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Using the trigonometric ratios, the value of cos F in the right angle triangle is 0.28 .

Right angle triangle are triangle that has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore,

cos F = adjacent / hypotenuse

adjacent = FE

hypotenuse = 50

50² - 48² = FE²

FE = √2500 - 2304

FE = √196

FE = 14

Therefore,

cos F = 14 / 50

cos F = 0.28

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Answer:

2,106 pi mm3

Step-by-step explanation:

Volume of the drill bit is equals to [tex]2,106\pi mm^{3}[/tex].

" Volume is defined as the total space occupied by a three dimensional object enclosed in it. It is measured in cubic unit."

Formula used

Volume of the cone =  [tex]\frac{1}{3} \pi r^{2}h[/tex]

Volume of the cylinder =[tex]\pi r^{2}h[/tex]

r = radius of the cone / cylinder

h = height of the cone / cylinder

According to the question,

Given,

Radius of the cylinder = 9 mm

Radius of the cone = 9 mm

Height of the cone = 24 mm

Height of the cylinder = 18 mm

Substitute the values in the formula to obtained the required volume,

Volume of the cone [tex]= \frac{1}{3} \pi (9^{2})(24)[/tex]

                                 [tex]= \pi (81)(8)\\=648\pi mm^{3}[/tex]

Volume of the cylinder [tex]= \pi (9^{2} )(18)[/tex]

                                       [tex]=1458\pi mm^{3}[/tex]

Required Volume of the drill pit

= Volume of the cone + Volume of the cylinder

[tex]= (648\pi + 1458\pi )mm^{3} \\= 2106\pi mm^{3}[/tex]

Hence, Option(B) is the correct answer.

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Answer:

The slope of the line is -1

Step-by-step explanation:

You need to use the slope formula

Slope Formula: y2 - y1 / x2 - x1

**The numbers represent subscripts but the subscripts aren't on computers**

Your Coordinate Points:

(7, -3) and (3, -7)

Do -7 - (-3) / 3-7

First, do -7 - (-3)

The negatives cancel to an addition problem.

-7 + 3

Now do -7 + 3. This is a subtraction problem that should be negative.

-7 + 3 = -4

Next, do 3 - 7

That should be 4

-4/4 is what we have right now.

Do -4 divided by 4 which has to contain a negative.

That is simply -1.

The slope of the line is -1

Answer:

Step-by-step explanation:

Let the Beth's score is x.

The average is 80.

Solve the following equation:

Beth's score was 75

Answer:

8 is the ans because it is 8

Here we would be using distance formula to calculate the distance between those two points.

Points are,

★ Distance Formula :

We have :

Substituting the values :

Centroid of a triangle :-

Midpoint of two points:-

Answer:

Step-by-step explanation:

When an exponential function is in the form ...

  y = ab^t

the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...

  b = 1 +r

In the alternate form, this can be written ...

  y = a·e^(kt)

Comparing the forms, we see that ...

  b = e^k   ⇒   k = ln(b)

__

  y = 22·1.35^t

  k = ln(1.35) ≈ 0.3001

  y = 22·e^(0.3001t)

The growth factor is greater than 1, so the function is growing.

__

The annual growth rate is ...

  r = 1.35 -1 = 0.35 = 35.00%

__

The continuous growth rate is ...

  k = 0.3001 = 30.01%

Answer:

Step-by-step explanation:

a.

[tex]2^3*2^{-3}=2^0\\b.\\\frac{2^3}{2^5} =2^{-2}\\c.\\2^{-3}*5^{-3}=10^{-3}[/tex]

Answer:

Perimeter of a rectangle = 2×(Length+Breadth)

(i) Length = 16.8 cm

Breadth = 6.2 cm

Perimeter = 2×(Length+Breadth)

= 2×(16.8+6.2) =46 cm

(ii) Length = 2 m 25 cm

=(200+25) cm (1 m = 100 cm )

= 225 cm

Breadth =1 m 50 cm

= (100+50) cm (1 m = 100 cm )

= 150 cm

Perimeter = 2×(Length+Breadth)

= 2×(225+150) =750 cm

(iii) Length = 8 m 5 dm

= (80+5) dm (1 m = 10 dm )

= 85 dm

Breadth = 6 m 8 dm

= (60+8) dm (1 m = 10 dm )

= 68 dm

Perimeter = 2×(Length+Breadth)

= 2×(85+68) =306

Answer:

[tex] \sf \: a5 = 769[/tex]

Answer:

Step-by-step explanation:

y - 9 = -2(x + 5)

y - 9 = -2x - 10

y = -2x - 1

If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder

Answer:

A . 900-1000

Step-by-step explanation:

Answer:

The

C

h

a

t

section

It's difficult to access

It's also really

sen-

sitive

to what you could type.

Answer:

It will take Lainey 9 seconds to travel from top to bottom

Further explanation:

The formula of speed will be used to calculate the time to reach from top to bottom of the slide.

Given

\begin{gathered}Distance=d=423\ feet\\Speed=s=47\ feet\ per\ second\end{gathered}

Distance=d=423 feet

Speed=s=47 feet per second

The formula for speed is:

s=\frac{d}{t}s=

t

d

Putting the values of distance and speed in the formula:

\begin{gathered}47=\frac{423}{t}\\t=\frac{423}{47}\\t=9\ seconds\end{gathered}

47=

t

423

t=

47

423

t=9 seconds

It will take Lainey 9 seconds to travel from top to bottom

Keywords: Speed, distance

Learn more about speed

f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9).

