Speed = distance / time
Speed = 200 meters / 20 seconds
Speed = 10 meters / second
1 meter per second = 3.6 km per hour
10 meters per second x 3.6 = 36 km per hour
Answer: 36 kilometers per hour
Step-by-step explanation: Average speed = total distance / total time.
Find the slope of the line containing the points (-2,5) and
(-2,0).
Answer:
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Step-by-step explanation:
Find the slope of the line between the points (-1, 3) and (5, 11).
Is the point (-4, -1) on the same line as the other two points? Use slope to justify your answer.
Answer:
Step-by-step explanation:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-1,\:3\right),\:\\\left(x_2,\:y_2\right)=\left(5,\:11\right)\\\\m=\frac{11-3}{5-\left(-1\right)}\\\\m =\frac{11-3}{5+1}\\\\m=\frac{8}{6}\\\\Simplify\\\\m=\frac{11-3}{5-\left(-1\right)}[/tex]
Yes (-4, -1) is on the same line with the other wo points.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\\\mathrm{Slope\:}\left(-4,\:-1\right),\:\left(5,\:11\right)\\\left(x_1,\:y_1\right)=\left(-4,\:-1\right),\:\\\left(x_2,\:y_2\right)=\left(5,\:11\right)\\\\m=\frac{11-\left(-1\right)}{5-\left(-4\right)}\\\\Simplify\\m=\frac{4}{3}\\\\\mathrm{Slope\:}\left(-1,\:3\right),\:\left(-4,\:-1\right)\\\\\left(x_1,\:y_1\right)=\left(-1,\:3\right),\:\\\left(x_2,\:y_2\right)=\left(-4,\:-1\right)\\\\m=\frac{-1-3}{-4-\left(-1\right)}\\\\Simplify\\\\m=\frac{4}{3}[/tex]
Which of these transformations occurs when the blades of a fan turn?
a. dilation
b. reflection
c. rotation
d. translation
Nathaniel invested $37,000 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $70,900?
Answer:
11
Step-by-step explanation:
\text{Compounded Daily:}
Compounded Daily:
A=P\left(1+\frac{r}{n}\right)^{nt}
A=P(1+
n
r
)
nt
Compound interest formula
A=70900\hspace{35px}P=37000\hspace{35px}r=0.057\hspace{35px}n=365
A=70900P=37000r=0.057n=365
Given values
70900=
70900=
\,\,37000\left(1+\frac{0.057}{365}\right)^{365t}
37000(1+
365
0.057
)
365t
Plug in values
70900=
70900=
\,\,37000(1.0001562)^{365t}
37000(1.0001562)
365t
Simplify
\frac{70900}{37000}=
37000
70900
=
\,\,\frac{37000(1.0001562)^{365t}}{37000}
37000
37000(1.0001562)
365t
Divide by 37000
1.9162162=
1.9162162=
\,\,1.0001562^{365t}
1.0001562
365t
\log\left(1.9162162\right)=
log(1.9162162)=
\,\,\log\left(1.0001562^{\color{blue}{365t}}\right)
log(1.0001562
365t
)
Take the log of both sides
\log\left(1.9162162\right)=
log(1.9162162)=
\,\,\color{blue}{365t}\log\left(1.0001562\right)
365tlog(1.0001562)
Bring exponent to the front
\frac{\log\left(1.9162162\right)}{\log\left(1.0001562\right)}=
log(1.0001562)
log(1.9162162)
=
\,\,\frac{365t\log\left(1.0001562\right)}{\log\left(1.0001562\right)}
log(1.0001562)
365tlog(1.0001562)
Divide both sides by log(1.0001562)
4164.8632402=
4164.8632402=
\,\,365t
365t
Use calculator
\frac{4164.8632402}{365}=
365
4164.8632402
=
\,\,\frac{365t}{365}
365
365t
Divide by 365
11.4105842=
11.4105842=
\,\,t
t
t\approx
t≈
\,\,11
11
Using compound interest, it is found that it would take 11 years for the value of the account to reach $70,900.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.Hence, the parameters are given as follows:
[tex]A(t) = 70900, P = 37000, n = 365, r = 0.057[/tex]
We have to solve for t, then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]70900 = 37000\left(1 + \frac{0.057}{365}\right)^{365t}[/tex]
[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = \frac{70900}{37000}[/tex]
[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = 1.91621622[/tex]
[tex](1.00015616)^{365t} = 1.91621622[/tex]
[tex]\log{(1.00015616)^{365t}} = \log{1.91621622}[/tex]
[tex]365t\log{1.00015616} = \log{1.91621622}[/tex]
[tex]t = \frac{\log{1.91621622}}{365\log{1.00015616}}[/tex]
t = 11.41
Rounding to the nearest year, it would take 11 years for the value of the account to reach $70,900.
