Express the trig ratios as fractions in simplest terms.

Answer:

Adjacent, x = 60°

Step-by-step explanation:

Adjacent angles are pairs of angles next to each other. Vertical angles make an x shape, are across from each other, and have the same measure. These are adjacent angles.

This is a 90° angles, which is signified by the little red box. To solve for x, make an equation by adding the two angles together and set them equal to 90.

x - 30 + x = 90

2x - 30 = 90

2x - 30 + 30 = 90 + 30

2x = 120

2x/2 = 120/2

x = 60°

Here, the angles x° and (x - 30)° both are complementary angles, so they will add upto 90°, thus we can obtain a equation as ;

[tex]{:\implies \quad \sf x^{\circ}+(x-30)^{\circ}=90^{\circ}}[/tex]

[tex]{:\implies \quad \sf 2x^{\circ}-30^{\circ}=90^{\circ}}[/tex]

[tex]{:\implies \quad \sf 2x^{\circ}=120^{\circ}}[/tex]

[tex]{:\implies \quad \sf x^{\circ}=\dfrac{120^{\circ}}{2}=\bf \boxed{60^{\circ}}}[/tex]

Hence, the required value of x is 60

Answer:

B

Step-by-step explanation:

The second option is the answer

Hope this helps :)

2

x-9 = -5

2=x 2+x + 4-2=2 2-6+

-4

2

X

Answer:

w = 60

Step-by-step explanation:

the midsegment SU is half the measure of side RV, then

SU =  RV , so

w - 30 =  w ( multiply through by 2 to clear the fraction )

2w - 60 = w ( subtract w from both sides )

w - 60 = 0 ( add 60 to both sides )

w = 60

Here it is

.,.,.,.,..,.,.,.

Answer:

ans is 24000

Step-by-step explanation:

frist convert 12 into mins

/ it with 45

now multiple it with 1500

now ans 24000

(Assuming it works at a constant rate)

45 minutes = 3/4 of an hour

If it works for 12 hours, it works for 12 : 3/4 = 16 times more than 45 minutes.

Since it works at a constant rate, it must also print 16 times more paper than in 45 minutes.

So, in 12 hours, the machine print 1500 x 16 = 24000 (papers)

Answer:

58.55Kg

Step-by-step explanation:

450 in Kg is 0.45.

0.45 + 4.5 = 4.95. 4.95 + 53.6 = 58.55.

Answer:

B. X

Step-by-step explanation:

The variable is the unknown term.

This is represented by a letter.

In this case, the variable is "x".

So the answer is B.

Answer:

B.

Step-by-step explanation:

1) the given equation is provided in slope-interception form, then

2) the interseption is '-3', it means the point (0;-3) - the correct answer is either B or C;

3) the slope of the given line is more that 1 (3/2>1), it means the angle is [45°;90°], then the line of the answer B is satisfies this condition.*

4) finally, the correct answer is B.

* - if to substitute the point (2;0) then it will be true equality 0=0.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{y = x^2 - 6x + 19}\\\mathsf{y = 6^2 - 6(3) + 19}\\\mathsf{y = 36 - 18 + 19}\\\mathsf{y = 18 + 19}\\\mathsf{y = 37}[/tex]

~~~~~~~~~~~~~~~~~

[tex]\mathsf{y = -2x^2 + 20x - 49}\\\mathsf{y = -2(3)^2 + 20(3) - 49}\\\mathsf{y = -2(9) + 60 - 49}\\\mathsf{y = -18 + 60 - 49}\\\mathsf{y = 42 - 49}\\\mathsf{y = -7}[/tex]

~~~~~~~~~~~~~~~~~~~~~

[tex]\mathsf{y = -4x^2 + 24x - 21}\\\mathsf{y = -4(3)^2 + 24(3) - 21}\\\mathsf{y = -4(9) + 72 - 21}\\\mathsf{y = -36 + 72 - 21}\\\mathsf{y = 36 - 21}\\\mathsf{y = 15}[/tex]

~~~~~~~~~~~~~~~~~~~~~

[tex]\mathsf{y = 2x^2 - 3x + 7}\\\mathsf{y = 2(3)^2 - 3(3) + 7}\\\mathsf{y = 2(9) - 9 + 7}\\\mathsf{y = 18 - 9 + 7}\\\mathsf{y = 9 + 7}\\\mathsf{y = 16}[/tex]

~~~~~~~~~~~~~~~~~~~~

[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

(3,-3) (5,-3) (3,-6)

Step-by-step explanation:

y=-1 is now a horizontal line passing through the point (0,-1)

I hope this helps!!

