Answer:
No.
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}\\\\= \text{50.91 mi/h}[/tex]
Step-by-step explanation:
First leg: d = r₁t₁
Second leg: d = r₂t₂
r₁t₁ = r₂t₂
Total distance: 2d = r₁t₁ + r₂t₂
Total time: t = t₁ + t₂
1. Equation for average rate
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}[/tex]
2. Average rate
Since r₁t₁ = r₂t₂,
[tex]t_{1} = \dfrac{r_{2}t_{2}}{r_{1}} = \frac{40}{70}t_{2} = \frac{4}{7}t_{2}\\\\\text{Average rate} = \dfrac{2r_{2}t_{2}}{\frac{4}{7}t_{2} + t_{2}} = \dfrac{2 \times 40t_{2}}{\frac{4t_{2}+ 7t_{2}}{7}}= 80t_{2} \times\frac{7}{11t_{2}} = \dfrac{560}{11}\\\\= \textbf{50.91 mi/h}[/tex]
We cannot say truthfully that the average rate is 55 mi/h.
The average rate of a body is the total distance travelled divided by the total time.
The cheetah runs at an average rate of 50.91mph, not 55mph
Let
[tex]d \to[/tex] distance
[tex]r \to[/tex] average rate
[tex]t \to[/tex] time
Given that:
[tex]d = r_1t_1 = r_2t_2[/tex]
So, we have:
[tex]r_1 = 70[/tex]
[tex]r_2 = 40[/tex]
The average rate (r) is calculated as follows:
[tex]r = \frac{Total\ Distance (D)}{Total\ Time (T)}[/tex]
Where:
[tex]D=d + d[/tex]
[tex]D = r_1t_1 + r_2t_2[/tex]
and
[tex]T =t_1 + t_2[/tex]
So, the average rate is:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
Recall that:
[tex]D = r_1t_1 + r_2t_2[/tex]
[tex]r_1t_1 = r_2t_2[/tex]
Make [tex]t_2[/tex] the subject
[tex]t_2 = \frac{r_1t_1}{r_2}[/tex]
Substitute values for [tex]r_1[/tex] and [tex]r_2[/tex]
[tex]t_2 = \frac{70t_1}{40}[/tex]
So, we have:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
[tex]r = \frac{70t_1 + 40 \times \frac{70t_1}{40}}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{70t_1 + 70t_1}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{140t_1}{t_1 + \frac{70t_1}{40}}[/tex]
Factor out t1
[tex]r= \frac{140t_1}{t_1(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{\frac{40+70}{40}}[/tex]
[tex]r= \frac{140}{\frac{110}{40}}[/tex]
Rewrite as:
[tex]r = \frac{140 \times 40}{110}[/tex]
[tex]r = 50.91mph[/tex]
Hence, the cheetah's average rate is 50.91mph, not 55mph
Read more about distance, average rates and time at:
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Help please :/.
What is the surface area of a cube where the length of each edge is 4 feet?
A) 12 sq ft
B) 24 sq ft
C) 64 sq ft
D) 96 sq ft
Answer:
the answer is 96 square feet
you could use
4×4=16
then times how many rectangle you have which is 6
Enter the equation for the graph.
Answer:
y = cos x
Step-by-step explanation:
The graph begins at (0, 1) and completes its first period at (2π, 1) Thus the period of this function is 2π. The amplitude is 1; this is the value that y takes on when x = 0.
Thus the equation of this graph is y = 1cos x, or y = cos x.
To cover a distance of 240 km has to increase a speed of 5 per hour to reach in time time. If the time Lost was 40 minutes during traffic find the original speed
Answer:
The initial speed is approximately 104.3 km
Step-by-step explanation:
Let Distance = 240 km
Time = ?
Speed =
Since
Speed = Distance/Time
Distance = Speed × Time
When arrival is late:
240 = S×T
When arrival is on time:
240 = (S+5)×T2
But 40minutes = 2/3 hours
So,
T2 = T - 2/3
240 = (S+5)×(T - 2/3)
240 = ST - 2S/3 + 5T - 10/3
ST - 2S/3 + 5T = 240 + 10/3
S(T - 2/3) + 5T = 730/3
S(T - 2/3) = 730/3 - 5T
S = (730/3 - 5T)/(T - 2/3)
But 240 = ST
S = 240/T
240/T = (730/3 - 5T)/(T - 2/3)
(T - 2/3)/T = (730/3 - 5T)/240
1 - 2/3T = 730/720 - 5T/240
1 + 73/72 = (2/3 + 5/24)T
145/72 = (7/8)T
T = 145/72 × 8/7
= 1160/504
T = 145/63
S = 240/S
= 240×63/145
= 3024/29
≈ 104.3km
Find a linear second-order differential equation F(x, y, y', y'') = 0 for which y = c1x + c2x4 is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c1 and c2. (Use yp for y' and ypp for y''.)
