Answer:
[tex] \dfrac{49}{4} = 12.25 [/tex]
Step-by-step explanation:
[tex] 4^{x-1} = [/tex]
[tex] = (2^2)^{x - 1} [/tex]
[tex] = 2^{2(x - 1)} [/tex]
[tex] = 2^{2x - 2} [/tex]
[tex] = 2^{x + x - 2} [/tex]
[tex] = 2^x \times 2^x \times 2^{-2} [/tex]
[tex] = 7 \times 7 \times \dfrac{1}{2^2} [/tex]
[tex] = \dfrac{49}{4} = 12.25 [/tex]
Solve exponential equation
1/16=64^4x-3
Answer: assuming that this was your equation;
[tex]\frac{1}{16} =64^{4x-3}[/tex]
You answer is x= 7/12
Step-by-step explanation:
First, rewrite 1/16 as 2^-4 and 64^4x-3 as 2^24x-18
This will leave you with;[tex]2^{-4} =2^{24x-18}[/tex]
Since bases are the same, set the exponents equal (eliminate the 2’s);
-4=24x-18
Move 24x to the left to get; -24x-4=-18
Move constant to the right to get -24x=-18+4
Add 4 to -18 to get; -24x=-14
Divide both sides by -24 to get you final answer for x which is 7/12
Hope this helps. Please rate and hit that thanks button. Cheers!
The required value of exponential equation is x = [tex]\frac{7}{12}[/tex].
Given that,
Exponential equation; [tex]\frac{1}{16} = 64^{4x-3}[/tex]
We have to determine,
The value of x.
According to the question,
To obtain the value of x by solving the exponential equation follow all the steps given below.
Exponential equation;
[tex]\dfrac{1}{16} = 64^{4x-3}[/tex]
Then,
[tex]\dfrac{1}{16} = 64^{4x-3}\\\\\dfrac{1}{2^{4}} = 2^{6(4x-3)}\\\\2^{-4} = 2^{24x-18}\\\\[/tex]
Since, bases are the same, set the exponents equation,
Then,
Equating the power of exponential equation,
[tex]-4 = 24x-18\\\\24x = -4+18\\\\24x = 14\\\\x = \dfrac{14}{24}\\\\x = \dfrac{7}{12}[/tex]
Hence, The required value of exponential equation is [tex]\frac{7}{12}[/tex].
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35 POINT QUESTION, WILL MARK BRAINLIEST. Which of the following options is a 3rd degree polynomial with exactly 1 real root?
Answer:
A. F(x) = x^3+9x^2+27x+27
Step-by-step explanation:
I am not 100% sure but I think this is right.
I found the root for this equation: x=-3
Hope this helps!
Answer:
The correct option is D.
Step-by-step explanation:
In option A,
The given function is
[tex]F(x)=x^3+9x^2+27x+27[/tex]
[tex]F(x)=x^3+3(3)x^2+3(3^2)x+3^3[/tex]
[tex]F(x)=(x+3)^3[/tex] [tex][\because (a+b)^3=a^3+3a^2b+3ab^2+b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x-3)=0\Rigtharrow x=-3[/tex]
The real root of this function is -3 with multiplicity 3. It means this function has 3 real roots.
In option B,
The given function is
[tex]F(x)=x^3+3x^2-9x-27[/tex]
[tex]F(x)=x^2(x+3)-9(x-3)[/tex]
[tex]F(x)=(x^2-9)(x+3)[/tex]
[tex]F(x)=(x+3)(x-3)(x+3)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x+3)=0\Rigtharrow x=-3,3,-3[/tex]
Therefore, this function has 3 real roots.
In option C,
The given function is
[tex]F(x)=x^3-9x^2+27x-27[/tex]
[tex]F(x)=x^3-3(3)x^2+3(3^2)x-3^3[/tex]
[tex]F(x)=(x-3)^3[/tex] [tex][\because (a-b)^3=a^3-3a^2b+3ab^2-b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x-3)(x-3)(x-3)=0\Rigtharrow x=3[/tex]
The real root of this function is 3 with multiplicity 3. It means this function has 3 real roots.
In option D,
[tex]F(x)=x^3+3x^2+9x+27[/tex]
[tex]F(x)=x^2(x+3)+9(x+3)[/tex]
[tex]F(x)=(x+3)(x^2+9)[/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x^2+9)=0[/tex]
[tex]x+3=0\Rightarrow x=-3[/tex]
[tex]x^2+9=0\Rightarrow x^2=-9\Rightarrow x=\pm 3i(Imaginary)[/tex]
The roots of this functions are -3, 3i and -3i. Since this function has exactly one real root, therefore option D is correct.
