Given:
The population of animals = 350
Growth rate = 5% each year.
To find:
The exponential function to model this situation.
Solution:
The general exponential growth model is:
[tex]f(t)=a(1+r)^t[/tex]
Where, a is the initial value, r is the growth rate in decimal and t is the time period.
Substituting [tex]a=350, r=0.05[/tex] in the above formula, we get
[tex]f(t)=350(1+0.05)^t[/tex]
[tex]f(t)=350(1.05)^t[/tex]
Therefore, the required exponential function is [tex]f(t)=350(1.05)^t[/tex], where f(t) is the number of animals after t years.
What is the radius of polygon JKLMN ?
Answer:
Radius of the circle is 5 units.
Step-by-step explanation:
JKLMN is a regular polygon inscribed in a circle.
Since, its a regular polygon,
JN = NM = 5.88 units
"Perpendicular drawn from the center of the circle to any chord is the bisector of the chord"
Therefore, PQ will be the perpendicular bisector of chord NM.
QM = [tex]\frac{1}{2}(NM)[/tex]
QM = [tex]\frac{1}{2}(5.88)[/tex]
QM = 2.94 units
By applying Pythagoras theorem in ΔPQM,
PM² = PQ² + QM²
PM² = (4.05)² + (2.94)²
PM = [tex]\sqrt{16.4025+8.6436}[/tex]
PM = [tex]\sqrt{25.0461}[/tex]
PM = 5 units
Therefore, radius of the circle is 5 units.
A team from the high school went on a science-and-math quiz show. The science questions were worth 10 points and the math questions were worth 3 points. The team answered a total of 10 questions and earned 65 points. How many questions did the team answer in each category?
Answer:
The answered 5 math questions, and 5 science questions.
5 * 3 = 15
5 * 10 = 50
15 + 50 = 65
Step-by-step explanation:
Select all expressions that equal −7−(−12) .
A
7+(−12)
B
−7+(−12)
C
−7+12
D
7+12
Answer:
C, -7+12
Step-by-step explanation:
-7--12= 5
-7--12 can also be -7+12
Answer:
The answer is c
Step-by-step explanation:
-7-(-12) = 5
If you added 2 circles to the left side, how many squares would you have to add to the right side to keep it balanced?
Answer: 2 circle to the right
Step-by-step explanation:
You would need to add 2 circles to keep it balanced.
?????????????????? find the value of x
Answer:
x = 17
Step-by-step explanation:
We can infer that the angles are equivalent based on the opposite angle theorem and we can set the equations equal to one another:
(8x-22)=(5x+29)
from here, we can subtract 5x from each side leaving us with:
3x-22=29
Now add 22 to both sides:
3x=51
Now divide both sides by 3, leaving us with the value of x:
x=17
If a point on the pre-image has coordinates (3, -4), and the coordinates of its image are (12, -16), what scale factor was used for the dilation?
A.4
B.1
C.4
D.1/4
Answer:
c 4i think soc 4 yu need to be add
Two sides of a triangle measure 25 meters and 13 meters. Which of the following measures could represent the perimeter of the triangle?
12meters
40meters
38meters
17meters
PLEASE HELP!!
Describe the relationship between expanding and factoring.
Answer:
To factor means to express as a product. To expand means to multiply something out.
Step-by-step explanation:
please answer my question for me pleaseeee
Solve the inequality 2m+10 < 40
Answer:
m < 15
Step-by-step explanation:
2m+10 < 40
Subtract 10 from each side
2m+10-10 < 40-10
2m < 30
Divide by 2
2m/2 = < 30/2
m < 15
Help me pls I need this to pass low key stuck
Answer:
m<F = 44°
length of FH = 15
length of GF = 21
Perimeter of ∆FGH = 50
Step-by-step explanation:
✔️Find m<F using the sum of triangle theorem:
The small box indicates angle 90°. Sum of a triangle is 180°. Therefore,
m<F = 180° - (90° + 46°)
m<F = 180° - 136°
m<F = 44°
✔️Find FH using trigonometric function:
Reference angle = 46°
Length of Opposite side = FH = ?
