Answer:
B. The population has increased by 105% each year since 1980.
D. Each year since 1980, the population is 105% of the population of the previous year.
E. Each year since 1980, the population is 1.05 times the population of the previous year.
Step-by-step explanation:
From the question, we are given the exponential function:
The exponential function P(t)=2000(1.05)^t models the population of the town since 1980.
Exponential growth rate =
P(t) = P(1 + r)^t
Where r = growth rate in percentage
P(t) = Size of the population after t years
t = time in years
Hence,
From the formula above, we can say =
1 + r = 1.05
r = 1.05 - 1
r = 0.05
Converting to percentage = 0.05 × 100 = 5%
1.05 can also converted to percentage and this = 1.05 × 100 = 105 %
The population has increased by 105% each year since 1980.
Hence, Options, B, D and E is correct
What is the equation of the line that passes through (-2, 92) and has a slope of −33/2 ?
A.) 33x + 2y = 75
B.) 33x + 2y = -24
C.) 33x + 2y = -57
D.) 35x + 2y = -75
A football team needs to move the ball at least 10 yards forward from the original starting point in order to get a first down. Angel runs for 6 yards on the first play. On the second play, he is sacked for −9 yards. At least how many yards does his team need on the third play to get a first down?
Answer:
13 yards
Step-by-step explanation:
Required distance moved from original position should be ≥ 10 yards in other to get a first down.
Run on first play = 6 yards
Second play = - 9yards
The least number of yards needed on third play :
Let yard needed on third play = x
First play + second play + third play = 10
6 + (-9) + x = 10
6 - 9 + x = 10
-3 + x = 10
x = 10 + 3
x = 13 yards
At least 13 yards is needed on third playbto get a first down.
A high school football team scored 39 points in the game last night, with a combination of touchdowns (6 points each), extra points (1 point each), and field goals (3 points each).
The team make 1 more extra point than field goals, represented by the equation e=f+1, where e is the number of extra points and f is the number of field points scored.
They also scored five times as many points on touchdowns as field goals, represented by the equation 6t=15f, where t is the number of touchdowns and f is the number of field goals scored.
Write a system of equations representing this situation and use it to complete the statement.
The team scored __ touchdowns, __ extra points, and __ field goals.
Answer:
39=6t+3f+e
39=19f+1
5 touchdowns, 3 extra points, and 2 field goals.
Step-by-step explanation:
e=f+1
6t=15f
39= 6t +3f +e
^ ^ ^
39=(15f)+(3f)+(f+1) | e=f+1 | 6t=15f
39=19f+1 | e=2+1 | 6t=15(2)
38=19f | e=3 | 6t=30
f=2 | | t=5
Show that x + y : x - y= 3 : 2
Answer:
x + y : x - y = (5/2+1/2) : (5/2-1/2)
x + y : x - y = 3 : 2
Therefore, x + y : x - y= 3 : 2 is proved.
Step-by-step explanation:
Given
x + y : x - y = 3 : 2
As
[tex]x + y = 3[/tex]
[tex]x - y = 2[/tex]
Solving to find x and y
[tex]\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}[/tex]
[tex]x-y=2[/tex]
[tex]-[/tex]
[tex]\underline{x+y=3}[/tex]
[tex]-2y=-1[/tex]
[tex]\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}[/tex]
solve for y
[tex]-2y=-1[/tex]
Divide both sides by 2
[tex]\frac{-2y}{-2}=\frac{-1}{-2}[/tex]
[tex]y=\frac{1}{2}[/tex]
[tex]\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=\frac{1}{2}[/tex]
[tex]x+\frac{1}{2}=3[/tex]
[tex]x+\frac{1}{2}-\frac{1}{2}=3-\frac{1}{2}[/tex]
[tex]x=\frac{5}{2}[/tex]
so
[tex]x=\frac{5}{2},\:y=\frac{1}{2}[/tex]
Thus,
x + y : x - y = (5/2+1/2) : (5/2-1/2)
x + y : x - y = 3 : 2
Therefore, x + y : x - y= 3 : 2 is proved.
What is the percent increase when 7,200 increases by 1,800?
A. 20 percent
B. 25 percent
C. 54 percent
D. 80 percent
Answer:
B.