Ms. Kincaid keeps a supply of dimes and quarters in her car to pay for highway tolls. A week’s supply of toll coins contains 5 more dimes than quarters and totals $4.00. How many quarters does Ms. Kincaid spend on highway tolls in one week
A. 10
B.15
C.16
D.40
Answer: (A) 10
Step-by-step explanation:
Value Quantity = TOTAL Value
dimes: .10 Q + 5 = .10(Q = 5)
quarters: .25 Q = .25Q
Dimes + Quarters = $4.00
.10(Q + 5) + .25Q = 4.00
.10Q + .50 + .25Q = 4.00
.50 + .35Q = 4.00
.35Q = 3.50
Q = 10
Quarters = 10
Dimes = Q + 5
= 10 + 5
= 15
Answer: Option A, she has 10 quarters.
Step-by-step explanation:
We have quarters of $0.25 and dimes of $0.10
We have 5 more dimes than quarters and a total of $4.00
How many quarters Ms. Kincaid has?
Q is the number of quarters and D the number of dimes.
We have the system of equations:
D = Q + 5
Q*$0.25 + D*$0.10 = $4.00
First, we can replace the first equation into the second and solve it for Q.
Q*$0.25 + (5 + Q)*$0.10 = $4.00
Q*($0.25 + $0.10) + $0.50 = Q*($0.35) + $0.50 = $4.00
Q = (4.00 - 0.50)/0.35 = 3.50/0.35 = 10
So she has 10 quarters.
The correct option is A.
Tim is making a fence in the shape of a triangle for his livestock. He wants one side of the triangle to be two times as along as another side and the thrid side to be 21 meters long. Tim wants the perimeter of the triangle to be more than 42 meters and less than 84meters
Answer:
Step-by-step explanation:
42 < 21+3x < 84
21 < 3x < 63
7 < x < 21
The measure of sides of a triangle lies between 7<x<21.
Given that, Tim is making a fence in the shape of a triangle for his livestock.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Let the measure of one side of a triangle be x meters.
One side of the triangle to be two times as along as another side and the third side to be 21 meters long.
Second side =2x meters and the third side =21 meters
Tim wants the perimeter of the triangle to be more than 42 meters and less than 84meters.
Now, 42<x+2x+21<84
21<3x<63
7<x<21
Therefore, the measure of sides of a triangle lies between 7<x<21.
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in a normal distribution what percentage of the data falls within 1 standard deviation of the mean?
Answer:
68.2% of the data falls within 1 standard deviation of the mean
Step-by-step explanation:
When we look at the curve for standard deviation, 34.1 % falls within 1 standard deviation below the mean and 34.1 % falls within 1 standard deviation above the mean.
34.1 + 34.1 = 38.2 %
68.2% of the data falls within 1 standard deviation of the mean
Answer:
68%
Step-by-step explanation:
Select the statement that is true for the graphs of all functions g(x). A. The graph of g(x + 1) is the graph of g(x) shifted right 1 unit. B. The graph of g(x + 1) is the graph of g(x) shifted up 1 unit. C. The graph of g(x + 1) is the graph of g(x) shifted left 1 unit. D. The graph of g(x + 1) is the graph of g(x) shifted down 1 unit.
Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
As per the given information option (A) is correct because it will shift to the right side by one unit when the function of [tex]g(x)[/tex] is [tex]g(x+1)[/tex].
For example:-
[tex]x=2[/tex]
So,
[tex]g(2)\\g(2+1)[/tex]
Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.
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Final answer:
The true statement for the graphs of all functions g(x) is that the graph of g(x + 1) is the graph of g(x) shifted left by 1 unit.
Explanation:
When considering the transformation of the graph of a function g(x) to g(x + 1), we are applying a horizontal shift to the graph. According to the principles of graph transformation, when we add a positive constant to the input of a function, every point on the graph shifts left by that amount. Therefore, the graph of g(x + 1) is the same as the graph of g(x), shifted to the left by 1 unit. This corresponds to the option C, which states that adding 1 to the input of the function shifts the graph to the left by 1 unit.
