Answers
Answer:
x=5
Step-by-step explanation:
x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.
Answer:
5
Step-by-step explanation:
Because this is a right triangle, you know that by the Pythagorean theorem:[tex]\sqrt{(x+7)^2+x^2}=x+8[/tex]
Squaring both sides to get rid of the square root:
[tex](x+7)^2+x^2=(x+8)^2[/tex]
Expanding all of the parentheses:
[tex]x^2+14x+49+x^2=x^2+16x+64[/tex]
Combine like terms:
[tex]x^2-2x-15=0[/tex]
Factor:
[tex](x-5)(x+3)=0[/tex]
Since x cannot be negative, it is equal to 5. Hope this helps!
Related Questions
If one box plot ranges from 25 to 85 and another boxplot ranges from 128 to 188, they will have the same range of what?
Answers
Answer:
They have the same range of 60.
Step-by-step explanation:
85-25=60
188-128=60
Two trains leave stations 390 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Answers
Answer:
Let's denote:
x: the time both trains traveled.
Then, we have:
70x + 80x = 390
=> 150x = 390
=> x = 390/150 = 2.6 hour
Answer:
2.6 hours ( or 2 hours 36 minutes).
Step-by-step explanation:
The combined speed is 70+80 = 150 mph.
Speed = distance / time, so time = distance / speed.
So the time when they will meet
= 390 / 150
= 2.6 hours.
Factor x2 – 8x + 15.
Which pair of numbers has a product of ac and a sum of b?
Answers
Answer:
(x - 5)(x - 3)
Step-by-step explanation:
[tex] {x}^{2} - 8x + 15 \\ = {x}^{2} - 5x - 3x + 15 \\ = x(x - 5) - 3(x - 5) \\ = (x - 5)(x - 3) \\ \\ ac = ( - 5) (- 3) = 15 \\ a + c = - 5 - 3 = - 8[/tex]
Work out the value of x
Answers
Answer:
x=40°
Step-by-step explanation:
Since the 2 sides of the triangle are equal, the angles are also equal. 180-110=70 so to find the angle measurement of x we have 180-70-70=40 x is 40°
A newspaper article stated that the US Supreme Court received 812 letters from around the country on the subject of whether to ban cameras from the courtroom. Of these 812 letters, 800 expressed the opinion that cameras should be banned. A statistics student was going to use this sample information to conduct a test of significance of whether more than 95% of all American adults feel that cameras should be banned from the courtroom. What would you tell this student
Answers
Answer:
a)This is a large enough sample to provide an accurate estimate of the American public's opinion on the issue.
Rewrite the function by completing the square. h(x)= 4 x^{2} -36 x +81
Answers
Answer:
4(x-4.5)^2
Step-by-step explanation:
h(x)=4x^2-36x+81
=4(x^2-9x)+81
=4(x^2-9x+20.25)-(4)(20.25)+81
=4(x-4.5)^2
For the following case, assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answer. The variable under consideration is very close to being normally distributed, and the sample size is 10. Choose the correct answer below. A. It is not reasonable to use the z-interval procedure in this case since it is very likely that with such a small sample size that there will be outliers in the sample. Knowing that the variable under consideration is very close to being normally distributed does not mean the sample is. B. It is reasonable to use the z-interval procedure in this case since both the sample is large (size 10 or greater) and the variable under consideration is very close to being normally distributed. C. It is reasonable to use the z-interval procedure in this case since, although the sample is small (size less than 15), the variable under consideration is very close to being normally distributed. D. It is not reasonable to use the z-interval procedure in this case because the sample is too small (size less than 15).
Answers
Answer:
B. It is reasonable to use the? z-interval procedure in this case? since, although the sample is small? (size less than? 15), the variable under consideration is very close to being normally distributed.
