Answer:
I believe the answer is x^8
Step-by-step explanation:
move x^-8 to the numerator in 1/x^-8 using the negative exponent rule 1/b-n = b^n.
Write the following equations as quadratics in standard form (with = 0). Make sure to remove any brackets and fractions present.
Question 1:
[tex]\frac{x}{2} = x^2 - \frac{3}{2}[/tex]
Question 2:
[tex]\frac{5}{x} + 1 = x[/tex]
Answer:
[tex]-2x^2+x+3=0[/tex]
[tex]-x^2+x+5=0[/tex]
Step-by-step explanation:
Algebraic Manipulation
Consists of applying basic rules of algebra to simplify or transform algebraic expressions into others.
We are required to rewrite two expressions as quadratics in standard form.
Question 1:
[tex]\displaystyle \frac{x}{2} = x^2 - \frac{3}{2}[/tex]
To get rid of the denominators, multiply by 2:
[tex]x=2x^2-3[/tex]
Move all the terms to the left side:
[tex]x-2x^2+3=0[/tex]
Order by degree:
[tex]\boxed{-2x^2+x+3=0}[/tex]
Question 2:
[tex]\displaystyle \frac{5}{x} + 1 = x[/tex]
Multiply by x (x must be different from 0):
[tex]5+x=x^2[/tex]
Move all the terms to the left side:
[tex]5+x-x^2=0[/tex]
Order by degree:
[tex]\boxed{-x^2+x+5=0}[/tex]
A 13-foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 10 feet above the ground?
The foot will be moving at ___ ft/sec
Answer:
[tex]\frac{db}{dt}=\frac{20\sqrt{69}}{69}\approx2.4077\text{ ft/s}[/tex]
Step-by-step explanation:
We know that the ladder is 13 feet long.
We also know that the top of the ladder is slipping down at a rate of 2ft/s.
And we want to find the rate at which the foot of the ladder is moving away when the top is 10 feet above the ground.
We can use the Pythagorean Theorem for this problem:
[tex]a^2+b^2=c^2[/tex]
Let's let a be the leg by the wall, and b be the leg on the ground.
Our hypotenuse is 13 and it stays 13. So, let's substitute 13 for c:
[tex]a^2+b^2=(13)^2=169[/tex]
Now, let's take the derivative of both sides with respect to t:
[tex]\frac{d}{dt}[a^2+b^2]=\frac{d}{dt}[169][/tex]
Evaluate. Use implicit differentiation:
[tex]2a\frac{da}{dt}+2b\frac{db}{dt}=0[/tex]
We know that the top of the ladder is slipping down at a rate of 2ft/s. So, da/dt is -2 (it's negative because it's slipping downwards).
We want to find db/dt when the top is 10 feet above the ground. So, substitute 10 for a.
Since a is 10 and we know that c stays constant at 13, we can figure out b using the Pythagorean Theorem:
[tex]10^2+b^2=13^2[/tex]
Evaluate:
[tex]100+b^2=169[/tex]
Solve for b:
[tex]b^2=69\\b=\sqrt{69}[/tex]
So, substitute -2 for da/dt, 10 for a, and √69 for db/dt. This yields:
[tex]2(10)(-2)+2(\sqrt{69})(\frac{db}{dt})=0[/tex]
Solve for db/dt. Multiply:
[tex]-40+2(\sqrt{69})(\frac{db}{dt})=0[/tex]
Add 40 to both sides:
[tex]2\sqrt{69}(\frac{db}{dt})=40[/tex]
Divide both sides by 2√69:
[tex]\frac{db}{dt}=\frac{20}{\sqrt{69}}[/tex]
Rationalize:
[tex]\frac{db}{dt}=\frac{20\sqrt{69}}{69}\approx2.4077\text{ ft/s}[/tex]
So, the foot will be moving at approximately 2.4077 feet per second.
10 points and marked brainliest!!! please help its a teat and due soon.
Answer:
27
Step-by-step explanation:
Answer:
ST=27 (Hope this helps)
Step-by-step explanation:
RT=100 (GIVEN)RS+ST=100
2x+7+x-6=100
3x+1=100
3x=99
x=33
ST=x-6 (GIVEN)ST=33-6
ST=27
what is the mean mark in5,8,4,3,7,6,2,9 and 1
Answer:
Mean= 5+8+4+3+7+6+2+9+1÷9
=5
Step-by-step explanation: The mean is 5
What are the rules to remember when dividing fractions?
