Answer:
x = 2.81 and 2.096
Step-by-step explanation:
Given the expression
10(2^x) + 7(3^x) = 6^x + 70
This can also be expressed as;
10(2^x) + 7(3^x) = (2*3)^x + 70
10(2^x) + 7(3^x) = 2^x*3^x + 70
Let a = 2^x and b = 3^x
10a + 7b = ab + 70
10a + 7b - ab = 70
10a-ab + 7b - 70 = 0
a(10-b)+7(b-10) = 0
a(10-b)-7(10-b) = 0
a-7 = 0 and 10-b = 0
a = 7 and b = 10
Since a = 2^x
7 = 2^x
log 7 = log2^x
log7 = xlog2
x = log7/log2
x = 2.81
Similarly
10 = 3^x
log 10 = log 3^x
log 10 = xlog3
x = log 10/log 3
x = 1/0.4771
x = 2.096
Hence the values of x that satisfies the equation are 2.81 and 2.096
HELP ASAP AND WILL MARK BRAINLIEST
Which similarity statement expresses the relationship between the two triangles?
Triangle E F G is similar to triangle J K L
Triangle G E F = Triangle K J L
Triangle F G E is similar to Triangle J K L
Triangle G F E = triangle L K J
Answer:
Triangle FGE is similar to Triangle JKL
Step-by-step explanation:
HELP!!! BRAINLYIEST!
3
Select the correct answer.
Emma starts a food blog. When the blog is launched, the number of site visits is 486. Every month, the number of site visits Increases by
one-third of the number of site visits in the previous month. At this rate, how many total site visits will there have been after 6 months?
OA. 6,734
OB.
2,731
Ос.
9,465
OD
728
Reset
Next
Answer:
6734
Step-by-step explanation:
1st month -> 486
2nd month->(1/3 x 486)+ 486
=648
3rd month->(1/3 x 648)+ 648
=864
4th month->(1/3 x 864)+ 864
=1152
5th month ->(1/3 x 1152)+ 1152
=1536
6th month ->(1/3 x 1536)+ 1536
=2048
486 + 648 + 864 + 1152 + 1536 +2048 = 6734
If the exponential model f(x)=14(5)x is written with the base e, it will take the form A0ekx. What is A0 and what is k?
Answer:
We have:
f(x) = 14*(5)^x
And we want to write this in the form:
g(x) = A*e^(k*x)
We want to have f(x) = g(x)
This is ratter easy.
The general case is:
A*(r)^x = B*e^(k*x)
Here we have:
A = B
Then:
(r)^x = e^(k*x)
Now we can remember the relation:
(a^x)^y = a^(x*y)
Then we can write:
e^(k*x) = (e^k)^x
Then we have:
(r)^x = (e^k)^x
Then we must have:
r = e^k
Now let's go to our case:
14*(5)^x = A*e^(k*x) = A*(e^k)^x
Then we have:
14 = A
5 = (e^k)
With this equation we can find the value of k.
ln(5) = ln(e^k) = k
ln(5) = k
Then the equation g(x) is:
g(x) = 14*e^(ln(5)*x)
Answer:
A0=14 k +ln9
Step-by-step explanation:
To rewrite the model with the base e, we use the fact that for all b>0,
b=eln(b)
Using this property, and then the power property of logarithms, on 9x, we find that
(9)x=eln(9x)=exln(9)=e(ln(9))x
So we find that
14(9)x=14eln(9)x
So A0=14 and k=ln(9).
Deanna says a common denominator for ¼ and ⅙ is 20. Do you agree? Explain why or why not
Answer:
no
Step-by-step explanation:
4 IS a factor of 20
BUT
6 IS NOT a factor of 20
a common denominator for 1/4 and 1/6 would be 12
In trapezoid MNPQ shown below, MN || QP, m&M = 108°, m&P = 4x - 5, and
mxQ = 3x + 21. What is the number of degrees in m«N.
Answer:
Answer:
The answer is below
Step-by-step explanation:
A trapezoid is a quadrilateral (has four sides and four angles) with a pair of opposite parallel sides. The pair of opposite parallel side is known as the base. Also, the angles on the same leg of a trapezoid (adjacent angles) are supplementary (add up to 180°).
In trapezoid MNPQ:
∠M + ∠Q = 180° (angles on the same leg are supplementary)
108 + (3x + 21) = 180
3x + 129 = 180
3x = 51
x = 17
Also:
∠N + ∠P = 180° (angles on the same leg are supplementary)
∠N + (4x - 15) = 180
∠N = 180 - (4x - 15)
∠N = 180 - 4x + 15
∠N = 195 - 4x
substitute x = 17°:
∠N = 195 - 4(17)
∠N = 127°
Work out the size of each of the angles. thank you!
Step-by-step explanation:
a=360°-300°=60°{reflex angle}
b=180°-40°=140°{straight angle}
hope it helps.
Step-by-step explanation:
For a
a + 300° = 360° { being complete turn }
a = 360° - 300°
a = 60°
For b
b + 40° = 180° { being linear pair }
b = 180° - 40°
b = 140°
Type the next number in this sequence:
6, 14, 32, 60, 98, 146, 204,
Answer: 272 I believe
A gas station sells 1600 gallons of gasoline per hour if it charges $ 2.70 per gallon but only 900 gallons per hour if it charges $ 2.95
per gallon. Assuming a linear model
(a) How many gallons would be sold per hour of the price is $ 2.90 per gallon?
