Justin recently drove to visit his parents who live 96 miles away. On his way there his average speed was 20 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 4 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.
Justin's average speed to his parents' house: __________ mph
Justin's average speed from his parents' house: __________ mph
Answer:
Justin's average speed to his parents' house: x= 40mph
Justin's average speed from his parents' house: x+20=60 mph
Step-by-step explanation:
Let the average speed be x +20
Then average speed from his parents' x
And the distance is S=96
Then we know :
[tex]\displaystyle \frac{S}{x+20} +\frac{S}{x} =4 \\\\\\ \frac{96}{x+20} +\frac{96}{x}=4 \ |\div 4 \\\\\\ 24\bigg(\frac{1}{x+20} +\frac{1}{x} \bigg) =1 \\\\\\ 24\cdot \frac{x+x+20}{(x+20)x} =1 \ |\cdot (x+20)x \ \ \\\\\\48x+480=x^2+20x \\\\ x^2-28x-480=0 \\\\ \rm D=28^2+4\cdot 480=2704 =52^2 \\\\ \boxed{x_1=\frac{28+52}{2} =40} \\\\x_2=\frac{28-52}{2} =-12 \ \ \varnothing[/tex]
Justin's average speed to his parents' house: x= 40mph
Justin's average speed from his parents' house: x+20=60 mph
If Cindy uses 1
1/2 cups of sugar to make 2 pints of Kool-aid, how much sugar would she need for 5 pints of Kool-aid?
Answer: 3.75
Step-by-step explanation:
5/2=2.5
1 1/2 = 1.5
1.5*2.5=3.75
What kind of question is this? To say you are in college...
Subtract (−3)−(−2) using the number line. Select the location on the number line to plot the difference.
Answer:
-1
Step-by-step explanation:
(-3)-(-2)= -1
Answer:
-1
Step-by-step explanation:
start at -3 and add 2 the answer is negative 1
Select the shapes that are similar to shape A
Answer:
Orange and pink, I'm not too sure
Answer:
Orange and pink.
Step-by-step explanation:
Because there shapes are same.
Prime numbers have, less than two factors, more than two factors, exactly two factors, less than or equal to two factors.
Answer:
exactly 2
Step-by-step explanation:
Prime numbers, the way I was taught to answer this question, has less than 2 factors. The reason is that 1 is considered a factor. However, I think the definition has changed and a prime has exactly two factors -- 1 and itself. 11 is a prime number: only 11 and 1 will divide into it.
Answer:
C exactly two factors.
Step-by-step explanation:
its 2 factors since 1 is considered a factor and 11 is a prime number so it be 2.
The total length of two ships is 2321 feet. The difference in their lengths is 17 feet. Find the length of each ship. If a football field has a length of 100 yards, determine the length of the longer ship in terms of number of football fields.
The length of the longer ship in terms of number of football fields is;
4 football fields
Let the length of ship 1 be x
Let the length of ship 2 be y
Total length of both ships is 2321 ft
Thus;
x + y = 2321 ----(eq 1)
The difference in their lengths is 17 ft
Thus;
x - y = 17 ----(eq 2)
Add eq 1 to eq 2 to get;
2x = 2338
Thus; x = 2338/2
x = 1169 ft
Put 1169 for x in eq 1 to get;
1169 + y = 2321
y = 2321 - 1169
y = 1152 ft
Longer ship = 1169 ft long
From conversion tables;
1 ft = 1/3 yards
Thus; 1169 ft = 1169 * 1/3 = 389.67 yards
A football field has a length of 100 yards
Then number of football fields for the length of the longer ship = 389.67/100 = 3.8967 ≈ 4 football fields.
Read more at; https://brainly.com/question/21804970
1.
15% of what number is 45?
Answer:
15% of 300 is 45
Answer:
300
Step-by-step explanation:
3.1.PS-16
Question Help
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A new health drink has 170% of the recommended daily allowance (RDA) for a certain vitamin. The
RDA for this vitamin is 30 mg. How many milligrams of the vitamin are in the drink?