Answer:
copy the first fraction, turn the division sign to a multiplication sign and flip the second fraction
Step-by-step explanation:
ex: 2/5 divided by 1/4
turn it to- 2/5 x 4/1
Answer:
Step-by-step explanation:
find reciprocal of second fraction then multiply the fraction after you find the reciprocal
Is analyzing a sequence challenging for you
Answer:
no
whats the point of this post?
HELPPPPPP MEEEE
After taking 4 pieces of fruit out of a bag, 12 pieces of fruit remained. How
many pieces of fruit were in the bag to start?
A. 12 ÷ f= 4
B. 12-4=f
C. 12+ f = 4
D. f÷4=12
E 4+f=12
F. f-4-12
Answer: B. 12-4=f
Step-by-step explanation: The correct answer is B. We can use subtraction to find the number of pieces of fruit that were taken out of the bag, which is 12 - 4 = 8. Then, we can add the number of pieces of fruit that remained to the number of pieces that were taken out to get the total number of pieces that were in the bag to start, which is 8 + 4 = 12.
Therefore, there were 12 pieces of fruit in the bag to start.
Hello!
unknown = f
After taking 4 pieces of fruit out of a bag = -4
12 pieces of fruit remained = 12
12 - 4 = f
A triangle with side lengths of 5 meters, 7 meters, and 9 meters
Answer:
It is not a right angled troagle
Step-by-step explanation:
Given
Sides: 5m, 7m and 9m
Required
Is it a right angled triangle?
A triangle is right angled if:
[tex]a^2 = b^2 + c^2[/tex]
Where a is the longest side and b,c is any of the other.
So, we have:
[tex]9^2 = 5^2 + 7^2[/tex]
[tex]81 = 25 + 49[/tex]
[tex]81 \neq 74[/tex]
Since they're not equal then it is not a right angled troagle
A box with a square base is needed to package 100 cm^3 of powdered milk. Find the dimensions of the box that will use the minimum amount of material.
the dimensions of the box that will use the minimum amount of material are 10 cm × 10 cm × 1 cm.
A box with a square base is required to package 100 cm³ of powdered milk. We must determine the dimensions of the box that will use the minimum amount of material.
To minimize the amount of material required to construct the box, we must minimize the surface area of the box. The surface area of a box with a square base can be expressed as follows:
SA = x² + 4xywhere S is the surface area, x is the length of one side of the base, and y is the height of the box. Since the box's volume is 100 cm³, the following equation can be used to solve for y:x²y = 100y = 100/x²Substituting this value of y into the equation for surface area, we obtain:
SA = x² + 4x(100/x²)
SA = x² + 400/x
Since we are trying to find the dimensions of the box that will use the minimum amount of material, we must find the value of x that minimizes the surface area. To do so, we must take the derivative of the surface area function with respect to x and set it equal to zero. This is because the derivative of a function at a minimum or maximum point is equal to zero.
dS A/dx = 2x - 400/x² = 0Solving this equation for x yields:
x = 10 cm
Substituting this value of x into the equation for y yields:
y = 1 cm
Therefore, the dimensions of the box that will use the minimum amount of material are 10 cm × 10 cm × 1 cm.
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How far would Maria have to travel to get to Valentina's house?
Answer:depends on the distance but we need info
Step-by-step explanation:
Determine the slope of the line that passes through the points M(-3,5) and N(1,
8). Represent the slope in decimal form.
Lisa has a credit card that charges 5% interest on a monthly balance. She buys a $120 bike and plans to pay for it by making monthly payments of $60. How many months will it take her to pay it off? Assume
Answer:
3 months
Step-by-step explanation:
Without the 5% interest it would take 2 months to pay it off but with the 5% interest added that's going to 5% of whatever the balance is.
After her 1rst payment of 60$ she will have 66$ left to pay: 120(1/20)+6-60
After her 2nd payment of 60$ she will have 9.3$ left to pay: 66(1/20)+ 3.3-60
so basically 2 payments of $60 and one payment of $0.47
In football, a kicker can score one point for the extra-point on a touchdown or three points for a field goal.
Logan is a kicker for his high school football team. The record number of points scored by a kicker in a single
game is 24. Logan is hoping to record his next game,
b) Using your previous graph, give two possible combinations extra-point kicks and field goals Logan could
score to beat the current record, (This would be any two points in the shaded region.)
