The divisibility rule for 7 says 10a + b is a multiple of 7 if only and only if a - 2b is a multiple of 7

Explain.

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Answer:

  169 ft

Step-by-step explanation:

The law of cosines can be used to find the distance from the outfielder to the pitcher. It tells you for triangle ABC, the length of side c can be found from ...

  c² = a² +b² -2ab·cos(C)

Here, we hve a=60.5, b=214, and C=36°. Then the desired distance is ...

  c = √(60.5² +214² -2·60.5·214·cos(36°)) ≈ √28507.56 ≈ 168.84

The outfielder throws the ball about 169 feet.

Answer:

[tex]\sqrt{48}[/tex]

all the other are RATIONAL ( can be expressed as a fraction)

Step-by-step explanation:

While other numbers in the option given are rational, only √48 is an irrational number

Rational number refers to all real numbers which can be expressed in the form x/y. Given that y ≠ 0.

Evaluating the values given :

Therefore, the only √48 does not belong to the group.

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Answer:

Step-by-step explanation:

g(x) = 3f(-2x)

     = 3*([-2x)² + (-2x) - 2)

    = 3 (4x² - 2x - 2)

   =   3 * (4x² - 4x  +2x - 2)        {Rewrite the middle term}

  = 3 *[ 4x(x - 1) + 2(x - 1)]

 = 3* [ (x -1) *(4x + 2)]

 = 3(x - 1)(4x + 2)

x - 1 = 0    ;   4x + 2 = 0

x = 1         ;      4x   = -2

                        x = [tex]\dfrac{-2}{4}=\dfrac{-1}{2}[/tex]

Roots:   x = 1 , (-1/2)

From The picture 2 barrels = 73 gallons

Divide by 2 for gallons per barrel:

73/2 = 36.5 gallons per barrel

Multiply gallons per barrel barrels:

36.5 x 0.045 = 1.6425 gallons.

Rounded to 2 decimals = 1.64

[tex] \sqrt{x + 6 } = x + 4[/tex]

now square both side

Answer:

29.

Step-by-step explanation:

We know that all functions of any angle must add up to be 180 degrees. using this knowledge we take 54 and subtract it by 180.

That leaves us with 126.

We can safely assume the measurement of angle B, using the angle measured as 97.

This is due to the law of corresponding angles.

97 and angle B; correspond, so they must measure the same.

our sum of 126 subtracted by angle B (97) leaves us with the sum of 29.

Answer:

2.5L of 10% salt solution and 7.5L of the 30% salt solution

Step-by-step explanation:

let the amount of L in the 10% solution be 'x'

let the amount of L in the 30% solution be '10-x'

* because they add up to a total of 10L

10%(x) + 30%(10-x) = 25%(10)

0.1x + 3 - 0.3x = 2.5

-0.2x = -0.5

x = 2.5

x =2.5

10-x = 7.5

2.5 of 10% solution and 7.5% of 30% solution

Answer:

14 cm

Step-by-step explanation:

from the right triangle we know that:

- A leg is 8 cm

- B leg is 11 cm

- angle between A and B leg is 90'

If we have one angle which is 90' we can use the following formula:

[tex]c = \sqrt{a^{2} + {b^{2} }[/tex]

[tex]c = \sqrt{8^{2} + {11^{2} }[/tex]

[tex]c = 13.60147[/tex]

Answer:

f(9) = - 59

Step-by-step explanation:

Substitute x = 9 into f(x) , that is

f(9) = - (9)² + 9 + 13

     = - 81 + 22

    = - 59

Answer:

-59

Step-by-step explanation:

f(x) =-x^2+x+13

Let x = 9

f(9) = - (9)^2 +9+13

       = -81 +9+13

      = -59

Answer:

A) The percentage is given by (The new value)/(The old value)*100 = 120%

B) The increase in value is $90000

C) The increase as a percentage is (90000/450000)*100=20%

a. The new value is 120% of the old value.

b. The increase in value over the three-year period is $90 000.

c. The increase in value over the three-year period is 20% of the original value.

