Answer:
Step-by-step explanation:
3ln(4) = 2ln(x)
ln(4³) = ln(x²)
4³ = x²
(2²)³ = x²
2⁶ = x²
x = ±√2⁶ = ±2³ = ±8
However, the argument of a logarithm must be positive, so x=8.
The solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}. Option D is correct.
To solve the equation, we can use the logarithmic identity that states:
n * log(a) = log(aⁿ)
Using this identity, we can rewrite the equation as:
In(4³) = In(x²)
Simplifying both sides using the natural logarithm properties, we get:
In(64) = In(x²)
Taking the exponential of both sides, we have:
[tex]e^{In 64} = e^{In x^2}\\64 = x^2[/tex]
Taking the square root of both sides, we get:
x = ±8
However, we must check if either of these solutions makes the argument of the natural logarithm negative, which is not allowed. Since the argument of the natural logarithm is positive for both x = 8 and x = -8, both solutions are valid.
Therefore, the solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}.
Learn more about logarithmic function here:
https://brainly.com/question/3181916
#SPJ7
(6n – 7) + (8n + 2) = 23
Answer:100
Step-by-step explanation:
2!2
Answer:
n = 2
Step-by-step explanation:
(6n - 7) + (8n + 2) = 23 (Combine like terms)
14n - 5 = 23 (Add 5 from both sides)
14n = 28 (divided 14 from both sides)
n = 2
Fill in the box to rewrite the expression 5x + 10
using the GCF.
5x + 10 = (
x) + (5 •
the segment joing C and D (-0.6, -0.8) is the tangent to the unit circle at D. what is the exact value of...
1. sin(t - 2pi)
2. tan(t + pi)
3. tan(t - 2pi)
Answer:
Tan(t+pi) = 3
Step-by-step explanation:
First let's find the slope of the line through the points and
Note: is the first point . So this means that x%5B1%5D=-2 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=3.
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.
m=%283-0%29%2F%280--2%29 Plug in y%5B2%5D=3, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=-2
m=%283%29%2F%280--2%29 Subtract 0 from 3 to get 3
m=%283%29%2F%282%29 Subtract -2 from 0 to get 2
So the slope of the line that goes through the points and is m=3%2F2
Now let's use the point slope formula:
y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula
y-0=%283%2F2%29%28x--2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=0
y-0=%283%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2
y-0=%283%2F2%29x%2B%283%2F2%29%282%29 Distribute
y-0=%283%2F2%29x%2B3 Multiply
y=%283%2F2%29x%2B3 Simplify
So the equation that goes through the points and is y=%283%2F2%29x%2B3
Notice how the graph of y=%283%2F2%29x%2B3 goes through the points and . So this visually verifies our answer.
Graph of y=%283%2F2%29x%2B3 through the points and
PLEAAASSSEE HELP!! ITS DUE IN 1 HOUR
Answer:
-4 and +4
Step-by-step explanation:
(- - - -) = -4
(+ + + +) = 4 or +4
Please give me the correct answer.Only answer if you're very good at math.
What is the relationship between toppings and price?
A:Fornos charges one euro for every topping.
B:Fornos charges one euro for a plain slice, and one-half euro for each extra topping.
C:Fornos charges one and a half euros for each topping.
D:Fornos charges one-half for each topping.
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
If a triangle has side lengths of 28,45, and 50, is the triangle acute,obtuse,or right?
Answer:
Acute i think
Step-by-step explanation:
Answer:
acute
Step-by-step explanation:
what is x and y? help
pleaseeee Answer! Will Mark as Brainliest for the Best Answer
Answer:
[tex]p^{4} s^{5} y^{-7} z^{-1}[/tex]
Step-by-step explanation:
[tex]\frac{1}{y^{7} } = y^{-7}[/tex]
[tex]\frac{1}{z} = z^{-1}[/tex]
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
The figure contains a right rectangular prism. The length of the prism is labeled 6 and one half centimeters, the width is labeled 2 and one half centimeters, and the height is labeled 2 and one half centimeters.
