Answer:
Data that we know:
He drove 504km in each direction.
Going, the average speed was 14km/h more than returning.
The total trip lasted 21 hours.
Ok, to solve this first:
Let's define the variables:
Sg = Average speed when going.
Sr = Average speed when returning.
Then we can write one of our relationships as:
Sg = Sr + 14km/h.
Now, you can recall the relation:
Time = Distance/speed.
Then we can write the equation that represents the total time of the travel as:
504km/Sg + 504km/Sr = 21h
Now we can replace the Sg by Sr + 14km/h, and get:
504km/(Sr + 14km/h) + 504km/Sr = 21h.
Now we must multiplacate by each denominator, in order to remove them:
504km*Sr + 504km*(Sr + 14km/h) = 21h*Sr*(Sr + 14km/h)
Sr*1008km + 7056km^2/h = 21h*Sr^2 + 294km*Sr
Now we can write a cuadratic equation, where i will ignore the units so it is easier to read, as:
21*Sr^2 -714*Sr - 7056 = 0
The solutions are given by the Bhaskara formula:
[tex]Sr = \frac{714 +- \sqrt{714^2 - 4*21*(-7056)} }{2*21} = \frac{714 +- 1050}{42}[/tex]
We have two solutions, one negative and one positive, and because Sr represents an average speed, it must be a positive number, then we choose the positive solution:
Sr = (714 + 1050)/42 km/h = 42km/h
Now we have the average speed for the returning, with this we can find Sg.
Sg = Sr + 14km/h = 42km/h + 14km/h = 56km/h.
Terrence drove to his sister's house, a distance of d miles. For the first 150 miles, he was able to drive relatively quickly, at 60 miles per hour. For the remaining distance, the road was rougher, and he had to slow his speed by 20 miles per hour. For each part of the journey, he was able to keep a steady speed. The time he spent driving at the faster speed was twice the time he spent driving at the slower speed.
Answer:
The total distance he drove is 350 miles, with an average speed of 46.67 miles/hour.
Step-by-step explanation:
Let [tex]t_1[/tex] and [tex]t_2[/tex] be the time of driving at a slower rate and at a faster rate respectively.
Given that the total distance = d
The speed for the first 150 miles = 60 miles/hour.
So, [tex]150=60\times t_1[/tex] [ as distance = speed x time]
[tex]\Rightarrow t_1=2.5[/tex] hours.
The remaining distance [tex]= d-150[/tex] miles.
Speed for the remaining distance = 60 miles/hour.
As the time he spent driving at the faster speed was twice the time he spent driving at the slower speed,
So, the time of driving at a faster rate, [tex]t_2 = 2t_1=2\times2.5=5[/tex] hours
So, [tex]d-150=60\times t_2[/tex] [ as distance = speed x time]
[tex]\Rightarrow d-150=20\times 5=100[/tex]
[tex]\Rightarrow d = 100+150=350[/tex] miles.
The average speed of the journey = (Total distance)/(Total time taken )
[tex]=d/(t_1+t_2)[/tex]
=350/(2.5+5)
=350/7.5
=46.67 miles/hour.
Hence, the total distance he drove is 350 miles, with an average speed of 46.67 miles/hour.
56 equals 128 reduced by z
Write the sentence as an equation.
Answer:
56 = 128-z
Step-by-step explanation:
Answer:
128-z=58
z=70
Step-by-step explanation:
Plz help!
The Gazelle football team made 5 plays in a row where they gained
3 yards on each play. Then they had 2 plays in a row where they lost 12 yards on each play. What is the total change in their position from where they started?
Answer:
3
Step-by-step explanation:
because 3 times 5 is 15 - 12 is 3
Jada is making lemonade for a get-together with her friends. She expects a total of 5 to 8 people to be there (including herself). She plans to prepare 2 cups of lemonade for each person. The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let represent the number of people at the get-together, the number of cups of water, the number of scoops of lemonade powder. Select all the mathematical statements that represent the quantities and constraints in the situation.
Answer: B,C,D,F
Step-by-step explanation:
All the correct mathematical statements that represent the quantities and constraints in the given situation are;
Option B; 5 ≤ n ≤ 8
Option C; c = 2n
Option D; l = c
Option F; 10 ≤ l ≤ 16
We are told that;
n = the number of people
c = the number of cups
l = the number of scoops of lemonade powder.