Length of Adjacent side = GH = 14
Apply TOA because we are concerned with the OPP and ADJ sides:
Tan 46° = Opp/Adj
Tan 46° = FH/14
14*Tan 46° = FH
14.4974243 = FH
FH = 15 (approximated to nearest whole number)
✔️Find GH by applying either a trigonometric function or just simply apply pythagorean theorem:
Pythagorean theorem is given as,
c² = a² + b²
c is the longest side (hypotenuse) = GF = ?
a = GH = 14
b = FH = 15
Thus:
GF² = 14² + 15²
GF² = 421
GF = √421
GF ≈ 21 (nearest while number)
✔️Perimeter of ∆FGH = GH + GF + FH
= 14 + 21 + 15
= 50
Given m||n, find the value of x.
+
>m
(5x+19)
(6x+1)°
Find each missing measure.
Answer:
m<A = 84
AC = 9
Step-by-step explanation:
We can find the measure of Angle A by using the sum of interior angles of a triangle theorem.
48+48+A=180
96+A=180
A=84
We can then use the isosceles triangle similarity theorem and reason that since this is an isosceles triangle and one of the side lengths (AB) is 9, the other (AC) would also be 9.
On a boat tour there are half as many children as there are adults. There are 30 people. How many children are there.
Answer:
10 children, 20 adults
Step-by-step explanation:
Children=1/2Adults
adults+children=30
adults + 1/2 adults=30
1 1/2 adults =30
adults = 20
children =1/2 adults
children = 1/2(20)
children=10
Question 38
Two cuboids are congruent. Which statement about their properties
a.Each face has the same area
b.One is larger than the other
c.They have the same volume
d.The sum of the angles is 360°
helppppppp meeeeeeee please
Answer:
33
Step-by-step explanation:
(3×3 )+(1/2 ×3×4) ×4 = 33
What of the following is NOT a formula for circumference?
a) C=2πr
b) C=πr
c) C=πd
Answer:
The formula for circumfernce is C=pixd D is diameter
Step-by-step explanation:
Find the equation of the line passing through the point (-6,4) that is perpendicular to the line 5x+3y=5
9514 1404 393
Answer:
3x -5y = -38
Step-by-step explanation:
The equation of the perpendicular line can be formed by swapping the coefficients of x and y in the given equation, negating one of them. The new constant will be the one that lets the given point satisfy the equation.
given: 5x +3y = 5
perpendicular: 3x -5y = constant
At the given point, the constant is ...
3(-6) -5(4) = -18 -20 = -38
So, the desired equation is ...
3x -5y = -38
Please help! I will give brainliest to the first correct answer!
Answer:
x=3 and y=1 so the answer is b
Step-by-step explanation:
hope it helped have a good day<3
Answer:
B
Step-by-step explanation:
image attached is the step by step "explanation
Joe can weed the garden twice as fast as his sister Janet. Together they can weed the garden in 2 hours. How long would it take each of them working alone?
A:[tex]\frac{1}{x}[/tex]
Answer:
Joe: 3 hrs
Janet: 6hrs
Step-by-step explanation:
joe takes x hours
so in 1 hr he does 1/x of the garden
janet takes 2x hours
so in 1 hr she does 1/(2x) of the garden
In one hour together they do 1/2 of the garden
1/x + 1/(2x) = 1/2
2/(2x) + 1/(2x) = 1/2
3/(2x) = 1/2
Cross multiply
6 = 2x
x = 3
Joe: 3 hrs
Janet: 6hrs
How. Many 5s is in 200989
Answer:
40197 these many 5s make up 200985 so 4 are left to make 200989
Step-by-step explanation:
Answer:
40197.8
Step-by-step explanation:
200989 ÷ 5
40197.8
Now, you do the math: Tell us if you can afford the apartment using the details below.
