Step-by-step explanation:
a)
Eric runs for 4 min and walks for 8 min.
The distance covered is
4*200 + 8*80 = 800 + 640 = 1440The goal of 1600 m is not met, needs additional 160 m
b)
The equation of distance is
d = 200x + 80yc)
For d = 1600, the equation is
200x + 80y = 1600Simplified form of it
2.5x + y = 20Some combinations of x and y to make the equation right
x = 2, y = 15x = 4, y = 10x = 6, y = 5d)
See the attached graph for more combinations, where the first coordinate represents running time and the second coordinate - walking time
Answer:
Part (a)Given:
Average running speed = 200 m/minAverage walking speed = 80 m/minIf Eric runs for 4 minutes ⇒ 200 x 4 = 800 m
If Eric walks for 8 minutes ⇒ 80 x 8 = 640 m
Total distance covered = 800 + 640 = 1440 m
Therefore, he is 160 m away from his 1600 m goal.
Part (b)Let x = number of minutes Eric runs
Let y = number of minutes Eric walks
Let d = total distance Eric covers
Equation: d = 200x + 80y
Part (c)Set d = 1600, then rewrite to make y the subject:
200x + 80y = 1600
⇒ 5x + 2y = 40
⇒ 2y = 40 - 5x
⇒ y = 20 - 2.5x
Now find ordered pairs (points on the line):
x-intercept (y = 0): 20 - 2.5x = 0 ⇒ x = 8 ⇒ (8, 0)y-intercept (x = 0): 20 - 2.5(0) = 20 ⇒ (0, 20)when x = 4: 20 - 2.5(4) = 10 ⇒ (4, 10)Part (d)Plot (8, 0) (0, 20) and (4, 10) and connect with a straight line.
(see attached graph)
From inspection of the graph, other combinations of running and walking times for which Eric would cover 1600 meters are:
2 minutes running, 15 minutes walking6 minutes running, 5 minutes walkingHelppppppppppppppppl
Answer: A
Step-by-step explanation: You're Welcome
*URGENT* PLEASE HELP
[tex] \frac{3z}{2} - 5 = 28 \\ [/tex]
[tex] \frac{2}{3} . \frac{3z}{2} = 33. \frac{2}{3} \\ [/tex]
[tex]z = 22[/tex]
Carlos ran 3 1/2 miles on Saturday and
2 1/2 miles on Sunday. How many yards
did Carlos run in all? Show your work.
Answer:
6 yard
Step-by-step explanation:
Since, it given that:
Carlos ran 3 1/2 miles on Saturday and 2 1/2 miles on Sunday.
And asking for how many yards carlos run in all
in all = add
3 1/2 + 2 1/2
Add the whole number
3 + 2 = 5
Since they have the same denominator we can just add them
1/2 + 1/2 = 1 whole
Since it a whole we can add to the whole number
5 + 1 = 6
Thus, Carlos run 6 yards.
Lenvy
Answer:
6 yards
Step-by-step explanation:
To Find:
How many yards did Carlos run in all?
Solution:
In all means addition in this question
Thus,
3 1/2 and 2 1/2
3 1/2 + 2 1/2
we can turn them into improper fraction and then find the answer
3 1/2 = 7/2 and 2 1/2 = 5/2
7/2 + 5/2 = 12/2
12/2 = 6
Hence, Carlos run 6 yards in all
[RevyBreeze]
A shape is made of 12 right triangles of equal size. Each right triangle has a base of 4cm and a height of 5cm. What is the total area, is square centimeters, of the shape?
Answer: 120 cm²
Step-by-step explanation:
Let's start by finding the area of one triangle
The formula for finding the area of a triangle is [tex]A=\frac{hb}{2}[/tex]
Where
A is the area
h is the height (5 for this)
and b is the base (4 for this)
Let's sub in our values and solve.
