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3 years ago

Write each ratio in simplest form 3 in. to 2 ft

Mathematics

1 answer:

Degger [83]3 years ago

4 0

$1ft=12in\to2ft=24in\\\\3in:2ft=3in:24in=3:24=\dfrac{3}{24}=\dfrac{3:3}{24:3}=\dfrac{1}{8}=1:8$

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2 years ago

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3 years ago

Find the minimum value of the function f(x)=x^2+5x-6

mash [69]

<h3><u>Explanation</u></h3>

Method 1 (Formula)

$\begin{cases}h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{2a} \end{cases}$

The vertex of Parabola is the maximum/minimum point depending on the value of a.

Find Vertex

<u>h-value</u>

$h = - \frac{5}{2(1)} \\ h = - \frac{5}{2}$

<u>k-value</u>

$k = \frac{4(1)( - 6) - {(5)}^{2} }{4(1)} \\ k = \frac{ - 24 - 25}{4} \\ k = \frac{ - 49}{4} \\ k = - \frac{49}{4}$

The minimum value is the value of k. Therefore the minimum value is - 49/4 at x = -5/2.

Method 2 (Derivative)

This is Calculus method. We simply differentiate the function then substitute y' = 0.

Differentiate Function

$f'(x) = 2 {x}^{2 - 1} + {5x}^{1 - 1} - 0 \\ f'(x) = 2x + 5$

Substitute f'(x) = 0

$0 = 2x + 5 \\ - 5 = 2x \\ - \frac{5}{2} = x$

Substitute x = -5/2 in the original equation.

$f(x) = {( - \frac{5}{2} )}^{2} + 5( - \frac{5}{2} ) - 6 \\ f(x) = \frac{25}{4} - \frac{25}{2} - 6 \\ f(x) = \frac{25}{4} - \frac{50}{4} - \frac{24}{4} \\ f(x) = \frac{25}{4} - \frac{74}{4} \\ f(x) = - \frac{49}{4}$

<h3><u>Answer</u><u /></h3>

<u> $\sf{the \: \: minimum \: \: value \: \: is \: \: - \frac{49}{4} \: \: at \: \: x = - \frac{5}{2} }$ </u>

4 0

3 years ago

Y’all pls help me :(

Ilia_Sergeevich [38]

Answer: B

Step-by-step explanation:

When you are multiplying exponents, if the base is the same, then you can directly add the exponents together.

We can see that both bases are 6. That means we can add the exponents.

$3+\frac{1}{4}$ [common denominator]

$\frac{12}{4}+\frac{1}{4}$ [add]

$\frac{13}{4}$

Now, we know that the answer will be $6^1^3^/^4$ .

6 0

3 years ago

Write anwsers as fractions using / as fraction bar and write the greater value first

puteri [66]

Answer:

Final answer is $\frac{3}{2}$ or $\frac{1}{2}$ .

Step-by-step explanation:

Given equation is $\log_x\left(8x-3\right)-\log_x\left(4\right)=2$

Now we need to solve that equation for x.

$\log_x\left(8x-3\right)-\log_x\left(4\right)=2$

Apply formula $\log_c\left(A\right)-\log_c\left(B\right)=\log_c\left(\frac{A}{B}\right)$

$\log_x\left(\frac{8x-3}{4}\right)=2$

Apply formula $\log_c\left(A\right)=b \Rightarrow c^b=A$

$x^2=\frac{8x-3}{4}$

$4x^2=8x-3$

$4x^2-8x+3=0$

$4x^2-2x-6x+3=0$

$2x(2x-1)-3(2x-1)=0$

$(2x-3)(2x-1)=0$

$2x-3=0$ or $2x-1=0$

$2x=3$ or $2x=1$

$x=\frac{3}{2}$ or $x=\frac{1}{2}$

Hence final answer is $\frac{3}{2}$ or $\frac{1}{2}$ .

6 0

3 years ago