Name the property of real numbers illustrated by the equation
Answer:
Distributive property
Step-by-step explanation:
Simplify f+g / f-g when f(x)= x-6 / x+7 and g(x)= x-7 / x+6
Answer:
C. 2x^2 - 85 / 13
Janice bought juice packed for the 15 players on the soccer team the juice packets come in boxes of 6 how many boxes did Janice buy
Answer:
It would be 90 because if there are 15 soccer people on the team and there are 6 in the packets then each would get 1 and if you multiply 15 times 6 you will get 90.
So the answer would be 90
Answer:
90
Step-by-step explanation:
just do 15x6
From the table below, determine whether the data shows an exponential function. Explain why or why not.
Answer:
Option a. No; the domain values are at regular intervals and the range values have a common sum 1.
Step-by-step explanation:
x1=3, x2=1, x3=-1, x4=-3
y1=1, y2=2, y3=3, y4=4
x1-x2=3-1→x1-x2=2
y2-y1=2-1→y2-y1=1
x2-x3=1-(-1)=1+1→x2-x3=2
y3-y2=3-2→y3-y2=1
x3-x4=-1-(-3)=-1+3→x3-x4=2
y4-y3=4-3→y4-y3=1
The data doesn't show an exponential function, because the domain values are at regular intervals and the range values have a common sum 1.
Answer:
a
Step-by-step explanation:
A mayoral candidate would like to know her residents’ views on a public open space before the mayoral debates. She asks only the people in her office. Her co-workers are an example of a ______.
census
population
convenience sample
simple random sample
Answer:
convenience sample
Step-by-step explanation:
Answer: Convenience Sample
Step-by-step explanation: Biased sample–Parts of the population are favored over others. She only asked people in her office
Please help with this Math Question...
Answer: A
Step-by-step explanation:
f(x) = x³ + 4x² + 7x + 6
possible rational roots are ±{1, 2, 3, 6}
Try x = -2
-2 | 1 4 7 6
| ↓ -2 -4 -6
1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0
The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.
a=1, b=2, c=3
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\dfrac{-(2)\pm\sqrt{(2)^2-4(1)(3)} }{2(1)}[/tex]
[tex]x=\dfrac{-2\pm\sqrt{4-12} }{2}[/tex]
[tex]x=\dfrac{-2\pm\sqrt{-8} }{2}[/tex]
[tex]x=\dfrac{-2\pm2i\sqrt{2}}{2}[/tex]
[tex]x = -1 \pm i\sqrt{2}[/tex]
[tex]x = -1 + i\sqrt{2}[/tex] [tex]x = -1 - i\sqrt{2}[/tex]
[tex]x - (-1 + i\sqrt{2})=0[/tex] [tex]x - (-1 - i\sqrt{2})=0[/tex]
The factors are:
[tex](x - 2)[x - (-1 + i\sqrt{2})][x - (-1 - i\sqrt{2})][/tex]
Can someone help me please
Add 1,1.5,1.25,2.5, and 3 to get D, or 9 and 1/4.
Answer:
9 and 1/4 hope this helps!!!!!
23/50 of Zanders friends prefer to stay home on Friday night what percent of Xander's friends prefer to stay home on Friday nights
Answer:
46% of Xander's friends prefer to stay home on Friday nights.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
[tex]\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.[/tex]
i.e
Zanders friends prefer to stay home on Friday night = 23
Total numbers of Zanders friends are 50.
Part value = 23
Total value = 50
Put in the formula
[tex]Percentage = \frac{23\times 100}{50}[/tex]
[tex]Percentage = \frac{2300}{50}[/tex]
Percentage = 46%
Therefore 46% of Xander's friends prefer to stay home on Friday nights.
Answer:
wasdd ada
Step-by-step explanation:
hey please help me with this
Answer:
Two real solutions
Step-by-step explanation:
z=-1.45
z=0.45
Answer:
ANSWER: Two real solutions
Step-by-step explanation:
its z=-1.45
its z=0.45
Melanie's trip was 500 miles long. She drove the same number of miles each day for 3 days. How many miles did she drive each day? Write the answer as a mixed number
Melanie drove a total of 500 miles over three days. To determine how many miles she drove each day, we divided total miles by total days. This gives us 166.67 miles or 166 2/3 miles as a mixed number.
Explanation:The subject of the provided question is related to simple division. Here, Melanie has traveled 500 miles in total over the course of three days, and she drove the same distance each day. Mathematically speaking, to find out how many miles Melanie drove each day, we need to divide the total distance by the number of days. Hence, we divide 500 miles by 3 days.