[tex]A=\frac{(5)(4)}{2}\\A=\frac{20}{2}\\A=10[/tex]
Since there are 12 triangles in the shape we must multiply our area for one triangle by 12 to find the total area of the shape
12×10=120
Graphing a linear equation of the form y=mx how do I plot y=-2x
a line through the origin with a slope of -2 (for every 1 unit to the right, move 2 units down)
when plotting, plug in values for x, i would recommend starting with 0, 1, and -1, then find y for each of these x values, then connect the points
8th Grade Math!!
find the area of the rectangle.
the area of the rectangle is __ square feet. (simplify your answer)
Answer:
[tex]48x^{13}\ ft^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the rectangle
To find the area of the rectangle we just need to do Length * Width which will give us the area in square feet (it really depends on the units that they are giving the L and W in).
[tex](8x^6) * (6x^7)[/tex]
[tex]((8*6)(x^6*x^7))[/tex]
[tex](48*x^{6+7})[/tex]
[tex]48x^{13}[/tex]
Answer: [tex]48x^{13}\ ft^2[/tex]
last number of 1²+2²+...+2007²
Answer:
4028054 is the last number when we operate it....
∠2 and ∠4 are "blank" angles.
Answer:
angles 4 and 2 are congruent
Step-by-step explanation:
the same
Divide $3600 among Nancy Beverly and Todd in the ratio 2:3:4?
Answer:
nancy: $800, beverly: $1200, todd: $1600
Step-by-step explanation:
finding the portion of one part of the ratio:
3600 ÷ 9 = 400 (9 came from 2 + 3 + 4 in the ratio)
Nancy: 2 x 400 = $800
Beverly: 3 x 400 = $1200
Todd: 4 x 400 = $1600
checking the answer:
1600 + 1200 + 800 = 3600
A water balloon is launched in the air from a height of 12 feet and reaches a maximum height of 37 feet after 1.25 seconds. Write an equation to represent the height h of the water balloon at time t seconds. Then, find the height of the balloon at 2 seconds.
The height of the balloon is given as h(t) = -16t² + 40t + 12 at 2 seconds, the height is 28 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of the water balloon after t minutes, hence:
h(t) = -16t² + vt + h₀
Where h₀ is the initial height = 12 feet and v is the initial velocity, hence:
h(t) = -16t² + vt + 12
The height of 37 feet after 1.25 seconds, hence:
37 = -16(1.25)² + v(1.25) + 12
v = 40 m/s
h(t) = -16t² + 40t + 12
After 2 seconds:
h(t) = -16(2)² + 40(2) + 12
h(2) = 28 feet
The height of the balloon at 2 seconds is 28 feet
Find out more on equation at: https://brainly.com/question/1214333
Can someone help me I need this done ASAP like TODAY… I know D. I just dont know A, B, C. Please helppppppppp meeeeeeeeee
Answer:
Please see explanation
Step-by-step explanation:
base= -3
the exponent is 5
in expanded form -3×-3×-3×-3×-3
evaluation = -3×-3×-3×-3×-3= -243
HELP MEEEEE THIS IS DUE IN 2 HOURSSS
4. Convert: 32 cups = gallons 10 gallons 3 gallons 2 gallons 1 gallon
Answer:
2 gallons
Step-by-step explanation:
:/
What is the distance between the points(-4,-1) and (-6,8) in simplest radical form.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6 - (-4)]^2 + [8 - (-1)]^2}\implies d=\sqrt{(-6+4)^2+(8+1)^2} \\\\\\ d=\sqrt{(-2)^2 + 9^2}\implies d=\sqrt{85}[/tex]
Find the product of the sum of 76 and 13 and the difference of 92 and 49.
3827
hope it helps...!!!
It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I
maintain the same speed, estimate how much longer I will be driving for.
If a giraffe eats 75 pounds of acacia leaves a day, how many grams would that be?
Answer:
34,050 grams
Step-by-step explanation:
To convert pounds to grams, you must multiply the mass (75) by 454.
454 * 75 = 34,050
34,050 grams is equal to 75 pounds.