The percentage is defined as a ratio expressed as a fraction of 100.

a. To find the new value as a percentage of the old value, we can divide the new value by the old value and multiply by 100 to get a percentage:

New value as a percentage of old value = (New value / Old value) x 100%

= ($540 000 / $450 000) x 100%

= 120%

Therefore, the new value is 120% of the old value.

b. To find the increase in value over the three-year period, we can subtract the old value from the new value:

Increase in value = New value - Old value

= $540 000 - $450 000

= $90 000

Therefore, the increase in value over the three-year period is $90 000.

c. To find the increase in value as a percentage of the original value, we can divide the increase in value by the old value and multiply by 100 to get a percentage:

Increase in value as a percentage of original value = (Increase in value / Old value) x 100%

= ($90 000 / $450 000) x 100%

= 20%

Therefore, the increase in value over the three-year period is 20% of the original value.

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Answer:

4x( x^3 +3x+2)

Step-by-step explanation:

4x^4 + 12x^2 + 8x

Factor out 4x

4x( x^3 +3x+2)

Answer:

- [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

Given

- [tex]\frac{7}{10}[/tex] ÷ [tex]\frac{2}{5}[/tex]

Leave the first fraction

Change division to multiplication

Turn the second fraction upside down

= - [tex]\frac{7}{10}[/tex] × [tex]\frac{5}{2}[/tex] ← cancel 5 and 10 by 5

= - [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{2}[/tex]

= - [tex]\frac{7(1)}{2(2)}[/tex]

= - [tex]\frac{7}{4}[/tex]

Answer:

Step-by-step explanation:

B = {p , q , r}

Number of subsets = [tex]2^{n}[/tex]

Her, n  is the number of elements in the set.

Number of subsets = 2³ = 8

Answer:

Sorry I don't know the answer

Step-by-step explanation:

First draw a lign segment like DF

Next keep the point on D make an arc by increasing the length of compass

As same keep the point on F make an arc lile same as before

Next there is apoint name it as any meeting on drew arc

connect it to the point with P

Answer:

We know he spent 5 sixths which is 50 minutes

Ten percent of 50 is 5

This means he spent 3 quarters of an hour in the office

Answer:

Sam spent 50 minutes at the office, and 1/10 (or 5 minutes) in the waiting room.

So, he spent 3/4 of an hour at the office but not in the waiting room.

Let me know if this helps!

Answer:

[tex]x = -6.5c[/tex]

[tex]c = -\frac{x}{6.5}[/tex]

Step-by-step explanation:

In both cases, you are simply isolating the variable you are trying to solve for:

[tex]\frac{-x}{c} = 6.5[/tex]

Solve for x. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply c to both sides, and then divide -1 from both sides:

[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c} * c = 6.5 * c\\-x = 6.5c\\\frac{-x}{-1} = \frac{6.5c}{-1}\\x = -6.5c[/tex]

Solve for c. Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Multiply -1/x to both sides of the equation:

[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c}(c)) = 6.5(c) \\-x = 6.5c\\\frac{-x}{6.5} = \frac{6.5c}{6.5}\\c = -\frac{x}{6.5}[/tex]

Answer:

x = -6.5c

-x/6.5 = c

Step-by-step explanation:

-x/c=6.5

Multiply each side by -c

-x/c * -c=6.5*-c

x = -6.5c

-x/c=6.5

Multiply each side by c

-x/c *c=6.5*c

-x = 6.5c

Divide each side by 6.5

-x/6.5 = 6.5c/6.5

-x/6.5 = c

Answer:

The price of the game is 33.75

Step-by-step explanation:

45% of 75

.45 * 75

33.75

The price of the game is 33.75

Answer:

Option D, 110

Step-by-step explanation:

first we find x

10x+20-80=2(2x+15)

or, x=15

now, 10x+20 = 170

so, z = 360-170-80 = 110

Answer:

See the diagram below:

                             Red  3/8  -----------------> Red-Red  = 4/9*3/8 = 1/6

Red 4/9            <

                            Orange 5/8 --------------> Red-Orange = 4/9*5/8 = 5/18

                            Red 4/8 --------------------> Orange-Red = 5/9*4/8 = 5/18

Orange 5/9      <

                           Orange 4/8 ----------------> Orange-Orange = 5/9*4/8 = 5/18

Answer:

Step-by-step explanation:

let the height of the room(h) = x

Length(l) = 3*x = 3x

length = 2 * breadth

breadth(b) = length /2 = 3x/2

Cost of whitewashing the 4  walls = ₹ 7200

Area of 4 walls = 7200 ÷ 50 = 144 m²   ------(I)

Area of walls = 2lh + 2bh

                      = 2*3x*x + 2  *[tex]\frac{3x}{2}[/tex] * x

                       = 6x² + 3x²

                        = 9x²

9x² = 144    {From (I)}

x²  = 144/9

x²  = 16

x = [tex]\sqrt{16}=\sqrt{4*4}[/tex]

x = 4 m

height = 4 m

length = 3*4 = 12m

Breadth = [tex]\frac{3}{2}*4=3*2=6 \ m[/tex]

Area of floor = l*b

                    = 12 * 6

                    = 72 m²

Cost of carpeting the floor = 72 * 325 = ₹ 23400

Answer:

8x^2 - 4x - 5

See the steps below for better explanation:

Answer 8

8+8²=72

8+64=72

72=72

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[tex]x - 12 = 14 \\ x = 14 + 12 \\ x = 26[/tex]

it was help to you ❤︎❤︎❣︎❣︎★★★

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

[tex]\huge\textsf{x - 12 = 14}[/tex]

[tex]\huge\text{ADD 12 to BOTH SIDES}[/tex]

[tex]\huge\textsf{x - 12 + 12 = 14 + 12}[/tex]

[tex]\huge\boxed{\bullet}\huge\text{ CANCEL out: 12 - 12 because it gives}\\\huge\text{you 0}[/tex]

[tex]\huge\boxed{\bullet}\huge\text{ KEEP: 14 + 12 because it gives you}\\\huge\text{the RESULT of the x-value}[/tex]

[tex]\huge\textsf{a = 14 + 12}\\\huge\boxed{\rightarrow}\huge\textsf{ 14 + 12 = a}[/tex]

[tex]\huge\textsf{14 + 12 = \bf 26}[/tex]

[tex]\boxed{\huge\textsf{Therefore, your answer is: a = 26}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

x + 14.7

Step-by-step explanation:

x + 6.2 + 8.5.

Combine like terms

x + 14.7

Answer:

S=(-2, -9)

T=(-8, -9)

U=(-9, -5)

V=(-6, -5)

Step-by-step explanation:

rotating counter clockwise 90 degrees has a simple formula: (-y, x) simply take your ordered pair and rearrange it to match this formula.

ex. (3, 4) would become (-4, 3)

(-y, x) the negative symbol in front of the y means to switch the sign from either positive or negative to its opposite. since there is no symbol in front of the x you keep that numbers sign the same.

Answer: -35

Step-by-step explanation:

You can check it by multiplying -3 and -35 you should get 105

Answer:

HF = 11.0

Step-by-step explanation:

We can use a ratio to solve

ED        EC

----- = ----------

HG       HF

23       36

----- = ----------

7         HF

Using cross products

23 HF = 36*7

23 HF = 252

Divide by 23

HF = 252/23

HF =10.95652

To the nearest tenth

HF = 11.0

Answer:

x= 16

4x+21 = 85 degrees

Step-by-step explanation:

The angles shown are vertical angles and vertical angles are equal

85 = 4x+21

Subtract 21 from each side

85 -21 = 4x+21-21

64 = 4x

Divide by 4

64/4 = 4x/4

16 = x

Answer:

16degrees

Step-by-step explanation:

As these angle are (vertically opposite angles)

So,85=4x+21,

85-21=4x

x=64/4

x=16degrees