Mathematics High School

Hi I have question on solving algebraic fractions. How would I find the LCD for this?

(x/x+1)+(x-1/4)=(11/12)

I tried multiplying the denominator by the opposites (x+1 and 4) to make them the same denominator and then add them and cross multiply, however, I never got the right answer

Answers

Answer 1

The value of x is either 2 or -7/3.

Given expression:-

(x/x+1)+((x-1)/4)=(11/12)

We have to find the value of x.

The LCM of (x + 1) and 4 is 4(x - 1).

We can write,

[4x + (x + 1)(x - 1)]/4(x + 1) = 11/12

[tex]\frac{4x+x^2-1}{4(x+1)}=\frac{11}{12}[/tex]

We can multiply 4 to the given equation, and get,

[tex]\frac{4x+x^2-1}{(x+1)}=\frac{11}{3}[/tex]

By cross multiplying, we can write,

[tex]12(4x+x^2-1)=11(4(x+1))[/tex]

12x + [tex]3x^2[/tex] -3 = 11x + 11

[tex]3x^2[/tex] + 12x - 11x -3-11 = 0

[tex]3x^2[/tex] + x-14 = 0

Using the middle-term split theorem, we can write,

[tex]3x^2[/tex] + 7x - 6x -14 = 0

x(3x + 7) - 2(3x + 7) = 0

(3x + 7)(x - 2) = 0

x = -7/3, 2.

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Related Questions

At one store Roberto bought 10 packages of batteries. Each package had 24 batteries. At another store, he bought 10 packages of batteries, but each

Answers

The answer is 240 trust me I got it correct

Write an equation that represents the line.
Use exact
numbers.

Answers

Answer:

y = -1/3x -3.5

Step-by-step explanation:

line interesects y axis at -3.5, distance between dots is down 1 and forward 3

PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table? PLEASE ANSWER BOTH Y AXIS AND SLOPE! And please give an explanation if possible

Answers

Answer:

24 and 11

Step-by-step explanation:

See attached worksheet.

Calvin has three alarm clocks which sound at different intervals. Clock A goes off every 10 minutes, clock B every 15 minutes, and clock C every 20 minutes.The three clocks sound together every _minutes.

Answers

Answer:

Given that,

Calvin has three alarm clocks which sound at different intervals.

Clock A goes off every 10 minutes

Clock B every 15 minutes

Clock C every 20 minutes.

To find: the three clocks sound together every _minutes

The three clock sounds together for every least common minutes of the 3 clocks (A,B,C)

To find LCM of 10,15,20.

we get,

LCM of 10,15,20 is 60

Therefore we get that,

The three clock sounds together for every 60 minutes.

Answer is:

The three clock sounds together for every 60 minutes.

Keenan travels 14 miles per hour. How long does it take him to travel 70 miles? Your answer should be in hours, accurate to at least the
nearest tenth.

Answers

Answer: 5 Hours

Step-by-step explanation:

14 miles x 5 hours = 70miles in 5 hours.

Hope this helps!

It's possible to build a triangle with side lengths of 3, 3, and 9.
O A. True
O B. False

Answers

it is possible to make a triangle with the sides 3, 3 and 9

true

Evaluate the following equation when x = {1, 2, 3, 4, 5} by filling in the table with the correct values for the function f (x) = (-3)^x

Answers

Step-by-step explanation:

In x you can put the value which can given in question.

A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in. If the container holds 1096 cubic feet of shipped goods, what percent is empty?

Answers

As per the volume of a rectangular prism, it is found that 34.76% of the container is empty.

Volume of a rectangular prism

The volume of the rectangle prism is calculated by multiplying the length, breadth and height of the prism.

The formula for the volume of rectangle prism is

V = l x w x h

where

l represents the length

w represents the width

h represents the height

Given,

A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in.

Here we need to find if the container holds 1096 cubic feet of shipped goods, what percent is empty

According to the given question,

Let us consider the length is 30ft, Width is 8ft and Height is 7ft.