What points will you go through on the graph
Determine the mean and standard deviation of the variable X in each of the following binomial distributions. a. n=5 and π=0.10 b. n=3 and π=0.40 c. n=5 and r=0.50 d. n=3 and π=0.80 a. When n=5 and π=0.10, determine the mean. μ= (Type an integer or a decimal. Do not round.)
The mean (μ) for the given binomial distribution is 0.50.
To calculate the mean (μ) of a binomial distribution, we multiply the number of trials (n) by the probability of success in a single trial (π). Let's examine each scenario in detail:
a. When n = 5 and π = 0.10:
μ = 5 * 0.10
= 0.50
For this binomial distribution, with 5 trials and a success probability of 0.10, the mean (μ) is 0.50. This means that, on average, we would expect to have 0.50 successes per trial.
b. When n = 3 and π = 0.40:
μ = 3 * 0.40
= 1.20
In this case, the mean (μ) of the binomial distribution is 1.20. It indicates that, on average, there would be 1.20 successes per trial when there are 3 trials and a success probability of 0.40.
c. When n = 5 and π = 0.50:
μ = 5 * 0.50
= 2.50
For a binomial distribution with 5 trials and a success probability of 0.50, the mean (μ) is 2.50. This means that, on average, we would expect to have 2.50 successes per trial.
d. When n = 3 and π = 0.80:
μ = 3 * 0.80
= 2.40
In this scenario, the mean (μ) of the binomial distribution is 2.40. It suggests that, on average, we would expect to have 2.40 successes per trial when there are 3 trials and a success probability of 0.80.
The mean (μ) provides a measure of the central tendency or the average number of successes in a binomial distribution based on the given parameters.
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On the interval 0 ≤ x ≤ 2π, what are the x-intercepts of y = sinx?
1.) 0, pi/2, and 3pi/2
2.) 0, pi, and 2pi
3.) pi/2 and 3pi/2 only
4. pi and 2pi only
Answer:
B. 0, π, and 2π
Step-by-step explanation:
on edge
The x-intercepts of y = sin x should be option b.
Given that,
The interval is 0 ≤ x ≤ 2π.Based on the above information, the calculation is as follows:
0 ≤ x ≤ 2π
Here the x-intercepts should be [tex]0, \pi, 2\pi[/tex]
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Find the coordinates of the point P that is 1/8 of the way from point M along MN if the points are M (-4, 7) and N (12, - 1) (1 point)
(14, - 2)
0 (-1,7)
0 (-2, 6)
O (10,0)
Answer:
i think its the 3rd one
Step-by-step explanation:
be care i might be wrong
Answer:
It is (10,0)
Step-by-step explanation:
I had the same q on my quiz
ASAP MULTIPLE CHOICE
What is the converse of the following statement?
"If Joe goes fishing, then he needs bait."
If Joe does not go fishing, then he does not need bait.
If he does not need bait, then Joe does not go fishing.
If Joe goes fishing, then he does not need bait.
If he needs bait, then Joe goes fishing.
Answer:
If he needs bait, then Joe goes fishing.
Step-by-step explanation:
If he needs bait, then Joe goes fishing.
Answer: If Joe does not go fishing, then he does not need bait.
Explanation: If Joe has to go fishing, then he needs bait. If he did not go fishing, then he will not need bait. These are total opposites. Hope this helps!
What is the opposite of -8 ?
Answer:
The opposite will be positive 8.
Step-by-step explanation:
Answer: +8
Step-by-step explanation:
i am looking for someone that is very handsome single and 15
Answer:
Abe lunch hshhshhshajskbdbd
Let f be a function. Use each statement to find the coordinates of a point on the graph of f. f (5) = 9
Answer:
5, 9
Step-by-step explanation:
I did it on Big Ideas Math. Plus, I looked it up on Slader.
When f(5) = -3 the coordinate of points are (5,-3).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
It is given that,
f (5) = 9
If f(x) = y
The coordinates of the functions are (x,y)
The coordination when f (5) = 9 is (5,9)
As a result the coordination when f(5) = -3 is (5,-3)
Thua,when f(5) = -3 the coordinate of points are f(5) = -3.
