Answers
Answer:
Yes, Elias got his food before reaching the potluck.
Step-by-step explanation:
Elias left home at 7:00 one morning, determined to make the ten-mile trip to Leaders on a bicycle. Soon thereafter, Elias' parent noticed he had forgotten his potluck dish on the kitchen table, got into the family car, and tried to catch up with the forgetful child. Elias had a fifteen-minute head start, and was pedaling at 12 mph, while the parent pursued at 30 mph. Was Elias reunited with his potluck food before reaching Leaders that day? If so, where? If not, at what time was the food delivered?
Let's set x as the time after the parent leaves as x (time after the first 15-minute headstart)
When the two meet, it means that the distance is equal. Remember, distance = time * speed.
Using this, we know that Elias had a 15-minute headstart at 12 mph, which means that he had 0.25 of an hour. Thus, Elias had a 0.25 * 12 mile headstart.
We can write this equation for the distance Elias traveled.
0.25 * 12 + 12 * x
And this equation for the distance his parent traveled.
30 * x
These equations need to be equal so that the two meet.
0.25 * 12 + 12 * x = 30 * x
Simplify.
3 + 12x = 30x
Subtract 12x from both sides.
3 = 18x
Divide both sides by 18.
x = 1/6
So, it took 1/6 of an hour, which is 10 minutes, for the parent and Elias to meet.
If Elias were to get the food before he reached the potluck, the distance he traveled (0.25 * 12 + 12 * x) needs to be less than 12.
Plug 1/6 in for x.
0.25 * 12 + 12 * 1/6 =
3 + 2 = 5
Elias traveled 5 miles before his parent met him.
So, Elias did get his food before reaching Leaders.
Just in case, let's double-check this answer.
Using the distance = speed * time formula, we know that time = distance/speed. Elias's parent had to travel 5 miles at 30 mph, so it would have taken 1/6 of an hour to drive 5 miles.
Elias traveled at 12 mph for 1/6 + 1/4 of an hour, so he traveled:
(1/6 + 1/4) * 12 =
(4/24 + 6/24) * 12 =
10/24 * 12 =
120/24 = 5 miles
Thus, the previous answer is right.
I hope this helps! Feel free to ask any questions!
Related Questions
349324923420 × 4π × 9π × 9908=?????
FREE AWARD!!!!!
Answers
1.2297528e+18
There ya go
which of the following is correct statement about this relation?
Answers
Given:
The relation is:
(-3,1),(-2,3),(-1,5),(0,7),(1,9),(2,11)
To find:
The slope and y-intercept for the given relation.
Solution:
Consider any two points from the given relation.
Let the two points are (0,7) and (1,9). So, the slope of the given relation is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{9-7}{1-0}[/tex]
[tex]m=\dfrac{2}{1}[/tex]
[tex]m=2[/tex]
The slope of the given relation is 2.
A point of relation is (0,7). It means the value of relation is 7 at x=0.
So, the y-intercept is 7.
Therefore, the correct option is D.
If f(x) = 5x2 – 6x + 13 and g(x) = 6 – 4(x – 1) which is an equivalent form of f(x) + g(x)?
Answers
Answer:
61-4-2. (3t-a)(at+1) f. 6x2 - 17x+10. 16x-5X(x-2) e x-2x*-*+2 x2{x-2)-1(x-2). (x-2)(x2_1). (x-2)x+1)(x-) hi ** +5x2 +6 ... Leave your answers in simplest radical form if needed. ... 4. Let 'n(x)=x2-Ox and g(x)=2x-7. Find all values of x, for which h(x) = g(x) ... p=2 4p=8. (x+6*=8(y+3) x+6X+36=8Y+24. X*+6x +12= By gx+x+1=Y. 13.
Step-by-step explanation:
Definition the value of a number regardless of its sign Definition
Answers
A company offers broadband for a one-off charge of £60 for every 3 months, then £28 per month after that. How much will 12 months' broadband cost?
Answers
Step-by-step explanation:
12 months with $60 every 3 months is $240
then add $28 "per month after that"
The revenue from selling x bracelets is f(x) = 8x.
