Which expression is equivalent to the following complex fraction?


2 minus StartFraction 1 Over y EndFraction divided by 3 + StartFraction 1 Over y EndFraction

StartFraction 3 y + 1 Over 2 y minus 1 EndFraction

StartFraction (2 y minus 1) (3 y + 1) Over y squared EndFraction

StartFraction y squared Over (2 y minus 1) (3 y + 1) EndFraction

StartFraction 2 y minus 1 Over 3 y + 1 EndFraction

The value of b is -3

Explanation:

The function is [tex]f(x)=\frac{1}{4} x^{2} +bx+10[/tex] and [tex]x=6[/tex]

The function is of the form [tex]y=a x^{2}+bx+c[/tex]

where [tex]a=\frac{1}{4}[/tex], [tex]b=b[/tex] and [tex]c=10[/tex]

Using the axis of symmetry formula, we can determine the value of b.

Thus, the axis of symmetry formula is given by,

[tex]x=\frac{-b}{2a}[/tex]

Substituting the values, we have,

[tex]6=-\frac{b}{2(\frac{1}{4}) }[/tex]

Multiplying the denominator, we get,

[tex]6=-\frac{b}{\frac{1}{2} }[/tex]

Dividing, we get,

[tex]6=-2b[/tex]

Dividing both sides by -2, we get,

[tex]-3=b[/tex]

Hence, the value of b is -3.

Answer:

-3

Step-by-step explanation:

Edge 2021

Answer:

x = (-7)/5

Step-by-step explanation:

Solve for x:

3 (x - 6) - 8 x = 5 (2 x + 1) - 2

3 (x - 6) = 3 x - 18:

3 x - 18 - 8 x = 5 (2 x + 1) - 2

Grouping like terms, 3 x - 8 x - 18 = (3 x - 8 x) - 18:

(3 x - 8 x) - 18 = 5 (2 x + 1) - 2

3 x - 8 x = -5 x:

-5 x - 18 = 5 (2 x + 1) - 2

5 (2 x + 1) = 10 x + 5:

-5 x - 18 = 10 x + 5 - 2

Add like terms. 5 - 2 = 3:

-5 x - 18 = 10 x + 3

Subtract 10 x from both sides:

(-5 x - 10 x) - 18 = (10 x - 10 x) + 3

-5 x - 10 x = -15 x:

-15 x - 18 = (10 x - 10 x) + 3

10 x - 10 x = 0:

-15 x - 18 = 3

Add 18 to both sides:

(18 - 18) - 15 x = 18 + 3

18 - 18 = 0:

-15 x = 3 + 18

3 + 18 = 21:

-15 x = 21

Divide both sides of -15 x = 21 by -15:

(-15 x)/(-15) = 21/(-15)

(-15)/(-15) = 1:

x = 21/(-15)

The gcd of 21 and -15 is 3, so 21/(-15) = (3×7)/(3 (-5)) = 3/3×7/(-5) = 7/(-5):

x = 7/(-5)

Multiply numerator and denominator of 7/(-5) by -1:

Answer: x = (-7)/5

Answer:

3.08    i turned it to a decimal

Step-by-step explanation:

2 3/4= 2.75

1/3=.33 and add them to get 3.08

in fraction form it is 3 1/12

Answer:

3

Step-by-step explanation:

Given 2 3/4 + 1/3

First change the mixed fraction to improper fraction .

That’s 2 2/3 becomes 8/3. Multiply the denominator 3 by the whole number 2 and then add it the numerator 3.

Now we have 8/3 + 1/3 .

We look for the lowest common multiple LCM of the denominators of the fractions.

The LCM is = 3

Now divide the denominator of each fraction by the LCM 3 and multiply the result by the numerator.

We have 8 + 1 /3 .

Everything divided by the LCM.

8 + 1 /3

9/3

3/1

3

Answer:

X=-3

Step-by-step explanation:

Answer:

vertex = (9, - 1 )

Step-by-step explanation:

Given a quadratic in standard form, y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = x² - 18x + 80 ← is in standard form

with a = 1 and b = - 18, thus

[tex]x_{vertex}[/tex] = - [tex]\frac{-18}{2}[/tex] = 9

Substitute x = 9 into the function for corresponding value of y

y = 9² - 18(9) + 80 = 81 - 162 + 80 = - 1

Vertex = (9, - 1 )

Answer:

55

Step-by-step explanation:

Yo sup??

This question can be solved by multiplying the numerator and denominator by 3^1/2

and the answer u will get will be

5*3^1/2-6^1/2)/3

Hope this helps

The price per square foot is 0.55$

Step-by-step explanation:

We can solve this problem by applying the rule of three.