Answer:
(b) What must the gasoline price be in order to sell 1300 gallons per hour?
Answer:
Geometry Need help/........
What is the place value of 9 in 9.08
Answer:
The whole number or tens place
Step-by-step explanation:
If u need any more help love to help
The requried place value of 9 in 9.08 is a unit place.
What is place value?The place of the value of digits is defined as in a number the place of digits is the location of the digit in that number.
Here,
We have to determine the place value of 9 in 9.08
Since 9 is present at the unit place of the number so the place value is given as unit place.
Thus, the requried place value of 9 in 9.08 is a unit place.
Learn more about place value here:
https://brainly.com/question/27734142
#SPJ5
Can someone help me with both of these? You can answer only one, however, If you answer both that is who gets brainliest. don't answer just to take my points or you will get reported.
Answer:
1. true
2. Associative
Step-by-step explanation:
1) Kayla is using mental math to find the given sum. Which equivalent
expression could she use?
A)
85 + 20
B) 90 - 13
C)
100 + 13
D) 105 - 2
John O'Sullivan has just completed his first year in business. His records show that he spent the following in advertising: Internet $600 radio $650 yellow pages $700 local flyers $400. what percent. of johns advertising was spent on the Yellow Pages? ( Round to the nearest hundredth percent.)
Answer:
29.787%
Step-by-step explanation:
The computation of the percentage that spend on yellow pages is shown below:
= Yellow pages ÷ Total advertising cost
= $700 ÷ ($700 + $600 + $650 + $400)
= $700 ÷ $2,350
= 29.787%
What percent of 40 is 50?
PLZ PLZ PLZ
What is the limit ?
- does not exist
- “infinity”
- “-infinity”
- 1
Answer:
Um i think it would be
does not exist
Step-by-step explanation:
sorry if wrong im a little bad at that
In how many ways can a quality-control engineer select a sample of3 transistors for testing frm a batch of 100 transistors?
Answer:
161700 ways.
Step-by-step explanation:
The order in which the transistors are chosen is not important. This means that we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
3 transistors from a set of 100. So
[tex]C_{100,3} = \frac{100!}{3!(100-3)!} = 161700[/tex]
So 161700 ways.
HELP PLEASEEEEEEEEEEE!!!
Answer:
The graph under the "U" graph
Step-by-step explanation:
Please will give brainliest and thanks for the problem
Answer:
X - INTERCEPT = (3.5, 0)
Y - INTERCEPT = (0, 2.5)
Step-by-step explanation:
X and Y intercepts are determined by where and when the point crosses x or y. Let's take a look at the graph,
Answer:
Y intercept- (0,2.5)
X intercept - (3.5, 0)
Step-by-step explanation:
I was summoned
4x.5x³.2x⁵ find the product
A house needs to be built and ready to move into by June 1 st . It takes 1 week to clear the land. After that, it takes 4 days to lay the foundation. It takes 2 ½ weeks to put up the framing of the house. The interior of the house will take 9 days to finish. When should the crew start work on the house?
Answer:
38
Step-by-step explanation:
7+4+14+4+9
if you multiply the number by 2 and add 4, then result you get will be the same as three times the number decreased by 7.
Answer:
Step-by-step explanation:
Let the number be x,
2x+4 = 3x-7
Collect like terms
2x-3x= -4-7
-x =. -11
Multiply both sides by -1
x. =. 11
PLEASE MARK BRAINLIEST.
1/10 of the counters in a bag are blue. 1/2 of the counters are red. 2/5 of the counters are yellow. Which of the ratios below shows the ratio of blue to red to yellow?
Answer:
well 1/10 are blue, 5/10 are red, and 4/10 are yellow.
1/10 blue
5/10 red
4/10 yellow
I don't really know how to answer this question but I hope me converting the ratios helps :)
Step-by-step explanation:
A student read the clock at 12:00. Then she read it again at 12:15. How many one degree turns has the minute hand made?
Answer
about 15
Step-by-step explanation:
Find the total cost, to the nearest cent, for a meal at a restaurant that cost $19.74 with
an additional sales tax of 7.5%
4 units 2 units 7 units 3 units what's the area
Answer:
15 units
Step-by-step explanation:
split the figure into two figures
one with 4x3 and the other with 1x3
then find the area for each and add the areas to get total area
4x3=12
1x3=3
12+3=15
hope this helps have a blessed day :)
Answer:
The answer has to be 168
Step-by-step explanation:
To find the Area you need to multiply all the lengths of each side together.
So 3x4x2x7=168
HOPE THIS HELPS!!!
PLEASE MARK BRAILIEST!!!
Joaquin can read one comic book in 15 minutes. Write and solve an equation to determine how many comic books he can read in 75 minutes.
what is this ???????/ 9.1 ∙ 102
Step-by-step explanation: 9.1 x 102 = 928.2.
what equation can be formed to determine the two numbers.
Answer:
If one is given a quadratic equation in the form x2 + bx + c = 0, the sought factorization has the form (x + q)(x + s), and one has to find two numbers q and s that add up to b and whose product is c (this is sometimes called "Vieta's rule" and is related to Vieta's formulas).
Step-by-step explanation:
Answer:
what numbers?
Step-by-step explanation:
Which is equivalent to 3/8 1/4
Answer:
Step-by-step explanation:
what is equivalent to
1/4: 2/8, 4/16, 8/32....... and etc-
3:8: 6/16, 9/24 and etc.......-
i was listening to rhinestone eyes while typing this-
ty :P