The cost of buying x bracelets is c(x) = 3x + 12.
The profit from selling x bracelets is p(x) = (x) - c(x).
Write a function for p(x), the profit from selling x bracelets.
O A. p(x) = 11x - 12
B. p(x) = 11x + 12
C. p(x) = 5x - 12
O D. p(x) = 5x + 12
Answers
We are given r(x) and c(x).
p(x) = 8x - (3x + 12)
p(x) = 8x - 3x - 12
p(x) = 5x - 12
Done.
Factorise 3x⁴-4y⁴ completely
Answers
Answer:
Step-by-step explanation:
[tex]3x^4-4y^4\\=(\sqrt{3}x^2)^2-(2y^2)^2)\\=(\sqrt{3}x^2+2y^2)(\sqrt{3}x^2-2y^2)\\=(\sqrt{3} x^{2} +2y^{2} )((3^{\frac{1}{4} } x)^2-(\sqrt{2} y)^{2} )\\=(\sqrt{3} x^{2} +2y^{2} )(3^{\frac{1}{4} } x+\sqrt{2} y)(3^{\frac{1}{4} } x-\sqrt{2} y)[/tex]
Hey guys can someone help me out?
Answers
Answer: yes with what
Step-by-step explanation:
PLEASE HELP ITS DONE IN 16 HOURSSS!!!
question: A substance with 12 negatively charged atoms combined with a substance that has 10 positively charge atoms. What is the total charge of the substance when the atoms are combined?
answer options:
+22
-22
+2
-2
Answers
Miss logan leaves school at 15:55 it takes her 1 hour and 20 mins to get home what time does she arrive home? answer using 24 hour time
Answers
Answer:
5:15
Step-by-step explanation:
15:55 = 3:55 in normal time
3:55 + 1 hr = 4:55
4:55 + 20 min = 5:15
Enter the pair of fractions 6/7 and 13/14 with the smallest common denominator between the two fractions
Answers
Answer:
25/14
Step-by-step explanation:
What is the average rate of change for f(x) = 2 ^ x + 10 over the interval 2 <= x <= 4
Answers
solve for x. x+53=99 A.36 B.46 C.47 D.152
Answers
Answer:
Hii, the answer B. 46
Step-by-step explanation:
x+ 53 = 99
So to find what x equals we just do simple subtraction
99 - 53 = 46
so x = 46
Hope this helps!
What is the distance between - 10
and 2 on the number line?
12 units
-8 units
5 units
8 units
Answers
Answer:
12 units
Step-by-step explanation:
Draw a number line and mark x = -10 and x = 2. You can readily see that the distance from -10 to the origin is 10 units, and from the origin to 2 is 2 units, in both cases measured from left to right. Adding these two positive quantities together, we get 10 + 2, or 12.
The distance from -10 to 2 on the number line is 12 units.
If a point on a coordinate plane is placed 5 lines to the right and 3 lines up, what would the ordered pair be?
Answers
Answer:
(5,3)
Step-by-step explanation:
Multiple Choice
Use the diagram below to answer questions 1–3.
Which angle is congruent to angle 1?
A. angle2
B. angle5
C. angle6
D. angle7
Answers
What is the value of x?
K
х
X-6
Q
P
5
ال)
L
J
Answers
Answer:
C
Step-by-step explanation:
The value of x is equal to 9
Need help with radius and diameter pls hurry points and I will give brainlest
Answers
Answer:
the radius is 9 and the diameter is 18
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
- 2
0
2
Use the function rule to complete the table.
- 10x + y = 4
Please help I’ve been stuck on this for an hour now PLEASEEEEE
Answers
Answer:
y= 10x + 4
Step-by-step explanation:
-10x + y = 4
-10x + y +10x = 10x + 4
y= 10x + 4
depending on what its asking usually this is what its asking for but im not sure exaclty what its asking so here.....
next step is to plug the numbers in
so for the first box it says that x is -2
plug it in.....
y = 10(-2) + 4
y = -20 + 4
y = -16
then keep doing it for the next boxes.....
second box:
y = 10(-1) + 4
y = -10 + 4
y = -6
third box:
y = 10(0) + 4
y= 4 because 10 times zero is zero (basically any number times 0 is zero)
fourth box:
y = 10(1) + 4
y = 10 + 4
y = 14
fifth box:
y = 10(2) + 4
y = 20 + 4
y = 24
Hope this helps!