We are told that number of people is a total of between 5 to 8 people. Thus, the inequality to represent this is; 5 ≤ n ≤ 8We are told that she wants to prepare 2 cups of lemonade for each person. This means when n = 1, c = 2 ; when n = 2, c = 4. Thus, this can be expressed as; c = 2nWe are told that the lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. That means 4 lemonade powder scoops = 4 cups. This can be expressed as; 4l = 4c. This can be simplified to; l = c
Since she is expecting between 5 to 8 people including herself. 2 lemonade scoops per person means;
the least amount of lemonade = 5 × 2 = 10
the maximum lemonade = 8 × 2 = 16
This can be written in inequality form as;
10 ≤ l ≤ 16
The only options that correspond with all the inequalities gotten above are; Options B, C, D, F.
Read more at;
Rashan says that –6 ÷ 2 = -3. Which multiplication expression can he use to check his answer?
a) 2(3)
b) –3(2)
c) 6(2)
d) –6(–3)
Answer:
b) –3(2)
Step-by-step explanation:
–3(2)
= –3 x 2
= –6
if |a+3|=4 which describes all possible values of a)
Answer:
1 and -1
Step-by-step explanation:
The absolute value means that the answer will always come out as positive, meaning that both 1 and -1 fit in this equation.
Answer:
-7 and 1.
Step-by-step explanation:
either a + 3 = 4 or a + 3 = -4
So a = 1 and a = -7.
which number line represents 3-5?
Answer:
?
please rewrite the question cause it seems unclear!
what is the likelihood of throwing a 4 with a single throw of adie
Answer:
1/6.
Step-by-step explanation:
As there are 6 sides to a die than answer is 1/6.
SOMEONE PLLLLZZZ HELP MMEEE!!!III BBEEGGGGG UUU!!!!
Answer:
y = x + 2
Step-by-step explanation:
Used slope formula to get a slope of 1
Line crosses y axis at (0,2)
What is the slope of a line parallel to y = -5x + 2?
Answer:
-5
Step-by-step explanation:
Parallel lines have the same slope, so it would just be -5
suppose you want to buy software for your computer. One piece of software costs $20.75. Another costs $10.59 and a third costs $18.25.
Use mental math to find the total cost. Explain.
How much more is the first piece of software than the second? Use mental math to decide.
Answer:
The total cost is 49.59 the answer for the second question is 10.16
Step-by-step explanation:
Part A. self explanatory, i just added all of the pieces together and got 49.59.
Part B. I just solved the expression 20.75 - 10.59 and got 10.16.
Each morning Soriano buys coffee and donut holes for his employees and clients. The following system represents the amount of coffee and donut holes bought this morning and the amount of money that he spent (in dollars). In the system, represents the number of cups of coffee that he bought and the number of cups of donut holes that he bought.
c+d=60
2.5+1.75=123.75
Part A: How many cups of coffee and donut holes did Soriano buy this morning?
Part B: How much does each cup of coffee cost?
Part C: How much does each cup of donut holes cost?
Part D: How much did Soriano spend in coffee and donut holes?
Part E: Use the elimination method to solve the system and determine the number of cups of coffee and donut holes that Soriano bought this morning.
Answer:
Part A: 60
Part B: Each cup of coffee costs 2.5 dollars
Part C: Each donut costs 1.75 dollars
Part D: Sonario spent 123.75 dollars in coffee and donut holes
Part E: The number of cups of coffee bought are 25 cups of coffee
The number of donut holes bought are 35 donut holes
Step-by-step explanation:
The given parameters are;
c + d = 60
2.5 × c + 1.75 × d = 123.75
Part A
Whereby the number of cups of coffee bought = c, and the number of donut holes bought = d, then, the total number of cups of coffee and donuts bought is c + d = 60
Part B:
From the second equation for the total cost of cups of coffee and holes of donuts, the coefficient multiplying the variable representing an item is the cost of the item
Therefore, each cup of coffee costs 2.5 dollars
Part C:
Using the method from above, each donut costs 1.75 dollars
Part D:
From the equation for the total cost, Sonario spent 123.75 dollars in coffee and donut holes
Part E:
By the elimination method, we have;
c + d = 60
∴ c = 60 - d
Eliminating c in the equation for the total cost gives;
2.5 × c + 1.75 × d = 2.5 × (60 - d) + 1.75 × d = 123.75
150 - 2.5·d + 1.75·d = 150 - 0.75·d = 123.75
150 - 123.75 = 0.75·d
26.25 = 0.75·d
d = 26.25/0.78 = 35
d = 35
c = 60 - d = 60 - 35 = 25
c = 25
∴ c = The number of cups of coffee bought = 25 cups of coffee
d = The number of donut holes bought = 35 donut holes
I need help on these questions who ever answers this question will be the brainliest!!
