You are told that in a billiards shot, the cue ball was shot at the eight ball, which was 8 inches away. As a result, the eight ball rolled into a pocket, which was 6 inches away.
Knowing that the angle made with the path of the cue ball and the resulting path of the eight ball is larger than 90°, it can be determined that the original distance from the cue ball to the pocket was greater than ____ inches
DISCLAIMER:
I know the answer is 10 but I don't know why, I thought I did the math right but I got 100. I'll give brainliest if you explain it well!

Answer:

The jar has 32 dimes and 18 quarters

Step-by-step explanation:

To solve this problem we can create a system of linear equations in terms of two-variables (say [tex]x[/tex] and [tex]y[/tex]) and solve it. To begin let us analyze the problem further. We know that the values of each coin type are:

Dimes ( [tex]x[/tex] )     = $0.10

Quarters( [tex]y[/tex] )  = $0.25

Total Value   = $7.70

Total Coins   = 50

Now let us set up our system of equations as:

[tex]0.10x+0.25y=7.70[/tex]      Eqn.(1)

[tex]x+y=50[/tex]                     Eqn.(2)

Lets take Eqn.(2) and rerrange it to solve for [tex]x[/tex] as:

[tex]x=50-y[/tex]                     Eqn.(3)

Now lets plug this, in Eqn.(1) so we get the value of [tex]y[/tex] as:

[tex]0.10(50-y)+0.25y=7.70\\\\5-0.10y+0.25y=7.70\\\\-0.10y+0.25y=7.70-5\\\\0.15y=2.7\\\\[/tex]

[tex]y=\frac{2.70}{0.15} \\\\y=18[/tex]

Plugging in [tex]y=18[/tex] back in Eqn.(3) we finally have:

[tex]x=50-18\\x=32[/tex]

Thus we conclude that in the jar the coins are:

Dimes ( [tex]x[/tex] ) [tex]=32[/tex]

Quarters( [tex]y[/tex] ) [tex]=18[/tex]

Answer:

an equal number of students chosen at random from each grade level

In statistics, a sample is a little amount that reveals how the remainder is or should be.

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.

A middle school contains sixth, seventh, and eighth graders each grade level contains approximately the same number of students the principal wants to find the answer to a survey question affecting each student in the school.

An equal number of pupils from each grade level were chosen at random.

We could simply collect the information of all the pupils by randomly picking some students such that there are an equal number of students from each grade.

More about the statistics link is given below.

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To simplify, remove the parentheses and combine like terms:

( y + 22) + 3

Y + 22 + 3

Answer: Y + 25

Answer:

4+5x<50

Step-by-step explanation:

5n < 50 <--- subtracts 4 from both sides

n < 10 <--- divides both sides by 5

Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works

testing n=10, 4 + 5(10) = 4 + 50 = 54.

testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.

X < 10, proven, verified, correct

The inequality 'Four more than 5 times the number x is less than 50' translates to '5x + 4 < 50'. By solving, we find the solution is 'x < 9.2', indicating that x must be less than 9.2.

The question "Four more than 5 times the number x is less than 50" can be translated into a mathematical inequality. The 'four more than' suggests addition, and '5 times the number x' indicates multiplication.

Therefore, we have the inequality 5x + 4 < 50. To find the range of values for x, we need to solve the inequality for x.

Step 1: Subtract 4 from both sides to isolate the term with x on one side of the inequality. 5x < 46.

Step 2: Divide both sides by 5 to solve for x. x < 9.2.

So, the solution to the inequality is that x must be less than 9.2. This inequality does not require the quadratic formula as suggested in some parts of the provided information.

The assumption that 'The value of x is not less than 5% of 0.50' is also not relevant to solving this particular inequality.

The two numbers are 15 and 6

Solution:

Let the two number be "a" and "b"

Let the first number be "a" and second number be "b"

Given that,

The difference between two numbers is 9

a - b = 9 -------- eqn 1

The first number plus twice the other number is 27

First number + twice the second number = 27

a + 2b = 27 ---------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

a = 9 + b ------ eqn 3

Substitute eqn 3 in eqn 2

9 + b + 2b = 27

3b = 27 - 9

3b = 18

Divide both sides of equation by 3

Substitute b = 6 in eqn 3

a = 9 + 6

Thus the two numbers are 15 and 6

[tex]\frac{5x-20}{14x^{2}-7x }[/tex]

Answer:

The answer is  [tex]9\times 10^{16}.[/tex]

Step-by-step explanation:

Given:

2 times 10 to the 16th plus 7 times 10 to the 16th in scientific notation.