In fact, we know that:

- The price per 1 gallon is $55

- The area covered by 1 gallon is [tex]100 ft^2[/tex]

So this means that the price per [tex]100 ft^2[/tex] (1 gallon) is $55.

Here we want to find the price per square foot, so we can write:

[tex]\frac{x}{1}=\frac{55}{100}[/tex]

And solving for x, the price per square foot, we find:

[tex]x=\frac{55}{100}=0.55[/tex]

So, the price per square foot is 0.55$.

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Final answer:

The price per square foot for paint that costs $55 per gallon and covers 100 square feet is $0.55.

Explanation:

To calculate the price per square foot for paint that costs $55 per gallon and covers 100 square feet, we need to divide the total cost by the total coverage area. Here is the step-by-step calculation:

Determine the total cost of one gallon of paint: $55

Determine the total coverage of one gallon of paint: 100 square feet

Calculate the price per square foot: $55 ÷ 100 sqft = $0.55 per sqft

Therefore, the price per sqft of paint is $0.55.

Answer:

Step-by-step explanation:

Check attachment for solution

Answer:

Measure of angle x = 74

Measure of angle y = 90

Step-by-step explanation:

The required measure of angle x in the triangle inscribed in the circle is 74°.

Following the given, there is a property of a circle that states that, the angle subtended through the endpoints of the longest chore of the circle(i.e. diameter) on the circumference of a circle is always 90°.
So, y = 90°
Now,
The measure of angle x is given as:
[tex]x + 90 + (180-148)/2 = 180[/tex]
x = 74

Thus, the requried measure of angle x in the triangle inscribed in the circle is 74°.

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Answer:

117 and 123.

Step-by-step explanation:

If the 2 numbers are x and y we have the system of equations:

x - y = 6

xy = 14391

From the first equation y = X - 6  so substituting:

x(x - 6) = 14391

x^2 - 6x= 14391

x^2 - 6x - 14391 = 0

The prime factors of -13491  are -3*3*3*13*41

Now  3*3*13 = 117 and -3 * 41 = -123,

so the factors are:

(x - 123)(x + 117) = 0.

x = 123, -117.

As x is a whole number we take the positive value 123.

So x = 123  and y = 123 - 6 = 117.

Answer012345

Step-by-step explanation:

Answer:

When you cube root x to the power of 6, x becomes squared, and the exponent, 5, makes it x to the power of 10.

Step-by-step explanation:

Answer:

12. Pentagon

13. The cross-section will have one pair of parallel sides and one pair of sides that are not parallel along with two opposite triangular faces.

Answer:

Step-by-step explanation:

eq. of line through (0,0) and (6,3)

[tex]slope=\frac{3-0}{6-0} =\frac{1}{2} \\y-0=\frac{1}{2} (x-0)\\y=\frac{1}{2}x\\when~x=2\\y=\frac{1}{2}*2=1[/tex]

Answer:

The correct option would be option D.) The retailer sent the customer a check for $12.50 directly.

Step-by-step explanation:

A customer bought an item from a retailer and eventually received a $12.50

rebate check in the mail after sending in a rebate form.

The transaction that occurred would be

D.)The retailer sent the customer a check for $12.50 directly

Answer:

the manufacturer of the item sent the customer a check for 12.50 directly.

Step-by-step explanation:

43.6% of the  area of lakes in north america is occupied by Lake superior and 13.6% of the area of lakes in north america is occupied by Lake Michigan.

Explanation:

13/50

26/100

52/200

etc.

Answer:

13/50

Step-by-step explanation:

26/100 = 13/50

Answer:

12² + 16² = 144 + 256 = 400 = 20²

So a triangle with side lengths of 12 in., 16 in., and 24 in. is not a right triangle.

The correct answer is False.

Final answer:

The algebraic equation 7(x-10)-2(x+5)=4x-7+6x-3 simplifies through distribution, combining like terms, and isolating x, resulting in the solution x = -14.

Explanation:

The student's question involves solving the algebraic equation 7(x-10)-2(x+5)=4x-7+6x-3. To solve this equation, we will simplify and solve for x, demonstrating the process step-by-step.

Step 1: Distribute and Simplify

First, distribute the numbers outside the parentheses:
7(x-10) becomes 7x - 70 and
-2(x+5) becomes -2x - 10.

The equation now looks like 7x - 70 - 2x - 10 = 4x - 7 + 6x - 3.