*srry in advance if its wrong
The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per
year. Which function shows the company's profit as a function of time in years?
a. f(t) = 100,000 0.012^t
b. f(t) = 100,000(1 + 1.2)^t
c. f(t) = 100,000(1 + 0.012)^t
d. f(t) = 100,000 - 1.2^t
Answers
Given:
Initial profit = $100,000
Increasing rate of profit = 1.2%
To find:
The function that shows the company's profit as a function of time in years.
Solution:
The exponential growth model is defined as:
[tex]f(t)=a(1+r)^t[/tex]
Where, a is the initial value, b is the growth rate and t is the time period.
Putting a=100,000 and r=0.012, we get
[tex]f(t)=100,000(1+0.012)^t[/tex]
Where, t is the number of years.
Therefore, the correct option is c.
Select all expressions that are equal to 3⋅3⋅3⋅3⋅3.
3^5
3^4 ⋅ 3
5 ⋅ 3
5^3
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3=\bf9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9=\bf81}\\\\\mathsf{81\times3=\bf result}\\\\\mathsf{= \bf \underline{243}}\large\checkmark[/tex]
[tex]\text{Option A. }\downarrow\\\mathsf{3^5}\\\\\mathsf{3^5= 3\times3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3 = 9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9 = 81}\\\\\mathsf{81\times3= 243}\\\\\large\text{\bold{Option A.} could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option B. }\downarrow\\\mathsf{3^4\times5}\\\mathsf{3^4 = 3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3}\\\\\mathsf{3\times3=9}\\\\\mathsf{9\times9= 81}\\\\\mathsf{81\times3=243}\\\\\large\text{Option B. could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option C. }\downarrow\\\mathsf{3\times5}\\\\\maths{3+3+3+3+3}\\\\\mathsf{3+3=6}\\\\\mathsf{6+6+3}\\\\\mathsf{6+6=12}\\\\\mathsf{12+3=15}\\\\\mathsf{15\neq243}\\\\\large\text{Option C is NOT your ANSWER}[/tex]
[tex]\text{Option D.}\downarrow\\\mathsf{5^3}\\\\\mathsf{5^3=5\times5\times5}\\\\\mathsf{5\times5\times5}\\\\\mathsf{5\times5=25}\\\\\mathsf{25\times5 = 125}\\\\\mathsf{125\neq243}\\\\\large\text{Option D. is NOT your ANSWER}[/tex]
[tex]\boxed{\boxed{\large\text{Answers: \boxed{\boxed{\mathsf{\bf{Option\ A.)\ 3^5 \ \& \ Option\ B.)\ 3^4 \times 3}}}}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
A) 3^5 B) 3^4*3
Step-by-step explanation:
HEY can You help me with this work pls i need help don't put random. if u don't know it pls guys.
Answers
1️⃣Remove parentheses
6a+6+3x-2+2a+4
2️⃣Collect like terms
(6a+2a)+(6-2+4)+3x
3️⃣Simplify
8a+8+3x
Answer: 8a+8+3x
QUESTION 21️⃣Remove parentheses.
-2z-3+4c+6y+y+3c
2️⃣Collect like terms.
-2z-3+(4c+3c)+(6y+y)
3️⃣Simplify
-2z-3+7c+7y
Answer: -2z-3+7c+7y
QUESTION 31️⃣Subtracting (7.8 - 5.1t) from (2.8 - 3.2t)
(2.8 - 3.2t) - (7.8 - 5.1t)
2️⃣Remove the parentheses.