Answer:
40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex]
Step-by-step explanation:
The figure is a rectangular prism, so the formula would be Volume = length x width x height.
length = 6 [tex]\frac{1}{2}[/tex] cm
width = 2 [tex]\frac{1}{2}[/tex] cm
height = 2 [tex]\frac{1}{2}[/tex] cm
If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm.
Without a calculator, I would first turn the mixed numbers into improper fractions.
6 [tex]\frac{1}{2}[/tex] = [tex]\frac{13}{2}[/tex]2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex]Volume = [tex]\frac{13}{2}[/tex] x [tex]\frac{5}{2}[/tex] x [tex]\frac{5}{2}[/tex]
When you multiply everything together you should get [tex]\frac{325}{8}[/tex].
As a mixed number, that would be 40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex].
You deposit $5,000 in a bank account that earns 4% simple interest. How much interest will you earn in 2 years?
Answer:
Step-by-step explanation:
triangle similarity i think ... picture included * SIN COS TAN
Answer:
d = 105tan(37°)Step-by-step explanation:
opposite (o) = d
adjacent (a) = 105
Angle A = 90 - 53 = 37°
Therefore,
the correct equation would be
tan(A°) = opposite/adjacent
tan(37°) = d/105
d = 105tan(37°) ✅d = 105 × 0.7535540501
d ≈ 79.12 units
______________
#IndonesianPride
- kexcvi
Can somebody help me? -2-7p<26
Answer: p>−4
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2−7p<26
Step 1: Simplify both sides of the inequality.
−7p−2<26
Step 2: Add 2 to both sides.
−7p−2+2<26+2
−7p<28
Step 3: Divide both sides by -7.
−7p
−7
<
28
−7
p>−4
Parallel Lines cut by a transversal
Answer:
110
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Set the two given equations equal to each other (alternate angles i think)
12x + 2 = 11x + 11
**simplify and pull x to one side**
x = 9
**now insert x=9 into one equation (I choose 12x+2**
12(9) + 2 = 108 + 2 =110
A
Write an equivalent expression in word form.
(1- 1/3) / 2
Answer:
21
Step-by-step explanation:
M=-1 and it has a y-intercept of (0,-6). Write the equation that represents the situation.
Answer:
y=-1x-6
Step-by-step explanation:
do you need a explanation aswell?
Which of the following table of values represent a function?
A. (-1,5) (1,5) (4,5) (-4,5) (1,-5)
B. (1,0) (0,2) (5,-4) (-2,-1) (1,5)
C. (2,2) (3,3) (4,4) (5,5) (6,6)
D. (1,-4) (4,2) (-4,0) (0,3) (-4,-2)
C is the answer
Step-by-step explanation:
but I think is C
6. Ria purchased a car for
$14,775. Sales tax in her
county is 6.8%.
a. What is the total price of
the car including tax?
b. If she puts $2,100 down,
how much will she be
financing?
c. What will her monthly
payment be if the term of
the loan is 72 months with
an APR of 3.5%?
9514 1404 393
Answer:
a) $15,779.70
b) $13,679.70
c) $210.92
Step-by-step explanation:
a) When tax is added, the total cost is ...
total = price × (1 +tax rate)
total = $14,775 × 1.068 = $15,779.70
__
b) The amount financed is the difference between the total cost and the down payment.
financed = total - down35
financed = $15,779.70 -2100 = $13,679.70
__
c) The monthly payment is found using the amortization formula. It can also be found using any of a number of financial calculators, spreadsheets, or apps.
A = P(r/12)/(1 -(1 +r/12)^-n) . . . . annual rate r, n monthly payments, principal P
A = $13,679.70(0.035/12)/(1 -(1 +0.035/12)^-72) ≈ $210.92
what 2 numbers can be added to make -40 as well as added to make -6?