Answer:
[tex]4y+ y"x^2-4y'x = 0[/tex]
↓
[tex]F(x, y, y', y'') = 0[/tex]
Step-by-step explanation:
From the information given:
[tex]y = c_1x + c_2x^4 \\ \\ y^1'= c_1 + 4c_2x^3 \\ \\ c_1 =y' - 4c_2x^3 \\ \\[/tex]
So;
[tex]y = y'x -4c_2x^4+c_2x^4 \\ \\ y - y'x - 3c_2x^4 \\ \\ y'= y"x+y'- 12c_2x^3 \\ \\ c_2= \dfrac{y"x}{12x^3} \\ \\ c_2= \dfrac{y"}{12x^2}[/tex]
∴
[tex]y = y'x- \dfrac{3x^4*y'' }{12x^2} \\ \\ \\ y = y'x - \dfrac{y" x^2}{4} \\ \\ \\ 4y+ y"x^2-4y'x = 0[/tex]
↓
[tex]F(x, y, y', y'') = 0[/tex]
$36/4oz is what and , 24/3oz is what , $20/2oz is what plz help
Answer:
see below
Step-by-step explanation:
$36/4oz = $9 per oz
24/3oz = $ 8 per oz
$20/2oz = # 10 per oz
*I WILL MARK YOU BRAINLIEST!!!!!!*
Answer:
A. is the correct answer
Step-by-step explanation:
the answer is 27
Answer:
A. 25
Step-by-step explanation:
f(x)= 8x - 7
f(4)= 8*4 - 7= 25
f(4)= 25
Question 19 / 50
In a class of forty students, one fifth of the students also play on the school's
football team. If four more students from the class join the football team, what
percentage of students in the class will be on the football team?
25%
30%
0 33%
O 35%
40%
Submit Answer
Answer: 30%
Step-by-step explanation:
1/5th of students = 1/5 x 40 = 8
If 4 more students join, they will be (8+4) 12 students
Percentage will be 12/40 x 100 = 30%
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4). Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.
Answer: - 2.5
Step-by-step explanation:
Using the attached number line has reference, the distance between each integer on the number line attached is 1, and the numbers are ordered in ascending order from - 10 to + 10. The point R exists in between the point marked - 2 and - 3 respectively. This shows that that point R is a number between the two integers, a number greater than - 3 but less than - 2.
From the picture attached the blue dot sits directly at the midpoint between - 3 and - 2. Hence the position can be a obtained by averaging the two integers.
(-3 + - 2) / 2 = - 5/2 = - 2.5
I need help with this problem.
Answer:
D
Step-by-step explanation:
[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]
Therefore, the correct answer is choice D. Hope this helps!
When a number is tripled, it gives the same result as when 32 is added to it.
What is the number?
Answer:
The number is 16.
Step-by-step explanation:
3x=32+x
2x=32
x=16
A number that when tripled, gives the same result as when 32 is added to it is 16.
Let the unknown number be x.In this exercise, you're required to solve for an unknown number, that when tripled has the same value as when 32 is added to it.
Translating the word problem into an algebraic expression, we have;
Tripling the number, we have:
[tex]3x[/tex] ....equation 1
Adding 32 to the number, we have:
[tex]32 + x[/tex] ....equation 2
Equating the two equations, we have:
[tex]3x = 32 + x\\\\3x - x = 32\\\\2x = 32\\\\x = \frac{32}{2}[/tex]
x = 16
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someone help please!
tell whether the red figure is a translation or rotation of a black figure
Answer:
The 2 figures have the same shape and the corresponding points are "lined up" so I would say that this is a translation.
Answer:
translation
see below
Step-by-step explanation:
translation because it didn't change direction of the figure
translation is sliding down or up rotation is moving in circle
Choose the two steps that are part of factoring the trinomial 6x2 + 17x + 5 by grouping.
a. 6x2 + 9x + 8x + 5
b. (3x + 1)(2x + 5)
c. x(6x + 17) + 5
d. 3x(2x + 5) + 1(2x + 5)
Answer:
b
Step-by-step explanation:
given
6x² + 17x + 5
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × 5 = 30 and sum = 17
The factors are 2 and 15
Use these factors to split the x- term
6x² + 2x + 15x + 5 ( factor the first/second and third/fourth terms )
= 2x(3x + 1) + 5(3x + 1) ← factor out (3x + 1) from each term
= (3x + 1)(2x + 5) → b
The two steps are [tex]3x(2x+5)+1(2x+5)[/tex] and [tex](3x+1)(2x+5)[/tex]. So, options b and d are correct.
