In triangle ABC, which side is the longest if these are the measures of the angles? m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
Answer:
AC
Step-by-step explanation:
First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:
60 + 3x - 2 + 2x + 7 = 180
5x + 65 = 180
5x = 115
x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.
In triangle ABC, the longest side is AC, since it is opposite the biggest angle ∠B.
What is the angle sum property of a triangle?According to the angle sum property of a triangle, the sum of the three interior angles is 180°.
What is the relation between sides' length and the size of the angle of a triangle?In a triangle, the longest side is on the opposite side of the biggest angle, and the shortest side is on the opposite side of the smallest angle.
How do we solve the given question?We are given the angles of the triangle ABC. We are asked to find the longest side in the triangle ABC.
By the angle sum property of a triangle, we know that,
m∠A + m∠B + m∠C = 180°
or, 60° + (3x - 2)° + (2x + 7)° = 180°
or, 5x + 65° = 180°
or, 5x = 180° - 65° = 115°
or, x = 115/5 = 23.
∴ m∠A = 60°.
m∠B = (3x - 2)° = (3(23) - 2)° = (69-2)° = 67°.
m∠C = (2x + 7)° = (2(23) + 7)° = (46 + 7)° = 53°.
∵ m∠B is the largest angle, the side opposite to it, that is, AC is the longest side of the triangle.
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0.9962 to the nearest hundredth
Answer:
1.00o2
Step-by-step explanation:
You dont need this explained come on
If the standard deviation for a Poisson distribution is known to be 3.60, the expected value of that Poisson distribution is
Answer: 12.96
Step-by-step explanation:
given data:
Poisson distributio = 3.60
solution:
The Poisson distribution expected value is same as Variance.
which is expressed as = SD^2
therefore;
the expected value
= SD^2
= 3.60^2
= 12.96
Madison leaves her house and bikes north at a constant speed of 10 miles per hour. If her dad leaves the same house two hours later, driving north at a constant speed of 15 miles per hour, how long will it take him, in hours, to reach Madison?
Answer:
It should take her father four hours to reach her.
Step-by-step explanation:
Since Madison takes an hour to travel 10 miles, by the time she reaches 3 hours, shes at 30 miles. (At this point her father has begun traveling towards her) And since he goes 15 miles per hour, four hours later (for her father), they will both be at the same distance.
(So in 6 hours, Madison goes 60 miles, and in 4 hours her father also goes 60 miles since hes faster)
Please tell me if I did anything wrong!
It will take the time that Madison's dad 8 hours to catch up with her.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Let's call the distance from Madison's house to the point where her dad catches up with her "D".
distance Madison traveled = rate × time = 10 mph × 2 hours = 20 miles.
This means that when Madison's dad starts driving, Madison is 20 miles ahead of him.
For Madison's dad, his rate is 15 mph, and the time it takes him to catch up to Madison is "t" hours.
So his distance traveled is:
distance traveled by Madison's dad = 15 mph × t
For Madison, her rate is 10 mph, and she has already traveled for 2 hours. So her distance traveled is:
distance traveled by Madison = 10 mph × (t + 2)
Now, their distances are equal to each other:
15t = 10(t + 2) + 20
Simplifying and solving for "t", we get:
15t = 10t + 40
5t = 40
t = 8
Therefore, it will take Madison's dad 8 hours to catch up with her.
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How many 5 ounce glasses of soda can you get from 3, 2 liter bottles of soda (6 liters total?
Answer:
21
Step-by-step explanation:
tcctvucycyccyctctctchu ycuvuvuvy t r y y g g t g
A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to Two-thirds of its maximum volume? Use π = 3.14 and V = four-thirds pi r cubed.
Answer: A
16 minutes
Step-by-step explanation:
The required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.
The rate of change is defined as the change in value with the rest of the time is called rate of change.