What number is 38% of 60
Answer:
63.333333333333 you could put 63.3
Step-by-step explanation:
How much is 38 out of 60 written as a percent value? Convert fraction (ratio) 38 / 60 Answer: 63.333333333333%
Answer:
38% of 60 is 22.8. that's the correct answer
I just took a science test and got a 80% on the test. CBA's are 50% of our grade and I had a 98% in science class. How much will my grade drop?, what will my new grade be?
Answer:
89%
Step-by-step explanation:
Answer:
Grade drops 9 percentage points.
New overall grade is 89%
Step-by-step explanation:
The test with a score of 80% accounts for 50% of the grade.
The current average of 98% accounts for the other 50% of the grade.
50% of 80% + 50% of 98% =
= 40% + 49%
= 89%
The new overall grade is 89%.
Since the previous overall grade, before the test, was 98%,
and 98% - 89% = 9%, then
the new grade is 9 percentage points lower than the previous overall grade.
What is the domain of the radical function shown on the graph?
The domain is the set of all possible x inputs. The blue curve stretches on forever in both directions along the x axis. This means that we can plug in any x value we want, and get some y output. We don't have to worry about dividing by zero, or applying the square root of a negative number, so there are no restrictions on the domain. We can take the cube root of a negative number with no issues. For example, the cube root of -8 is -2.
A camera is marked down from $36 to $27. What is the percent of the markdown
Answer:
75%
Step-by-step explanation:
You have to put 27/36 and multiply 27/36 by 100/1 and then you get 2700/36 and divide it and you get 75 so that is how you get 75%
Ron is saving money for college. Each month he deposits 10% of his net income plus
an additional $50 into a savings account. His net income, after taxes have been taken
out, is 80% of his gross income. Find the amount that Ron saves a month when his
gross income is $2400.
Answer:
$242
Step-by-step explanation:
His Gross income a month is $2400.
Now, we are told that his net income, after taxes have been taken out, is 80% of his gross income.
Thus;
Net income a month = 80% × 2400 = $1920
Now, Each month he deposits 10% of his net income plus an additional $50 into a savings account.
This means amount saved each month is = (10% × 1920) + 50 = 192 + 50 = $242
Determine the correct answer when you round to the nearest hundred. "5,264"
I need an answer as soon as possible, please.
Answer:
5,300
Step-by-step explanation:
5 or more raise the score, 4 or less let it rest.
Answer:
5,300
Step-by-step explanation:
buddy im not sure if this is right but i want you to knwo that no one is perfect and i tried plz and thank you
e. How many feet are there in 14.0 yards? (3 ft = 1 yd)
Answer:
42
Step-by-step explanation:
i smart
Answer:
Step-by-step explanation:
1 yard = 3 ft
To find 14 yards, just multiply 14 by 3
14 yards = 14 x 3 = 42 ft
Solve m +1.4 = 0.6.
What does m equal?
Answer:
m=0.8
Step-by-step explanation:
Answer:
0.8
Step-by-step explanation:
1.4-0.6=m
If f(x) = 5x - 75, find f(-2).
Answer:
-85
Step-by-step explanation:
No. 2 BAC and 2 CAD remain congruent, and m 2 DAB is still the sum of mZBAC and m2 CAD.
AN
Question 4
Move point C so that ZBAC and CAD form a pair of supplementary angles, or angles whose sum is 180°. Record each of the angle measurements
for this case.
Answer:
I’m srry I don’t know about question 2 but here’s the answer to Question 4
When the two angles are supplementary, m<BAC = m<CAD = 90° and m<DAB = 180°
Step-by-step explanation:
Answer from Plato
Answer:
No. ∠BAC and ∠CAD remain congruent, and m∠DAB is still the sum of m∠BAC and m∠CAD.
Step-by-step explanation:
This is the answer for question 2
А
Question 5
Dwight owns 1600 acres of farmland. He wants to split the PLEASE HELP TIMED TEST !!
land into fourths and sell off each of the parcele, which expression shows the amount of acres that each parcel will contain? Select ALL that apply
1600 =
1600-4
1600
B
С
D
16.4
E
1600-
1600+
F
Answer:
Options (B) and (C)
Step-by-step explanation:
Farmland owned by Dwight = 1600 acres
He wants to divide his farmland into four equal parts.