Step 2: Combine Like Terms

On the left side of the equation, combine 7x and -2x to get 5x. Also, combine -70 and -10 to get -80.
On the right side, combine 4x and 6x to get 10x, and -7 with -3 to get -10.

Step 3: Further Simplification and Solving for x

Now, the equation is 5x - 80 = 10x - 10. Subtract 5x from both sides to get -80 = 5x - 10. Adding 80 to both sides gives us 0 = 5x + 70. Subtract 70 to get 5x = -70. Finally, divide by 5 to find that x = -14.

In conclusion, through the steps of distribution, combining like terms, and isolating x, we find the solution to the original algebra problem to be x = -14.

Answer:

124 plants

Step-by-step explanation:

7.25*4.25=30.8125

30.8125*4=123.25

Since you can't buy 1/4 of a plant, you must round up to 124.

Answer:

d

Step-by-step explanation:

Answer:

there will be one less than three, so two zeros

3500

Step-by-step explanation:

The right answer is Option C.

Step-by-step explanation:

Given,

Area of post it note = A square inches

Width of post it note = 4 inches

Length of post it note = X

We know that;

Area = Length * Width

[tex]A=X*4\\A=4X[/tex]

As we have to find length, we will divide both sides by 4

[tex]\frac{A}{4}=\frac{4X}{4}\\\\\frac{A}{4}=X\\\\X=\frac{A}{4}[/tex]

The equation [tex]X=\frac{A}{4}[/tex] represents the length of post it notes in inches.

The right answer is Option C.

Keywords: area, multiplication

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Answer:

Length = 30√2 yards.

Step-by-step explanation:

There is a plot of land of square shape that has 30 yards on each side. Jules owns this plot. He plans to divide the land in half by building a fence along the diagonal of the plot.

We have to calculate the length of the fence.

Now, the length of the diagonal will be the length of the fence.

So, the length = [tex]\sqrt{30^{2} + 30^{2}} = 30\sqrt{2}[/tex] yards. (Answer)

Answer:

C. 30√2 yd

Step-by-step explanation:

infinity numbers above 12

The inequality x > 12 has infinitely many solutions as it represents all numbers greater than 12 without any upper limit.

The inequality x > 12 actually has infinitely many solutions, since any number greater than 12 satisfies the inequality condition.

In mathematics, inequalities that do not contain restrictions other than the comparative operator (in this case, '>') have a set of solutions that can be represented on a number line extending infinitely in one direction.

For example, if x > 12, then numbers such as 13, 14.5, 100, and 1234 are all solutions.

This can be visualized on a graph where x > 12 would be shown as an open interval starting from 12 and extending to the right toward infinity.

Answer:

x=12, y=4. (12, 4).

Step-by-step explanation:

x-y=8

x/y=3

--------

x=y+8

(y+8)/y=3

y+8=3y

8=3y-y

8=2y

y=8/2

y=4

x-4=8

x=8+4

x=12

x=12, y=4. (12, 4) is the two numbers.

Here given that,

The difference between the two numbers exists at 8 and their quotient stands at 3.

Step 1

x-y=8

x/y=3

--------

x=y+8

(y+8)/y=3

y+8=3y

Simplifying,

8=3y-y

8=2y

y=8/2

Hence,

y=4

x-4=8

x=8+4

Thus,

x=12

Therefore, x=12, y=4. (12, 4) is the two numbers.

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Final answer:

To find out how many children like each drink in a year group of 60 pupils, calculate each fraction of the total. 45 pupils like Coke, 12 pupils like Sprite, and 18 pupils like Tango.

Explanation:

In a year group of 60 pupils, to find out how many children like each drink, you need to calculate the fractions of the total number of pupils.

Therefore, 45 pupils like Coke, 12 pupils like Sprite, and 18 pupils like Tango.

Final answer:

45 children like Coke, 12 children like Sprite, and 18 children like Tango.

Explanation:

To find out how many children like each drink, we can use the given fractions and the total number of children in the year group.

Let's calculate the number of children who like Coke:

Total children in the year group = 60

Fraction who like Coke = 3/4

Number of children who like Coke = (3/4) x 60 = 45

Similarly, we can calculate the number of children who like Sprite and Tango:

Fraction who like Sprite = 1/5

Number of children who like Sprite = (1/5) x 60 = 12

Fraction who like Tango = 3/10

Number of children who like Tango = (3/10) x 60 = 18

Therefore, 45 children like Coke, 12 children like Sprite, and 18 children like Tango.

Answer:  The Area of this shape is 32.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = 1/2 ×(a+b)h

a = 4, b = 12, h = 4

Area = 1/2 × (4+12)4

Area = 2(16)

Area = 32square unit