A sum of money is to shared among Betty, Luke and John in the ratio 4 : 7 : 9. If Luke's share amounts to $1295, calculate the total sum of money to be shared.​

Answer:

14 : -17 : 2

Step-by-step explanation:

8 + (9 · 2 – 3) : 25 – 4 2 : 2

= 14 : -17 : 2

Answer:

- 12.4

Step-by-step explanation:

[tex]8 + \frac{9 * 2 - 3}{25} - \frac{42}{2}[/tex]

[tex]8 + \frac{18 - 3}{25} - 21[/tex]

[tex]8 + \frac{15}{25} - 21[/tex]

[tex]8 + \frac{3}{5} - 21[/tex]

[tex]8 \frac{3}{5} - 21[/tex]

[tex]-12 \frac{2}{5}[/tex]

Step-by-step explanation:

QR--DE

RS--- EF

RQ-----DE

Answer:

-166

Step-by-step explanation:

Answer:

A. [tex]UPC = 0-03700-80049-9[/tex]

Step-by-step explanation:

Given

[tex]ID = 037000[/tex]

[tex]Item\ Number = 80049[/tex]

Required

The valid UPC

First, the UPC is represented as:

UPC = ID followed by item number followed by the checksum

So, we have:

[tex]upc = 0-03700-80049-X[/tex]

To calculate X (the checksum)

Add up digits at odd positions

[tex]Odd = (0 + 7 + 0) + (8 + 0 + 9)[/tex]

[tex]Odd = 24\\[/tex]

Multiply by 3

[tex]Product = Odd * 3[/tex]

[tex]Product = 24 * 3[/tex]

[tex]Product = 72[/tex]

Add up digits at even positions

[tex]Even = (3 + 0 + 0) + (0 + 4)[/tex]

[tex]Even = 7[/tex]

Add the product and the sum of even

[tex]Result = Product + Even[/tex]

[tex]Result = 72+7[/tex]

[tex]Result = 79\\[/tex]

The last digit of the UPC is 9.

Hence, the UPC is:

[tex]UPC = 0-03700-80049-9[/tex]

No, The third line does not necessarily be a transversal.

What is Equation of line?

The equation of line with slope 'm' and y intercept at point 'b' is given as;

⇒ y = mx + b

Given that;

Two lines intersected by a third line.

Since, When two lines are parallel to each other and two lines intersected by a third line then, third lines are transversal.

So, Here it is not given two lines are parallel.

Thus, Third line is not necessarily a transversal.

Hence, The third line does not necessarily be a transversal.

Learn more about the transversal visit:

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Answer:

x^2-2x+5

Step-by-step explanation:

5x^2 -4x +8 + -4x^2 +2x -3

Combine like terms

5x^2-4x^2-4x+2x+8-3

x^2-2x+5

Answer:

Step-by-step explanation:

3x - 14 = 46

   + 14   +14

3x = 60

3x/3 = 60/3

x = 20

Answer:

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos theta = 8/20

cos theta = 2/5

Taking the inverse cos of each side

cos^-1 (cos theta) = cos ^-1 ( 2/5)

theta =66.42182152

To the nearest degree

theta = 66 degrees

Answer:

[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]

Step-by-step explanation:

we would like to factor the following:

[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]

let a²+b²=x

thus substitute:

[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]

rewrite the middle term as 4x-22x:

[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]

factor out x:

[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]

factor out -22:

[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]

group:

[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]

substitute back:

[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]

and we are done!

Answer:

Division property of equality

Step-by-step explanation:

7q=49

Divide each side by 7

7q/7 = 49/7

q = 7

Step-by-step explanation:

everything can be found in the picture

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

The graph ranges vertically between 9 and 15, starting at 9 (the minimum) when x=0. The minimum appears again at x=350.

This means the vertical offset is (9+15)/2 = 12, and the amplitude is (15 -9)/2 = 3. The period is 350, so the coefficient of x is (2π/350). All of the answer choices agree on these parameters.

