MATHEMATICS HIGH SCHOOL

What is .333 written in its simplest fraction form?

Answers

Answer 1
Answer:

The simplest fraction form of 0.333 will be 333/1000 .

Given,

Decimal form: 0.333

Now,

To convert decimal form into fraction form,

When the decimals are to be removed from the decimal form we divide the number by 10 , 100 , 1000 depending on the place of decimal .

Here the decimal is placed after 3 places from right side .

Thus the division will be done of 1000 .

So,

0.333 = 333/1000

333/1000 is the simplest form as it can not be reduced further .

Thus the simplest form in fraction is 333/ 1000 .

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Answer 2
Answer: .333 in simplest fraction form is 333/1000.

{\boxed{(333)/(1000)}

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Solve x^2 - 8x + 3 = 0 by completing the square. Which equation is used in the process? (x - 4)^2 = 0 (x - 4)^2 = 13 (x - 4)^2 = 19 Match the following items by evaluating the expression for x = -3
Express 35.4% as a demical
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If y = x - 6 were changed to y = x + 8, how would the graph of the new function compare with the first one?

Answers

The graph of the new function compared with the first one is the graph would be shifted upward.

What is the equation?

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

The given equations are;

y = x - 6

y = x + 8

To compare the equation substitute the value of x = 0 and solving for the value of y.

y = x - 6

x = 0

y = 0 -6

y = -6

And y = x + 8

y = 0 + 8

y = 8

So the function would be shifted upward.

Hence, the graph of the new function compared with the first one is the graph would be shifted upward.

Learn more about the equation here;

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The first one would have a y-intercept of (0,-6) and the second one would have a y-intercept of (0,8) and x (the slope) would still be the same.
y=x-6 would have points with (0,-6) (2,-4) (4,-2) (6,0)
y=x+8 would have points with (0,8) (-2,6) (-4,4) (-6,2)
In other words shifted up. Hope this helps!

anna bakes 12 blueberry muffins, 20 bran muffins, and 8 apple muffins. what percent of the muffins are blueberry?

Answers

Answer:

\%_B_b=(3)/(10) =0.3=30\%

Step-by-step explanation:

When we talk about percentages, we refer to that amount, which, proportionally, refers to a part of the total. In this sense, the total amount of muffins would equal 100%. And we need to find what is the percentage of the amount of blueberry muffins, so:

Let:

Bb=Amount\hspace{3}of\hspace{3}blueberry\hspace{3}muffins\nB=Amount\hspace{3}of\hspace{3}bran\hspace{3}muffins\nA=Amount\hspace{3}of\hspace{3}apple\hspace{3}muffins\n\%_T=Total\hspace{3}percentage=100\%\n\%_B_b=Percentage\hspace{3} of \hspace{3}blueberry\hspace{3} muffins

T=Total\hspace{3}amount\hspace{3}of\hspace{3}muffins

Using  cross-multiplication we can find the what percent of the muffins are blueberry:

(\%_T)/(\%_B_b)= (Bb+B+A)/(Bb) \n\n(100\%)/(\%_B_b) =(12+20+8)/(12)

Solving for \%_B_b

\%_B_b=(12*100)/(12+20+8)=(1200)/(40)=30\%
30%. You want to add up all the muffins (which is 40) and make that your denominator. then as the numerator you make it as many blueberry muffins Anna has. (which is 12) you divide 12÷40×100. and that gives you a percent of 30.

Find the slope of the line 7x-9y=5

Answers

7/9 or seven ninths

Answer:

7/9

Step-by-step explanation:

Question: Find the x-intercepts for the parabola defined by this equation:y = 2x²
- 8x + 10
Write your answer as two ordered pairs:
(x1, y1), (×2, y2)
Separate the values with a comma.
Round, if
necessary, to the nearest hundredth.

Answers

Answer:

To find the x-intercepts of the parabola defined by the equation y = 2x² - 8x + 10, you need to set y equal to zero (because x-intercepts occur when y is zero) and solve for x.

So, you have:

0 = 2x² - 8x + 10

Now, you can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 2, b = -8, and c = 10. Plug these values into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Since the discriminant (the value inside the square root) is negative, there are no real solutions, which means this parabola does not have x-intercepts in the real number system.

So, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts because there are no x-intercepts for this parabola in the real number system.

Step-by-step explanation:

Certainly, let's find the x-intercepts step by step for the equation:

y = 2x² - 8x + 10

Step 1: Set y to zero because x-intercepts occur when y equals zero:

0 = 2x² - 8x + 10

Step 2: Now, we want to solve this equation for x. We can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this formula:

a is the coefficient of the x² term (which is 2 in this case).

b is the coefficient of the x term (which is -8).

c is the constant term (which is 10).

Step 3: Plug the values of a, b, and c into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

Step 4: Simplify the equation inside the square root:

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Step 5: Now, notice that we have a square root of a negative number (√(-16)). In the real number system, we can't take the square root of a negative number. This means there are no real solutions for x.

Step 6: Since there are no real solutions, there are no x-intercepts for this parabola in the real number system. Therefore, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts in this case.

Solve for x
log(x–4)+log(x+3)=2logx

Answers

D:x-4>0 \wedge x+3>0 \wedge x>0\nD:x>4 \wedge x>-3 \wedge x>0\nD:x>4\n\n\log(x-4)+\log(x+3)=2\log x\n\log(x-4)(x+3)=\log x^2\n(x-4)(x+3)=x^2\nx^2+3x-4x-12=x^2\n-x=12\nx=-12\n-12\not\in D\n\Downarrow\n\boxed{x\in\emptyset}

The steamboat River Queen travels at the rate of 30km/h in still water. If it can travel 45 km up stream in the same amount of time that it takes to go 63 km down stream what is the rate of the current.

Answers

x-the\ rate\ of\ the\ current\nt-time\n\n \left\{\begin{array}{ccc}(30-x)t=45\n(30+x)t=63\end{array}\right\n \left\{\begin{array}{ccc}t=(45)/(30-x)\nt=(63)/(30+x)\end{array}\right\n\n(45)/(30-x)=(63)/(30+x)\n\ncross\ multiply\n\n63(30-x)=45(30+x)\n1890-63x=1350+45x\n-63x-45x=1350-1890\n-108x=-540\ \ \ \ /:(-108)\nx=5\n\nAnswer:The\ rate\ of\ the\ current\ is\ 5\ km/h.
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