given that y= 6 cm and θ= 32 °, work out x rounded to 1 dp.


(not drawn to scale)

The complete question is

"A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°, 17.5°, 72.5°,73.3°"

The value of angle x would be 16.7 degrees.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

In order to find the value of x, a tan would be used.

This is because we have given the opposite and adjacent sides as 10 ft and 3 ft.

Tan Ф = opposite / adjacent

Tan Ф =  (3/10)

= 16.7 degrees

The value of angle x would be 16.7 degrees.

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Answer: the answer is 16.7°.

Step-by-step explanation: it show below.

Answer:

D.

Step-by-step explanation:

0.45*5=2.25

0.25*9=2.25

2.25*2=4.50

Hope this helps!

If not, I am sorry.

Answer:

  B.  180° about the origin

Step-by-step explanation:

You are given a figure and its image, and asked to determine the angle of rotation. All of the answer choices indicate the center of rotation is the origin.

__

You have two clues that the rotation is 180° about the origin:

__

To find the angle of rotation, you can look at the angle formed by a point, the center of rotation, and the image of the original point. Here, the angle UOU' is a straight angle, so the angle of rotation about O is 180°--the measure of that angle. (It can be convenient to use points close to the center of rotation, but any corresponding points on preimage and image will do.)

Answer:

c

cuz it is

first of all 4,3 + 0,0 = 4,3

2,1+0,0 = 2,1

and which is the answer

Answer:

x = 100

Step-by-step explanation:

[tex]4x^{2} -371=29\\[/tex]

      + 371   +371

[tex]4x^{2} =400[/tex]

[tex]\sqrt{4x^{2} } =\sqrt{400}[/tex]

[tex]4x=400[/tex]

Divide both sides by 4.

x = 100

Hope it helps!

The probability that none of the prizes is a $10 gift certificate is; 7/99

The expected number of $20 gift certificates drawn is 2.083

This is a question of picking objects from a mixture without replacement. The modelling distribution is the hypergeometric distribution, given by the formula:

P(a) = C(A,a) * C(B,b)/C(A+B,a+b)

Where;

a = number of good objects picked

b = number of bad objects picked.

A = number of good objects in the given batch.

B = number of bad objects in the given batch.

a + b = total number of objects picked without replacement.

A + B = total number of objects in the batch.

A) In this question;

A = 4 ($10, good)

B = 3 + 5 = 8 ($20, $50, "bad")

a = 0, b = 5

a + b = 5

Thus;

P(a = 0) = C(4, 0) × C(8, 5)/C(12, 5)

P(a = 0) = 1 × 56/792

P(a = 0) = 7/99

B) $20 is the "good" prize.

Thus;

A = 5

B = 3 + 4 = 7

a + b = 5 (total number of prizes drawn)

Thus;

E[$20] = (5/(5 + 3 + 4)*5)

E[$20] = (5/12)*5

E[$20] = 25/12

E[$20] = 2.083

Complete Question is;

The door prizes at a dance are four $10 gift certificates, five $20 gift certificates, and three $50 gift certificates. The prize envelopes are mixed together in a bag, and five prizes are drawn at random.

What is the probability that none of the prizes is a $10 gift certificate?

What is the expected number of $20 gift certificates drawn?

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[1] t ≥ 45

   Since Isabel exercises more ("no less") than 45 minutes a day, we will use greater than or equal to.

-> because being equal is not less, hence still "no less"

[2] f ≥ 45

   Because the vehicle's fuel is "at least" that means it can also be equal too, hence the user of greater than or equal to.

Answer:

16 feet

Step-by-step explanation:

her first try is 2 and you multiply by 2 every time so her first would be 2 which we would multiply to get 4 which we would multiply again to get 8 which we would multiply AGAIN to get the final answer of 16

Answer:

14

29  as a fraction

Step-by-step explanation:

Based on the given conditions, formulate:

14=19+14+6）

2 Calculate

14

9+14+6

Calculate

14

23+6

Calculate the sum or difference

14

29

X

Calculate the sum or difference

14

29

Alternative forms

~ 0.482759, ~ 48.275862%,

4.827586 × 10

Hope it help :)

Answer:

0.125 times larger

Step-by-step explanation:

given the scale factor of 2 solids is k , then the volume  factor = k³

here k = 0.5 , so

volume factor = (0.5)³ = 0.125

Answer:

56

Step-by-step explanation:because 12345

The equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

The expression is given as:

9q^ 2 - 2/3(3q - 7) + 5q^2

Open the bracket

9q^ 2 - 2q - 14/3 + 5q^2

Evaluate the like terms

14q^ 2 - 2q - 14/3

Hence, the equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

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Answer:

P(5 ≤ X ≤ 8)  = a  rectangle  with a width of 3  and height of .15   = 3(.15)  = .45

P( 4 ≤ X ≤ 5)  =  a triangle  with a base of 1  and a height of (0.15 -0.05) = .10

So....this area  =   (1/2)(1)(.10)  = .05

And  another rectangle with a width of 1 and height of .05  = (1) (.05) = .05

So

Adding these areas

P( 4 ≤ X ≤ 8 )  =  .45 + .05 + .05   =  .55

Step-by-step explanation:

Hoped this helped!