So the area of each part of the land will be = [tex]\frac{\text{Area of the farmland}}{\text{Number of parts of the farmland}}[/tex] = [tex]\frac{1600}{4}[/tex]
This expression can be written in different ways,
[tex]\frac{1600}{4}=[/tex] 1600 ÷ 4
[tex]=1600\times \frac{1}{4}[/tex]
Therefore, Options (B) and (C) will be the correct options.
What value should go in the empty boxes to complete the calculation for finding the product of 0.59 × 0.37? Both numbers are the same; however, only input the number one time in your answer. 0.59 times 0.37 gives two unknown partial products. The first product is 413. The second product is 1 thousands, an unknown value in the hundreds place, an unknown value in the tens, and 0 ones. These products are being added. Numerical Answers Expected! Answer for Blank 1:
Answer:
1 7 _7 0
Step-by-step explanation:
From this Given information:
We are to find the product of:
0.59
× 0.37
However, the first product is given as 413;
Also, the second product is 1 thousand, an unknown value in the hundreds place, an unknown value in the tens, and 0 ones.
Mathematically; i.e. 1 __ __ 0
i.e.
0.59
× 0.37
4 1 3
+ 1 __ __ 0
So, to work out the unknown; we look for the multiplication of:
0.59
× 0.37
This is calculated as:
0.59
× 0.37
4 1 3
1 7 7
0 0 0
1 1 8 3
Thus:
1183 - 413 = 770
i.e
the unknown value in the hundreds place is highlighted in bold format = 700
the unknown value in the tens place is highlighted in bold format = 70
Let cot(x) = StartFraction 5 Over 8 EndFraction, with 0 < x < 90°. What is sin(x)?
StartFraction 5 Over StartRoot 89 EndRoot EndFraction
StartFraction 8 Over StartRoot 89 EndRoot EndFraction
StartFraction StartRoot 89 EndRoot Over 8 EndFraction
StartFraction StartRoot 89 EndRoot Over 5 EndFraction
Answer:
B. 8/square root of 89
Step-by-step explanation:
got it right on edge :)
Value of sin(x) = 8 / √89, 0 < x < 90.
What are trigonometric functions?Trigonometric functions can be simply defined as the functions of an angle of a triangle where 0 < x < 90°.
Formula used
In right angled triangle ABC , ∠B = 90° , ∠C = x°
cot (x )= ( Base ) / ( perpendicular)
sin ( x) = ( perpendicular ) / ( Hypotenuse )
Pythagoras theorem
(Hypotenuse)² = (Base)² + (perpendicular)²
(AC)² = (AB)² + (BC)²
Given that
cot (x) =5 / 8 , 0< x< 90
Therefore, by comparing the given values of trigonometric function with the formula ,
Base = 5
perpendicular = 8
Substitute the value in the Pythagoras theorem,
(Hypotenuse)² = 5² + 8²
⇒ (Hypotenuse)² = 25 + 64
⇒ Hypotenuse = √89
Therefore,
sin(x) = 8 / √89
Hence Value of sin(x) = 8 / √89, 0 < x < 90
To learn about trigonometric function: https://brainly.com/question/26719838
#SPJ2
Sum of twice a number and 15 is greater than 3
The number with the algebraic sum of its double and 15 is greater than 3 is described by; x > -6
From the question given;
The Sum of twice a number and 15 is greater than 3.In essence;
Let the number in discuss be; x so the we have;2x + 15 > 3By solving;
2x > 3 -152x > -12x > -6.Read more on inequalities;
https://brainly.com/question/14361489
Which polygon has two or more right angles?
Answer:
c
Step-by-step explanation:
Sarah purchased $28.75 worth of coffee that sold for $11.50 per pound. How
many pounds of coffee did Sarah buy?
Answer:
She bought 2.5 pounds
Answer:
2.5 lb
Step-by-step explanation:
If Sarah has not made any loss or profit then amount of coffee = total cost/cost per pound 28.75/11.5= 2.5
Evaluate 1/3 x 5/6.
A. 1/15
B. 6/15
C. 5/18
D. 3/30
Answer:
C
Step-by-step explanation:
1x5=5
3x6=18
and you can't simplify 5/18.
Answer:
5/18
Step-by-step explanation:
1 times 5 equals 5. 3 times 6 equals 18.