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zysi [14]
3 years ago
6

How do you solve these problems?

Mathematics
1 answer:
Rzqust [24]3 years ago
6 0
A)

\bf log_4(x)=3\\\\
-----------------------------\\\\
log_{{  a}}{{  a}}^x\implies x\qquad \qquad 
\boxed{{{  a}}^{log_{{  a}}x}=x}\impliedby 
\begin{array}{llll}
\textit{we'll use this}\\
\textit{cancellation rule}
\end{array}\\\\
-----------------------------\\\\
4^{\cfrac{}{}log_4(x)}=4^3\implies x=4^3

b)

\bf 3^{2y}=81\qquad 
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^{2y}=3^4\impliedby 
\begin{array}{llll}
\textit{same base}\\
exponents\\
must\ be\\
the\ same
\end{array}
\\\\\\
2y=4\implies y=\cfrac{4}{2}\implies y=2
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Mrs. larnell is making snack packs for a class picnic. She puts 1/4 pound of apples, 1/8 pound of nut mix, and 1/16 pound of cho
Leona [35]
The answer is 10.5 pounds. No there is no other solutions.

24 divided by 1/4 = 6 lbs
24 divided by 1/8 = 3 lbs
24 divided by 1/16 = 1.5 lbs

6+3+1.5= 10.5 lbs of food
5 0
3 years ago
What is -4 (-6x + 3) = 12
IgorC [24]

Answer: x = 1

Step-by-step explanation:

Simplifying

-4(-6x + 3) = 12

Reorder the terms:

-4(3 + -6x) = 12

(3 * -4 + -6x * -4) = 12

(-12 + 24x) = 12

Solving

-12 + 24x = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12' to each side of the equation.

-12 + 12 + 24x = 12 + 12

Combine like terms: -12 + 12 = 0

0 + 24x = 12 + 12

24x = 12 + 12

Combine like terms: 12 + 12 = 24

24x = 24

Divide each side by '24'.

x = 1

Simplifying

x = 1

6 0
2 years ago
Read 2 more answers
Iteration - Maths Question attached
Ivanshal [37]

Answer:

7.8

Step-by-step explanation:

First I will try 50. I got 127,550, so that was way too big.

Let me try a smaller number. How about 5. I got 155, so that was a bit too small.

Now I'll try 20. I got 8420. Looks like the number is between 5 and 20.

How about 7. I got 399.

Let me try 8. I got 584! That's really close. It's just a little too big.

I tried 7.5, and got 485.624. So close! Just a little higher.

Putting in 7.8 yields <u>543.192!</u> That's our answer.

8 0
3 years ago
Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned i
jolli1 [7]

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

0.3·X = $3,600

X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

Therefore, the amount invested at 7% = $12,000 and the amount invested at 10% = $8,000.

7 0
3 years ago
Read 2 more answers
Help pls
konstantin123 [22]

Answer:

40 minutes

Step-by-step explanation:

We simply want to find the least common multiple (lcm) of the two times (5 and 8). Which is 40 minutes

For a more visual representation every 5 minutes Georgia will cross the starting line while it will take Susana 8 minutes to cross after starting at the same time.

So Georgia will cross at (5, 10, 15, 20, 25, 30, 35, 40) minutes

While Susana will cross at (8, 16, 24, 32, 40) minutes

4 0
3 years ago
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