-20 x 2 or -10 x 4 both equal -40
-2 x 3 = 6
The temperature at 5:00 am functions
Answer:
t2 = 37 °F
Step-by-step explanation:
t
1
=52
∘
F
g=3
∘
F/hr
Factor the GCF out of each term of the polynomial.
Answer For The Number 22: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22. 3.
Answer For The Problem 2x3 (Divide it by the numbers I give you meaning divide the number two by what I give yo and the other number 3 by it.
The common factors for 2,3 are −1,1 . The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors −1,1 is 1 .The number is one.
Answer For The Problem 2x5 is also 1 so decide both 2&5 by 1 then multiply. After doing that for answers 2&3 add them. last if you then subtract 22 that might be the answer so put that & also put the answer of the greatest common factor of 22 which is 3. Make sure to include that the one where you subtracted 3 was the greatest common factor for 22.
Dare to do this if you are geiness
Express 750×900as a product of it prime factors using exponents
Who did this get a follow and marked as brainliest
Answer:
2^3 x 3^3 x 5^4
Step-by-step explanation:
750 x 900 = 675000
675000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 5
Which in product of prime factors is = 2 to the power of 3 x 3 to the power of 3 x 5 to the power of 4
Please answer this! I need a quick answer with work.
Equations -
1. Input u!
[tex] \frac{2.6 - ( - 1)}{5.8} [/tex]
Solve the problem!
[tex] \frac{3.6}{5.8} [/tex]
[tex] \frac{3.6}{5.8} =0.62[/tex]
Answer:
0.44827586
Step-by-step explanation:
(2.6)(−1)/-5.8=-2.6/-5.8 so you get 0.44827586
help0000000000000000000
Answer:
The answer is going to be C.
Step-by-step explanation:
To help you in the future with any question like this one, you can always use Desmos Calculator.
Overview
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Question Progress
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Oilsee
Homework Progress -
26 / 28 Marks
D
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Here is a list of numbers:
20 29 30 33 37 40
41
46
50
Use four of the numbers to make a sequence and describe the rule
for continuing your sequence.
I
equences - Term-to-Term Rule
Overview
0
Answer:
20 292 02 202 202
Step-by-step explanation:
In ΔOPQ, the measure of ∠Q=90°, PQ = 1.8 feet, and OP = 7.4 feet. Find the measure of ∠P to the nearest degree.
Answer:
P=75.922 ≈ 76
∘Step-by-step explanation:
What function uses the ADJACENT and the HYPOTENUSE?
SOH-CAH-TOA
cos P = adjacent/hypotenuse= 1.8/7.4
Pcos^-1 = (1.8/ 7.4)
P=75.922 ≈ 76
The total population of a town is 128200 if 55% men are find the number of all the six pairs of corresponding
Pls help
Answer:
Here is the answer bro
Find the unit rate for each Lean Cuisine Entree. Show your
work
Please show work worth 40 points
Answer: 60
Step-by-step explanation:10 x 6 = 60 ( Also, 6x6x6x6x6x6x6x6x6x6 = 60
plz help asap I'll mark brainliest!!!
One number is 4 more than another, and their sum is 60. What is the smaller number?
If x = the larger number and y = the smaller number, then which of the following systems could be used to solve the problem?
x + y = 60 and -x + y = 4
x + y = 60 and x + y = 4
x + y = 60 and x - y = 4
Unlimited Attempts Remain
Answer:
Step-by-step explanation:
The system is
x+y=60 and x-y=4
If we get the difference between the two equations above we get
x+y-x+y=60-4
2y=56
y=28
If f(x)=3x+2, what is f(3)-7
Answer:
[tex] \orange{ \bold{f(3) - 7 = 4}}[/tex]
Step-by-step explanation:
[tex]f(x) = 3x + 2 \\ \\ plug \: x = 3 \\ \\ f(3) = 3(3) + 2 = 9 + 2 \\ \\ f(3) = 11 \\ \\ f(3) - 7 = 11 - 7\\ \\ \purple{ \bold{f(3) - 7 = 4}}\\ \\ [/tex]