So, the selection comes down to an understanding of how the sine and cosine curves vary. The sine curve starts at zero and increases from there. The cosine curve starts at its maximum (1) and decreases. Here, the curve starts a its minimum and increases, so could be the opposite of the cosine function.

  y = -3cos(2πx/350) +12 . . . . . . matches choice C

Answer:

4(9a^4+4y^2)

Step-by-step explanation:

factor out common term

Answer:

17th term

Step-by-step explanation:

For some nth term, both series have same term. So,

6n - 21 = 4n + 13

Subtract 4n from both sides

6n - 4n - 21 = 13

  2n - 21 = 13

Add 21 to both sides

2n = 13+21

2n = 34

Divide both sides by 2

n = 34/2

n = 17

Check:

6n - 21 = 6*17 - 21 = 102 - 21 = 81

4n + 13 = 4*17 + 13 = 68 + 13 = 81

17th term both the series is 81

Answer:

The answer is n = 17

Step-by-step explanation:

You first have to substitute a number for n. You put in a number and calculate. If the 2 are not equal, then it is not correct. When you substitute 17,

4(17) + 13 = 81. 6(17) - 21 = 81.

Because of this, 17 would be the correct term for n.

Answer:

The difference is 3 for 4-7, and 39 for 52-91. So basically its a change of 3 for every 4-7 I think this is what you ask for. Let me explain and show results and then pick what you need.

Step-by-step explanation:

So, we know 4 to 7 is 3.

52 to 91 is 39.

So one is a change in 3. the other is a change is 39.

However, could these be the same, just bigger?

Lets divide the 52 to 91 with a change of 39 by 4 to 7 with a change of 3:

52/4 to 91/7 with a change of 39/3 =

13 to 13 with a change of 13.

So this tells us that the 52 to 91 with a chang eof 3 is 13 times bigger than 4 to 7 with a change of 3.

Hope this helps!

Answer:

x = -6

Step-by-step explanation:

All three angles are equal, so all three sides are equal, making this an equilateral triangle

5x+10 = 2x-8

Subtract 2x from each side

5x-2x +10 = 2x-8-2x

3x+10 = -8

Subtract 10 from each side

3x+10-10 = -8-10

3x = -18

Divide by 3

3x/3 = -18/-3

x = -6

Given:

Initial number of participants = 128

During each round, half of the players are eliminated.

To find:

The number of players remain after 5 rounds.

Solution:

It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.

If half of the players are eliminated, then half of the players are remained.

So, the initial value is 128 and the decay factor is [tex]\dfrac{1}{2}[/tex].

The general exponential decay model is:

[tex]y=a(b)^x[/tex]

Where, a is the initial value and b is the decay factor.

Putting [tex]a=128[/tex] and [tex]b=\dfrac{1}{2}[/tex] in the above model, we get

[tex]y=128\left(\dfrac{1}{2}\right)^x[/tex]

Here, y is the number of remaining players after x rounds.

Substituting [tex]x=5[/tex], we get

[tex]y=128\left(\dfrac{1}{2}\right)^5[/tex]

[tex]y=128\left(\dfrac{1}{32}\right)[/tex]

[tex]y=4[/tex]

Therefore, the required model is [tex]y=128\left(\dfrac{1}{2}\right)^x[/tex] and the number of players remain after 5 rounds is 4.

2√2 i.e OPTION A is the correct answer

Answer:

the answer would be 193.77

Step-by-step explanation:

literally, subtract 45.87 from 239.64.

you get 193.77.

(you put 44 instead of 45, so the sum with 44 would be 194, that is incorrect.)

Answer:

60 yd

Step-by-step explanation:

C⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

perimeter=46.5 inches

Step-by-step explanation:

[tex]width=2\frac{3}{4}[/tex]

[tex]=\frac{5*4+3}{4}[/tex]

=[tex]=\frac{23}{4}[/tex]

[tex]length=3(\frac{23}{4} )[/tex]

[tex]=\frac{23*3}{4}[/tex]

=[tex]\frac{69}{4}[/tex]

perimeter of rectangle =2(l+b)

[tex]=2(\frac{69}{4} +\frac{24}{4} )[/tex]

[tex]=2(\frac{69+24}{4} )[/tex]   (since their denominator are same u can add their numerator)

[tex]=2(\frac{93}{4})[/tex]

[tex]=\frac{93*2}{4}[/tex]

[tex]=\frac{186}{4}[/tex]

[tex]=46.5[/tex]   inches

Answer: both roots are greater than zero

Step-by-step explanation:

If this is factored, you can find the roots.

(x-3)(x-5)=0

Set each factor equal to zero and solve.

x-3=0

x=3

Answer:

Step-by-step explanation:

the sign must have a line underneath itself to show that it can be equal and unequal. 2/5 times a number (from my understanding) is 2/5 times a variable, plus 7.

Translation into inequality of negative nine is greater than or equal to the sum of two-fifths times a number, and seven is -9 ≥ (2/5x) + 7.