More can be learned about compound interest at https://brainly.com/question/25781328
#SPJ2
Which graph describes the relation {(3, –1), (1, –2), (–3, –2), (5, –5)}?
Does the table represent a function? Then represent
the relationship using words, an equation, and a
graph.
I need crucial help!
Answer:
This table represents a function
y is 1.3 times x
y=1.3x
Step-by-step explanation:
Stephanie's cable company charges $29.95 per month, plus $3.00 for each on-demand
movie rented. If Stephanie's cable bill last month was $44.95, how many on-demand
movies did she rent last month?
Pls help me plssssssss
Answer:
5
Step-by-step explanation:
44.95-29.95=15/3=5
NEED ANSWER ASAP PLEASE HELP!!!
What composition of transformations is equivalent to a rotation of 180°?
Open-ended question
Answer:
90 is correct good job
Step-by-step explanation:
PLEASE HELP!!! GIVING BRAINLIST
If x + 2y = 8 and x/2 -y= 10, then x = ?
A)-3
B) 0
C) 10
D) 14
Answer:
D. 14
make y the subject of the formula in equation 1 and then substitute it in equation 2
-1/4 [p+16]=2 help me pls
Answer:
6p
Step-by-step explanation:
HELPPPPPPP I WILLL GIVE THE BRAINLIESTTTTTTTTTTTT
At Open Skate Night, admission is $4.50 with a membership card and $5.00 without a membership card. Skate rentals are $2.00.
Aidan paid the admission for himself and two friends at Open Skate Night. Aidan had a membership card, but his friends did not. Aidan paid with a $20 bill. How much change should Aidan receive?
Aidan should receive
$_________ in change.
Answer:
50 cents
Step-by-step explanation:
4.50 + 5.00 + 5.00 + 2.00 x 3 = ?
^
20.00 - ?
Simplify the following expression. (19x + 4y) + (49x + 32y)
Answer: 68x + 36y
Step-by-step explanation:
Combine Like Terms:
= 19x + 4y + 49x + 32y
= (19x + 49x) + (4y + 32y)
= 68x + 36y
Hope this helped you!
Answer:
68x + 36y
Step-by-step explanation:
You can compeletely get rid of the parenthesis because it is addition through and thorough.
You have 19x + 4y + 49x + 32y
You can combine like terms to get
19x +49x which is 68x
and
4y + 32y which is 36y
You now have 68 + 36y which cannot be simplified anymore because the variables are different.
Hope this helps!
what is 10m-2?
Variables are really hard for me so if anyone can help me with this problem that would be really great
Answer:
tytyty
Step-by-step explanation:
A person can pay $9 for a membership to the history museum and then go to the museum for just $1 per visit. For a member of the history museum, what is the total cost of 23 visits?
Answer:
$32Step-by-step explanation:
Step one:
Given that membership is $9 and the cost per visit is $1
let the number of visits be x
and the total cost be y
the total cost for the situation is modeled as
y=mx+c-----equation of a line
Step two:
given that x=23, we can solve for the totals cost as
by substituting we have
y=1*23+9
y=23+9
y=32
The total cost for 23 visits is $32
Log. 216 = Y
Solve for Y
Solve for g.
18 = 3(g + 19)
Find an expression for the nth term (tn) in each of the following sequence:
2, 6, 10, 14, 18…
Answer:
The answer is 34
Step-by-step explanation: I just have a big brain
Answer: [tex]t_n = 4n - 2[/tex]
===========================================
Work Shown:
The first term is a = 2 and the common difference is d = 4, since we're adding 4 to each term to get the next term.