There are
mg of the vitamin in the drink.
Answer:
Answer:
51 mg
Step-by-step explanation:
A new health drink has 170% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 30mg.
The above question is calculated as:
RDA of the vitamin × 170%
The RDA for this vitamin is 30mg
Hence:
30mg × 170%
= 51 mg
Therefore, the milligrams of the vitamin that are in the drink is 51 mg
-7/6 or -11/15
which is the greatest?
Answer:
-11/15 is the greatest because ita in negative
Answer:
-11/15 is > -7/6
Step-by-step explanation:
PLEASE SHOW YOUR WORK
FIRST TO ANSWER GETS BRAINLIEST!
Answer:
Carlton: 731 feet tall
Burj Khalifa: 2716 feet tall
Q1 Tower: 1059 feet tall
The Shard: 1017 feet tall
Willis Tower: 1450 feet tall
Gran Torre: 984 feet tall
(note: this is all rounded up answers)
Work:
223 x 3.28 = 731
828 x 3.28 = 2716
323 x 3.28 = 1059
310 x 3.28 = 1017
442 x 3.28 = 1450
300 x 3.28 = 984
How do you get the right answer?
A scientist drops a probe in the water. The depth of the probe changes −1 1/2 feet every second. How many seconds will it take for the probe to reach the bottom at a depth of −114 feet?
of all the trees planted last year by a landscaping firm, only 1 in 10 trees died within a month. suppose a new landscaping firm is hired to plant 15 new trees. Let X denote the number of trees planted out of the 15 that died.
What is the lowest value of X that is consistent with the belief that the tree died due to mishandling?
The number of trees that died is an illustration of proportions.
The lowest value of X that is consistent with the belief that the tree died due to mishandling is 1.5
From the question, we have: 1 out of 10 died
This means that, the mean number of trees that died are:
[tex]\mathbf{\bar x =\frac{1}{10}}[/tex]
In 15 trees, the number (n) of trees expected to die is:
[tex]\mathbf{n = \bar x \times 15}[/tex]
So, we have:
[tex]\mathbf{n = \frac{1}{10} \times 15}[/tex]
[tex]\mathbf{n = 1.5}[/tex]
Hence, the lowest value of X is 1.5
Read more about mean and proportions at:
https://brainly.com/question/1139885
solve {-20-5x}-70=-40
Answer:
x = -10
Step-by-step explanation:
Antonia is using the calculator shown to find the value of 1,035 × 6. What key on the calculator should she press after clearing the calculator?
1
+/–
C
/
WILL MARK BRAINLIEST FOR BEST ANSWER
for real numbers x and y what is the largest possible value of 5 - (x-y)^2
Answer:
5−x²+2xy−y²
Step-by-step explanation:
5 - (x-y)²
Rewrite
(x−y)² as (x−y)(x−y) so
5−((x−y)(x−y))
Expand (x−y)(x−y) using the FOIL Method
Apply the distributive property.
5−(x(x−y)−y(x−y))
Apply the distributive property
5−(x⋅x+x(−y)−y(x−y))
Apply the distributive property
5−(x⋅x+x(−y)−yx−y(−y))
Simplify and combine like terms
Simplify each term
5−(x²−xy−yx+y²)
Subtract yx from −xy
5−(x²−2xy+y²)
Apply the distributive property
5−x²−(−2xy)−y²
Multiply −2 by −1
5−x²+2xy−y²
Find the odd one out
1. 33
2. 57
3. 79
4. 13
5. 93
6. 52
Answer:
52
Step-by-step explanation:
All of these are odd numbers 52 isn't not a odd number so it doesn't belong...
Find the value of m if 2y³+my²+11y+m+3 is exadly divisible by (2y-1)
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that:
[tex]\sf p(y) = 2y^3+my^2+11y+m+3 [/tex]
We are also given that, p(y) is divisible by 2y - 1.
