The denominator of a fraction is greater than its numerator by 7. If
the numerator is increased by 1 and the denominator is increased by
4, the fraction becomes 1/3

. Find the original fraction.

Answer:

y-1 = 2(x+2)

Step-by-step explanation:

Point slope form of a line is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y -1 = 2(x - -2)

y-1 = 2(x+2)

Answer:

- 12 and - 187

Step-by-step explanation:

To evaluate f(- 7) substitute x = - 7 into f(x)

f(- 7) = 2(- 7) + 2 = - 14 + 2 = - 12

Similarly for g(- 4)

g(- 4) = 3(- 4)³ + 5 = 3(- 64) + 5 = - 192 + 5 = - 187

Answer

IS 2/4

Step-by-step explanation:

1/3 = 4/12  1/4 = 3/12  4/12+3/12= 6/12 = 2/4

Answer:

-2/5

Step-by-step explanation:

( -8/ 125) ^ 1/3

We know (a/b) ^ 1/3 = a^ 1/3  / b^1/3

( -8) ^ 1/3  / ( 125) ^ 1/3

Rewriting

( -2^3) ^ 1/3  / ( 5^3) ^ 1/3

We know that a^b^c = a^(b*c)

-2^(3* 1/3)  / 5^(3 * 1/3)

-2 / 5

Answer:

-2/5

Step-by-step explanation:

Answer: we wont be able to answer if there is no fill out box

Step-by-step explanation:

Answer:

Can you complete the sentence?

Step-by-step explanation:

Let the increase in the size of the length and breath be 'x'.

The area of the rectangle = 12in × 8in

=96 in²

From the question,

(12+x)(8+x)=96×2 in²

or, 96+12x+8x+x²= 192

or, x²+20x+96-192=0

or, x²+20x-96=0

or, x²+24x-4x-96=0

or, x(x+24)-4(x+24)=0

or, (x-4)(x+24)=0

Either, Or,

x-4=0 x+24=0

Therefore, or, x= –24 (Which is impossible)

x=4

So the new dimensions are 12+4=16 inch and 8+4=12 inch.

Answer:

Angle A: 28 degrees

Angle B: 24 degrees

Step-by-step explanation:

Hi there!

The angle that measures 52 degrees (angle DCA) is one of the exterior angles of a triangle. An exterior angle of a triangle is equal to the sum of the opposite interior angles, which in this case would be angles A and B. Knowing this, we can set up the following equation:

[tex]4y-4+3y=52[/tex]

1) Solve for y

[tex]4y-4+3y=52[/tex]

Combine like terms

[tex]7y-4=52[/tex]

Add 4 to both sides to isolate 7y

[tex]7y-4+4=52+4\\7y=56[/tex]

Divide both sides by 7

[tex]\frac{7y}{7}=\frac{56}{7} \\y=8[/tex]

Therefore, y is equal to 8.

2) Solve for angles A and B

Angle A:

[tex]4y-4\\=4(8)-4\\=32-4\\=28[/tex]

Angle B:

[tex]3y\\=3(8)\\=24[/tex]

I hope this helps!

Answer and Step-by-step explanation:

To find the answer, we need to first think of what length in the rectangle can make the longest path, then use the Pythagorean Theorem.

The diagonal in a rectangle (going from one corner to another) is the longest distance.

If we were to split that rectangle by its diagonal, we would get a triangle. By the Pythagorean Theorem, we can find the length of that diagonal (the hypotenuse of the triangle).

[tex]A^2 + B^2 = C^2\\\\110^2+80^2 = C^2\\\\12100 + 6400 = C^2\\\\18500 = C^2\\\\10\sqrt{185} = C = 136.0147 yards[/tex] <- This is the answer (the decimal version or this ^ version).