This comes out to be 166.67 miles, which is the decimal format of the distance traveled by Melanie each day. However, the question asks for the answer to be written as a mixed number. Therefore, 166.67 miles can be expressed as 166 2/3 miles per day, as a mixed number. This is calculated by expressing the decimal .67 as a fraction.
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The table below shows four systems of equations:
System 1
4x − 5y = 2
3x − y = 4
System 2
4x − 5y = 2
10x − 21y = 10
System 3
4x − 5y = 2
24x − 47y = 22
System 4
4x − 5y = 2
10x + 3y = 15
Which pair of systems will have the same solution?
System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1
System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2
System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to three times the second equation in system 1
System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to three times the second equation in system 2
Answer:
System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2
Step-by-step explanation:
We are given four systems of equations. We are asked to find which two sets have the same solution.
We find that in all the 4 systems, first equation 4x-5y =2 remains the same.
I option is wrong because
Equation I + 2times equation 2 in II system
gives 10x-7y =10 but given is 10x-21y =10 hence wrong.
Now compare 2 and 3
In system 2, I equation +2times second equation gives
24x-5y-42y =2+20 or
24x-47y =22
Hence system 2 and 3 are the same set of equations and give the same solution.
Could I get some help on this question?
Answer:
The triangles are similar, because the angles are congruent and the sides are proportional.
Step-by-step explanation:
The first step to see if the triangles are similar is to see if the angles are the same.
The third angle in the large triangle is
30 + 65+ unknown = 180
95 + unknown = 180
Subtract 95 from each side
unknown = 180-95
unknown = 85
So the angles are the same.
Lets check the ratio of the the sides
14 10
------ = ----------
7 5
Both simplify to 2/1 so the ratio's are the same.
The triangles are similar because the angles are congruent and the sides are proportional.
Use substitution to find the solution to the system of equations. 5x+7y=-29 y=x+1
Answer:
(x, y) = (- 3, - 2)
Step-by-step explanation:
given the 2 equations
5x + 7y = - 29 → (1)
y = x + 1 → (2)
substitute y = x + 1 into (1)
5x + 7(x + 1) = - 29 ( distribute and simplify left side )
5x + 7x + 7 = - 29
12x + 7 = - 29 ( subtract 7 from both sides )
12x = - 36 ( divide both sides by 12 )
x = - 3
substitute x = - 3 into (2)
y = - 3 + 1 = - 2
solution is (- 3, - 2 )
Answer:
(-3,-2)
Step-by-step explanation:
At the beginning of the week Fayez writes drown the mileage of his limousine - 2529 At the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during the week. The handbook states that the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limousine used 1 gallon of petrol for every 20 miles this week 1 gallon = 4.54 litres Did his limo use 1 gallon of petrol for every 20 miles that week? Explain answer in full Please help!!
Antonio earns $5 an hour for raking leaves. He also has $35 in savings. Which equation shows the amount of money, m, Antonio will have after raking leaves for a number of hours, h?
Answer:
35 + 5h = m
Step-by-step explanation:
PLEASE PLEASE HELP PLEASE
Answer:
arc ≈ 25.13 feet
Step-by-step explanation:
arc length = circumference × fraction of circle
= 2 πr × [tex]\frac{\frac{4\pi }{3} }{2\pi }[/tex] ← cancel 2π
= 6 × [tex]\frac{4\pi }{3}[/tex] = 8π ≈ 25.13 feet
Kimberly got 3 problems wrong on a test of 25 questions. What percent of the questions did she get correct
Answer:
88%
Step-by-step explanation:
if she got 3 problems wrong, so she got (25-3)=22problems correct,
22/25=x/100,x=88
The percent of the questions did she get correct will be 88%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Kimberly got 3 problems wrong on a test of 25 questions.
Then the number of the correct question will be
⇒ 25 – 3
⇒ 22
Then the percent of the questions did she get correct will be
⇒ (22 / 25) x 100
⇒ 0.88 x 100
⇒ 88%
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George has 600 basketball cards Jocelyn has 1/5 as many basketball cards as George how many basketball cards does joycelyn have
Answer: he has 3000
Step-by-step explanation: just multiply 600 by 5
Answer:
120
Step-by-step explanation:
all you do is 600 x 1/5
but u have to turn 1/5 into a decimal which is .20
so 600 x .20= 120
The sales tax in your city is 8.8\%8.8%, and an item costs \$63$63 before tax. How much tax would you pay on that item? Round to the nearest hundredth or cent.
please help? i honestly don't know
a population of bacteria doubles every 15 hours, initially the population of bacterica is 40. what is the population of the bacteria after 40 houra?