2.8 - 3.2t - 7.8 + 5.1t
= 5.1t - 3.2t + 2.8 - 7.8 (we have now shown the difference in another way)
3️⃣Subtracting the like terms, will give:
1.9t - 5
4️⃣Recall
(2.8 - 3.2t) - (7.8 - 5.1t).
(-3.2t + 2.8) - (-5.1t + 7.8)
Answer:
a. (-3.2t + 2.8) - (-5.1t + 7.8)
b. 1.9t - 5
c. (-3.2t + 2.8) - (-5.1t + 7.8)
QUESTION 41️⃣Simplify
1/2p-(1/4p-4)
2️⃣Simplify
p2-(p/4-4)
3️⃣Simplify
p2-p/4+4
4️⃣Combine Terms
(p/2-p/4)+4
5️⃣Combine Terms
p/4+4
Answer: p/4+4
Done ✔
An archer releases an arrow with an initial velocity of 20 feet per second at a height of 12 feet. The path the arrow takes can be modeled using the function f(x)=−16x2+20x+12, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. What is the maximum height, in feet, reached by the arrow? Round your answer to the nearest hundredth if necessary. Do not include units in your answer
Answers
Answer: 18.25
Step-by-step explanation:
The arrow reaches its highest point at the y-value of the turning point. Thus, we need to find the maximum quadratic function.
-16x^2+20x+12
We know that the maximum( or minimum) of a parabola is reached at x= -b/(2a)= -20/ 2(-16)= 18.25
Showing that the object will reach a maximum height of 18.25 feet
Question
what's 10÷0=_
Answer please
Answers
Answer:
Undefined
Step-by-step explanation:
Answer:
you cant divide by 0
Step-by-step explanation:
no solution
y=3x-4 slope intercept form
Answers
Answer:the slope is 3 and the y intercept is -4
Step-by-step explanation:
Function A and Function B are linear functions. Compare the two functions and choose all that are correct. Can someone help?
Answers
Answer:
(b) and (c) are true
Step-by-step explanation:
Given
Function A and B
First, calculate the slope of A
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{24 - -21}{8- -7}[/tex]
[tex]m = \frac{45}{15}[/tex]
[tex]m =3[/tex]
The equation of function A is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 3(x - 8) + 24[/tex]
[tex]y = 3x - 24 + 24[/tex]
[tex]y = 3x[/tex]
The general form of a function is:
[tex]y = mx + b[/tex]
Where [tex]m = slope[/tex] and [tex]b = y\ intercept.[/tex]
This implies that:
[tex]Slope = 3[/tex]
[tex]Y\ intercept = 0[/tex]
For function B:
[tex]y = 4x - 3[/tex]
[tex]Slope = 4[/tex]
[tex]Y\ intercept = -3[/tex]
By comparison:
(b) and (c) are true
At an Auto Repair shop, 4 of the 16 cars received oil changes. What percent of the cars received oil changes?
Answers
Answer:
its 25 percent
Step-by-step explanation:
want an explanation cuz im happy to give you 1
I need help with this one.
Answers
9514 1404 393
Answer:
1,563.5 in³904.8 yd³2,144.7 mm³1,288.2 cm³434.9 in³Step-by-step explanation:
The formula for the volume of a sphere is ...
V = (4/3)πr³
When you have several of these calculations to do, it is convenient to let a graphing calculator or spreadsheet do them. A spreadsheet can do the rounding for you, too. The results are attached. The units are the cube of the units of the radius.
Example calculation:
(4) Radius = diameter/2 = 13.5 cm/2 = 6.75 cm
V = (4/3)π(6.75 cm)³ = 4.18879 × 307.547 cm³ = 1288.2 cm³
Note that the constant (4/3)π ≈ 4.18879 remains the same for each calculation. All you need to do is multiply that by the cube of the radius.
Consider a graph of the equation y = x + 6. What is the y-intercept? (5 points) 6 −1 1 −6
Answers
D I am not 100% sure, If I am wrong sorry
Please help me I wanna go to sleep
What is true about this sequence?
8000, 4000, 2000, 1000, ...
Answers
Answer:
B
Step-by-step explanation:
each consecutive term is divided by 2