Answer:

The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

anything with 10^n multiplied by a number from 0 to 10 is

Answer:

Step-by-step explanation:

Applying the formula for volume of a rectangular prism and volume of a cube, we would have:

a. 6/125 cm³

b. 8/125 cm³

c. 1/125 cm³

d. 36/125 cm³

a. Volume of rectangular prism = length × width × height = (1/5) × (2/5) × (3/5)

Volume of rectangular prism = 6/125 cm³

b. Volume of cube = (side length)³ = (2/5)³

Volume of cube = 8/125 cm³

c. Volume of cube = (side length)³ = (1/5)³

Volume of cube = 1/125 cm³

d. Volume of rectangular prism = length × width × height = (3/5) × (4/5) × (3/5)

Volume of rectangular prism = 36/125 cm³

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[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{0}~~,~~\stackrel{y}{9})\qquad \implies 9=ab^0\implies 9=a(1)\implies 9=a~\hfill \underline{y=9b^x} \\\\\\ (\stackrel{x}{10}~~,~~\stackrel{y}{9216})\qquad \implies 9216 = 9b^{10}\implies \cfrac{9216}{9}=b^{10}\implies 1024=b^{10} \\\\\\ \sqrt[10]{1024}=b\implies 2=b~\hfill \underline{y=9(2)^x}[/tex]

The Exponential function is [tex]y = 9(2^{x} )[/tex]

The mathematical expression for an exponential function is f (x) = aˣ where “x” denotes a variable and “a” denotes a constant that is the base of the function and ought to be greater than 0. The most regularly utilized remarkable capability base is the supernatural number e, which is roughly equivalent to 2.71828.

Given function

y = abˣ

and coordinates (0, 9) and (10, 9216)

when x = 0,  y = 9

[tex]y = ab^{x}[/tex]

substitute values

9 = ab⁰

9 = a

and [tex]y = ab^{x}[/tex]

when x= 10 and y = 9216

9216 = 9(b)¹⁰

1024 = b¹⁰

[tex]\sqrt[10]{1024}[/tex] = b

b = 2

[tex]y = 9(2^{x} )[/tex]

Hence equation is [tex]y = 9(2^{x} )[/tex].

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Answer:

Average speed = 40 mph.

Step-by-step explanation:

Step-by-step explanation:

Given:

32^(1/6)

To Find:

Convert to Radical form 32^(1/6)?

Solution:

here, given that- 321/6

Since, we know that - If n is a positive integer

that x and a is a real number or a factor, then

an = Vu?

=

now, using this rule to convert 321/6 to a radical,

where a=32, x=1 and n=6

√32

Hence,

Exact form:

32

Decimal Form:

2

The area of the sandbox is 5 x 5 = 25 square feet.

the cost of the sand = 25 square feet x 1.47 = $36.75

Answer: $36.75

Answer:

36.75

Step-by-step explanation:

5*5=25 ft^2

(area)

25*1.47=36.75

sand cost

The line RS would extend in both direction, while the ray TV would extend in one direction

A line is an undefined term of geometry; and it can only be defined through examples. However, the general notion is that a line extends in both directions without end

Rays are extracts from a line; that have a fixed point and an endless point

Using the above definitions, we can draw the line RS such that the point T is located on line RS and the point T extends to point V to form a ray TV

See attachment for the diagram

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Answer:

Question 1 )

given ,

height of cylinder = 9 cm

diameter of cylinder = 10 cm

[tex]\dashrightarrow \: radius = \frac{10}{5} \: cm \\ [/tex]

now ,

[tex]Volume \: of \: cylinder = \pi \: r {}^{2} h \\ \\ substitutng \: the \: values \: of \: h \: and \: r \: \\ \\ \dashrightarrow \: \pi \: \times (\frac{10}{2} ) {}^{2} \times 9 \\ \\ \dashrightarrow \: \pi \: \times 25 \times 9 \\ \\ \dashrightarrow \: 225\pi \: cm {}^{3} [/tex]

therefore ,

option (C) is correct.

______________________________________

______________________________________

Question - 2 )

dimensions of the rectangular prism are 2 × 3 × 4

[tex]Lateral \: surface \: area = 2h(l + b) \\ \\ \dashrightarrow \: 2 \times 3(4 + 2) \\ \\ \dashrightarrow \: 6(6) \\ \\ \dashrightarrow \: 36 \: cm {}^{2} [/tex]

hope helpful :D

The volume of the cylinder is 225 [tex]\rm cm^3[/tex]  and the lateral surface area of the rectangular prism is 36 square cm.

It is given that the radius of the cylinder is 10 cm and height is 9 cm.

It is required to find the volume of the cylinder.

It is defined as a three-dimensional space enclosed by an object or thing.

