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3 years ago

Which shows the decimal 0.16 expressed as a fraction in simplest form?

Mathematics

1 answer:

nata0808 [166]3 years ago

3 0

$0.\underbrace{16}_{2}=\dfrac{16}{1\underbrace{00}_{2}}=\dfrac{16}{100}=\dfrac{16:4}{100:4}=\dfrac{4}{25}$

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NEED RN, WORTH 20! What is the value of x?

max2010maxim [7]

Answer:

$x = 5.625$

Step-by-step explanation:

Step 1: Make an expression

$\frac{3}{4} = \frac{x}{7.5}$

Step 2: Cross Multiply

$\frac{3}{4} = \frac{x}{7.5}$

$4 * x = 7.5 * 3$

$4x = 22.5$

Step 3: Divide both sides by 4

$4x / 4 = 22.5 / 4$

$x = 5.625$

Answer: $x = 5.625$

5 0

3 years ago

Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6

Oksi-84 [34.3K]

Answer:

$-1/3$

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

$9x^2-15x$

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

$9x^2-15x=6$

Subtract 6 from both sides:

$9x^2-15x-6=0$

Divide everything by 3:

$3x^2-5x-2=0$

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

$3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0$

Find the x using the Zero Product Property:

$3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2$

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

$x=-1/3$

Assume that the correct symbol is >. Thus,

$x>-1/3$

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

$9x^2-15x$

0 is indeed less than six, so our first correct solution is:

$x>-1/3$

For the second one, do the same thing. We have:

$x=2$

Assume that the correct symbol is <. Thus:

$x$

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

$9x^2-15x$

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

$x>-1/3 \text{ and } x$

Together, we can write them as:

$-1/3$

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

6 0

3 years ago

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

MissTica

It must be an obtuse triangle

4 0

3 years ago

Sixteen is seven plus three times a number find the number

Mama L [17]

Answer: x=3

Step-by-step explanation:

16 = 7 + 3x

9 = 3x

3 = x

4 0

3 years ago

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What i

Nata [24]

Answer: 42.25 feet

Step-by-step explanation:

We know that after "t" seconds, its height "h" in feet is given by this function:

$h(t) = 52t -16t^2$

The maximum height is the y-coordinate of the vertex of the parabola. Then, we can use the following formula to find the corresponding value of "t" (which is the x-coordinate of the vertex):

$x=t=\frac{-b}{2a}$

In this case:

$a=-16\\b=52$

Substituting values, we get :

$t=\frac{-52}{2(-16)}\\\\t=1.625$

Substituting this value into the function to find the maximum height the ball will reach, we get:

$h(1.625) = 52(1.625) -16(1.625)^2\\\\h(1.625) =42.25\ ft$

4 0

3 years ago

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