Hope this helps:)
Simplify: ^6 square root x times ^4 square root y^3
The expression [tex]\sqrt[6]{x} \times \sqrt[4]{y^3}[/tex] is an illustration of an algebraic expression
The simplified expression of [tex]\sqrt[6]{x} \times \sqrt[4]{y^3}[/tex] is x^1/6y^3/4
How to simplify the expression?The expression is given as:
[tex]\sqrt[6]{x} \times \sqrt[4]{y^3}[/tex]
Rewrite the expressions as exponents
x^1/6 * y^3/4
Multiply the expresions
x^1/6y^3/4
Hence, the simplified expression of [tex]\sqrt[6]{x} \times \sqrt[4]{y^3}[/tex] is x^1/6y^3/4
Read more about expressions at:
https://brainly.com/question/723406
Answer:
Step-by-step explanation:
edge
please help me with this question
what can you add to get negative 8 and multiple to get positive 7
Step-by-step explanation:
-1 and 8 Below we prove the -1 and 8 multiple to -8 and add up to this -1 × 8= -8
Help me for 10 help me please
Answer:
Answer:
what do u need help in?
4 to the 5th power times 4 to the -7th power divided by 4 to the -2nd power
Answer:
1
Step-by-step explanation:
4^(5)×4^(−7)÷4^(−2)
=4^(5+(-7)-(-2))
=4^(5-7+2)
=4^(0)
=1
Hey!
Your answer is 1.Heres how i got the answer
4^(5)×4^(−7)÷4^(−2)
=4^(5+(-7)-(-2))
=4^(5-7+2)
=4^(0)
Hope this helps!
Five friends share 4 bags of trail mix equally.
What fraction of a bag of trail mix does each friend get?
A photograph has a length that is 6 inches longer than its width,x. So it's area is given by the expression x(x+6) square inches.
Answer:
The width of the photograph is 8 inches
Step-by-step explanation:
hopefully im right
2. Brian thinks that 1.75 x 10-3 is less than 1.25 10-2. Is he correct? Justify your answer.
Answer:
Yes
Step-by-step explanation:
Triangle ABC is a right triangle, and mC is 78°.
What is mA?
A. 2°
B. 12°
C. 22°
D. 32°
Answer:
[B] 12°
Step-by-step explanation:
Given:
Triangle ABC is a right triangle, and m∠ C is 78°.
Solution:
Knowing that Triangle = 180 degree
Square in a right angle = 90° angle.
Thus,
78+90 =168
180-168 is 12
Hence, the answer is [B] 12 degree
Kavinsky
Answer:
the answer is
Step-by-step explanation:
B
If you draw out a red marble, keep it, then draw out a
blue marble, is it independent or dependent probability?
Independent
Answer:
dependent
Step-by-step explanation:
the probability of drawing the blue marble was changed when you drew the red marble and did not put it back
can someone help mepleace
Answer:Click on the file below
Step-by-step explanation:
Complete the two-way frequency table below, which shows the
distribution of blood types for students in their first year at a local
college.
O AB AB Total
Male (M) 210 17474 42
Female (F)|31526111163
Total
What is P(ABM), and are the events "the student is male" and "the
student has blood type AB" independent events? (7 points)
а
21
; they are independent because P(M N AB) = P(M)
250
· P(AB)
Ob
T!
; they are dependent because P(M NAB) P(M) · P(AB)
5
Ос
21
; they are independent because P(M N AB) = P(M)
625
P(AB)
Od
1
--; they are dependent because P(M N AB) = P(M) · P(AB)
4
Answer:
a.
Step-by-step explanation:
Probability that is a AB type blood given is a Male
P(AB/M) = 42/500 = 21/250
Probability that they are Male with an AB type blood out of all AB type blood people = Probability that is a Male out of all students
P(M∩AB) = P(M)
(42/105) = (500/1,250)
.4 = .4 ✅
The events "the student is male" and "the student has blood type AB" are independent events.
Jack went to baseball practice at 5:45 p.m. He returned home at 8:22 p.m. How long was he gone for? SHOW YOUR WORK PLEASE
Answer:
2 hours and 37 mins
Step-by-step explanation:
you want to get to a full hour so 5:45 closes hour would be 15 minutes later which would be 6:00 and then you add 2 hours which would be 8:00 and you have 22 minutes to get 822 p.m. so you add the minutes together 15 + 22 which you'll get 37 and you'll have the 2 hours on the side so it would be 2 hours and 37 minutes