Here the value 3ft refers the depth.

That one is also multiplied with the volume.

Therefore, the volume of the container is

=> 8 x 7 x 30

=> 1680

Therefore, the volume of the container is 1680 cubic feet.

So, here we have to percentage of the empty space for that we have to find the difference of them and convert it into percentage,

=> 1680 - 1096

=> 584

The percent of empty space is,

=> x% of 1680 = 584

=> x% = 584/1680

=> x% = 0.3476

=> x = 34.76

Therefore, 34.76% of rectangular prism container is empty.

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Given the function f(x) = 8x + 7, find each of the following. f(1), f(-9), f(0)

Answers

IN THE PLACE OF X YOU INSERT THE NUMBER GIVEN AS F(X<<<) AND SIMPLIFY .

[tex]f(1) = 8(1) + 7 \\ f(1) = 8+ 7 \\ f(1) = 15[/tex]

[tex]f( - 9) = 8( - 9) + 7 \\ f( - 9) = - 72 + 7 \\ f( - 9) = - 65[/tex]

[tex]f(0) = 8(0) + 7 \\ f(0) = 0 + 7 \\ f(0) = 7[/tex]

GOODLUCK !!

The temperature of a day at the end of winter starts in the morning at -2 degrees Fahrenheit. The weather report notes that the temperature increases 10 degrees
by midday. At 5:00 pm, the temperature has doubled since midday. What was the temperature at 5:00 pm?

A 24 degrees

B16 degrees

C-16 degrees

D10 degrees

Answers

Answer:

B. 16 degrees

Step-by-step explanation:

First, we find temperature at miday:

- 2 (Temperature at morning) + 10 (Increase in temperature by midday) = 8 degrees (Temperature at midday)

Now, for temperature at 5:00 pm:

8 x 2 (At 5 pm temperature is double since midday) = 16 degrees (Temperature at 5:00 pm)

Answer:

B 16 degrees

Step-by-step explanation:

Find the temperature

We start at -2

We increase 10 degrees by noon

-2 + 10 = 8

at 5pm the temperature doubles

8*2 = 16

1 (a). Determine if each of the following is true or false. Explain your reasoning.i. There are 12 cubic inches in a cubic foot.ii. There are 144 squares inches in a square foot. iii. If I triple the length and width of a rectangle, then the area increase by a factor of 3.iv. If I triple the length and width and height of a cube, then the volume increases by a factor of 27.

Answers

(i)

1 cubic foot is equivalent to 1728 cubic inches, this is why the statement is false.

(ii)

1 square foot is equivalent to 144 square inches, so the second statement is also false.

(iii)

The third statement is also false because if we triple both dimensions of a rectangle, the area will be increased by a factor of 9.

[tex]A=3w\times3l=9wl[/tex](iv)

This statement is true because when we multiply 3x3x3 we actually get a factor of 27

[tex]V=3w\times3l\times3h=27\text{wlh}[/tex]

PLEASE HELP!!!!!! It’s algebra

Answers

Answer:

Y=3X-4

Step-by-step explanation:

1. Find the slope using matching (x,y) values. (5,11) and (2,2) for example. (Change in Y)/(Change in X) [tex]\frac{11-2}{5-2}[/tex] = [tex]\frac{9}{3}[/tex] = 3

2. Use the point-slope form to find the equation. Pick a matching (x,y) value. (2,2) for example. and plug it in for Y₁ and X₁ in the equation Y-Y₁=M(X-X₁)

with M as the slope. Y-2=3(X-2).

3. Simplify

Y-2=3X-6

Y=3X-4

2- x+2/x-3 - x-6/x+3

A=
B=

It can be written in the form is like ax+b/x^2-9
so we only need the A and B.