Here,
radius = 55 / 2 = 27.5
Since volume is directly proportional to the cube of the radius,
So,
For maximum volume,
V ∝ R³
and
2/3V = v
2/3R³ = r³
r = 27.5 ∛2/3
r = 24
Now,
the radius increases at a rate of 1.5 feet per minute.
Time to reach a radius of 24 feet,
= 24 / 1.5
= 16 minutes
Thus, the required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.
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Need help!!! A rocket scientist is designing a rocket to visit the planets in the solar system. The velocity that is needed to escape a planet’s gravitational pull is called the escape velocity. The escape velocity depends on the planet’s radius and its mass, according to the equation V escape=square root(2gR where R is the radius and g is the gravitational constant for the particular planet. The rocket’s maximum velocity is exactly double Earth’s escape velocity. The earth’s gravitational pull is 9.8 m/s^2 The earth’s radius is 6.37 x10 ^6 For which planets will the rocket have enough velocity to escape the planet’s gravity?
Answer:
Mercury, Venus, Earth, Mars, and Uranus
Step-by-step explanation:
Calculate the escape velocity for each planet, using the equation v = √(2gR).
[tex]\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right][/tex]
The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s. So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.
16. In the adjoining figure, if ll|m, then find the value of angle x
Step-by-step explanation:
Hey, there!!
Let's solve it simply,
angle ONP = 60°+55° { as exterior angle is equal to the sum of opposite interior angle}.
Therefore, angle ONP = 115°.
Now, let's solve for x,
x+ 115°=180° { because the sum of co-interior angle is 180°}.
x= 180°-115°
Therefore, the measure of angle x is 65°.
Hope it helps...
Answer:
[tex]\Huge \boxed{{x=65\° }}[/tex]
Step-by-step explanation:
l and m are parralel lines.
The third angle in the triangle is also x, because of corresponding angles.
Angles in a triangle add up to 180 degrees.
Create an equation and solve for x.
x + 60 + 55 = 180
Add the numbers.
x + 115 = 180
Subtract 115 from both sides.
x = 65
given directed line segment AB find the coordinates of p such that the ratio of ap to pb is 2:1 plot point p
Answer:
[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]
Step-by-step explanation:
The question is incomplete; However
[tex]A = (-2, -4)[/tex]
[tex]B = (6, 1)[/tex]
Required
Determine coordinates of P
When line segment is divided in ratios, the following formula calculates the coordinates;
[tex]P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}[/tex]
In this case;
[tex]m:n = 2:1[/tex]
[tex](x_1,y_1) = (-2, -4)[/tex]
[tex](x_2,y_2) = (6, 1)[/tex]
So, the coordinates of P is calculated as thus
[tex]P(x,y) = \{\frac{2 * 6 + 1 * (-2)}{2+1}, \frac{2 * 1 + 1 * (-4)}{2+1}\}[/tex]
[tex]P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}[/tex]
[tex]P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}[/tex]
Hence, the coordinates of P is
[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]
The question is incomplete, the points A and B are:
A = (-2, -4)
B = (6, 1)
We want to find a point P in the segment AB such that the ratio of AP to PB is 2:1
We will find that:
[tex]P = (\frac{2}{3} , \frac{7}{3} )[/tex]
The general formula for two points (x₁, y₁) and (x₂, y₂), the coordinates of a point that separates the segment in a ratio j:k is
[tex]P = (\frac{j*x_1 + k*x_2}{j + k} , \frac{j*y_1 + k*y_2}{j + k})[/tex]
So we only need to use that general formula:
[tex]P = P = (\frac{2*(-2) + 1*6}{3} , \frac{2*(-4) + 1*1}{3})\\\\P = (\frac{2}{3} , \frac{7}{3} )[/tex]
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Micah was given $200 for his birthday. Each week he spends $15 on comic books. In how many weeks will his birthday money be gone?
Answer:
13 weeks
Step-by-step explanation:
V = -15 x + 200 x 213.33 weeks 6 = -15x + 200 after 13 weeks.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
The number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.