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could you please help solve this math question
Q.5) (10 p.) Solve the differential equation given as d'y dy dy +2- dr² da dr Y
The general solution to the given differential equation is y = -2r + Cy + D, where C and D are constants.
The given differential equation is d²y/dy² + 2d²r/da dr = 0. In order to solve this equation, we will need to find the general solution that satisfies the equation.
To solve the given differential equation d²y/dy² + 2d²r/da dr = 0, we can start by rearranging the terms. Let's separate the variables and rewrite the equation as d²y/dy² = -2d²r/da dr.
Next, we integrate both sides of the equation with respect to the corresponding variables. Integrating d²y/dy² with respect to y gives us y', and integrating -2d²r/da dr with respect to r gives us -2r'.
Now we have the equation y' = -2r' + C, where C is the constant of integration.
To further simplify the equation, we can rearrange it as dy/dy = -2dr/da + C.
Integrating both sides with respect to y, we obtain y = -2r + Cy + D, where D is another constant of integration.
Therefore, the general solution to the given differential equation is y = -2r + Cy + D, where C and D are constants.
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Show and explain work
What is the solution to 3x+2.42 >3.0?
O x20.2
O x20.6
0 x 1.8
O X2 2.5
Answer:
I believe the answer is x>0.2
) Rory sold T-shirts at a festival for $15 each. He paid $100 in materials and fees.
Rory's profit after the festival was $350. He wants to know how many shirts he sold.
Answer:
The number of shirts sold, 15s-100=350, s=30
Step-by-step explanation:
Question 7
After you reflect a figure, the image is
congruent.
O never
O Always
sometimes
Plssssss helpppp A$AP (rocky)
Answer:
a
Step-by-step explanation:
d
Determine if (-3,2) is a solution to the system x+2y=11 and 3x+7y=5
write yes or no
Answer:
#3x + 2y = 11# and #x - 2 = -4y#?.
Step-by-step explanation:
what price should the company charge for each unit in order to sell 4500 units? (
The company should charge approximately $33.33 per unit in order to sell 4500 units, based on the given assumptions.
To determine the price per unit that the company should charge in order to sell 4500 units, we need additional information such as the total cost and desired profit margin. The price per unit can be calculated using the following formula:
Price per unit = (Total cost + Desired profit) / Number of units
Let's assume that the total cost is $100,000 and the desired profit is $50,000. We can substitute these values into the formula to find the price per unit:
Price per unit = ($100,000 + $50,000) / 4500
Price per unit = $150,000 / 4500
Price per unit ≈ $33.33
It's important to note that the actual price per unit may vary depending on the specific cost and profit margin considerations of the company.
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Decreasing the sample size from 750 to 375 would multiply the standard deviation by. (b) √2. (a) 2. (c) 1/2. (d) 1√2 (e) none of these.
Decreasing the sample size from 750 to 375 would multiply the standard deviation by √2. The correct answer is (b) √2.
The sample size is the number of individuals in a study. If the population is extremely large, the sample size should be larger than if it were smaller. As a result, the larger the sample size, the better, since it leads to higher accuracy and a lower margin of error. For example, let’s say you want to know the proportion of people who wear glasses. If you only ask three people, you may get lucky and find all three wear glasses or unlucky and get none of them to wear glasses. If you ask 30 people, your estimate of the proportion of people who wear glasses will be much better.
The effect of sample size on standard deviation: Standard deviation measures how much spread there is in the data. Larger samples provide better estimates of the population, and therefore, the standard deviation is smaller for larger samples than for smaller ones. This is because a larger sample will have more data points, which will help to better estimate the true population standard deviation. Decreasing the sample size will not only make the standard deviation larger but also introduce more variability in the data. In fact, the standard deviation will be multiplied by the square root of the ratio of the two sample sizes. In this case, it will be multiplied by √2. Therefore, the answer is (b) √2.
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26. 50 students sit in a class room. Each student
requires 9 m² on floor and 108 m in space. If the
length of the room is 25 m, find its breadth and
height.
Plz explain
Nina is training for a marathon. She can run
kilometers in
of an hour. At this pace, how many kilometers can Nina run in 1 hour?
Answer:
She can run 9 kilometers per hour.
Step-by-step explanation:
4 1/2 = 1/3 kilometers
4 1/2 = 9/2
9/2 x 1/3
27/6 x 2/6 = 54/6
54/6 = 9 kilometers per hour.
