Marco runs 4 kilometers every morning. He takes 2 minutes for the first 500 meters, 4 minutes for the next 2000 meters, 1 minute for the next 700 meters, and 3 minutes for the rest.
Marco’s average speed for the entire run is__320___ meters per minute. Hint : One kilometer is the same as 1,000 meters.
Answer: 400 meters per minute.
Formula to find average speed: total time / total distance
Total time taken is 2+4+1+3 which is 10 minutes.
Total distance traveled is 4 kilometers.
(Unitary method)
In 10 minutes Marco runs 4 kilometers.
In 1 minute Marco will run 4/10 (0.4)kilometers.
Now to convert 0.4 kilometers to meters,multiply it by 1000.
0.4 * 1000 is 400 meters
so the final answer is he will run 400 meters in 1 minute.
The sum of two integers is 2. Their difference is 10. What are the two integers?
Answer:
6 and -4
Step-by-step explanation:
a + b = 2
a - b = 10
Solve:
from the first eq.
a = 2 - b
replacing this value in the second eq.
(2-b) - b = 10
2 - 2b = 10
-2b = 10 - 2
-2b = 8
b = 8/-2
b = -4
from the second eq.
a - b = 10
a - (-4) = 10
a + 4 = 10
a = 10 - 4
a = 6
Check:
from the first eq.
6 + (-4) = 2
6 - 4 = 2
Solve the equations below. Give exact solutions only. Show your work.
a) 5x^2 - 7 = 72
b) x(x + 2) = 5
c) 3x^2 + 2x - 4 = 0
Answer:
A. 5x² - 7 - 72 = 0
5x² - 79 = 0
x = ± √-4ac / 2a
x = ± √- 4 (5) (-79) / 2 (5)
x = ± √ 1580 / 10
x = ± 39.749/10
x = + 39.749/10 x = -39.749/10
= 3.9749 = - 3.9749
B. x² + 2x - 5 = 0
x = - b ± √b² - 4ac / 2a
= - 2 ± √2² - 4 (1) (-5) / 2 (1)
= - 2 ± √4 + 20 / 2
= - 2 ± √ 24 / 2
x = - 2 + 4.898 /2 x = - 2 - 4.898 / 2
= 2.898/2 = -6.898/2
= 1.449 = - 3.449
C. 3x² + 2x - 4 = 0
x = - b ± √b² - 4ac / 2a
= - 2 ± √2² - 4 (3) (-4) / 2 (3)
= - 2 ± √4 + 48 / 6
= - 2 ± √ 52 / 6
x = - 2 + 7.211 /6 x = - 2 - 7.211 / 6
= 5.211/6 = - 9.211 /6
= 0.869 = - 1.535
Hope that helps
Please to re-check answers
Plz help (MATH)...................
Answer:
2.8 pounds
Step-by-step explanation: For this one, I rounded the answer, but what you need to do is divide 20 by 7.
20/7 = 2.85714285714
2.85714285714 ≈ 2.8 pounds
What is the difference (how far apart on a number line are the solutions) between the sum of roots versus the product of the roots of the equation:
(x-5)(x+2)=0?
answer should be a number only
Answer:
7
Step-by-step explanation:
(x - 5)(x + 2) = 0
x = 5 & -2
Now,
given
r > s
r = 5, s = -2
Now,
=> r - s
=> 5 - (-2)
=> 5 + 2
=> 7
4. Kayla graphed a scatter plot of the number of hours she drove her car
(x) and the distance traveled (y). She drew the trend line and calculated its
equation to be y = 50x + 2. What is the predicted distance Kayla would
drive if she drove for 3.5 hours?
how do I write an equation of a line that is parallel to 2x-3y=15
If there are 42 boys and 54 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
42:54,54:42
Step-by-step explanation:
Determine which of the following terms are considered to be like terms with the expression 3xy. Select all situations that apply.
A) 3 x ∙ y
B) 1/2( xy)
C) -2 ∙ x ∙ y
D) 4 ∙ x + y
E) ( x)( y)
F) 2 x^2 y
Answer: Down there there is the correct answer step by step
I hope it helps you!
Find the area of the figure.
Answer:
780ft²
Step-by-step explanation:
I'd cut that lower part off into a separate section, and then its width would be the difference of 40 and 30, and its height the difference of 24 and 18. Then, with just 2 rectangles, you can easily calculate the area of each and add them up.
[tex]40-30=10\\24-18=6[/tex]
The lower rectangle is 10' × 6'.
Upper rectangle:
[tex]40\times18=720[/tex]
Lower rectangle
[tex]10\times6=60[/tex]
Add them up:
[tex]720+60=780[/tex]
780ft²
Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)2 = 19
=
A. x= -V19+
B. X= -
V14
3
O c. x=
114
3
O D. x= -119 +5
3
E. x = V19+
+
3
V19 +5
O F. X=
3
The solutions are x = (5 + √19)/3 and x = (5 - √19)/3. These match options E and F in your question.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given that;
The function (3x - 5)2 = 19
Now,
To find the solutions to the equation (3x - 5)^2 = 19, we need to use the following steps:
Take the square root of both sides to get 3x - 5 = ±√19
Add 5 to both sides to get 3x = 5 ±√19
Divide both sides by 3 to get x = (5 ±√19)/3
Therefore, the solutions of the equations will be x = (5 + √19)/3 and x = (5 - √19)/3.
Learn more about solving equations here:
https://brainly.com/question/13072448
#SPJ7
40% of _______ is 16.
Answer:
40% of ___ is 16
So then 10% of ___ is 4
Then do 4 x 10 = 40
So 40% of 40 is 16.
Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?