Important information:
The given trinomial is [tex]6x^2+17x+5[/tex].Factoring:Splitting the middle term, we get
[tex]6x^2+15x+2x+5[/tex]
After grouping, we get
[tex](6x^2+15x)+(2x+5)[/tex]
Taking out common factors, we get
[tex]3x(2x+5)+1(2x+5)[/tex]
Now, it can be written as:
[tex](3x+1)(2x+5)[/tex]
Therefore, the correct options are b and d.
Find out more about 'Factoring' here:
https://brainly.com/question/2416165
What is the value of p?
Answer:
[tex]p = 43 \: \: \: degrees[/tex]
Answer A is correct
Step-by-step explanation:
[tex]90 + p = 133[/tex]
the sum of the exterior angles in a triangle is equal to the sum of opposite interior angles.
[tex]p = 133 - 90 \\ p =4 3 \: \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
David wants to find the solutions of this system of equations: –4x – 7 = y x2 – 2x – 6 = y Which statement is true? Plz its urgent!!
Answer:
(-1, -3)
Step-by-step explanation:
The given equations are:
[tex]-4x-7=y ...... (1)[/tex]
and
[tex]x^2 - 2x - 6 = y ....... (2)[/tex]
Equating (1) and (2):
[tex]-4x -7 =x^{2}-2x-6\\\Rightarrow x^{2}-2x-6+4x+7=0\\\Rightarrow x^{2}+2x+1=0\\\Rightarrow (x+1)^2=0\\\Rightarrow x = -1[/tex]
The two values of x are repeating in nature i.e. x = -1
So, value of [tex]x[/tex] is -1.
Putting value of [tex]x[/tex] in equation (1):
[tex]-4 \times (-1)-7=y \\\Rightarrow y=-3[/tex]
The solution is represented as ([tex]x,y[/tex])
So, the solutions are :
(-1, -3)
Answer:
2
Step-by-step explanation:
give brainliest
Which equation is equivalent to -2(2 − 2x) = 4 − 8(1 − x)
0 = 4x
8 = 4x
4 = -4x
16 = -4x
Answer:
8 = 4x OR 0 = 4x
Step-by-step explanation:
I not %100 sure or it could be 0 = 4x
EITHERONE
Tony wants to put $318,000 in his retirement savings account. It earns an interest rate of 7.1% compounded quarterly. He wants to determine how much he will have in the account after 5 years, even if he makes no additional contributions or withdrawals to the account
A. $448099.52
B. $347242.34
C. $452115.44
D. $341186.28
which answer correct
Answer:
C. $452115.44
Step-by-step explanation:
To solve this, we will follow the steps below;
first write down the formula for compound interest
A= P [ 1 + [tex]\frac{r}{n}[/tex]]^nt
where A is the ending amount
P represent the principal
r represent the interest rate
n represent the number of compounding a year
t represent the time {in years)
from he question above
p= $318 000
r = 0.071
n = 4 since is quarterly
t= 5
we can now proceed to insert the values into the formula
A= P [ 1 + [tex]\frac{r}{n}[/tex]]^nt
=318 000 [1+[tex]\frac{0.071}{4}[/tex]] ^4(5)
= $318 000 [1+[tex]\frac{0.071}{4}[/tex]] ^20
=$318 000 [1+0.01775] ^20
= $318 000 [1.01775] ^20
=$318 000× 1.421747
≈$452 115.44
He will have $452 115.44 in the account
Evaluate 10x^2y^–2 for x = –1 and y = –2.
Answer:
10
Step-by-step explanation:
10x^2y^-2
10(-1)^2(-2)^2=10
I have a test in 2 days please do quickly!!! What is a ratio???!!??
Answer:
A ratio is when 2 values that come from related things are compared in the form of x:y
Answer:
comparison between things
Step-by-step explanation:
for example:
16 girls and 8 boys in a class room
the ratio would be 2:1 (girls:boys)
f=
4m + 3
m – 1
make m the subject
Answer:
m = [tex]\frac{f+1}{7}[/tex]
Step-by-step explanation:
f = 4m + 3m -1
f = 7m - 1
Adding 1 to both sides
f+1 = 7m
Dividing both sides by 7
m = [tex]\frac{f+1}{7}[/tex]
Answer:
m= (f+3)/(f-4)
Step-by-step explanation:
It is not clear from the question, but I assume it is:
f= (4m+3)/(m-1)so the solution is:
f= (4m+3)/(m-1)f(m-1)=4m+3fm-f= 4m+3fm- 4m= f+3m(f-4)= f+3m= (f+3)/(f-4)I need explanation and help me plz !!!!
