step-by-step explanation:

cos(x)=9/16

x=55.8

The angle of elevation of the ladder is approximately 60.5 degrees.

To find the angle of elevation (x) of the ladder, we can use trigonometry. The ladder, the side of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse of the right triangle, and the distance from the bottom of the ladder to the house is one of the legs.

Using the tangent function:

tan(x) = opposite/adjacent

tan(x) = 16 ft / 9 ft

Now, solve for x:

x = arctan(16/9)

Using a calculator, we find

x ≈ 60.5 degrees

So, the angle of elevation of the ladder is approximately 60.5 degrees.

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Answer:

-8+2i and -8+2i

Step-by-step explanation:

here simply we'll use general formula

x= (-b +or - √ b^2-4ac)/2a

Answer:

Step-by-step explanation:

The graph of f(x) = –x^2 + 5 is that of an upside-down parabola with vertex (0, 5) and x-intercepts (-√5, 0) and (+√5, 0).  Plot the vertex (0, 5) and then draw a smooth curve through it and through the x-intercepts.

The function f(x) = -x2+5 is thus represented by the quadratic functions in the first graph.

A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero.  Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.

here calculation

The function provided is f(x) =  -x2+5

.... (1) (1)

We must locate the function's graph.

The quadratic function's vertex form is f(x)= a(x-h)2 + k.... (2)

When we compare (1) and (2), we obtain

h=0 , k=5

It denotes that the function's vertex is (0,5).

The values list is

x           y

-2            1

-1            4

0            5

1            4

2           1

Place all ordered pairings on a coordinate plane, and then use a free-hand curve to link them.

The function f(x) = -x2+5 is thus represented by the quadratic functions in the first graph.

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Answer: $5 per calculator

Step-by-step explanation: divide 125 and 25

Answer:

5$

Step-by-step explanation:

Given:

25 calculators cost 125.00

So:

_______ DIvide the cost of calculators by the number of calculators, and we get 5$

Answer:

~~~~~~~~~~~~~~~~~~~~~~~~~.~~~~~~~~~~~~~~~~~~~~~~~~~

Step-by-step explanation:

Answer:

y = 48

Step-by-step explanation:

Start with the given 3y = 150.

Solve this for y by dividing both sides by 3:  y = 50

Then y - 2 = 50 - 2, or

        y    =    48

The value of y-2 is 48,

Two expressions connected by an equal sign makes an equation.

Given is an equation, 3y = 150

Solving for y,

3y = 150

y = 150 / 3

y = 50

therefore, y-2 = 50-2

= 48

Hence, the value of y-2 is 48,

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Answer:

The work done is 202.50Nm

Step-by-step explanation:

Given

[tex]F =450N[/tex]

[tex]x_1 = 30cm[/tex]

[tex]x_2 = 60cm[/tex]

Required

The work done

First, we calculate the spring constant (k)

[tex]F = kx_1[/tex]

[tex]450N = k *30cm[/tex]

[tex]k = \frac{450N}{30cm}[/tex]

[tex]k =15N/cm[/tex]

So:

[tex]F = kx_1[/tex]

[tex]F(x) = 15x[/tex]

The work done using Hooke's law is:

[tex]W =\int\limits^a_b {F(x)} \, dx[/tex]

This gives:

[tex]W =\int\limits^{60}_{30} {15x} \, dx[/tex]

Rewrite as:

[tex]W =15\int\limits^{60}_{30} {x} \, dx[/tex]

Integrate

[tex]W =15 \frac{x^2}{2}|\limits^{60}_{30}[/tex]

This gives:

[tex]W =15 *\frac{60^2 - 30^2}{2}[/tex]

[tex]W =15 *\frac{2700}{2}[/tex]

[tex]W =15 *1350[/tex]

[tex]W =20250N-cm[/tex]

Convert to Nm

[tex]W =\frac{20250Nm}{100}[/tex]

[tex]W =202.50Nm[/tex]

Answer:

41

Step-by-step explanation:

The minimum value of the data set is located at the end of the whisker on the left side of the box plot.

The minimum value is 41

9514 1404 393

Answer:

  D

Step-by-step explanation:

The inequality symbol is < (not ≤), which means the end point of the graph will be an open circle.

After dividing by the coefficient of x, you have an inequality of the form ...

  x +( ) < ( )

which means the solution will be left of the (open circle) end point of the graph. Only one graph has that form.

__

If you actually work through the numbers, you get ...

  x +8 < 9 . . . . . . divide both sides by 2.9

  x < 1 . . . . . . . . . subtract 8 from both sides

9514 1404 393

Answer:

  {5, 10, 15, 20}

Step-by-step explanation:

Multiples of 5 are of the form 5n, where n is an integer. The ones of interest will satisfy ...

  0 < 5n < 23

  0 < n < 4.6

That is, the multiples of 5 we want are for values of n that are 1 through 4. The set is ...

  5 × {1, 2, 3, 4} = {5, 10, 15, 20}

Answer:

here

Step-by-step explanation:

C and D is the answer

Answer:

y=5

y int

x=0

y=2(0)^2-8(0)+5

y=5

note everything multiplied by 0 is 0

No, 50 by 50 chance.

Answer:

The equation is x = 5

Answer:

x = 5

Step-by-step explanation:

Answer:

[tex] {x}^{2} = 5 - x \\ { \tt{ {x}^{2} + x - 5 = 0 }} \\ \\ { \bf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ \\ { \tt{x = \frac{ - 1± \sqrt{21} }{2} }} \\[/tex]

9514 1404 393

Answer:

  Tim is correct. 5/8 > 1/2

Step-by-step explanation:

By taking 5/8 of the lasagna, Tim will be taking more than half (4/8) of it. No remaining share can be larger. Any remaining share will be 3/8 or less, so will be smaller than a 5/8 share.

Tim's 5/8 share is the largest.

9514 1404 393

Answer:

  A

Step-by-step explanation:

It is usually sufficient to look at one section of the graph to answer a question like this. Often the best choice is the section that has a solid dot at the end of the curve. Here, that is the right section.

The left end of the right section is at x=-2, so that part of the function is defined for x ≥ -2. The line to the right has a positive slope, so the coefficient of x will be positive.

Only one answer choice has a positive x-coefficient for x ≥ -2.

  [tex]\textbf{A. }\begin{cases}-x-2&\text{if }x<-2\\x+4&\text{if }x\ge-2\end{cases}[/tex]

Answer:

Step-by-step explanation:

This graph is made up of two different, separate line segments.  In other words, it comes in two pieces which can be described as a pair of linear functions.

We call this a "piecewise linear" function.  Choice A is the best one.

Answer:

11. (a) 3/4+1/2=5/4

   (b) 4/5= 8/10 , 16/20

12. 8 children don't like choc ice cream

Step-by-step explanation:

11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)

12. 3/5 of 20 = 12

     20-12=8

Answer:

[tex]\sin(G) = \frac{8}{17}[/tex]

Step-by-step explanation:

Given

[tex]\angle H = 90^o[/tex]

[tex]FH = 8[/tex]

[tex]GF = 17[/tex]

[tex]HG = 15[/tex]

See attachment for illustration

Required

The ratio of [tex]\sin(G)[/tex]

[tex]\sin(G)[/tex] is calculated as:

[tex]\sin(G) = \frac{Opposite}{Hypotenuse}[/tex]

From the attachment, we have:

[tex]\sin(G) = \frac{FH}{GF}[/tex]

This gives:

[tex]\sin(G) = \frac{8}{17}[/tex]

The percent of 10.2 gram of 32 mg is gotten to be; 31.875%

When we are trying to find the percentage with the expressions "if" and "of", we will use the formula;

is/of *100%

Now, we want to find the percentage of 10.2 gram of 32 mg. Thus, the percentage is expressed as;

10.2/32 * 100% = 31.875%

Thus, the percent of l0.2 gram of 32 mg is gotten to be 31.875%

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9514 1404 393

Answer:

  D

Step-by-step explanation:

Multiplying the inequality by 2 will eliminate the fraction and give you ...

  x ≤ 36

The "or equal to" part of the symbol means the end dot will be solid. The "less than" part of the symbol means the graph is shaded to the left of the end dot, which is at x=36. This description matches the graph shown below.

Answer:   24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Volume is length times width times height so you just have to multiply 3 by 4 by 2 to get 24.

Answer:

/ROB.UX ME 1,000,000,000

Step-by-step explanation:

Answer:

.073398

Step-by-step explanation:

It's easiest to use a binomial distribution here

We have...

14C8*.75⁸*(1-.75)⁶= .073398

Answer:

Ŷ = -1.7391+0.8913X

Step-by-step explanation:

Given the data :

husband 23,27 ,28,28,29, 30,31,33,35,36

wife 18,20,22,27,21,29,27,29,28,29​

Taking :

Husband as (X)

Wife as (Y)

We could use technology to fit the data and obtain a regression model.

Using technology ; the regression equation obtained is:

Y = -1.7391+0.8913X

Where

Y = wife

X = husband

Slope = 0.8913

Intercept = - 1.7391

Answer:

[tex]n(A\ u\ B) = 10[/tex]

[tex]n(A'\ u\ C) = 10[/tex]

[tex]n(A\ n\ B)' = 6[/tex]

Step-by-step explanation:

Given

[tex]n(U) = 12[/tex]

[tex]n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6[/tex]

[tex]n(A\ n\ B\ n\ C)=4[/tex]

[tex]n(A\ u\ B\ u\ C)=10[/tex]

Required

Solve a, b and c

There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)

Solving (a):

[tex]n(A\ u\ B)[/tex]

This is calculated as:

[tex]n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)[/tex]

From the attachment

[tex]n(A) = 0+2+4+2 = 8[/tex]

[tex]n(B) = 0+2+4+2 = 8[/tex]

[tex]n(A\ n\ B) = 4 +2 = 6[/tex]

So:

[tex]n(A\ u\ B) = 8 + 8 - 6[/tex]

[tex]n(A\ u\ B) = 10[/tex]

Solving (b):

[tex]n(A'\ u\ C)[/tex]

This is calculated as:

[tex]n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)[/tex]

From the attachment

[tex]n(A) = n(U) - n(A) = 12 - 8 = 4[/tex]

[tex]n(C) = 0+2+4+2 = 8[/tex]

[tex]n(A'\ n\ C) = 2[/tex]

So:

[tex]n(A'\ u\ C) = 4 + 8 - 2[/tex]

[tex]n(A'\ u\ C) = 10[/tex]

Solving (c):

[tex]n(A\ n\ B)'[/tex]

This is calculated as:

[tex]n(A\ n\ B)' = n(U) - n(A\ n\ B)[/tex]

[tex]n(A\ n\ B)' = 12- 6[/tex]

[tex]n(A\ n\ B)' = 6[/tex]

Answer:

B) this line has zero slope.

Step-by-step explanation:

it doesn't increase or decrease. it is a constant; zero

Answer:

This line has zero slope.

Step-by-step explanation:

The slope of the line doesn't change it just stays straight.