x₁ = - 1
x₂ = 2
Step-by-step explanation:2²ˣ⁺¹ - 9ₓ2ˣ + 4 = 0
2²ˣₓ2 - 9ₓ2ˣ + 4 = 0
2ˣ = n
2n² - 9n + 4 = 0
2n² - n - 8n + 4 = 0
n(2n - 1) - 4(2n - 1) = 0
(2n - 1)(n -4) = 0
2n - 1 = 0 => n₁ = 1/2
n - 4 = 0 => n₂ = 4
2ˣ = 1/2 => 2ˣ = 2⁻¹ => x₁ = - 1
2ˣ = 4 => 2ˣ = 2² => x₂ = 2
A car enters a highway driving 60 mph. A truck enters the highway 6 minutes later and drives 65 mph. The vehicles travel a total of 56 miles and arrive at the same time. How far did the car travel?
Answer:
65 or 60
Step-by-step explanation:
I am not really positive about my answers so please take this into consideration.
The school production of Our Town' was a big success. For opening night. 434 tickets were sold. Students paid $4.00 each, while non students paid $6.00 each. If a total of $2032.00 was collected, how many students and how
many non students attended
The number of students was (Simplify your answer)
The number of non-students was (Simplify your answer)
Answer:
286 students attended
148 non students attended
Step-by-step explanation:
Given
[tex]Tickets = 434[/tex]
[tex]Students = \$4.00[/tex]
[tex]Non-Students = \$6.00[/tex]
[tex]Total = \$2032.00[/tex]
Solving (a): Number of students
Represent students with S and non students with N
So:
[tex]S + N = 434[/tex] --- (1)
[tex]4S + 6N = 2032[/tex] --- (2)
Make N the subject of formula in (1)
[tex]N = 434 - S[/tex]
Substitute 434 - S for N in (2)
[tex]4S +6(434 - S) = 2032[/tex]
Open Bracket
[tex]4S + 2604 - 6S = 2032[/tex]
Collect Like Terms
[tex]4S - 6S = 2032 - 2604[/tex]
[tex]-2S = -572[/tex]
Divide through by -2
[tex]S = 286[/tex]
Hence; 286 students attended
Solving (b):
Recall that
[tex]N = 434 - S[/tex]
[tex]N = 434 - 286[/tex]
[tex]N = 148[/tex]
148 non students attended
What is 57 divided by 20
Answer:
2.85
Step-by-step explanation:
Answer: 2.85
Step-by-step explanation:
57/20 = 2.85
Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided.
4(2x-3) + 8(x-4) = 2(2x+6)
Answer: 4 2/3
Step-by-step explanation:
Because I said so
The graph models projected populations, in thousand, of two towns after x years. Both towns experience a 1.9% annual growth rate. Which equation represents g(x) as a translation of f(x)?
The image of the graph is missing, so i have attached it.
Answer:
g(x) = 5/3 * f(x)
Step-by-step explanation:
We want to find the equation represents g(x) as a translation of f(x).
From the graph, the y = f(x) function curve has the following observations,
- At x = 0, y = f(0) = 30
- At x = 10, y = f(10) = 36
Similarly, from the graph, the y = g(x) function curve has the following observations,
- At x = 0, y = g(0) = 50
- At x = 10, y = g(10) = 60
From those coordinates on the graph, we can see that;
f(0) = 30 and g(0) = 50
It means that for us to make g(x) as a translation of f(x), g(0) = fraction * f(0)
Fraction = g(0)/f(0) = 50/30 = 5/3
Thus;
g(x) = 5/3 * f(x)
Let's confirm with the second coordinate;
Thus;
g(10) = 5/3 * f(10)
g(10) = 5/3 * 36
g(10) = 60
This value is same as what is on graph, thus we can conclude that;
The equation represents g(x) as a translation of f(x) is; g(x) = 5/3 * f(x)
ILL GIVE YOU BRAINLIST !!! HAVE TO GET IT RIGHT
Evaluate the expression given the replacement values
Moving the slider to 9 inches shows that 9 inches is equivalent to 22.86 centimeters. 1 inch is 2.54 times bigger than a centimeter.
Solve each system of equations by using a table.
y= 3x - 4
y = -2x + 11
Answer:
Step-by-step explanation:
3x - 4 = -2x + 11
5x - 4 = 11
5x = 15
x = 3
3(3) - 4 = 9 - 4 = 5 = y
(3, 5)
Answer:
1.)y=3x-4=5
2.)y=4x-1=7
If you averaged 400 miles per day, about how many days would a trip of 1990 miles take?
A. about 6 days
B. about 5 days
c. about 3 days
D. about 4 days
E. about 3 dayS
Answer:
B. about 5 days.
Step-by-step explanation:
If you average;
400 miles per day
1990 miles trip would take?
Cross multiplying gives;
[tex]\frac{1990 * 1}{400}[/tex] = 4.975 days
Rounding off the answer to nearest day gives 5 days.