The relationship between two non-equal values is defined by inequalities. Equal does not mean unequal, though. In most cases, the "not equal sign" is used.

Negative nine is greater than or equal to the sum of two-fifths times a number, and seven can be written as,

-9 ≥ (2/5x) + 7

Therefore, Translation into inequality of negative nine is greater than or equal to the sum of two-fifths times a number, and seven is -9 ≥ (2/5x) + 7.

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Answer:

x = 3.24, x = -1.24

Step-by-step explanation:

The standard form for a quadratic equation is [tex]ax^2+bx+c=0[/tex]. For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is [tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex].

Plug in a = 1, b = -2, and c = -4 into the formula.

[tex]=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]

We'll do the top part first:

[tex]\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}[/tex]

Apply rule [tex]- (-a) = a[/tex]

[tex]=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}[/tex]

Apply exponent rule [tex](-a)^{n} =a^n[/tex] if [tex]n[/tex] is even

[tex](-2)^2=2^2[/tex]

[tex]=\sqrt{2^2+4\cdot \:1\cdot \:4}[/tex]

Multiply the numbers

[tex]=\sqrt{2^2+16}[/tex]

[tex]2^2=4[/tex]

[tex]=\sqrt{4+16}[/tex]

Add

[tex]=\sqrt{20}[/tex]

The prime factorization of 20 is [tex]2^2*5[/tex]

20 divides by 2. 20 = 10 * 2

[tex]=2*10[/tex]

10 divides by 2. 10 = 5 * 2

[tex]=2* \:2*5[/tex]

2 & 5 are prime numbers so you don't need to factor them anymore

[tex]=2*2*5[/tex]

[tex]=2^2*5[/tex]

[tex]=\sqrt{2^2\cdot \:5}[/tex]

Apply radical rule [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]

[tex]=\sqrt{5}\sqrt{2^2}[/tex]

Apply radical rule [tex]\sqrt[n]{a^{n} } =a[/tex]; [tex]\sqrt{2^2} =2[/tex]

[tex]=2\sqrt{5}[/tex]

[tex]=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}[/tex]

Because of the [tex]\pm[/tex] you have to separate the solutions so that one is positive and the other is negative.

[tex]x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}[/tex]

Positive x:

[tex]\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}[/tex]

Apply rule [tex]-(-a)=a[/tex]

[tex]=\frac{2+2\sqrt{5}}{2\cdot \:1}[/tex]

Multiply

[tex]=\frac{2+2\sqrt{5}}{2}[/tex]

Factor [tex]2+2\sqrt{5}[/tex] and rewrite it as [tex]=2\cdot \:1+2\sqrt{5}[/tex]. Factor out 2 because it is the common term. [tex]=2\left(1+\sqrt{5}\right)[/tex].

[tex]=\frac{2\left(1+\sqrt{5}\right)}{2}[/tex]

Divide 2 by 2

[tex]x=1+\sqrt{5}[/tex] or [tex]x=3.24[/tex] (You'll probably have to use a calculator for the square root of 5)

^Repeating the process of positive x for negative x in order to get [tex]x=1-\sqrt{5}[/tex] or [tex]x=-1.24[/tex]

Answer:

Step-by-step explanation:

Decreased students = 1050 - 798 = 252

Decreased percentage = (decreased students ÷ number of last year students) * 100

= [tex]\frac{252}{1050}*100[/tex]

= 24%

Answer:

24%

Step-by-step explanation:

% change = [tex]\frac{difference}{original amount}[/tex] x 100

; 1050 - 798 = 252

% change = [tex]\frac{252}{1050}[/tex] x 100

% change = 0.24 x 100

% change = 24

the percentage decrease in the number of students enrolled is 24%

Answer:

(3,6.3), (7, 14.7)

Step-by-step explanation:

For this question, you want to find the values where 2.1×x is the same as y. It's mostly just trial and error.

x is always first in the bracket, so by multiplying it by 2.1, you would get y (the second value) if it applies.

3*2.1=6.3, so the first one is true.

6.3*2.1=13.23, so the second one is false.

2.1*2.1=4.41, so the third one is false.

7*2.1=14.7, so the fourth one is true.

10.5*2.1=22.05, so the fifth one is false.

14.7*2.1=30.87, so the sixth one is false.

This leaves the first one (3,6.3) and the fourth one (7, 14.7) as true.

** This is mostly algebra, so you may want to look at that. If this question was supposed to be done without a calculator, look at multiplying decimals too. I'm always happy to help!

Answer:

They are (3, 6.3) and (7, 14.7)