Step-by-step explanation:
The percent increase when 7200 increases by 1800 is 25 %
work out
a. 5 x 1/8
b.1/7 x 6
plzz help
Answer:
Step-by-step explanation:
5 * 1/8= 5/8
1/7*6= 6/7
Place the whole number over 1 and multiply.
what is the measure of <x
Answer:
X=17
Step-by-step explanation:
73+x=90 90-73=17
A cab company charges $2.75 per mile, plus an extra surcharge. Bernardo took a cab to the
airport, which was 8 miles from his home. His total fare came to $29.50. Let x represent the
number of miles and y represent the total cost of the cab ride.
a. What is the slope-intercept equation of the line that fits this information?
b. If a customer paid $35, how many miles did they travel in the cab?
Answer:
a) $7.50
b) 10 miles
Step-by-step explanation:
a)
y=mx+b
y=$29.50
x=8
m=$2.75
b=unknown
29.50=2.75(8)+b
29.50-22=22-22+b
7.50=b
Check:
2.75(8)+7.50=29.50
b)
y=$35
x=unknown
m=2.75
b=7.50
35-7.50=2.75x+7.50-7.50
27.5/2.75=2.75/2.75x
10=x
Mary was able to make 3 necklaces and 2 bracelets in 30 minutes. It takes her 5 minutes longer to make a necklace than a bracelet. How long does it take to make each necklace and each bracelet?
A. Bracelets take 3 minutes to make, and Necklaces take 8 minutes to make.
B. Bracelets take 8 minutes to make, and Necklaces take 3 minutes to make.
C. Bracelets take 15 minutes to make, and Necklaces take 20 minutes to make.
D. Bracelets take 20 minutes to make, and Necklaces take 15 minutes to make.
Answer:
A. Bracelets take 3 minutes, and necklaces take 8 minutes.
Step-by-step explanation:
If Mary made 3 necklaces at that rate, it would add up to 24 minutes. A bracelet takes 3 minutes to make, and she made 2, so that would take 6 minutes. Add 24 to 6 and you'll get 30 minutes. I hope this helped :^)
Answer:
23 56
Step-by-step explanation:
yt
The seventh grade enrollment at Goddard, increased from 380 to 456 students. What is the percent of increase?
Answer:
20%
Step-by-step explanation:
Calculate percentage change
from V1 = 380 to V2 = 456
(V2−V1)|V1|×100
=(456−380)|380|×100
=76380×100
=0.2×100
=20%change
=20%increase
I bought 24 donuts for 44dhs how much does each donuts cost?? 24 divided by 44 =
Answer:
54 cents
Step-by-step explanation:
The best way to solve this is by writing this as a fraction...
24/44
Next, we should divide both sides by their GCF (Greatest Common Factor) Which in this case is 4.
Now, our fraction is...
6/11
So, our final answer is 6/11 or 0.54 repeating or 54 cents
Hope this Helps!!! :)
Let me know in the comment section if I should change anything or if this answer was perfect!!!
Need help. Forgot how to do this type
Answer:
AB=707
Step-by-step explanation:
what is the equation of the line in slope intercept form
Answer:
y=-3/2+1
Step-by-step explanation:
Byron's MP3 player holds 75 songs. He has space for 26 more songs. Write an equation to find how many songs are already on Byron's MP3 player.A.) 75 + s = 26 B.)75/s = 26 C.) 26s = 75 D.)s + 26 = 75
Answer:
D
Step-by-step explanation:
let the number of songs Byron have be s songs.
s + 26 = 75
Answer:
D
Step-by-step explanation:
s= number of songs played.
s+26=75
s-26=75-26
s=49
6. The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measures, while angle C is 57 degrees larger than the other two angles. Find the measure of angle C. a. 41 degrees b. 98 degrees c. 82 degrees d. 139 degrees Answer:
Answer:
well, if we want to know the measure angle c. we need to know the other angles measures. We know that c. is 57 more than a. and b.
So, if the triangle is 180 degrees in total, than we need to subtract 57 frm 180 to get 123. Now we divide that by 2 because that is what the other 2 angles will measure. 123 divides by 2 is 61.5.
now we subtract 61.5 from 180 to get 118.5
now to subtract 61.5 again because the 2 angles are the same measure. 118.5-61.5 is 57. so it cant be any of the answers you provided if angle a and b are the same
Step-by-step explanation:
plz mark brainliest!