Answer:
the bacteria's population is 120
Step-by-step explanation:
Answer:
After 40 hrs it is 213.333 bacterias
Approximately 213 bacterias
Step-by-step explanation:
Initial population of bacteria is 40
And it doubles every 15 hrs
If 15 hrs is double
1 hrs is 0.13333
Then 10 hrs is 1.3333
So the first 15 hrs
It multiplies to 40*2= 80
The second 15 hrs it multiplies by 80*2=160
The next 10 hrs it multiplies by
160*1.33333= 213.333
A total of 60 60 children signed up for hockey. There were 3 3 boys for every 1 1 girl who signed up. How many of the children who signed up for hockey were girls?
Answer: 15
Step-by-step explanation:
Boys : Girls
3x + 1x = 60
4x = 60
x = 15
Girls (1x) = 1(15) = 15
Answer:
The answer is 15
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 152. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 12. Ten more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
Answer:
Number of restaurant-purchased meals eaten in a restaurant = 70
Number of restaurant-purchased meals eaten in a car = 22
Number of restaurant-purchased meals eaten in a home = 60
Step-by-step explanation:
Let the number of people that will eat in a restaurant be R.
Let the number of people that will eat in a car be C.
Let the number of people that will eat in a home be H.
From the information given in the problem we have,
R+C+H = 152 ____equation (1)
C+H-R = 12 ____equation (2)
R = H+10 ____equation (3)
1) Plugging in R=H+10 from equation 3 into the equation 2, we get
C+H-R=12
=> C+H-(H+10)=12
=> C+H-H-10=12
2) Cancelling out +H and -H, we get
C-10=12
3) Add 10 to both sides
C-10+10=12+10
4) Cancelling out -10 and +10, we get
C=22
5) Plugin C=22 in equation 1, we have
R+C+H = 152
=> R+22+H=152
Subtract 22 from both sides,
R+22+H-22=152-22
Cancelling out +22 and -22 from the left side, we get
R+H=130 ____let it be equation (4)
6) Plugin C=22 in equation 2, we have
C+H-R = 12
22+H-R = 12
Subtracting 22 from both the sides, we get
22+H-R-22 = 12-22
Cancelling out +22 and -22 from the left side,
H-R = -10 ____let it be equation (5)
7) Adding equation 4 and equation 5, we get
(R+H)+(H-R) = 130 + (-10)
=> R+H+H-R = 130-10
8) Cancelling out R and -R from the left side, we get
2H = 120
9) Dividing both sides by 2, we get
[tex]\frac{2H}{2} = \frac{120}{2}[/tex]
10) Cancelling out the 2's from the left side, we have
H=60
11) Plugging in C=22 and H=60 in the equation 1, we have
R+C+H = 152
=> R+22+60=152
=> R + 82 = 152
12) Subtracting 82 from both the sides, we get
R + 82 -82 = 152 -82
13) Cancelling out +82 and -82 from the left side, we get
R = 70
So, C=22, H=60, R=70
Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.
1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.
Answer:
1) [tex]2s+s\leq18[/tex]
2) 6 years old
Step-by-step explanation:
Let Hannah's age be [tex]h[/tex] and her sister's age be [tex]s[/tex]
Hannah is 2 times her sister’s age:It means [tex]h=2s[/tex]
The sum of their ages is no more than 18 years:It means the sum is LESS THAN or EQUAL TO 18. So we can write:
[tex]h+s\leq18[/tex]
1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,
[tex]h+s\leq18\\2s+s\leq18[/tex]
2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,
[tex]2s+s\leq18\\3s\leq18\\s\leq\frac{18}{3}\\s\leq6[/tex]
Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.
The perimeter of a rectangle is 62 feet.If the width of the rectangle is 19 feet.What is the length of the rectangle
l - length
19 ft - width
62 ft - perimeter
l + l + 19 + 19 = 2l + 38 - perimeter
The equation:
2l + 38 = 62 subtract 38 from both sides
2l = 24 divide both sides by 2
l = 12 ft
Answer: The length = 12 ft.