Hence the 1990 miles journey should take about 5 days.
A trip of 1990 miles would take around 5 days if you averaged 400 miles each day. Option B is correct.
What is average?It is described as the single number that embodies the mean value for the specified collection of data or the closed value for each item in the specified set of data.
It is given that, you averaged 400 miles per day,
We have to find the days would a trip of 1990 miles takes.
The number of days is obtained by taking the ratio of the total distance we have to travel to the distance traveled by the person in one day.
Suppose the number of days needed to complete the trip will be x,
x=Total distance/distance in one day
x=1990 / 400
x= 4.975 days
x≈5 days
If you averaged 400 miles each day, a trip of 1990 miles would take around 5 days.
Thus, option B is correct.
Learn more about the average here:
brainly.com/question/24057012
#SPJ2
Complete the equation describing how x and y are related.
Answer:
5
Step-by-step explanation:
o+5=y=5
1+5=y=6
2+5=y=7
.:y=x+5
If two lines intersect, then they intersect in exactly one _____ point. line. postulate. plane.
Answer: the answer is A. point
Which shows how to find the value of this expression when X=-2 and Y = 5?
(3x®y-2)2
32 (-2)
54
3(-2)6
54
32(5) 6
(-2)
3
(2) 854
Answer:
i think it's b
Step-by-step explanation:
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brody is working two summer jobs, making $10 per hour babysitting and making $15 per hour cleaning tables. In a given week, he can work a maximum of 13 total hours and must earn at least $150. If x represents the number of hours babysitting and y represents the number of hours cleaning tables, write and solve a system of inequalities graphically and determine on possible solution.
Answer:
10x+15y≥150
Step-by-step explanation:
Graph y≤13−x (shading down)
graph y≥10− 3/2x (shading up)
Write each fraction in simplest form if the fraction is already in simplest, form write simplifyed 4 over 14
Answer:
2/7 or 2 over 7
Step-by-step explanation:
4/14 can be simplified. We know this because both 4 and 14 can be divided by 2. 4 divided by 2 = 2 and 1 divided by 2 = 7, thus the answer is 2 over 7.
The Black Panther climbed a height of 15 ft and dropped 20 ft. Write each number as an integer and solve.
Answer:
-5
Step-by-step explanation:
15-20
Answer:
-5
Step-by-step explanation:
15-20=-5
integer means whole number
Suppose a set of data about the spread (in hundreds of acres) of a food-borne bacteria (after t weeks) in lettuce has the following percentage rates of change: 0.9%, 1.3%, 1.1%, 1.0%, 1.3%, 1.0%; and the following average rates of change: 2.9, 2.4, 3.7, 3.1, 3.6, 3.2. Based only on the information given, and without doing any calculations, what type of model would you use? Why? (NOTE THAT the information given is not the actual data set. I have calculated the two types of rate of change for you. You should NOT BE CALCULATING ANYTHING!) Comment:What tells you that the relation is best fit by a linear model? Use principles about what kinds of functions have consistency in which types of rates of change?
Answer:
A sinusoidal model would be used
The kind of function that have consistency in the periodic rate of change is the Average rate of changes
Step-by-step explanation:
The type of model that would be used is sinusoidal model and this is because there is periodic change in the values given ( i.e the rate of changes given )
For percentage rate of changes :
starting from 0.9% there is an increase to 1.3% then a decrease to 1.1% and a further decrease to 1% before an increase to 1.3% and another decrease to 1%
For Average rate of changes:
starting from 2.9 there is a decrease to 2.4, then an increase to 3.7 and another decrease to 3.1 followed by an increase to 3.6 and a decrease back to 3.2
This relation ( sinusoidal model ) is best suited for a linear model because there is a periodic rate of change in the functions
The kind of function that have consistency in the period rate of change is the Average rate of changes
8x - 7x + 6 = 6 help you guys pleases
Steps to solve:
8x - 7x + 6 = 6
~Combine like terms
x + 6 = 6
~Subtract 6 to both sides
x = 0
Best of Luck!
Answer:
0
8x0=0 7x0=0
6+0=6
Step-by-step explanation:
2x+5(3x-4)=14
Step by step please
Answer:
x=2
Step-by-step explanation:
2x+5(3x-4)=14
Distribute
2x + 15x -20 = 14
Combine like terms
17x -20 = 14
Add 20 to each side
17x-20+20 =14+20
17x = 34
Divide by 17
17x/17 = 34/17
x=2
a missile is fired with 96% accuracy. Each firing is independent of the other. If four missiles are fired what is the probability only the second one misses
Answer: 0.03538944
Step-by-step explanation:
Given, The accuracy of missile = 96%
i.e. The probability that it will hit the shot = 0.96
Probability of missing the shot = 1-0.96= 0.04
Now, each missile is independent of other.
