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3 years ago

How do you simplify 16^2/24^7

Mathematics

1 answer:

quester [9]3 years ago

5 0

Answer:

1/(2¹³·3⁷)

Step-by-step explanation:

16²/24⁷

Factor the terms = (2⁴)²/(8×3)⁷

Apply the Power Rule = 2⁸/(2³×3)⁷

Apply the Power Rule = 2⁸/(2²¹ × 3⁷)

Apply the Quotient Rule = 1/(2¹³·3⁷)

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For what value of k will the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent?

konstantin123 [22]

Answer:

After solve the equations we get value of k=3

Step-by-step explanation:

We need to find value of k for which the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent.

If the lines are concurrent, they pass through same point.

Let:

$x+2y=0--eq(1)\\ 3x-4y-10=0--eq(2)\\ 5x+ky-7=0--eq(3)$

First solving equation 1 and 2 to find values of x and y

From eq(1) we find value of x and put it in eq(2)

$From \ eq(1) x+2y=0\\x=-2y\\Put x=-2y \ in \ eq(2)\\3x-4y-10=0\\3(-2y)-4y-10=0 \\-6y-4y=10\\-10y=10\\y=\frac{10}{-10}\\y=-1$

After solving we get value of y=-1

Now putting in eq(1) to get value of x

$x+2y=0\\x+2(-1)=0\\x-2=0\\x=2$

So, Value of x= 2

Now put value of x=2 and y=-1 into eq(3) to find value of k

$5x+ky-7=0\\5(2)+k(-1)-7=0\\10-k-7=0\\-k+3=0\\-k=-3\\k=3$

So, After solve the equations we get value of k=3

4 0

3 years ago

Help pls it’s really hard

slavikrds [6]

Answer:

1 acute and 2 right (the last option)

3 0

3 years ago

In planning her retirement, Liza deposits some money at 3.5% interest, with twice as much deposited at 4.5%. Find the amount

KATRIN_1 [288]

a = amount deposited at 3.5%

b = amount deposited at 4.5%

we know that "b" is twice as much as "a", thus b = 2a.

$\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.5\% of a}}{\left( \cfrac{3.5}{100} \right)a}\implies 0.035a \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.5\% of 2a}}{\left( \cfrac{4.5}{100} \right)2a}\implies 0.045(2a)$

we also know that whatever "a" amount is, their sum is 2250, thus

$0.035a+0.045(2a) = 2250\implies 0.035a+0.09a=2250\implies 0.125a=2250 \\\\\\ a=\cfrac{2250}{0.125}\implies \boxed{a=18000}~\hspace{10em}\boxed{\stackrel{2a}{b=36000}}$

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2 years ago

A rectangular garden has length and width as given by the expressions below. Length: 4 − 7(3x + 4y) Width: 3x(−2y) Write a simpl

liraira [26]

Answer:

Step-by-step explanation:

Length of the garden = 4 - 21*x - 28*y

Width of the garden = -6*x*y

Perimeter of the garden = 2*(Length + Width)

P = 8 - 42*x - 56*y - 12*x*y

4 0

3 years ago

What is 3 root of − 1331 end root ?

NNADVOKAT [17]

∛-1331
∛-11 · (-11) · (-11)
∛-11∛-11∛-11
-11

7 0

3 years ago