Step-by-step explanation:
answer b is considered to be correct because we know that the population is normal and the standard deviation is known, which allows using the interval z, the answer A is not correct because although the option to use the interval z is given, which is correct, the large sample is not favored, the answer C and D are incorrect because they both reject the use of the z interval and in d it is further rejected that although there is a normal distribution the sample is not, which is false
Assuming the population variance is known in this case, and examining it using the z-interval approach to obtain a confidence interval for the mean is fair, which can be defined as follows:
Using the z-interval procedure is appropriate in this case because, despite the small sample size (less than 15), the variable in the examination is almost distributed normally. Conformity is fulfilled because the population is normal, and we may utilize the z-interval because the population standard deviation was known.Therefore the final answer is "Option C".
Learn more about the analysis of variance:
brainly.com/question/14265451
An aquarium 7 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.)
Answers
Answer:
8575 joules
Step-by-step explanation:
We have that the volume is given as follows:
v = 7 * 1 * delta x
v = 7 * delta x
we know that the density: mass / volume
therefore the mass is:
mass = volume * density
replacing:
mass = 7 * delta x * 1000
mass = 7000 * delta x [kg]
now we know that force equals mass * acceleration:
F = 7000 * delta x * 9.8 m / s ^ 2
F = 68600 * delta x [N]
Now, we multiply by x meters, to calculate the work:
W = F * x
W = 68600 * delta x * x
W = 68600 * delta x [J]
We know that the portion of the chian x to x + delta x to be the following
limit when n tends to infinity of the sum of i = 1 up to n = infinity of 68600 * xi * delta x
therefore, the total work done to pump half of the water out of the aquarium is:
To the integral of 68600 * x * dx from 0 to 1/2, applying the integral we have:
68600 * x ^ 2/2 [x = 0 to x = 1/2]
68600 * ((1/2) ^ 2) / 2 - 68600 * (0 ^ 2) / 2 = 8575
That is to say that the work is 8575 joules
Factor the expression 4x + 32. Explain each step you
take in the process.
Answers
Answer:
4(x+8)
Step-by-step explanation:
4x + 32
Factorization:
4x: 2×2×x
32: 2×2×2×2×2
Highest common factor: 2×2 = 4
4x + 32
(4×x) + (4×8)
Using distributive property:
4(x + 8)
Answer:
The GCF of 4x and 32 is 4, so the first step is to divide each term by 4. The quotients are x and 8. The factored expression will be 4(x + 8).
Which set of numbers shows all the factors of 18?
1.2.3.6. 9.18
1.3.6.18
9.18. 27. 36
18. 36, 54, 72, 90
My Progress >
Answers
Answer:
the first set of numbers
Step-by-step explanation:
the first set if numbers shows all the factors of 18
Can anyone help please? With questions 4 please
Answers
Answer:
a. The area of the garden is 11.68 [tex]m^{2}[/tex]
b. $192 and then $177
Step-by-step explanation:
a. 7.5-2.6 = 4.9, so the rectangular part is 4.9 x 1.3 = 6.37
then [tex]\pi r^{2}[/tex] is the area of a circle, but the 2 ends together are 1/2 the circle
so [tex]\pi *1.3^{2}[/tex] = 5.31, The area of the garden is 11.68 [tex]m^{2}[/tex]
b. 11.68/.75=15.57, so you have to buy 16 bags (can't buy a partial bag)
16*$12=$192, then 5($33)+$12=$177
The speeds in miles per hour of seven randomly selected qualifiers for the Indianapolis 500 (in 2012) are listed below. Estimate the mean qualifying speed with 95confidence. Round your answers to four decimal places.
223.684 222.929 226.240 224.037 226.484 225.172 223.422
Answers
Answer:
Mean qualifying speed
= 224.5669mi/hr
Speed that passed the average/mean
= 226.240mi/hr ,224.037mi/hr 226.484mi/hr, 225.172 mi/hr
Step-by-step explanation:
Let's understand what mean is then understand what mean qualifying speed is.
First mean is like the average of the seven speed listed below.