Given,
Micah was given $200 for his birthday.
Each week he spends $15 on comic books.
We need to find in how many weeks will his birthday money be gone.
How to compare two units in proportion?We need to make sure we get the required value on the left side.
If 1 week = 7 days
Find how many days in 2 weeks
2 weeks = 2 x 7 days = 14 days
We have 2 weeks on the left side.
If 2 items = $5
5/2 x 2 items = 5/2 x $5
5 items = $25/2 = $12.5
Find the total amount Micah has.
= $200
Find the amount spend each week.
= $15
Find how many weeks she must spend to spend $200.
We have,
$15 = 1 week
Multiply 200/15 on both sides.
200/15 x $15 = 200/15 x 1 week
$200 = 13.33 weeks
This means 13 weeks.
Thus the number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.
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i need help with this can someone help me
Answer:
#9 x=21
#10 a. QP b. 8 c. 18
Step-by-step explanation:
#9 use the theorem where the ratio between a midline and the base of the triangle is 1:2
as we know the midline and the base is 1:2
this means
2(4x-65)=2x-4
4x-65=x-2
3x=63
x=21
---------------------------------------------------------------
#10
a. RS|| QP (Remember to write the letters accordingly)
b. 8 (As mentioned before of the ratio 1:2)
c. 18
After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The population on the island grows exponentially according to the model n(t)-ne", where n(t)is the number of rats at time t in months. After 15 months there are 280 rats on the island a. Find a function that models the population t months after the arrival of the rats. b. What will the population be 3 years after the shipwreck? Round to a whole number. c. When will the population reach 2000 rats?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]n(t) = 120 e^{(0.056t)}[/tex]
b
[tex]n(36) = 901 \ rats[/tex]
c
[tex]t = 50 \ months[/tex]
Step-by-step explanation:
From the question we are told that
The original number of rats that swim from the wreckage to a deserted island is
The population on the island grows exponentially according to the model
[tex]n(t) = n_o e^{rt}[/tex]
The number of rats after t = 15 months is 280
So
[tex]n(15) = 120 e^{15 * r } = 280[/tex]
=> [tex]120 e^{15 * r } = 280[/tex]
=> [tex]e^{15r} = 2.33[/tex]
=> [tex]15r = 0.8459[/tex]
=> [tex]r = 0.056[/tex]
Therefore the population t months after the arrival of the rats is mathematically represented as
[tex]n(t) = 120 e^{(0.056t)}[/tex]
Here t is in months
Considering question b
For t = 3 years = 12 * 3 = 36 months
Then the number of rats that will be present is mathematically represented as
[tex]n(36) = 120 e^{0.056 * 36 }[/tex]
[tex]n(36) = 901 \ rats[/tex]
Considering question c
Now the number of rats considered is n(t) = 2000
So
[tex]n(t) = 2000 = 120e^{0.056t}[/tex]
=> [tex]2000 = 120e^{0.056t}[/tex]
=> [tex]16.67 = e^{0.056t}[/tex]
Taking natural log of both sides
=> [tex]0.056 t = 2.81[/tex]
=> [tex]t = 50 \ months[/tex]
Which of the following expressions does not represent "four more than one-third x"?
Options:
1/3x + 4
x/3 + 4
1/4x + 3
Please explain well so I can understand it. Thanks! :)
Answer:
1/4x + 3
Step-by-step explanation:
The question said one-third(1/3) not one-fourth(1/4).
1/3x + 4 can also be written as x/3 + 4.
Answer:
1/4x + 3
Step-by-step explanation:
expressions does not represent "four more than one-third x"
1/3x + 4 --- No.
x/3 + 4 --- No.
1/4x + 3 --- Yes. it does not represent 4 + 1/3x. you can tell it by +3
Find an equation of the line containing the centers of the two circles whose equations are given below.
x2+y2−2x+4y+1
=0
x2+y2+4x+2y+4
=0
A mountain biker gets halfway up a hill and realizes he forgot his water, so he returns to his starting point.