To answer the questions, we need to know what functions are

A function is a mathematical expression that shows the relationship between two variables.

Since f(x) = (2x³ + 1 + x²)/(x² + 9).

Its odd part g(x) = [f(x) - f(-x)]/2

So, g(x) =  [f(x) - f(-x)]/2

= [(2x³ + 1 + x²)/(x² + 9) - (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2

= [(2x³ + 1 + x²)/(x² + 9) - (-2x³ + 1 + x²)/(x² + 9)]/2  

= (2x³ + 1 + x² + 2x³ - 1 - x²)/2(x² + 9)  

= 4x³/2(x² + 9)  

g(x) = 2x³/(x² + 9)  

Its even part h(x) = [f(x) + f(-x)]/2

So, h(x) =  [f(x) + f(-x)]/2

= [(2x³ + 1 + x²)/(x² + 9) + (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2

= [(2x³ + 1 + x²)/(x² + 9) + (-2x³ + 1 + x²)/(x² + 9)]/2  

= (2x³ + 1 + x² - 2x³ + 1 + x²)/2(x² + 9)  

= 2(1 + x²)/2(x² + 9)  

h(x) = (1 + x²)/(x² + 9)

So, f(x) = g(x) + h(x)

f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9)  

So, f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9).

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Answer:

[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]

[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]

Step-by-step explanation:

'x² - 9' is an even.

Break up the numerator into odd an even parts to get your answer.

'2x³' is odd and 'x² + 1' is even.

[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]

[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]

Answer:

57mm

Step-by-step explanation:

Length of missing side= perimeter- known lengths

= 152mm- (30+20+45)mm

= (152 - 95)mm

= 57mm

This is one single number just a bit under 175 thousand. Delete the comma if needed.

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

Work Shown:

x = number of total doctors

24.7% of x = number of female doctors

0.247x = 43200

x = 43200/(0.247)

x = 174,898.785425101 approximately

x = 174,899 when rounding to the nearest whole number

Answer:

D

I really wish is right!!!

Answer:

B 5

Step-by-step explanation:

it is the same ratio as the red

In a trapezoid, the segment at the midpoint is the average of the other two bases.

In other words: YZ = (QR + TS) / 2

5x + 1 = ( (2x + 7) + 19 ) / 2

2(5x + 1) = 2x + 26

10x + 2 = 2x + 26

8x = 24

x = 3

YZ = 5x + 1

YZ = 5(3) + 1

YZ = 15 + 1

YZ = 16

Hope this helps!

Answer:

104 feet

Step-by-step explanation:

Answer:

1 hour=55 miles

Step-by-step explanation:

Answer:

55 mph

Step-by-step explanation:

605 miles/11 hours

605/11 mph

55 mph

Hope this helps!

f(x+1)

Answer:

Rational

Step-by-step explanation:

5.74 is the same as 5.74 over 1. In other words, 5.74 can be written with a numerator and denominator, like this:

 5.74  =  5.74/1

5.74 x 100/ 1 x 100

You can multiply the numerator and denominator of any fraction by the same number and keep the value of the fraction the same. Here we will multiply the numerator and denominator by 100 to get rid of the decimal point.

5.74 × 100/ 1 × 100

When we calculate the numerator and the denominator above, we get this fraction:

574/100

The fraction above is the same as 5.74. Furthermore, the numerator and the denominator of the fraction above are integers. Therefore, we can conclude that the answer to "Is 5.74 a rational number?" is yes.

Answer:

Step 1. Plot x-intercept

Step 2. Plot y-intercept

Step 3. Connect dots

y = |x|

x-intercept = (0,0)

y-intecept = (0,0)

y = |x + 3|

x-intercept = (-3,0)

y-intecept = (0,3)

y = |x - 2|

x-intercept = (2,0)

y-intecept = (0,2)

Answer:

t = 7.46, 0.42

Explanation:

h = 126t - 16t²    [ "h" is height, "t" is time ]

when height is 50 feet

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

[tex]\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

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

[tex]\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}[/tex]

[tex]\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}[/tex]

[tex]\Longrightarrow \sf t = 7.46, \ 0.42[/tex]

Let's find

Put h=50

Use quadratic formula

[tex]\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}[/tex]

[tex]\\ \rm\Rrightarrow t=7.5s,0.4s[/tex]

Answer:

find the common factor in the given algebraic expressions 4 (x-y) , 6(y-x)

Answer:

[tex]x=20\\\\m\angle B = 92^{\circ}\\\\m\angle C = 40^{\circ}[/tex]

Step by step explanation:

[tex]~~~m\angle A +m\anglee B + m\angle C =180^{\circ}\\\\\implies 48+6x-28+2x = 180\\\\\implies 8x +20 = 180\\\\\implies 8x = 180 -20 = 160\\\\\implies x = \dfrac{160}8=20\\\\\\m\angle B = (6x -28)^{\circ} = (6\cdot 20 -28)^{\circ}=92^{\circ}\\\\m\angle C = (2x)^{\circ} = (2\cdot 20)^{\circ}=40^{\circ}[/tex]

A unit ounce is 0.16

If 36 ounces worth 5.79, 1 ounce will be

= 5.79 / 36

= 0.1608