So let's find the mean.
Mean = (223.684+ 222.929+ 226.240
+224.037 +226.484+ 225.172
+223.422)/7
Mean = 1571.968/7
Mean = 224.5669
So the mean qualifying speed is those speed that qualifies when the mean is taken, i.e the speed that crossed the average.
Mean qualifying speed are
=226.240 ,224.037,226.484
, 225.172
A boat sailed 560 km in 8 hours. It took three hours to travel
the first 150 km. What was its average speed for the
remaining journey?
km/h
Answers
Step-by-step explanation:
150 km in 3 hours
= 150 ÷ 3 = 50km/h
Remaining distance = 560 - 150 = 410
Remaining hours = 8 - 3 = 5
Then average speed = 410 ÷ 5 = 82 km / h
1.4.2 Suppose a car dealership offers a low interest rate and a longer payoff period to customers or a high interest rate and a shorter payoff period to customers, and most customers choose the low interest rate and longer payoff period, does that mean that most customers want a lower interest rate? Explain.
Answers
Answer:
Yes, customers that deal on cars
But no, if not car customers.
Step-by-step explanation:
Most customers of cars want lower interest rate because it gives them opportunity to work for a longer period and gradually make the profit and pay back.
Even if it will take time that was why the dealer made it longer time.
But this might not apply to customer to other services because they might have their own principles or government/policies or interest rate to their customers.
A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity. A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity. The 95% confidence interval to estimate the population proportion is _______.
Answers
Answer:
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 200, \pi = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.2365[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.3635[/tex]
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
a clock chimes once at 1, twice at 2
Answers
Answer:
3 times at 3
Step-by-step explanation:
simplify the expression (3k / 8)^2
Answers
Answer:
9k/64^2 (9k^2/64^2)
Step-by-step explanation:
Answer:
9k^2/64
Step-by-step explanation:
3*3=9
k*k=k^2
8*8=64
Which describes the role of oxygen in photosynthesis?
It is a reactant, so it is released by the plant.
It is a product, so it is released by the plant.
It is a reactant, so it enters the plant.
It is a product, so it enters the plant,
Answers
Answer:
the answer is the first one.
Step-by-step explanation:
Answer:
b: It is a product, so it is released by the plant.
Step-by-step explanation:
good luck
I'll give you brainiest
Explain how to translate the statement into an equation. Use n for the variable.
Sixty-three is the product of nine and a number.
Answers
Answer:
9n= 63
n=7
Step-by-step explanation:
hope this helps, good luck. :)))
brainliest ?? :)))
Based on the statement sixty-three is the product of nine and a number, the equation will be 9n = 63.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between.
WE have been given that sixty-three is the product of nine and a number, Use n for the variable.
We need to find the statement into an equation.
The equation in this case will be as follows;
9n = 63
n = 63/9
n = 7
Therefore, the equation is 9n = 63 and the value of n is 7.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ6
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answers
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
Pls answer the last question thank you! Number 5.
Answers
Answer:
1/2 x 4/1 x 2/1 = 4
4th should be 1/6 btw
Step-by-step explanation:
Answer:
Step-by-step explanation:
We'll say the fraction is 4 1/2 so: The length is 6 blocks the width is 2 blocks and we'll say the height is 3 blocks so the length would be 27 the width is 9 and the height is 13 1/2 now 27*9*13 1/2=3280 1/2
(you might have to draw this cube just sayin idk exactly what it wants)
A spinner is divided into 8 equal sections numbered 1 to 8. About how many times would you expect the pointer to land on a number less than 6 if the pointer is spun 30 times.