Answer:
True
Explanation:
1/2 (up the hill) - 1/2 (down the hill) = 0
10. Hank bought a four-family residence for rental property. Hank put 20% down on the $300,000 rental unit. How much will he be able to depreciate
using the class recovery period for residential rental property each year?
A. $9,809.09
O B. $15,609.09
O C. $11,893.09
D. $10,909.09
Mark for review Will be highlighted on the review page)
Answer:
D. $10,909.09
Step-by-step explanation:
The class recovery period for residential rental property each year = 27.5 years
The cost basis for the residential property = $300,000
The amount he will be able to depreciate
= Cost basis/ Number of years
= $300000/ 27.5 years
=$10, 909.090909
Approximately ≈ $10,909.09
The amount he will be able to depreciate using the class recovery period for residential rental property each year is: D. $10,909.09.
Using this formula
Depreciation=Rental unit amount/ MACRS residential rental property recovery period
Where:
Rental unit amount=$300,000
MACRS Residential rental property recovery period=27.5 years
Let plug in the formula
Depreciation=$300,000/27.5
Depreciation=$10,909.09
Inconclusion the amount he will be able to depreciate using the class recovery period for residential rental property each year is: D. $10,909.09.
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2. Find the slope and y-intercept.
a. y = 3x - 4 b. 4x - 5y = 15
What are equivalent fractions for 8/11 and 1/10 using the least common denominator?
Answer:
2/10 because if the two fraction
The equivalent fractions of 8/11 = 16/22 , 24/33 , 32/44
The equivalent fractions of 1/10 = 2/20 , 3/30 , 4/40
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the first fraction be represented as A
Now , the value of A = 8/11
Let the second fraction be represented as B
Now , the value of B = 1/10
And , the equivalent fractions of A is given by
A = 8/11 , 16/22 , 24/33 , 32/44
And , the equivalent fractions of B is given by
B = 1/10 , 2/20 , 3/30 , 4/40
Hence , the fractions are solved
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Find the least whole number that can replace _
to make the statement true.
_ ÷ 17 > 99
The _ can be replaced with?
Answer:
1684
Step-by-step explanation:
x ÷ 17 > 99
x > 17 * 99
x > 1683
The least whole number that is greater than 1683 is 1684.
Answer: 1684
Answer:
1683
Step-by-step explanation:
To undo the problem you do 99 times 17 which is 1683. Then you know that 1683 divided by 17 is 99.
Kara needs to fence her yard. How many feet of fencing is needed?
A. 370 feet
B. 500 feet
C. 13, 700 feet
D. 15, 000 feet
Answer:
newzz new new me he new new
Answer:
oiuhj90pkomnjhb vcfgtyu789i0op,lmkn bvghyu7890opklmnjbhgvfty67890-p[lkjhngvty67u890-op[l;',
Step-by-step explanation:
Identify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest percent. Original: 170 New: 90 %________
Answer:
the percent decrease is approximately 47 %
Step-by-step explanation:
Since the quantity started at 170 and then changed to 90, there was clearly a decrease in its value.
We use the following formula to calculate the percent of decrease:
[tex]\%\,decrease = \frac{original-final}{original} \,100\\\%\,decrease = \frac{170-90}{170} \,100\\\%\,decrease = \frac{80}{170} \,100\\\%\,decrease \approx 47\,\%[/tex]
The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this average and decided to sample 30 citizens in her neighborhood. Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311. What is the p-value of the test statistic? Answer choices are rounded to the hundredths place.