We know the volume of a cylinder given by:

[tex]\rm V = \pi r^2 h[/tex]

We have diameter = 10 cm

Radius r = 10/2 = 5 cm

and height h = 9 cm

Volume will be:

[tex]\rm V= \pi \times5^2 \times 9[/tex]

V = 225π cubic cm

For the lateral surface area = 2h(l+b)

= 2×3(4+2)

= 36 square cm

Thus, the volume of the cylinder is 225 [tex]\rm cm^3[/tex]  and the lateral surface area of the rectangular prism is 36 square cm.

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Answer:

B and D    

Step-by-step explanation:

in D 15x+9=15x+9

in B x=0

Answer:What is the probability of spinning a 2 on the spinner?

Image result for You roll a number cube and then spin a spinner with two equal-sized sections. What is the probability of rolling a number greater than 3 and spinning red? A. 1/4 B. 1/6 C. 1/3 D. 1/2

There are 2 sections on the spinner that contain a '2'. The probability of spinning a 2 is 2 / 8 . The probability of spinning a 3 is also 2 / 8

Step-by-step explanation:

The probability of rolling a number greater than 3 and spinning red is 1/4.

We need to determine the favorable outcomes (the outcomes that satisfy both conditions) and the total possible outcomes.

The numbers greater than 3 and corresponding to the red section are: 4R, 5R, and 6R. So, there are 3 favorable outcomes.

Since we have a number cube with 6 sides and a spinner with 2 sections, the total possible outcomes are the product of the number of sides on the cube and the number of sections on the spinner, which is 6 × 2 = 12.

The probability is calculated by dividing the number of favorable outcomes by the total possible outcomes.

Probability = Favorable outcomes / Total possible outcomes

= 3 / 12

= 1 / 4

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As the histogram is skewed to the right because there is less data on the right side. So, she is correct that is option D.

A histogram graph is a graphical representation of given data. It is a bar graph that represents a frequency distribution by rectangles separated from each other with equal spaces.

A graph shows several dogs labeled 0 to 2 on the horizontal axis and frequency on the vertical axis.

here, we can see from a given data that as the number of dogs increases the frequency on the vertical axis decreases. At 0 dogs the frequency is 20, at 1 dog the frequency is 15, At 2 dogs the frequency is 12.

The histogram is skewed to the right because there is less data on the right side as the frequency decreases.

Therefore, the histogram is skewed to the right because there is less data on the right side. So, she is correct that is option D.

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Answer:

d

Step-by-step explanation:

Answer:

3 cups. 15 cookies to 1 cup of flour.

Step-by-step explanation:

The answer is 3 cups. The first thing you do is find the unit rate. Divide 30 by 2 and you know that 1 cup of flour makes 15 cookies. Then divide 45 by 15 which is 3 and which tells you that 3 cups of flour makes 45 cookies.

The kinetic energy that the coaster must have before it goes up is: 13.3megajoules.

Kinetic energy refers to the energy that a body possesses due to its motion. It's known to be the energy needed to move a body of a given mass from rest to its stated velocity.

We can calculate the kinetic energy of the Kingda Ka roller in the following way:

K.E = Potential Energy

K.E = mgh

Where: m = mass = 9750

g = acceleration due to gravity = 9.8m/s²

h = height = 139m

Thus: K.E = 9750 x 139 x 9.8 = 13,281,450J

= 13.3megajoules.

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Answer:

2 electrons

Step-by-step explanation:

2 electrons is the answer

If u need explanation do mention in comments

Answer:

*2 electrons more*

Explanation:

Otherwise, it will have charge and form ions.   [ ignore the neutrons ]

Here,

The electron and proton is unbalanced, In order to make them same.

2 more electrons need to be added to make total 6 electrons.

Answer:

871 miles

Step-by-step explanation:

737/11= 67

67 x 13= 871

Answer:

The range is the best measure of variability because the distribution has an outlier.

Either the IQR or the range are good measures of variability because the distribution has no outliers.

The IQR is the best measure of variability because the distribution has an outlier.

Step-by-step explanation:

is this what you was looking for

Given A room is half as long again as it is broad

Let the breadth of the room x m

length of the room x + x/2 = 3x/2m

Area of the room , x × 3x/2 = 3x²/2m

Given , cost of carpeting the room at Rs. 3.25m⁻²

So , total cost , 3x²/2 × 3.25

But , Total cost of carpeting is given as 175.50 so ,

let the height of the room H m

Area of the four wall = 2(L+ b)× h 2(6+9)× H

= 30H m²

Area of the of the one door and two window is 8m²

8m² Area to be prepared = Area of four wall - area of two window and 1 door = (30H - 8) m²

Given cost of preparing wall is Rs. 1.40m²

total cost of preparing wall is (30H - 8) × 1.40

Total cost of preparing wall is given as 240.80

comparing , (30H - 8 ) × 1.40 = 240.80

Hence, Dimensions of the room are lengths 9m , breadth 6m and height 6m