Answers
Answer:
The answer is
6.25×30= 18.75
I'm not sure but this is what I think
Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a
horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to
right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in
inches) as a function of time t (in seconds)
a=
Answers
Answer:
Step-by-step explanation:
amplitude of oscillation a = 12 / 2 = 6 inches.
time period T = 2 s
b = angular frequency = 2π / T
= 2π / 2
= π
so putting the values in the equation
d = a cos ( b t )
d = 6 cos ( π t )
Answer:
there are two more questions and the answers are 0.5 is the least positive amount of the pendulum and 4.243=y when x=4.25
Step-by-step explanation:
Given the speeds of each runner below, determine who runs the fastest.
Noah runs 15 feet per second.\text{Noah runs 15 feet per second.}
Noah runs 15 feet per second.
Jake runs 101 feet in 8 seconds.\text{Jake runs 101 feet in 8 seconds.}
Jake runs 101 feet in 8 seconds.
Debbie runs 1 mile in 455 seconds.\text{Debbie runs 1 mile in 455 seconds.}
Debbie runs 1 mile in 455 seconds.
Stephanie runs 869 feet in 1 minute.\text{Stephanie runs 869 feet in 1 minute.}
Stephanie runs 869 feet in 1 minute.
Answers
Answer:
Stephanie runs the fastest.
Step-by-step explanation:
Answer:
noah
Step-by-step explanation:
What is the GCF of 45 and 72?
Answers
Answer:
The common factors of 45 and 72 are 9, 3, 1
Step-by-step explanation:
Answer:
The GCF of these two numbers is nine.
Step-by-step explanation:
They share three common factors: 1, 3 and 9. The greatest out of all of those is 9. Hope this helps!
if you had a sale price of $40 and the percent of your discounts 25% what was the original price.
Answers
Answer:
$ 50
Step-by-step explanation:
Original price = Sale price + discount
= 40 + 25% of 40
= 40 + 0.25 * 40
= 40 + 10
Original price = $50
Elijah and Bentley go to the movie theater and purchase refreshments for their friends.
Elijah spends a total of $59.00 on 4 bags of popcorn and 10 drinks.
Bentley spends a total of $90.00 on 8 bags of popcorn and 6 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answers
Answer:
x4+y10=59
Step-by-step explanation:
Answer: let P stand for the popcorn and D stand for the drink. Use substitution method
equation: 4P+10D=59 and 8P+6D=90
One drink is 2 dollar and one popcorn is 9.75 dollar.
Step-by-step explanation:
Start with 8P+6D=90, subtract 6D from both side and you will get 8P=90-6D then divide both side by 8 and you will get P=(45/4)-(3/4D) then substitute the P in the 4P+10D=59 with (45/4)-(3/4D) and the equation will be 4(45/4)-(3/4D)+10D=59. then distribute the 4 and get 45-3D+10D=59 then add the like term and get 45+7D=59 then subtract 45 from both side and get 7D=14 the divide 7 on both side and you will end up with D=2. then substitute the D in the 8P+6D=90 with 2 and the equation will be 8P+6(2)=90 then you distribute the 6 and get 8P+12=90 then subtract both side to get 8P=78 then divide both side by 8 and get 9.75. Popcorn cost $9.75 and drink cost $2.
Brainliest giving to who gets this CORRECT first. Check all that apply.
Answers
Answer:
D.
Step-by-step explanation:
a² -b²= (a-b)(a+b)
100x²-49y²= (10x-7y)(10x+7y)
Answer:
Answer is D
Step-by-step explanation:
The difference of the squares method is a short-cut method that is expressed a2 - b2 = ( a + b ) *(a-b). In this case, a2 and b2 should be perfect squares in which a and b are the square roots. In this case, 100 and 49 are perfect squares, hence the answer is D.
Is p = –11 a solution to the inequality below?
p
> –5
Answers
Answer:
not a solution
Step-by-step explanation:
p > -5
Let p = -11
-11 > -5
This is a false statement
It is not a solution
solve for x
4x+5(5x-39)=153
Answers
Answer:
x=12
Step-by-step explanation:
4x+5 (5x-39) = 153
4x + 25x - 195 = 153
29x - 195 = 153
29x = 348
x = 12