So, 2y - 1 is a factor of p(y).
[tex]\sf\longmapsto 2y-1=0[/tex]
[tex]\sf\longmapsto y=\dfrac{1}{2}[/tex]
So, 1/2 is a zero of p(y).
[tex]\sf\longmapsto p(1/2) =0 [/tex]
[tex]\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
So,
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{5m+35}{4}[/tex]
[tex]\sf\longmapsto 5(m+7)=4\times0[/tex]
[tex]\sf\longmapsto 5(m+7)=0[/tex]
[tex]\sf\longmapsto m+7=0[/tex]
[tex]\longmapsto\bf m=-7[/tex]
Therefore, the value of m is -7.
If Kamina can do a job in 43 hours and Simon and Kamina working together can do the same job in 15 hours, find how
long it takes Simon to do the job alone.
hours
Answer:
Answer:
645/28 hours
Step-by-step explanation:
In 1 hour, Kamina does 1/43 of the job.
Simon takes x hour to do the job alone.
In 1 hour, Simon does 1/x of the job.
Together, they do the job is 15 hours, so in 1 hour, they do 1/15 of the job.
1/43 + 1/x = 1/15
15x/(645x) + 645/(645x) = 43x/(645x)
15x + 645 = 43x
28x = 645
x = 645/28
The perimeter of a regular pentagon is 4 1/7
cm. Find the length of its each side
Answer:
29/35 cm for each of the 5 sides
Step-by-step explanation:
The perimeter is the length of all the sides added together. A pentagon has 5 sides. So you'd need to divide 4 1/7 by 5.
It might be easier to divide 4 by 5 and then divide 1/7 by 5 then add the two numbers together.
4/5 = 0.80 or 8/10
1/7 divided by 5 is written as (1/7) / (5/1)
When you divide a fraction by a fraction, you flip the fraction in the denominator over and multiply the new fractions.
So (1/7) / (5/1) turns into 1/7 x 1/5 = 1 / 35
Adding 8/10 + 1/35, you first need to find the common denominator which would be 70.
8/10 would turn into 56/70
1/35 would turn into 2/70
Add them together now and you get 58 / 70. This can be reduced down to
29 / 35.
Before doing the question let's recall that their are two types of shapes mostly , irregular and regular . Regular shapes have all their sides equal while irregular doesn't have. And here The given shape is pentagon so it will have 5 sides . Also , it's perimeter is given i.e sum of it's all sides , If we assume it's one side to be s then perimeter will be (s+s+s+s+s) more conveniently 5s . Now , heading to our question ,
[tex]{:\implies \quad \sf 5s=4\dfrac{1}{7}}[/tex]
[tex]{:\implies \quad \sf 5s=\dfrac{4\times 7+1}{7}}[/tex]
[tex]{:\implies \quad \sf 5s=\dfrac{28+1}{7}}[/tex]
[tex]{:\implies \quad \sf 5s=\dfrac{29}{7}}[/tex]
[tex]{:\implies \quad \sf s=\dfrac{29}{7\times 5}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{Each\:\: Side=\dfrac{29}{35}\:\: cm}}}[/tex]
A farmer sold did he sell? of his sheep. His original flock was 300 sheep. How many sheep did he sell?
all of his sheep
Hope that helps :)
Suppose two trains leave a certain station, at the same time, traveling in opposite directions. One train travels 30 mph faster than the other. In 2.5 hours, the trains are 205 miles apart. Find the speed of each train
9514 1404 393
Answer:
56 mph, 26 mph
Step-by-step explanation:
The trains are separating at the rate of (205 mi)/(2.5 h) = 82 mi/h. If we let s represent the speed of the slower train, then that sum of their speeds is ...
s + (s+30) = 82
2s = 52 . . . . . . . . . . subtract 30
s = 26 . . . . . . . . . divide by 2
s +30 = 56 . . . the speed of the other train
The speeds of the two trains are 56 mph and 26 mph.