Your gross paycheck is $2100 per month.
You're looking at a very small one-bedroom apartment that rents for only $650 per month.
The electric bill runs about $60 per month for power.
You'll pay about $10 per month for gas.
An Internet line will cost you $20 per month.
You have to rent a parking space for your old buggy at $20 per month.
Can you afford to get this apartment?
Yes.
No.
If no, how much can you afford to pay in rent plus housing expenses?
Answer:
I think yes because u will have 760 leftover
please help. i don’t know what to dooooooooooo
Answer:
x = 48 degrees
Step-by-step explanation:
(2x + 2) + (x + 34) = 180
3x + 36 = 180
3x = 180 - 36
3x = 144
x = 144 / 3
x = 48 degrees
I hope this helps :)
Answer:
B. x = 48
Step-by-step explanation:
(x + 34)+(2x + 2) = 180°. Angles on a straight line
x+2x = 180 - (34+2)
3x = 180 - 36
3x ÷3 = 144 ÷3
x = 48°
You invest $8,000 in an account that earns 4% compounded monthly. How much money are you going to have in 5 years?
5-ſ
To rationalize the denominator of
9-14 · you should multiply the expression by which fraction?
5+√7
9-14
9- V14
9-√14
9+ 14
9+ V14
14
14
We should multiply the expression by (9+√14) fraction.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
To rationalize the terms, we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 9-√14 and its conjugate is; (9+√14).
(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)
= (5-√7)(9+√14)/(9²-14)
= (45 + 5√14 - 9√7 - √98)/(81-14)
= (45 + 5√14 - 9√7 - √98)/67
= (45 + 5√14 - 9√7 - 7√2)67
This is the rationalized expression.
The denominator is (9-√14) and its conjugate is (9+√14).
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ7
Answer each question and round your answer to the nearest whole number
Answer:
New width = 12 in.
Step-by-step explanation:
Original height = 2 in.
Original width = 3 in.
New height = 8 in.
New width = x = ?
The shape of the original painting and the shape of the new painting are similar, therefore, the ratio of their corresponding linear measurement will be equal.
Thus:
New height/original height = new width/original width
8/2 = x/3
Cross multiply
2x = 3*8
2x = 24
2x/2 = 24/2
x = 12
New width = 12 in.
PLEASE ANSWER QUICKLY
An isosceles triangle has an angle that measures 40°. Which other angles could be in that isosceles triangle? Choose all that apply. 70, 100,80,40
Given:
An isosceles triangle has an angle that measures 40°.
To find:
The other possible angles of the triangle.
Solution:
Case 1: 40° is the measure of base angle of isosceles triangle.
Then, the other base angle is 40°.
Let x be the measure of third angle.
The sum of all interior angles of a triangle is 180 degrees. So,
[tex]x+40^\circ+40^\circ=180^\circ[/tex]
[tex]x=180^\circ-40^\circ-40^\circ[/tex]
[tex]x=100^\circ[/tex]
So, the possible angles are 40° and 100°.
Case 2: 40° is the measure of vertical angle of isosceles triangle.
Let y be the measure of base angles, then
[tex]y+y+40^\circ=180^\circ[/tex]
[tex]2y=180^\circ -40^\circ[/tex]
[tex]y=\dfrac{140^\circ}{2}[/tex]
[tex]y=70^\circ [/tex]
So, the possible angles are 40° and 70°.
Therefore, the correct options are A, B and D.
Sam, Raj and Jade have 12 sweets each. One quarter of Sam's sweets are blue. How many blue sweets does he have?
Step-by-step explanation:
Sam, Raj and Jade have 12 sweets each
(one person has 12 sweets)
Sam has 12 sweets
one quarter of Sam sweet is blue
1/4 = one quarter
1/4 * 12 = 3
Sam has 3 blue sweets.