#teamtrees #PAW (Plant And Water)

Answer:

f/9

Step-by-step explanation:

n + 5/5 = f + 9/9

do cross multiplication

5(f+9)=9(n+5)

5f+45=9n+45

5f=9n+45-45

5f=9n+0

f/9 = n/5

Answer:

9

Step-by-step explanation:

because volume of a prism is area × length

so area of triangle is 4*4/2=8 so 72÷8=9.

hope this helps:)

Answer:

C

Step-by-step explanation:

The interior angles means the angles inside the triangle

Answer:

{x,y}={5,-3}

Step-by-step explanation:

Answer:

4.7

Step-by-step explanation:

3.21 + 3.62 ÷ 2.43

[tex]3\frac{21}{100}+1\frac{119}{243}[/tex]

[tex]4\frac{ 17003}{24300}[/tex]

[tex]4\frac{ 17003}{24300}=4.6997119341564[/tex]

4.6997119341564 rounds to

4.70

Answer is 4.70

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

3.21 + 3.62 ÷ 2.43

Convert decimal into fraction,

[tex]\dfrac{321}{100} + \dfrac{362}{100}\div\dfrac{242}{100}[/tex]

[tex]\dfrac{321}{100} + \dfrac{362}{242}[/tex]

[tex]\dfrac{(321)(242)+(362)(100)}{(100)(242)}[/tex]

[tex]\dfrac{77682+36200}{24200}[/tex]

[tex]\dfrac{113882}{24200}[/tex]

[tex]4.7[/tex]0

Learn more about Arithmetic operations here:

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Answer:

profit(n) = n * .50

Profit(10) = 5.00

Step-by-step explanation:

Profit = amount of candy bars sold * profit per candy bar

profit(n) = n * .50

Let the number of candy bars sold be 10  ( n=10)

Profit(10) = 10 * .50

               = 5.00

When you added you only added 9  .50 terms which is why you only got 4.50 for your answer.

Answer:

Oki Doki, read below this will be long.

Step-by-step explanation:

So, lets start with mr moy.

First off, we need to figure out the total hours that mr moy worked.

Throuhgout the 7 days of the week, he worked 5 days. These were his hours:

8, 8, 8, 8, 9

Adding these together, you get a total of 41 hours.

Next we have total wage.

To find this, multiply the total hours by the hourly income. We know the hourly income is 12.5, and the total hours is 41:

12.5*41=512.5

So 512.5 is the total wage.

Lets do this for the next four people, I am just going to speed it up a bit:

Ms wong - hours - 8+8+7+9+9 =41. Hourly income - 9.5. Total income: 9.5*41:

389.5 is total income

41 is total hours

Maria - hours - 5+5+6+8+9=33. Hourly income - 7.5. Total income: 7.5*33:

247.5 total income

33 total hours

Tom - 4+4+4+4+4+8+8=36. Hourly income - 7.5. Total income: 7.5*36:

270 total income

36 total hours

Jacob - 5+5+5+7+7 =29. Hourly income - 7.5. Total income: 7.5*29:

217.5 total income

29 total hours

OK, now for the total sums:

Total hourly wages - 7.5+7.5+7.5+12.5+9.5=44.5

Total of the total hours - 41+41+33+36+29=180 hours

Total of total wages - 217.5+512.5+389.5+270+247.5=1637

Ok, thats it for the first page.

On the next pages, I was slightly confused. But Ill try my best.

A - for each employ, calculate total hours and wages. We already did this before.

B - What is the total amount that is paid out in wages in a week. We already did this before(1637)

C - which day is the busiest day of the week - Saturday. The slowest? Monday

So we know the slowest day has to be monday, since the total employment hours is 8+8+4=20. WHich is lower than the rest.

We also know the busiest day has to be saturday, since the total employment hours is 9+9+8+5=31. Which is higher than the rest.

Now to the the third page.

What is the average employe wage?

Lets add up all the wages, and divide by the amount of wages:

7.5+7.5+7.5+9.5+12.5=44.5

44.5/5

=

8.9

This is the average wage.

I dont totally understand part b or c of this answer.