Answer:
0.10
Step-by-step explanation:
Average age of Iowa residents = 37 years
Amy believes that the average age in her hometown in Iowa is not equal to this average
Alternative hypothesis : µ ≠ 37
Sample size = 30
t - test statistic = 1.311
The p-value of the test statistic can be obtained using the online p-value calculator :
The p- value obtained using a t-test statistic value of 1.311 and a degree of freedom (df =N-1; 30 - 1 = 29) at a 0.05 significance level = 0.100072 = 0.10 ( nearest hundredth)
Answer:
0.20
Step-by-step explanation:
In order to find the p-value we first need the degrees of freedom because we are running a t-test. The df = n-1 = 30-1 = 29. If Amy is using the alternative hypothesis, µ ≠ 531, this is a two-tailed test. In order to find the p-value, we simply need to find the probability of being as extreme or more extreme as our current test statistic in one-tail and then multiply it by 2. Another way to describe this is it is the tail probability/area. If we go to the df row of 29 and then scan to the right we see 1.311 is in the 0.10 column. So if we multiply this by 2, we find 0.20 or 20% in both of the tails. So the p-value is 0.20.
Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. PART B: Gunnar’s car is close to empty and only has 0.98 gallon of gas left. He stops at a gas station that charges $2.05 per gallon of gas. How much does it cost for Gunnar to refill his tank? Round your answer to the nearest penny.
Answer:
399.17 miles
Step-by-step explanation:
Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.
Gunnar's car travels with one gallon of gas = 22.4 miles
He can travel with 17.82 gallon of gas = 17.82 × 22.4
= 399.168 ≈ 399.17 miles
Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.
Solve and graph the following inequality
Answer:
x is greater than 4
Step-by-step explanation:
4x + 5 is greater than 13
you want to find out what x is
4 - 4 x + 5 is greater than 13 - 4 ( whatever you do to one side you have to do to the other)
x + 5 is greater than 9
x + 5 - 5 is greater than 9 - 5
x is greater than 4
How many atoms in human body?
Solve the simultaneous equation,
2p - 3q = 4
3p + 2q = 9
Answer:
p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]
Step-by-step explanation:
Given equations:
2p - 3q = 4 -----------(i)
3p + 2q = 9 ------------(ii)
Let's solve this equation simultaneously using the elimination method
(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;
[2p - 3q = 4] x 3
[3p + 2q = 9] x 2
6p - 9q = 12 -------------(iii)
6p + 4q = 18 -------------(iv)
(b) Next, subtract equation (iv) from equation (iii) as follows;
[6p - 9q = 12]
- [6p + 4q = 18]
-13q = -6 -----------------(v)
(c) Next, make q subject of the formula in equation (v)
q = [tex]\frac{6}{13}[/tex]
(d) Now substitute the value of q = [tex]\frac{6}{13}[/tex] into equation (i) as follows;
2p - 3([tex]\frac{6}{13}[/tex]) = 4
(e) Now, solve for p in d above
Multiply through by 13;
26p - 18 = 52
Collect like terms
26p = 52 + 18
26p = 70
Divide both sides by 2
13p = 35
p = [tex]\frac{35}{13}[/tex]
Therefore, p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]
Find the value of 83 - [59 - (22 - 18)].
Answer:
28
Step-by-step explanation:
83 - [59 - (22-18)]
= 83 - [59 - 4]
= 83 - 55
= 28
How far does Kai have to walk to school if he takes the nature trail?
School
Nature Trail
15 yd
20 yd
Kai's
House
A. 13.3 yd
B. 25.0 yd
C. 625.0 yd
D. 35.0 yd
Answer:
D?
Step-by-step explanation:
¯\_(ツ)_/¯
Write the algebraic expression without parentheses. - (- 7 + 7 y) 7 + 7y 7 - 7y -7 + 7y 49y
the answer is 7-7y i think if not the it should be 7+7y
If "a" is a negative number, and "ab" is a positive
answer, then what is the sign of "b”?
Answer:
b would be a negative number
Answer: The sign of b is negative or -
Step-by-step explanation:
If you multiply two negative numbers you will have a positive number. And if you multiply a positive and negative numbers you will have a negative answer.