1. COORDINATE GEOMETRY Classily AABC with vertices A-2, -1), B(-1,3), and C(2,0) as scalene, equilateral or isosceles.
Answer:
I'm pretty sure its a equilateral
Step-by-step explanation:
I graphed it
Hey luvs I NEED HELP ON THIS
Answer:
F. Outta. Here
Step-by-step explanation:
Answer:
a. 260m
b. 50m
Step-by-step explanation:
First, triangle POQ and triangle PNR are similar triangles, b/c they have one same angle(OQP), and OQ//NR.
Therefore, OP/OQ = NP/NR.
NP = OP + ON = 175 + 175 = 350
(a) 175/130 = 350 /NR, NR = 260
(b) 175/ (X+10) = 350/ (3X+5) , x = 15, NR = 50
please help asap, will give brainiest. TY! :3
Answer:
Page 1::1 & 3 & 4
Page 2:6
Page 3:8/1
Page 4:15 3/4
Step-by-step explanation:
HOPE THIS HELPS!!
Please help with this question, thank you so much.
The normal to the curve y =root x, at the point where x=1 and x=4 meet at P, find the coordinates of P.
The curve is y = sqrt{x}.
Replace x in the curve with 1 and then with 4 to find your point.
y = sqrt{1}
y = 1
First point (1, 1).
y = sqrt{4}
y = 2
Second point (4, 2).
Take it from here.
Find the value of x for which m parallel n 3x - 38 and 2x + 24
Answer:
35x
26x
Step-by-step explanation:
it help to understand..:)
Jamal drew the function below. Which explains whether or not his function is linear?
On a coordinate plane, a line with negative slope goes through points (0, 1.5) and (1.5, 0).
Answer:
"line" a straight line graph is always linear once the line isn't straight, it'll no longer be called a line and will never be linear anymore
Answer:
it is linear because it has a constant rate of change
Step-by-step explanation:
What is the value of x in this equation? 2x + 2 = -46
Answer:
x = -24
Step-by-step explanation:
1. Subtract 2 from -46 to cancel out the addition. 2x = -48
2. Divide both sides by 2. x = -24
7y + 8y can be simplified to 15y true or false
Answer:
True
Step-by-step explanation:
7y and 8y are like terms, so you can add them together
True.
How? By combining like terms.
7y + 8y = what?
We keep the variable y and simply add the numbers.
7 + 8 = 15
We now include y in our answer.
So, 7y + 8y = 15y.
Write an equation in slope-intercept form for the line with slope 6 and y-intercept -8 .
Answer:
y=6x-4
Step-by-step explanation:
The equation of line in the slope intercept form is y = 6x - 8 , where the slope of the line is m = 6
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the slope of the line m = 6
Let the y intercept of the line be = -8
Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
y = 6x - 8 be equation (1)
Hence , the equation of line is y = 6x - 8
To learn more about equation of line click :
https://brainly.com/question/14200719
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what is the equation of the line in slope intercept form
Answer:
y=2/7x+-9
Step-by-step explanation:
I need to go soon
Answer:
y=2/7x-9
Step-by-step explanation:
Goes to the right by 7 units, and goes up by two so 2/7. Line intercepts at -9.
Davaughn has 24 coins that are all dimes and quarters. The value of the coins is $3.75. How many dimes and how many quarters does Davaughn have?
Answer: 9 quarters and 5 dimes
Step-by-step explanation:
PLEASE HELP I NEED THIS TODAY!!
Answer: 201.06
Step-by-step explanation: The formula is pi times the radius squared.
Peter buys 12 bunches of bananas for $9.00. Use a ratio table to determine how much Peter will pay for 8 bunches.
Find the equation of the circle passes the following three
points?
a) (1,0) (0,1) and (2, 2)
Answer:
2.2
Step-by-step explanation:
the equation was not the only way that could change in a single year of growth
we have:(x, y1)=(1,0)
(x2,y2)=(0,1)
then the equation of circle is
(x-1)(x-x2)+(y-y1)(y-y2)=0
=(x-1)(x-0)+(y-0)(y-1)=0
=x2-x+y2-y=0
=x2++y2-x-y=0.
Hence this is the answer.