I cannot draw or make a graph and table right now, so I cannot finish your answers.

I hope these help though!

Answer:

221

Step-by-step explanation:

Substitute x = 7 and y = 8 into the expression

5(7)² - 3(8)

= 5(49) - 24

= 245 - 24

= 221

Answer:

3.44.

Step-by-step explanation:

We can see that in this square, the radii of the semicircles are 2. Using that, we can calculate that the area of each one is 6.58. Both combined is 12.56. Now, the original area of the circle was 16. 16 minus 12.56 is equal to 3.44, so the area of the shaded region is 3.44.

Answer:

3.44

Step-by-step explanation:

enter it just like that in ape x

Step-by-step explanation:

everything can be found in the picture

Answer:

C. a = 6√3, b = 12, c = 6√2

Step-by-step explanation:

First let's find b using the cos. The cos is the adjacent side if the angle divided by the hypotenuse. We know the value of the adjacent side and we know that cos(60°) = 1/2 = 0.5:

cos(60°) = 6/b

0.5 = 6/b

b = 6/0.5

b = 12

Now we can find a using the Pythagorean theorem:

b² = 6² + a²

12² = 6² + a²

144 = 36 + a²

a² = 144 - 36

a² = 108

a = √108

a = 6√3

And now we can find c using cos again:

cos(45°) = c/b

√2/2 = c/12

c = 12•√2/2

c = 6√2

Answer:

2015-2010=5

50÷5=10

120-50=70

2017-2015=2

2*10=20

70-20=50mg

2018=50mg

Answer:

d = 9.9 units

Step-by-step explanation:

Picture a right triangle with one acute vertex at (1, -5) and the other at (-6, 2).  Going from one to the other, we see a change in x (run) of 7 and a change in y of 7.  Applying the Pythagorean Theorem, we find the distance between the two points as follows:

d = √(7² + 7²) = 7√2, or approximately 9.9 units.

Answer:

$1.50

Step-by-step explanation:

25% of 6 is basically just 6/4, which is 1.5.

This is money we're talking about, so the answer is $1.50

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

it the only one that make sense

Answer:

b on edge 2021

Step-by-step explanation:

From the calculations, the length of CY in the parallelogram is 15 feet.

A diagonal is a line that runs from one end to another in a quadrilateral. We know that in such quadrilaterals as the parallelogram, the diagonals bisect each other.

Hence;

CY =WC

And

2x - 7 = x + 4

collecting like terms;

2x - x =  4 + 7

x = 11

Thus

CY = 2x - 7

= 2*11 - 7

= 22- 7

= 15

Learn more about diagonals:https://brainly.com/question/13702073

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Answer:

let kiran's age be x

kiran's father's age is 65

acc.to ques

kiran's father is 8 years older than 3 times kiran's age ....which gives us the equation as follows

8+3x =65

therefore

3x =65-8

3x =57

x =57/3

x= 19 ans

so kiran's age is 19 years.

Answer:

kiran is 19 years old.

Step-by-step explanation:

kiran's father age = 65

let kiran's age be x

kiran's father is 8 years older than three times kiran's age means 8 + 3x

so according to the question equation is

65 =  8 + 3x

65 - 8 = 3x

57/3 = x

19 = x

therefore kiran's age is 19 years.

Answer:

21 cm²

Step-by-step explanation:

Applying,

A = (a+b)h/2............. Equation 1

Where A = area of the trapezium, a = length of the first parallel side, b = length of the second parallel side, h = height.

From the diagram

Given: a = 5 cm (5 grids), b = 9 cm (9 grids), h = 3 cm (3 grids)

Substitute these values into equation 1

A = 3(5+9)/2

A = 3(14)/2

A = 3×7

A = 21 cm²

Answer:

x = y − 4

Step-by-step explanation:

y=x+4

Step 1: Flip the equation.

x+4=y

Step 2: Add -4 to both sides.

x+4+−4=y+−4

x=y−4

Answer:

x=y−4