The range of the exponential function will be y ≥ 250,0003. Then the correct option is B.

The domain means all the possible values of x and the range means all the possible values of y.

The Population Of Center City Is Modeled By Exponential Function F, Where X Is The Number Of Years After The Year 2015.

The graph is given below.

We know that the exponential function is given as

y = abˣ

For x = 0, y will be 250,000

250,000 = a

For x = 40, y will be 400,000

400,000 = 250,000b⁴⁰

           b = 1.0118

Then we have

y = 250,000 (1.0118)ˣ

Then the range of the exponential function will be y ≥ 250,0003.

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Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:

all real numbers greater than 0.

It is the set that contains all possible output values for the function.

In this problem, the function is:

[tex]f(x) = 9^x[/tex]

For exponential functions without vertical shifts, as is the case in this problem, the range is given by:

all real numbers greater than 0.

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The total purchase price of the dictionary and the software package is  $61.47.

The total purchase price is the sum of the dictionary, software package and taxes.

Total cost of  the dictionary and the software package = $27.65 + $29.80 = $57.45

Total cost after the taxes = ( 1 + 0.055 + 0.015) x $57.45 = $61.47

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Answer:

375 plates were sold

Step-by-step explanation:

$2400 (profit) - $150 (advertising) = $6 (profit per plate $8 cost - $2 expense) times x

2400 - 150 = 6x

Simplify the left side: 2400 - 150 = 2250

2250 = 6x

Divide both sides by 6

2250/6 = 375

Answer:

The height of the ladder is 6.9 meter

Explanation:

Given:

As opposite and hypotenuse given, use sine rule:

[tex]\rightarrow \sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\rightarrow \sf sin(60) = \dfrac{6}{h}[/tex]

[tex]\rightarrow \sf h = \dfrac{6}{sin(60)} = 4\sqrt{3} = 6.928 \ meters \quad \approx \ 6.9 \ meters \ \ (one \ decimal \ place)[/tex]

Answer:

1

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]

The current equation of the perpendicular line;

 ⇒ is the slope-intercept form: [tex]y= mx + b[/tex]

Now for the point-slope form, we need a point on the line and the slope of the line:

⇒ we have

Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]

 ⇒ where the (x₁,y₁) is the point on the line and m is the slope

    [tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]

To convert the equation to slope-intercept form:

  ⇒ must isolate 'y' to one side and everything to the other side

      [tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]

Answer: [tex]y = -\frac{3}{2}x+1[/tex]

Hope that helps!

The boat suspended by wire ropes AB and AD, AC is 4 units high.

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

The gradient of AB is 0.8, hence:

AC / BC = 0.8

Since BC = 5, therefore:

AC / 5 = 0.8

AC = 4

The boat suspended by wire ropes AB and AD, AC is 4 units high.

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Answer: B.

Step-by-step explanation:

   See attached. We examine the equation and decide which situation, or problem, models it correctly.

El volumen es una cantidad escalar tridimensional. El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.

Un volumen es un número escalar que expresa la cantidad de espacio tridimensional encerrado por una superficie cerrada.

El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm será,

Volumen del cilindro = (π/4)×diámetro ²×altura

                                = (π/4)×(50cm)²×30cm

                                = 58,904.863cm³

Por lo tanto, el volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.

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If ɑ and β are the roots of x² + bx + c = 0, then we can write

x² + bx + c = (x - ɑ) (x - β)

Expanding the right side gives

x² + bx + c = x² - (ɑ + β) x + ɑβ

so that ɑ + β = -b and ɑβ = c.

Recall that for all real numbers m and n,

(m + n)² = m² + 2mn + n²

a) It follows that

(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c

(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c

b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is

(x - (ɑ² + β²)) (x - (ɑ - β)²)

Using the results from part (a), this becomes

(x - (b² + c)) (x - (b² - c))

and expanding, we get

x² - (b² + c + b² - c) x + (b² + c) (b² - c)

= x² - 2b² x + b⁴ - c²

Answer: 36

Step-by-step explanation:

[tex]g(2)=2^{2}=4\\g(3)=3^{2}=9\\g(2) \cdot g(3)=4 \cdot 9=\boxed{36}[/tex]

Answer: number 1 and number 2 and 4 and 5

Step-by-step explanation:

Answer:

the solution  is (1,-4)

Step-by-step explanation:

Answer:

reason 1.) This is the original expression

reason 2.) you subtract 4 from both sides

reason 3.) you divide both sides by 2 to get x=5

Answer:

Step-by-step explanation:

Part A

Neighborhood A :

2, 2, 2, 4, 4, 5, 5, 5, 5

mean = [tex]\frac{2+2+2+4+4+5+5+5+5}{9}[/tex] = [tex]\frac{34}{9}[/tex] ≈ 3.8  

median = 4

mode = 5

range = 3

[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 2 = 3

===================

Part B.

Neighborhood B :

1, 1, 2, 2, 3, 4, 5, 5, 12

mean = ( 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 12 ) ÷ 9 = [tex]\frac{35}{9}[/tex] ≈ 3.9

median = 3

mode = 1, 2, 5

range = 11

[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 1.5 = 3.5

Outlier = 12