For each graphically defined function below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.


Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?

Answer:

See below ~

Step-by-step explanation:

Question 4

Finding the lateral area :

⇒ Lateral area = 2πrh

⇒ Lateral area = 2π(8)(20)

⇒ Lateral area = 320π cm²

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

Finding the surface area :

⇒ Surface area = Lateral area + 2 × area of the circle

⇒ Surface area = 320π + 2 × π(8)²

⇒ Surface area = 320π + 128π

⇒ Surface area = 448π cm²

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

Question 5

⇒ In this scenario, the part that is painted is the lateral area

⇒ Area painted = 6 × 4 × 170

⇒ Area painted = 24 x 170

⇒ Area painted = 4,080 mm³

Answer: 5+10-15=30

5=35

=7

х=49

5√49+10-15=30

30=30

+1+7=4

=-4

it is no solution

Step-by-step explanation:

Answer:

2nd option, (6x + 8)(x - 1) = 0

Step-by-step explanation:

Answer:

[tex](6x+8)(x-1)[/tex]

Step-by-step explanation:

We can separate the 2x into -6x + 8x. Then this will give us [tex]6x^2 - 6x + 8x - 8 = 0[/tex]. Now we can factor out a 6x and an 8 to give us [tex]6x(x-1) + 8(x-1) = (6x+8)(x-1)[/tex] by the distributive property.

Hope this helps! :)

Answer:

[tex]=15km[/tex]

Explanation:

[tex]12[/tex] [tex]km[/tex] ÷ [tex]4[/tex]

[tex]=3[/tex] [tex]km[/tex] per trip to school

Now that we know that Layla walks 3 km to walk to school, we multiply that by 10

[tex]3[/tex] [tex]km[/tex] × [tex]5[/tex] [tex]trips[/tex]

[tex]=15[/tex] [tex]km[/tex]

∴ Layla walked 15 km in total

Answer:

I think 24.

Step-by-step explanation:

Answer:

They bought 32 pencils

Step-by-step explanation:

5.76 divided by 0.18 = 32

Answer:

≈ [tex]\sf 203[/tex]

The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

The equations are given as:

tan(x)=sin38°

cosec( x+10°)=1.345​

In tan(x)=sin38°, we have:

tan(x)=0.6157

Take the arc tan of both sides

x = 31.6

Also, we have:

cosec(x+10°)=1.345​

Take the inverse of both sides

sin(x+10°) = 0.7434

Take the arc sin of both sides

x+10 = 48.0

Subtract 10 from both sides

x = 38.0

Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

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Answer:

Linear

Step-by-step explanation:

X = X + 1

Y= Y *3

A table of data is linear if there is a constant average rate of change between all pairs of points

There is because X is being added one every time and Y is being multiplied by 3 every time.

Hope this helps!

Answer:

  3

Step-by-step explanation:

The difference of the two y-coordinates is found by ...

  a) identifying the y-coordinates

  b) computing their difference.

__

Each ordered pair lists the y-coordinate second.

  (0, 3)   ⇒   y-coordinate = 3

  (4, 0)   ⇒   y-coordinate = 0

The difference of the y-coordinates is ...

  3 -0 = 3

Answer:

A or 2

Step-by-step explanation:

Reason:

The 5's cancel out leaving the 2 behind as the final answer.

Another way to look at it is that the 5*2 up top multiplies to 10, then we divide that by the 5 in the denominator to end up with 10/5 = 2

If you are a visual learner, then draw a circle and divide it into 5 equal slices. Do this a total of five times. Each pizza having 2 slices, and 5 pizzas total, gives 2*5 = 10 slices overall. These ten slices can be rearranged into making 2 full pizzas.

See below.

Answer:

The answer should be 420.

~

Step-by-step explanation:

Answer:

The triangle is a right triangle.

Step-by-step explanation:

Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:

[tex]a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256[/tex]

Therefore, the triangle is right.

Answer:

17,964.9 cubic meters

Step-by-step explanation:

Hey there!

The formula for finding the area of a sphere is:

[tex]V=(4/3)\pi r^3[/tex]

Where V is volume, and r is radius

The question already tells us that the diameter is 32.5m

*Remember, the diameter isn't the radius. It is the radius times two*

Now, we have to divide 32.5 by 2 to get the radius

32.5/2 is 16.25

Now we can plug this into the formula

16.25 cubed is 4291 after being rounded to the nearest tenth

Now we multiply 4291 by 3.14 (pi)

4291 x 3.14 is 13473.7 after being rounded to the nearest tenth

Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere

13473.7 x 4/3 is 17964.93333333...

Since it is asking us to round to the nearest tenth of a cubic meter;

The volume of the sphere will be 17,964.9 cubic meters

[tex]\rule{300}{1}[/tex]

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?

[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

We are asked to find the volume of a sphere, which we can find using the following formula:-

[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]

[tex]\bold{r=d\div2}[/tex]

Replace d with 32.5:-

[tex]\bold{r=32.5\div2}[/tex]

Therefore, the sphere's radius is as follows:-

[tex]\bold{r=16.25}[/tex] m

[tex]\rule{300}{1}[/tex]

Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-

[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]

Replace r with 16.25:-

[tex]\bold{V=\dfrac{4}{3} \pi (4291)}[/tex]           Next, we replace π with 3.14:-

[tex]\bold{V=\dfrac{4}{3} \times3.14\times4291}[/tex]

On simplification,

[tex]\bold{V=\dfrac{4}{3} \times13,473.74}[/tex]

On further simplification,

[tex]\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}[/tex]

[tex]\rule{300}{1}[/tex]

using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]

Indices in mathematics can be defined as a value that takes up in index form but still retain its magnitude.