A sample survey of discount brokers showed that the mean price charged for a trade of shares at per share was . The survey is conducted annually. With the historical data available, assume a known population standard deviation of . a. Using the sample data, what is the margin of error associated with a confidence interval (to decimals)
Using the z-distribution, it is found that the margin of error of the confidence interval is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, it is stated that the population standard deviation is known, thus, the z-distribution is used.
The margin of error of a z-confidence interval is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
z is the critical value. [tex]\sigma[/tex] is the population standard deviation. n is the sample size.A similar problem is given at https://brainly.com/question/25214883
5. The number that is to be divided in a division problem is the
_______________
Answer:
z I need this in essay form......
Phaeton, who has just discovered that is he is the son of the sun god, pays a visit to his father and makes a special request. In this passage consider how the author uses literary elements such as plot and language to reinforce the theme of the dangers of pride.
Answer:
dividend
Step-by-step explanation:
answer - dividend
What is the median of this data set? {15, 14, 6, 10, 7, 15, 7, 8} Enter your answer in the box.
Answer: 9
Step-by-step explanation:
took the k12 quiz
what is the approximate length of segment PR?
25
11
125
18
Answer:
18
correct me if I'm wrong❌
solve the inequality 2x + 3 < 7
A. x < 2
B. x > -2
C. x < -2
D. x > 2
Answer:
A. x < 2
Step-by-step explanation:
solution:
=2x<7-3
=2x<4
=x<2
What is the sum of the roots of the quadratic equation x²+6x-14=0?
Sum of Roots = ___ Product of Roots = ____
Answer:
Sum of Roots = (-8) Product of Roots = (-84)Step-by-step explanation:
[tex] {x}^{2} + 6x - 14 = 0[/tex]
Roots :- 6 and -14
Sum of the roots :
[6 + (-14)]
= (-8)//
Product of the roots :
[(6)(-14)]
= (-84)//
ey bud can you help me?
Answer:
sup everybody how's it been for yall?
Step-by-step explanation:
this is the last few hours of my free brainly premium so I just wanted to say if you love brainly you'll love brainly premium
A
Learning Task 3. Inside each wet and subsets, write at least 5 amples of
kind of numbers
Interpers
Who
Rational
Marafina
Natural
Solve the following word problem.
1. Mikey worked on her mathematics homework for hour and her science
homework for 7/8 hour. How long did she spend in all doing homework?
2. There are 60 students in a class. Three-fourths of them are girls. How many
boys are there?
3. One day in Baguio, the temperature went from - 2 °C to 8°C. What is the
change in temperature?
4. The elevation of Mt. Everest is 29 028 ft. The elevation of the Dead Sea is -485
ft. Find the difference in the elevation between Mt. Everest and the Dead Sea
1
5. Angie cleans of the yard. Alex cleans of the remaining. What fraction of
the yard is left unclean?
3
Matinong sagot po please
The following questions are related to problems on simple fraction and arithmetic. Hence, the solutions to the questions are as follows :
1.)
Time on mathematics = 1 hour
Time on science homework = 7/8 hours
Total time spent = (1 + 7/8) = [tex] 1 \frac{7}{8}[/tex]
2.)
Total number of students = 60
Fraction of girls = 3/4
Fraction of boys = 1 - 3/4 = 1/4
Number of boys = 1/4 × 60 = 15 boys
3.)
Initial temperature = - 2°C
Final temperature = 8°C
Change in temperature = Final temperature - Initial temperature
Change in temperature = (8 - (-2)) = 8 + 2 = 10°C
4.)
Elevation of everest = 20028 feets
Elevation of dead sea = - 485 feets
Difference in elevation = (20028 - (-485)) = 20513 feets
5.)
Question is missing key values.
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