Answer:
sam has 3 blue sweets
Step-by-step explanation:
[tex]\frac{1}{4} of 12 = 3[/tex]
if sam has 12 sweets and one quarter are blue then we need to work out one quarter of the twelve sweets. you need to do [tex]\frac{1}{4} of 12[/tex] which is 3 and [tex]\frac{1}{4} of 12[/tex] is the same as [tex]\frac{1}{4} times 12[/tex]
Please help me thanks :)
Answer:
A
Step-by-step explanation:
To sovle this we must combine the numbers togther and the variables togther.
We have:
8c+6-3c-2
Lets take out the c's and combine them:
8c -3c
=
5c
Now lets take out the numbers:
6-2
=
4
Now lets put these back together and we get the expression:
5c+4
This looks like A.
Hope this helps! :D
The table below shows three special sequences (A to C) of numbers.
A 1; 4; 9; 16; 25; 36 ...
B 1:8; 27; 64; 125; 216...
C 1:3; 6; 10; 15; 21; ...
3.1 Write down the next THREE terms of the respective patterns.
3.2.
Identify the pattem (sequence of numbers) represented by each letter.
3.3
Determine the formula for the general term of each sequence.
3.4
Determine the 100 term of each respective pattern.
Answer:
3.1 A) 49; 64; and 81
B) 343; 512; and 729
C) 28; 36; and 45
3.2 A) 1²; 2²; 3²...
B) 1³; 2³; 3³...
C) 1; 1+2; 1+2+3; ...
3.3 A) aₙ = n²
B) aₙ = n³
C) aₙ = n·(n + 1)/2
3.4 A) 10,000
B) 1,000,000
C) 5,050
Step-by-step explanation:
The given sequences are;
A 1; 4; 9; 16; 25; 36...
B 1; 8; 27; 64; 125; 216...
C 1; 3; 6; 10; 15; 21;...
3.1 A) The terms, aₙ, of sequence 'A' are given as follows;
aₙ = n², where, n = 1, 2, 3,...
The next three terms of sequence 'A' are therefore;
a₇ = 7³ = 49, a₈ = 8² = 64, and a₉ = 9² = 81
The next three terms of sequence 'A' are ; 49; 64; and 81
B) The terms, aₙ, of sequence 'B' are given as follows;
aₙ = n³, where, n = 1, 2, 3,...
The next three terms of sequence 'B' are therefore;
a₇ = 7³ = 343, a₈ = 8³ = 512, and a₉ = 9³ = 729
The next three terms of sequence 'B' are; 343; 512; and 729
C) The terms, aₙ, of sequence 'C' are given as follows;
aₙ = n·(n + 1)/2, where, n = 1, 2, 3,...
The next three terms of sequence 'A' are therefore;
a₇ = 7×(7 + 1)/2 = 28, a₈ = 8×(8 + 1)/2 = 36, and a₉ = 36 + 9×(9 + 1)/2 = 45
The next three terms of sequence 'A' are ; 28; 36; and 45
3.2 A) The pattern of the numbers in sequence 'A', consists of squaring (raising to the power of 2) each number in the sequence of natural numbers
B) The pattern of the numbers in sequence 'B', consists of raising to the power of 3 each number in the sequence of natural numbers
C) The pattern is the triangular number sequence and consists of finding half the number dots that are present in a n by (n + 1) rectangle, which is given by finding the sum of the natural numbers up to the given term in the sequence
3.3 A) The formula for the general term of sequence, A, is aₙ = n²
B) The formula for the general term of sequence, B, is aₙ = n³
C) The formula for the general term of sequence, C, is aₙ = n·(n + 1)/2
3.4 A) The 100th term of sequence 'A', a₁₀₀ = 100² = 10,000
B) The 100th term of sequence 'B', a₁₀₀ = 100³ = 1,000,000
C) The 100th term of sequence 'C', a₁₀₀ = 100 × (100 + 1)/2 = 5,050.