Please reply to this ASAP

Answers

Step-by-step explanation:

so, if I understand your text correctly, we need to bring

2 - (x+2)/(x-3) - (x-6)/(x+3)

into a form

(ax + b)/(x² - 9)

what we notice immediately is

(x+3)(x-3) = x² - 9

that makes sense, as we want to transform all terms into fractions with the same denominator.

and the necessary "criss-cross" multiplication leads to (x² -9) as denominator.

so, let's transform every term to a fraction with that denominator, and then we add or subtract them all up as per the original expression.

2 :

multiply by (x²-9)/(x²-9)

2(x²-9)/(x²-9) = (2x²-18)/(x²-9)

(x+2)/(x-3) :

multiply by (x+3)/(x+3)

(x+2)(x+3)/(x²-9) = (x²+3x+2x+6)/(x²-9) =

= (x²+5x+6)/(x²-9)

(x-6)/(x+3) :

multiply by (x-3)/(x-3)

(x-6)(x-3)/(x²-9) = (x²-3x-6x+18)/(x²-9) =

= (x²-9x+18)/(x²-9)

for the whole expression we get then

(2x²-18)/(x²-9) - (x²+5x+6)/(x²-9) - (x²-9x+18)/(x²-9) =

= (2x²-x²-x² -5x+9x -18-6-18)/(x²-9) =

= ( 0 + 4x - 42 )/(x²-9)

a = 4

b = -42

Shawn borrows $600 to be paid back in one year with 8% simple interest. How much interest will Shawn pay?

Answers

Answer:

Step-by-step explanation:

0.08 × 600 =48

for the percent you move the decimal forward twice.

Select the correct answer. Consider the function f(x) = 3x and the function g, which is shown below. How will the graph of g differ from the graph of f? A. The graph of g is the graph of f shifted 2 units up. B. The graph of g is the graph of f shifted 2 units to the left. C. The graph of g is the graph of f shifted 2 units to the right. D. The graph of g is the graph of f shifted 2 units down.

Answers

The graph of g will differ from the graph of f as the graph of g is the graph of f shifted 2 units to the right. Option C

This is further explained below.

What is a function?

A relation between a collection of inputs and one output for each of those inputs is the definition of a function.

A function is a connection between inputs in which each input is associated with precisely one output.

To put it another way, a function is a relationship between inputs. Each function has both a domain and a codomain or range that it operates inside.

Generally, The progression towards

g(x) = f(x -h) +k

depicts a translation with k units added on top and h units added to the right.

Since you have h equal to 0 and k equal to -2, this means that the graph is moved 0 units to the right and 2 units in the opposite direction of up.

The graph of g may be found by shifting f's graph down by two units.

Answers

If Jenny studies one hour both for economics and history she can gain 10+15=25 points

What is meant by Increasing?

Increasing: Growing larger or greater. Therefore, if the derivative of a function is positive, then the function is increasing. Let's consider our example of g(x) = x2. The derivative of g(x) = x2 is g'(x) = 2x. Since we are multiplying x by the positive number 2, it's easy to see that g ' is positive when x is positive and negative when x is negative.

Jenny will receive 15 points if she simply studies economics, which equates to 10 points in the first hour and 5 points in the second.

Jenny will earn 20 points if she exclusively studies history, which equates to 15 points in the first class and 5 points in the second.

Jenny should study economics for one hour, which will get her 10 points, and history for one hour, which will gain her 15 points, for a total of 25 points in the two hours

So we concluded that if Jenny studies one hour both for economics and history she can gain 10+15=25 points

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What is the y-intercept?

Answers

Please provide a picture, I'm not seeing one.

The y-intercept is when the x-value equals zero. (0, y)

You can find the y intercept if you plus in 0 for the c value

wo horses start a race at the same time. Horse A gallops at a steady rate of 32 feet per second and Horse B gallops at a steady rate of 28 feet per second. After 5 seconds, how much farther will Horse A have traveled? Explain or show your reasoning.

Answers

Answer:

Step-by-step explanation:

Multiply 32 by 5 = 160

Multiply 28 by 5 =140

subtract 140 from 160

Answer Horse A would have traveled 20 feet farther the Horse B

1/2 + 1/4= write as a fraction and as a decimal.