Now, to solve in scientific notation.

So, we change into scientific notation:

2 times 10 to the 16th

[tex]=2\times 10^{16}[/tex]

7 times 10 to the 16th

[tex]=7\times 10^{16}[/tex]

Now, to add:

[tex]2\times 10^{16}+7\times 10^{16}[/tex]

As, we see the powers are same so we add the numbers in this standard form:

[tex]=(2+7)10^{16}[/tex]

[tex]=9\times 10^{16}.[/tex]

Therefore, the answer is [tex]9\times 10^{16}.[/tex]

Answer:

x=0 or x=6/10

Step-by-step explanation:

10x^2=6x ⇔ 10x^2 - 6x = 0 ⇔ x(10x-6)=0 ⇔ x=0 or x= 6/10

Answer:

b

Step-by-step explanation:

Answer:

The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.

Answer:

13

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

44+4=48

48/3=16

Volume of a rectangular prism is V = L x W x H

The length for the small prism is 6

The width for the small prism is 4

The height for the small prism is 3

So 6 x 4 x 3 = 72

The length for the large prism is 16

The width for the large prism is 9

The height for the large prism is 2

So 16 x 9 x 2 = 288

Now you add the two volumes together: 288 + 72 = 360 ft cubed.

Answer:

Option B.) 3 inches

Step-by-step explanation:

Let us first express some principles that we can use to solve our problem. Generally, the Volume of a Box is given by:

[tex]V=h*w*l[/tex]

where

[tex]V[/tex] : is the volume

[tex]h[/tex]   : is the height

[tex]w[/tex]   : is the width

[tex]l[/tex]   : is the length

Now we know that:

Volume of Box A ( [tex]V_{A}[/tex] )  is Equal to Volume of Box B ( [tex]V_{B}[/tex] ) so we have:

[tex]V_{A}=(2in)(3in)(6in)\\V_{A}=36 in[/tex]

So now we can find the Length ( [tex]l_{B}[/tex] ) of Box B easily, as we now the volume along with the height and the width, as follow:

[tex]V_{A}=V_{B}=36in\\\\36in = (3in)(4in)l_{B}\\\\36in=(12in)l_{B}\\\\l_{B}=\frac{36in}{12in}\\ \\l_{B}=3in[/tex]

So the Length of Box B is 3 inches, thus Option B. is correct.

Answer: [tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{7}[/tex]

Step-by-step explanation:

To find the inverse , all we need do is to make x the subject of the formula.

y = 7x - 10

Add 10 to both sides

y + 10 = 7x

divide both sides by 7

Therefore:

x = y + 10 / 7 , that is

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{7}[/tex]

Answer:

Step-by-step explanation:

y=7x-10  calculate x :  7x-10 =y

7x = y+10

x = 1/7 y +10/7

the inverse of y=7x-10 is ; y = 1/7 x +10/7

Answer:

4 hours.

Step-by-step explanation:

If Robbie earns 12 dollars per hour, it will take him 4 hours to earn 48 dollars. This is because 48/12 = 4.

48/12=hours

12+12+12+12=hours

4 hours

Answer:

His Age is 4 years old

Step-by-step explanation:

His brother is 7

Answer: 4

Step-by-step explanation:

If Tyler is 4 years old then his brother would be 7 and 7+4=11

Answer:

D. 4.1 inches

Step-by-step explanation:

Answer:

14 cm

Step-by-step explanation:

10 plus 8 plus 6

perimeter means add up the sides

Answer:

Step-by-step explanation:

1. reg pay: 8.96,week days: 1.5 overtime pay, sat: double pay, sun: triple pay

38 hrs regular pay : 38 * 8.96 = 340.48

15 hrs overtime during week : 15 * 1.5(8.96) = 15 * 13.44 = 201.60

3 hrs overtime on saturday: 3 * 2(8.96) = 3 * 17.92 = 53.76

2 hrs overtime on sunday: 2 * 3(8.96) = 2 * 26.88 = 53.76

Gross wage = (340.48 + 201.60 + 2(53.76) = 649.60 <====

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

2. reg pay : 14.60, weekday pay: 1.25,sat pay: 1.5 , sun pay: double

(a) basic wage = 40(14.60) = 584 <==

(b) overtime wage : 15 * 1.25(14.60) + 6 * 1.5(14.60) + 5 * 2(14.60) = (15 * 18.25) + (6 * 21.9) + (5 * 29.2) = 273.75 + 131.40 + 146 = 551.15 <==

(c) gross wage : 584 + 551.15 = 1135.15 <==

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

3. basic work wk: 40 hrs...earned 518...overtime 148

(a) basic pay rate : (518 - 148) / 40 = 370/40 = 9.25 per hr <==

(b) if overtime is paid for at double time.....so overtime pay is (2 * 9.25) = 18.50 per hr....and he got paid 148....148/18.5 = 8 hrs <==

The gross wage of the man who worked overtime from Monday to Friday, on Saturday, and on Sunday is $582.40.

In order to determine the gross wage of the man, we need to calculate the wages for each type of overtime worked. Let's start with the basic wage calculation for each scenario:

The man worked 15 hours overtime on week-days, so he will receive 15 x 8.96 = $134.40 for week-day overtime.

He also worked 3 hours overtime on Saturday, so he will receive 3 x (2 x 8.96) = $53.76 for Saturday overtime.

Lastly, he worked 2 hours overtime on Sunday, so he will receive 2 x (3 x 8.96) = $53.76 for Sunday overtime.

Now let's calculate the gross wage by adding the basic wage and the overtime wages together:

Gross Wage = Basic Wage + Week-day Overtime Wage + Saturday Overtime Wage + Sunday Overtime Wage

= (38 x 8.96) + 134.40 + 53.76 + 53.76

= $340.48 + $134.40 + $53.76 + $53.76

= $582.40

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Answer:2.0994

Step-by-step explanation:

You would want to set up the equation like this

120°×π/180 which will then be 2.094rad

120 degrees is equal to 2π/3 radians. You can convert degrees to radians by using the conversion factor π/180. This method simplifies to 2π/3 for 120 degrees.

Converting Degrees to Radians

To convert an angle from degrees to radians, you can use the conversion factor that 360° is equal to 2π radians. Therefore, 1 degree is equal to π/180 radians. To convert 120 degrees to radians, you can follow these steps:

Therefore, 120 degrees is equal to 2π/3 radians. This method ensures accurate conversion and is useful in various mathematical calculations.

Greater than bc the pieces is bigger

Answer:

It could be -111 and -173

Step-by-step explanation:

-111 is 62 more than -173 and together they are -284.

There are a couple different dates that people say WW2 started but the main start of the war was when the Nazi’s invaded Poland September 1, 1939

The slope is always rise/run and has a variable. In this case, 2/3x is the slope.

The y-intercept is always the number at the end, which is the y-value. This would mean that 5 is the y-intercept.

Answer:

Step-by-step explanation:

Y = ⅔X + 5

Comparing with y = mx + c

Where m is the slope and c is the intercept

m = ⅔ and c = 5

Answer:

E

Step-by-step explanation:

The pattern is 3 letters before.

Answer:  38.46

Step-by-step explanation:

400/10.4= 38.46

The solution is (-4,4)

Step-by-step explanation:

Given equations are:

[tex]4x-9y = 20\ \ \ \ Eqn1\\2x-6x = 16\ \ \ \ Eqn2[/tex]

In linear combination method, we have to make coefficients of any one variable opposites by multiplying with an integer

So multiplying 2nd equation by -2

[tex]-2(2x-6y=16)\\-4x+6y=-32\ \ \ \ Eqn3[/tex]

Adding Equation 1 and Equation 3:

[tex]4x-9y-4x+12y = 20-32\\3y = -12[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3} = \frac{-12}{3}\\y = -4[/tex]

Putting y=-4 in equation 1

[tex]4x-9(-4) = 20\\4x +36= 20\\4x = 20-36\\4x = -16[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4} = \frac{-16}{4}\\x = -4[/tex]

Hence,

The solution is (-4,4)

Keywords: Linear combination, linear equations

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