Answer:
52
Step-by-step explanation:
There are a total of 380+240+110 people. (730)
0.52 are in stage 3.
0.33 in stage 2.
0.15 in stage 1.
52 people from stage 3 should be in the group.
Find the equation of the line shown.
Answer:
y = x+1
Step-by-step explanation:
draw a table / write down ratios of the values of x and y. Then, you will notice the difference/ similarity
Answer:
y = x + 1
Step-by-step explanation:
equation of the line :
y = my + p ; m is the slope and p is the y-intercept.
The line cross the —axis at the point (0,1) then
p = 1
the line passes through (0,1) and (1,2) then
m = (2-1)/(1-0) = 1/1 = 1
conclusion:
y = x + 1
People pay to visit a stately home [tickets age 16 and over : £18.60 ..under 16:£12.80] 155 people pay and 49 of these people are under 16. How much money is collected
Answer: £2598.80
Step-by-step explanation:
Let those under 16 be x
Those over 16 be y
49 + y = 155
y = 155-49
y = 106 = over 16
for over 16, y * 18.60
= 106 * 18.60 = 1971.60
For under 16, x * 12.80
= 49 * 12.80 = 627.20
The function has a y-intercept of (0, 4) and a multiplier of 0.8. 1) Whats the initial value? 2) Is it exponential growth or decay? 3) What is the exponential equation?
Answer:
1) 4
2) exponential decay
3) [tex]y = 4(0.8)^x[/tex]
Step-by-step explanation:
1) The initial value or an exponential function is the y-intercept.
Let us consider a standard exponential function of the form y(x) = a•bˣ , if you put in x = 0 (initial value) we get:
y(0) = a•bˣ = a•b⁰ = a•1 = a , so the y-intercept is a , which is called the initial value.
Therefore the y intercept is 4
2) Since the multiplier is greater than 0 and less than one, it is an exponential decay
3) standard exponential function of the form y(x) = a•bˣ, at (0,4),
4 = a(b)⁰
a = 4
b = multiplier = 0.8
Therefore: [tex]y = 4(0.8)^x[/tex]
– 4 vc2, when v = –7 and c = –2
Answer:
[tex] \boxed{112} [/tex]
Step-by-step explanation:
[tex]Evaluate - 4v {c}^{2} \: where \: v= - 7 \: and \: c= - 2 : \\ = > - 4v {c}^{2} \\ = > - 4( - 7) {( - 2)}^{2} \\ \\ {( - 2)}^{2} = 4: \\ = > - 4( - 7)4 \\ \\ - 4( - 7) = 28: \\ = > 28 \times 4 = 112[/tex]
if f(x)=6x^2-4 and g(x)=2x+2 find (f-g)(x)
Answer: [tex](f-g)(x)=6x^2-2x-6[/tex]
Step-by-step explanation:
[tex]f(x)=6x^2-4\\g(x)=2x+2\\(f-g)(x)=[/tex]
Take each function and subtract them.
[tex](f-g)(x)=(6x^2-4)-(2x+2)[/tex]
The trick here is that the negative sign changes all of the signs inside the parentheses.
[tex](f-g)(x)=6x^2-4-2x-2[/tex]
Combine like terms;
[tex](f-g)(x)=6x^2-2x-6[/tex]
Five times one number minus two times a second number is 11. Three times the first number minus two times the second number is 1. what are the numbers?
Answer:
first number is 5
second number is 7
Step-by-step explanation:
let x and y represent the first and second number
5x - 2y = 11 ........ equation 1
3x - 2y = 11.......... equation 2
so by elimination, equation 1 minus equation 2
5x - 3x - 2y - 2y = 11 - 1
2x = 10
x = 5
therefore the first number is 5
put x = 5 into equation 1
5x - 2y = 11
5(5) - 2y = 11
25 - 2y = 11
-2y = 11 - 25
-2y = - 14
y = 7
therefore the second number is 7
hope it helps .
The length of the unknown slide is?
Answer: 10.8
Step-by-step explanation:
We can use the Pythagorean Theorem to solve this.
a^2 + b^2 = c^2
6^2 = 36
9^2 = 81
36 + 81 = 117
square root of 117 is 10.8
rearrange to make x the subject a= 4x/t -p
Answer:
x = [tex]\frac{t(a+p)}{4}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{4x}{t}[/tex] - p ( isolate term in x by adding p to both sides )
a + p = [tex]\frac{4x}{t}[/tex] ( multiply both sides by t )
t(a + p) = 4x ( divide both sides by 4 )
[tex]\frac{t(a+p)}{4}[/tex] = x
Please help asap!!
Graph (x, y): x + 2y 6