It is writing big or complicated values in a simpler and smaller way.

Indices is so important for simplicity purposes.

in conclusion, using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]

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Answer:

Step-by-step explanation:

The parameter of interest can be found by putting the given values into the appropriate volume or area formula for a pyramid, then solving for the unknown. The relevant formulas are ...

  V = 1/3s²h . . . . . s is the base length; h is the height

  A = s(s +2h) . . . . s is the base length; h is the slant height

__

Using the given values for the volume and the length of the base, the formula becomes ...

  V = 1/3s²h

  96 m³ = 1/3(6 m)²h . . . . . . . . . . use the given values for V, s

  (96 m³)/(12 m²) = 8 m = h . . . . . divide by the coefficient of h

The height of the pyramid is 8 meters.

__

Using the given values for area and the length of the base, the formula becomes ...

  A = s(s +2h)

  47.25 in² = (3.5 in)(3.5 in + 2h) . . . . use the given values for A, s

  13.5 in = 3.5 in + 2h . . . . . . . . . . . divide by 3.5 in

  10 in = 2h . . . . . . . . . . . . . . . . . subtract 3.5 in

  5 in = h . . . . . . . . . . . . . . . . divide by 2

The slant height of the pyramid is 5 inches.

Answer:

4

Step-by-step explanation:

The ratio of the area of sector abc to the area of sector dbe is 4:3

The formula for calculating the area of a sector is expressed as:

A = r²Ф

where:

For the sector ABC

A1 = (2r)²β
A1 = 4r²β

For the sector DBE
A2 = (r)²3β
A2 = 3r²β

Take the ratios

Ratio= A1/A2
Ratio = 4r²β/3r²β
Ratio = 4/3

Hence the ratio of the area of sector abc to the area of sector dbe is 4:3

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Answer:

Step-by-step explanation:

Y=6x - 7

6x - 7 = Y

6x = Y + 7

6x/6 = Y + 7/6

X = Y + 7

Answer:   Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B

Step-by-step explanation:

* Lets revise the vertical and horizontal stretch with reflection

- A vertical stretching is the stretching of the graph away from the

x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

by multiplying each of its y-coordinates by k.

- If k should be negative, the vertical stretch is followed by a reflection

across the x-axis  

- A horizontal stretching is the stretching of the graph away from

the y-axis

- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally

stretched by dividing each of its x-coordinates by k.

- If k should be negative, the horizontal stretch or shrink is followed

by a reflection in the y-axis

* Lets solve the problem

∵ G(x) = sin x

∵ F(x) = -5.8 sin x

∴ F(x) = -5.8 G(x)

- From the rule above

∴ G(x) is stretched vertically by scale factor -5.8

∵ The scale factor is negative

∴ The vertical stretch is followed by a reflection across the x-axis  

* The transformation is:

 Vertical stretch by a factor of 5.8 , reflection across x-axis

To find a certain part of the arc:

   ⇒ we find a fraction of the circumference

Based on the diagram and information given:

         ⇒ which spans 116 degrees of the entire 360 degrees the whole

             arc covers

Thus let's solve:

  [tex]Length_.of_.arc = (\frac{116}{360})*(2*\pi *14)[/tex] ≈ [tex]28.34_.meters[/tex]

Answer: 28.34 meters

Hope that helps!

The value of cot x/2 is √3/√5.

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations.

given:

cos x=-1/4

sin x= √15/4

cosec x= 4/√15

and, cot x= -1/√15

Now, cot x/2= cosec x+ cot x

= 4/√15-1/√15

= 3/√15

= √3/√5

Hence, the value of cot x/2 is  √3/√5.

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Answer:

₹165.79

Step-by-step explanation:

Given:-

No. of electric bulbs = 1000

cost of each electric bulb = ₹ 150

No. of bulbs broken = 50

Selling price of each bulb = x

Profit percentage = 5%

To Find:-

The selling price of each bulb.

Solution:-

Cost price of 1000 electric bulbs,

= 1000 × ₹150

= ₹1,50,000

5% profit on the total cost price,

= {5}/{100}× ₹150000

= ₹7500

Total selling price = ₹157500

No. of bulbs remaining = 950

Therefore, selling price of each bulb,

= {₹157500}/{950}

= ₹165.79

Therefore,

Selling price of each bulb = ₹165.79

Answer:

If I'm right, the answers should be 40.

Answer:

Step-by-step explanation:

Figure Interpretation:

m∠CBA + m∠CDE = 180

m∠BCA = (180-m∠CBA)/2

m∠DCE = (180-m∠CDE)/2

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

Then

m∠BCA + m∠DCE = (180-m∠CBA)/2 + (180-m∠CDE)/2

                                = [360-(m∠CBA+m∠CDE)]/2

                                = [360 - 180]/2

                                = 90

finally,

m∠ACE= 180 - (m∠BCA + m∠DCE)

             = 180 - 90

             = 90

Answer:

IQR = 9

Step-by-step explanation:

Q3 = 24

Q1 = 15

24-15=9

Give brainliest, please!

Hope this helps :)