Answer:
f(x) = x^2 is a classic example
f( 3 ) = 9 and
f( -3 ) = 9, but
f^(-1)[9] is undefined because the result can be 3 and -3
What -3/4 equals 2/3
Answer:
17/12= 1 5/12
Step-by-step explanation:
make the denominator the same as 12
_______ -9/12 =8/12
so add 8+9 to get 17.then keep the denominator as 12. last simpfie it to 1 5/12
1 L = 0.26 gal
How many liters are in 13.39 gallons?
Answer: 50.686664
Step-by-step explanation: hope this helps :)
What is the distance between the following points?
Answer choices
A 9
B 10
C square root of 21
D square root of 58
Answer: 9 is incorrect the anwser is acactually D . The square root of 58
Step-by-step explanation:
1,348.439 rounded to the nearest one’s
Answer:
1348
Step-by-step explanation:
decrease eight times a number by twice the same number
Answer:
6x
Step-by-step explanation:
8x-2x
In a survey, 3 out of 20 students were left-handed. Based on this information, if 300 students were interviewed, how many of them could be expected to be left-handed?
Based on the information given, from the fraction, it can be noted that the number of left-handed people will be 45.
From the information given, it was stated that in the survey, 3 out of 20 students were left-handed.
Therefore, in a population of 300 people, the number of left handed people will be:
= 3/20 × 300.
= 3 × 15
= 45
There are 45 left handed people.
Learn more about fractions on:
https://brainly.com/question/13763238
Find the output for f(x) = -3 |2x - 9| + 4.
When x = -5
SHOW EVERY STEP!
Hey there!
f(x) = -3|2x - 9| + 4
y = -3|2x - 9| + 4
y = -3|2(-5) - 9| + 4
y = -3|-10 - 9| + 4
y = -3|19| + 4
y = -57 + 4
y = -53
Therefore, your answer should be: f(x) = -53
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A basketball player makes 75% of her free throws. If she made 84 free throws this season, how many has she attempted?
A. 112
B. 105
C. 63
D. 168
Answer:
A
Step-by-step explanation:
84 / 0.75 = 112
112 x 0.75 = 84
Answer:
Its A
Step-by-step explanation:
Solve: 4|x| = 32
–8 or 8
8
24
no solution
Answer:
-8 or 8
Step-by-step explanation:
We are given the absolute equation:
[tex]\displaystyle \large{4|x|=32}[/tex]
First, divide both sides by 4 which leaves [tex]\displaystyle \large{|x|=8}[/tex]
Absolute Value Definition
[tex]\displaystyle \large{|x|=\begin{cases} x \ \ \ (x\geq 0)\\ -x \ \ \ (x<0) \end{cases}}[/tex]
So from |x| = 8, break into two intervals/conditions.
(1) when x ≥ 0
x = 8
(2) when x < 0
-x = 8
x = -8
From (1) and (2), the solution to 4|x| = 32 is 8 or -8
Subtract and simplify your answer. 3/4 - 1/6
Answer:
7/12
Step-by-step explanation:
3/4 - 1/6
18/24 - 4/24 = 14/24
14/24 = 7/12
Answer:
[tex]\frac{7}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}- \frac{1}{6}[/tex] ⇒ [tex]\frac{9}{12}- \frac{2}{12}[/tex]
[tex]=\frac{7}{12}[/tex]
Hope this helped! :)
Three boards are placed end to end to make a walkway. The first board is 2 feet 8 inches long, the second board is 6 feet 10 inches long, and the third board is 4 feet 9 inches long. How long is the walkway?
Answer:
The walkway is 14ft and 3in
Step-by-step explanation:
v = 128 – 32t
v is the velocity in ft/sec. It is NOT the height of
the ball.
t is the number of seconds after the ball is
thrown.
With what initial velocity is the ball thrown?
128 seconds
s
What is the y-intercept of the equation?
IS
[ Select]
What does the y-intercept mean?
t
[ Select ]
What is the x-intercept of the equation?
[ Select]
What does the x-intercept mean?
Select]
7
10
-
-
с
80°F
Answer: The Y intercept is 128 as well, which is the original velocity. Technically it should be v - intercept but whatever. The y / v intercept is the original velocity. The X intercept should be the t intercept but again whatever. The x/t intercept is 4, meaning that the velocity is zero when t is 4
Step-by-step explanation: y/v intercept is when t = 0. v = 128 - 32(0) = 128
It is the initial velocity at t = 0. The X/t intercept is when v = 0. 0 = 128 - 32t, so 32t = 128, so t = 4. The x intercept means when the velocity is zero, which means that the ball is at its highest/farthest point.
"Four times the difference of a number and
seven is at least -52."
Tell if each statement about the equations y = log5x and y = 5% are true or false.
Explain your answers.
a) The graphs of the equations are symmetric to each other over line y = 0.
b) The equation y = 5* is the exponential form of y = log5x.
c) The functions are not inverses of each other.
d) The equations are symmetric over the line y = x.
Answer:
a) false b) false c) false d) true
Step-by-step explanation:
Answer:
a) false b) false c) false d) true
Step-by-step explanation:
Eric needs to make a total of 20 deliveries this week. So far he has completed 13 of them. What percentage of his total deliveries has Eric completed?
Answer:
65%
Step-by-step explanation:
13/20 is equivalent to 65% because half of it will be half of the percentage so that's why it is 65%
Which of the following could be used to solve the triangle below?
Answer:
sine
Step-by-step explanation:
Kindly Simplify this Question
Step-by-step explanation:
(3⁵×2^-5×5^-5×2×3²)/(5⁵×3^-2×2^-2)
[3^(5+2+2)][2^(-5+1+2)][5^(-5-5)]
3⁹×2^-2×5^-10.
hope this helps you.