Therefore, the probability only the second one misses = (probability that first will hit the shot) x (probability that second one misses ) x (probability that third will hit the shot)x (probability that fourth will hit the shot)
Thus, the probability only the second one misses is [tex](0.96)(0.04)(0.96)(0.96)=0.03538944[/tex]
Hence, the required probability = 0.03538944
Please help!!!! This question is on my plato
Answer:
Its D
Step-by-step explanation:
29/1000= 0.029
Answer:
C.
Step-by-step explanation:
29/999 is 0.02929292929292929
what is the factor of
[tex] {x}^{2} - 6x - 27[/tex]
Answer:
9 is correct answer
Step-by-step explanation:
[tex] {x}^{2} - 6x - 27 \\ = {x}^{2} - 9x + 3x - 27 \\ = x(x - 9) + 3(x - 9) \\ = (x + 3)(x - 9)[/tex]
x=9
Answer:
(x - 9)(x + 3)
Step-by-step explanation:
Given
x² - 6x - 27
Consider the factors of the constant term (- 27) which sum to give the coefficient of the x- term (- 6)
The factors are - 9 and + 3, since
- 9 × 3 = - 27 and - 9 + 3 = - 6, thus
x² - 6x - 27 = (x - 9)(x + 3)
PLEASE HELP - Determine the slopes of the lines passing through each pair of points. - (-6,-3) and (4,1)
Answer: -4/10
Step-by-step explanation:
Since we are finding the slope, we have to do the rise over run strategy. In this case, rise (y) are the numbers -3 and 1 and the run (x) is the numbers -6 and 4. After that, we subtract them. So, -3 - 1 and -6 - 4. We get -4 over -10 (or - 4/10) which is your slope.
On the game show "The Price is Right", the highest winning amount was $262,743. The next largest winning amount was only 81.4012% of the highest. What was the second highest winning amount rounded to the nearest dollar?
Answer:
[tex]Second = \$213876[/tex]
Step-by-step explanation:
Given
Highest Winning = $262,743
Second Highest Winning = 81.4012% of the first
Required
Determine the value of the second highest winning
Recall that
[tex]Second\ Highest\ Winning = 81.4012\%\ of\ the\ first[/tex]
Substitute $262,743 for the first highest winning
[tex]Second = 81.4012\%\ of\ \$262,743[/tex]
[tex]Second = 81.4012\%\ * \$262,743[/tex]
[tex]Second = \$213875.954916[/tex]
Approximate
[tex]Second = \$213876[/tex]
Hence, the second highest winning is approximately $213876
Help i dont understand Pls Help :( Given h(x)=-3x-4h(x)=−3x−4, find h(0)h(0).
Answer:
-4
Step-by-step explanation:
So we have the function:
[tex]h(x)=-3x-4[/tex]
To find h(0), substitute 0 for x. Thus:
[tex]h(0)=-3(0)-4[/tex]
Multiply:
[tex]h(0)=0-4[/tex]
Subtract:
[tex]h(0)=-4[/tex]
And we're done!
[tex] \sqrt{2 + \sqrt{2 + \sqrt{2} } } [/tex]
Midpoint (10,4) Endpoint (9,-4), find the coordinates of the other endpoint.
Answer:
(11, 12)
Step-by-step explanation:
Mid point coordinates:
x = (x₁ + x₂)/2y = (y₁ + y₂)/2Since midpoint and one endpoint given (10, 4) and (9, -4), the other endpoint:
x₂ = 2x - x₁ = 2*10 - 9 = 11y₂ = 2y - y₁ = 2*4 - (-4) = 12So the other endpoint is: (11, 12)
The surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell. Express S as a function of r.
Answer:
[tex]S(r)=4\pi r^2[/tex].
Step-by-step explanation:
It is given that, the surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell.
We need to express S as a function of r.
Let r be the radius of the cell and S(r) be the surface area of single-celled organism when radius is r.
According to the question,
[tex]S(r)=4\pi \times r^2[/tex]
[tex]S(r)=4\pi r^2[/tex]
Therefore, the required function is [tex]S(r)=4\pi r^2[/tex].
what is the slope of y=-3
Answer:The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 0 .
Step-by-step explanation:
Answer:
The slope of y=-3 is 0.
y=-3 is a horizontal line.
Let me know if this helps :)
You have a balance of $213 in a savings account you withdraw $68 one day and $128 the next day without making any deposit what is the new balance
Step-by-step explanation:
Here hope this helps........
What is the product of 2 and q
Answer:
2q
Step-by-step explanation:
Product is the answer to a multiplication equation or expression. So you could put it like 2 x q but it would be easier and more understanding to do 2q...Or even 2(q).
At a country concert, the ratio of the number of boys to the number of
girls is 2:5. If there are 250 girls, how many boys are at the concert?
Answer: There are 100 boys at the concert
Step-by-step explanation:
If the the ratio of boys to girls is 2:5 and and there are 250 girls then a number was multiplied by 5 to get 250 and that number needs to be multiply by 2 to find the number of boys.
So to find that number we will divide 250 by 5.
250/ 5 = 50
50 * 2 = 100