[tex]t_n = \text{nth term of arithmetic sequence}\\\\t_n = a+d(n-1)\\\\t_n = 2 + 4(n-1)\\\\t_n = 2 + 4n - 4\\\\t_n = 4n - 2[/tex]
Which is the answer.
--------------------------------
If you were to plug in say n = 3, then we get
[tex]t_n = 4n - 2\\\\t_3 = 4(3) - 2\\\\t_3 = 12 - 2\\\\t_3 = 10[/tex]
showing that 10 is the third term, which matches with what the original sequence shows. I'll let you check the other values of n to fully confirm the answer.
ILL GIVE BRAINLY THING
Answer:
the slope is -4/3
Step-by-step explanation:
you can either use the graph or algebra to find the slope.
to use the graph, simply count how many spaces up/down and to the left/right that you go.
to use algebra, take the coordinates of your two points and do (y2-y1)/(x2-x1).
In the souvenir shop, Gary finds a shirt and a key chain he would like to buy. The shirt costs $13.75 and the key chain costs $2.33. What will be the total of Gary's souvenirs?
Answer:
$16.08
Step-by-step explanation:
13.75+2.33=16.08
x+9;x=6
find the value of why for the given value of x
Answer:
-5
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
x+9=6 when x=6
6+9=15
15=15
Find the ratios x:y:z if x:y=9:10 and y:z=5:3
Answer:
Step-by-step explanation:
Answer:
x : y : z = 9 : 10 : 6
Step-by-step explanation:
Expressing the ratio y : z = 5 : 3 in fractional form, that is
[tex]\frac{y}{z}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )
5z = 3y ( divide both sides by 5 )
z = [tex]\frac{3}{5}[/tex] y = [tex]\frac{3}{5}[/tex] × 10 = 3 × 2 = 6
Thus
x : y : z = 9 : 10 : 6
7thh grade math help me plzzzzzzz
Answer:
aren't sufficiently brief
Step-by-step explanation:
The irony is when he was supposed to write a "brief" summary
Angie uses the equation E=0.03s + 25,000 to find her yearly earning E based on her total sales s. What is the independent variable
Answer:
25000
Step-by-step explanation:
it's independent because it's not related with her total sales s
The science center has 200 people in attendance on Monday. The center expects Saturday’s attendance to be 140 percent of Monday’s attendance. Natasha is trying to figure out how many people will be in attendance. Her work is shown below. StartFraction part Over whole EndFraction = StartFraction 140 Over 100 EndFraction StartFraction 140 divided by 2 Over 100 times 2 EndFraction = StartFraction question mark Over 200 EndFraction 140 divided by 2 = 70 70 people will be in attendance. What mistake did Natasha make? Natasha should have multiplied 140 by 2. Natasha should have divided 100 by 2. Natasha should have added 140 and 200. Natasha should have multiplied 140 and 200.
Answer:
A
Step-by-step explanation:
I did math
Answer:
a
Step-by-step explanation:
hope yall have a good day going back to school
Urgent please help, I will truly be grateful
Answer:
I can barley see it but i think i know what to do.
Step-by-step explanation:
First i have to write down on a piece of paper:D
QUICK WHAT IS 3 2/5X 2 1/3
Answer: 119/15 = 7 14/15
A bus travels at a speed of 40 miles per hour and reaches Hogville in 40 minutes. If a cab takes 35 minutes to reach the same spot, determine the speed at which it traveled.
Answer:
45.7miles per hour
Step-by-step explanation:
40mins = 2/3 hour
the bus travelled (2/3 x 40) miles = 80/3 miles
the cab took 35 mins (which is 7/12 hour) so it's speed is (80/3)/(7/12) miles/hour = 45.714 miles/hour (5 s.f.)
20 points to answer and extra if it’s right!
Answer:
C
Step-by-step explanation:
Money lost. Keyword "lost". Ages, people, and height can't be negative. ( I guess people can be negative mentally but not physically)
у = 3х – 7
у = 3х + 1
pula pays 419.92 for 2.4 pounds of walnuts .What is the price per pounof waluts ?