Answers

1/2 + 1/4 =

2/4 + 1/4 = = 3/4 = 0.75

The graph below represents the number
of containers and liters of water contained
in the containers. What is the constant of
proportionality?

Answers

The answer is: 4
Show work: 40-20/10-5

Sarah invests £400 at 3%
interest for 6 years
Circle the correct calculation to
work out how much she has now.

Answers

Answer: £900

Step-by-step explanation:

which measurements are equivalent to 3 yards

Answers

The equivalent measures to 3 yards are;

108 inches and ; 6 ft 36 inches

Here, we want to get the values of the measurements that are equivalent to 3 yards

To do this, we need to know how to convert between the various measure types

We proceed as follows;

Mathematically, 1 yard is 36 inches; also, 1 yard is 3 feet

So, 3 yards is (3*36) = 108 inches

Also, 3 yards is (3*3) = 9 feet

Also, 1 ft is 12 inches;

So, 6 ft 12 inches is 7 feet

108 inches is as seen above, so 3 yards equal this

3 yards is not 108 feet as calculated above

6 ft 36 inches

36 inches is 3 ft; so by addition; 6 ft 36 inches is 9 ft

So, the correct answers here are 108 inches and 6 ft 36 inches

Which 3 measurements could be the dimensions of a right triangle?
(a² + b² = c²)

Answers

Answer:

5, 12, 13

Step-by-step explanation:

let a = 5 , b = 12 , c = 13 , then

5² + 12² = 25 + 144 = 169

13² = 169

so a² + b² = c²

Answer:

3, 4, 5

Step-by-step explanation:

In a right triangle, we have 2 legs and a hypotenuse. The hypotenuse equals c, while the other 2 legs are a and b.

Lets say a = 3, b = 4, and c = 5

The formula is a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

Therefore, 3, 4, and 5 can be dimensions of a right triangle.

Danielle earns $36.80 for 4 hours of yardwork. How much does Danielle earn for 10 hours of yardwork

Answers

Firstly he earns 36.8 dollars in 4 hours
So how much does he earn per hour?
Decide 36.8 by 4 => 9.2 dollars
Now he earns 9.2 dollars for every he so he’ll earn 9.2(10) I.e. 92 dollars in 10 hours

$36.80 x 2 = $73.60

$36.80 / 2 = $18.40

4hr + 4hr + 2hr = 10hr

$73.60 + $73.60 + $18.40 = $165.60

A giant tortoise can travel 0.17 miles in 1 hour. At this rate, how long would it take the tortoise to travel 1.1 miles?
It would take the tortoise
hours.
(Type an integer or decimal rounded to one decimal place as needed.)
...

Answers

Answer:

1.07

friend me? anyone

Answer:

6.5 hours

Step-by-step explanation:

distance = rate times time

1.1 = .17t t stands for time Divide both side by .17

my calculator shows 6.47058823527 We need to round to one decimal place

time = 6.5 hours or 6 1/2 hours

4y+3z=19
-x+z=27
x-3y=-19

Solve the system of equations

Answers

4
y
+
3
z
=
19
−
x
+
z
=
27
x
−
3
y
=
−
19
4
y
+
3
z
=
19
-
x
+
z
=
27
x
-
3
y
=
-
19
divide
4
y
+
3
z
=
19
−
x
+
z
=
27
x
−
3
y
=
−
19
4
y
+
3
z
=
19
-
x
+
z
=
27
x
-
3
y
=
-
19
by
2
2
.
4
y
+
3
z
=
19
−
x
+
z
=
7
x
−
3
y
=
−
19

Answer:

x = -262/13, y = -5/13, z = 89/13

Step-by-step explanation:

Solve the following system:

{3 z + 4 y = 19 | (equation 1)

z - x = 27 | (equation 2)

-3 y + x = -19 | (equation 3)

Swap equation 1 with equation 2: