Answer:
In this problem and with any rational number, the zero product property will be applied. If ab = 0, then either a = 0 or b = 0, or both. A product of factors is zero if and only if one or more of the factors is zero.
And excuse me, but where's the other 75 points?
Which of these sets could represent the side lengths of a right triangle?
Group of answer choices
{4, 8, 12}
{6, 8, 10}
{6, 8, 15}
{5, 7, 13}
Answer:
{6, 8, 10} is a set which represents the side length of a right triangle.
Step-by-step explanation:
In a right triangle:
[tex](Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}[/tex]
Now, in the given triplets:
(a) {4, 8, 12}
Here, [tex](4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94[/tex]
So, third side of the triangle 8.94 ≠ 12
Hence, {4, 8, 12} is NOT a triplet.
(b) {6, 8, 10}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10
Hence, {6, 8, 10} is a triplet.
(c) {6, 8, 15}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10 ≠ 15
Hence, {6, 8, 15} is NOT a triplet.
(d) {5, 7, 13}
Here, [tex](5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60[/tex]
So, third side of the triangle 8.60 ≠ 13
Hence, {5, 7, 13} is NOT a triplet.
the sum of two numbers is 126 and their difference is 42. what are two numbers
Answer:
84, 42Step-by-step explanation:
[tex]x,\ y-numbers\\\\\text{The system of equations:}\\\\\underline{+\left\{\begin{array}{ccc}x+y=126\\x-y=42\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=168\qquad\text{divide both sides by 2}\\.\qquad x=84\\\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\84+y=126\qquad\text{subtract 84 from both sides}\\y=42[/tex]
Final answer:
The two numbers that have a sum of 126 and a difference of 42 are 84 and 42.
Explanation:
To find the two numbers whose sum is 126 and whose difference is 42, we can set up a system of equations:
x + y = 126 (Sum of the numbers)
x - y = 42 (Difference of the numbers)
By adding these two equations, we can eliminate y and solve for x:
x + y + x - y = 126 + 42
2x = 168
x = 84
Now that we have the value of x, we can find y by substituting x back into either of the equations. For example:
84 + y = 126
y = 126 - 84
y = 42
Therefore, the two numbers are 84 and 42.
I NEED HELLPPPP!!!!!!
Find (3 × 104) − (5 × 102).
A) 2.905 × 102
B) 2.905 × 104
C) 2.95 × 102
D) 2.95 × 104
Answer:
-198
Step-by-step explanation:
you will deal with the ones in the bracket first
that is [3×104]=312
[5×102]=510
312-510=-198
according to me there is no answer in your option my answer is negative198
A basketball team sells tickets that cost $10, $20 or for VIP seats $30. The team has sold 3239 tickets overall. It has sold 282 more $20 tickets than $10 tickets. The total sales are $63,720. How many tickets of each kind have been sold?
Answer:
The number of tickets that cost $ 10 is 923
The number of tickets that cost $ 20 is 1205
The number of tickets that cost $ 30 is 1111
Step-by-step explanation:
Given as :
The total number of three different tickets cost $ 10 , $ 20 and VIP seats $ 30
The total number of all tickets sold = 3239
The sale price for the tickets = $ 63720
Let The type of ticket for $ 10 = x
And The type of ticket for $ 20 = y
And The type of VIP ticket = v
According to question
The number of $ 20 tickets = The number of $ 10 tickets + 282
I.e y = x + 282
And x + y + v = 3239
Or, v = 3239 - ( x + y )
I.e v = 3239 - ( x + x +282 )
Or, v = 2957 - 2 x
Now ,
x × $ 10 + y × $ 20 = v × $ 30
Or, x × $ 10 + ( x + 282 ) × $ 20 = ( 2957 - 2 x ) × $ 30
or, 10 x + 20 x + 5640 = 88710 - 60 x
Or, 30 x + 60 x = 88710 - 5640
or, 90 x = 83070
∴ x = [tex]\frac{83070}{90}[/tex]
I.e x = 923
So, The number of tickets that cost $ 10 = x = 923
Similarly
y = x + 282
or, y = 923 + 282
I.e y = 1205
So, The number of tickets that cost $ 10 = y = 1205
And
v = 2957 - 2 x
∴ v = 2957 - 2 × 923
I.e v = 1111
So, The number of tickets that cost $ 30 = v = 1111
Hence
The number of tickets that cost $ 10 is 923
The number of tickets that cost $ 20 is 1205
The number of tickets that cost $ 30 is 1111
Answer
Answer:
1021 of the $10 tickets, 1303 of the $20 tickets and 915 of the $30 tickets.
Step-by-step explanation:
We have 3 types of tickets:
ones that cost $10, others that cost $20 and others that cost $30.
If A is the number of $10 tickets sold, B is the number of $20 tickets sold and C is the number of $30 tickets sold we have that:
A + B + C = 3239
B = A + 282
A*10 + B*20 + C*30 = 63720
We need to solve this system of equations.
From the second equation we have B isolated, we can replace it in the other equations:
A + (A + 282) + C = 3239
A*10 + (A + 282)*20 + C*30 = 63720
Now we can isolate one of the variables in the first equation and replace it in the second, lets isolate C.
C = 3239 - 2*A - 282 = 2957 - 2*A
the third equation is now:
A*10 + (A + 286)*20 + (2957 - 2*A)*30 = 63720
Now we solve it for A:
A*10 + A*20 - A*60 + 282*20 + 2957*30 = 63720
-A*30 + 94350 = 63720
A*30 = - 63720 + 94350 = 30630
A = 30639/30 = 1021
So they sold 1021 tickets of $10.
Now we can replace it in the equation:
C = 2957 - 2*A = 2957 - 2*1021 = 915
They sold 915 $30 tickets
They sold 1303 tickets of $20.
B = A + 282 = 1021 + 282 = 1303.
It took Nora 10 hours to walk a 30 mile trail. How long did it take her to walk 9 miles at the same speed
Answer: 3 hours
Step-by-step explanation: 30 miles/10 hours=3 miles per hour. 9 miles/3 miles per hour= 3 hours.
Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.
Carter's song played on 7 commercials and 5 movies.
Step-by-step explanation:
Earning per commercial = $50
Earning per movie = $130
Total earned = $1000
Total commercial and movies = 12
Let,
x be the number of commercials
y be the number of movies
According to given statement;
x+y=12 Eqn 1
50x+130y=1000 Eqn 2
From Eqn 1
x=12-y Eqn 3
Putting value of x from Eqn 3 in Eqn 2
[tex]50(12-y)+130y=1000\\600-50y+130y=1000\\80y=1000-600\\80y=400[/tex]
Dividing both sides by 80
[tex]\frac{80y}{80}=\frac{400}{80}\\y=5[/tex]
Putting y=5 in Eqn 1
[tex]x+5=12\\x=12-5\\x=7[/tex]
Carter's song played on 7 commercials and 5 movies.
Keywords: linear equation, substitution method
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Carter had his songs played in 7 commercials and 5 movies to earn $1000 in royalties. This was determined by solving a system of linear equations.
Carter is dealing with a system of linear equations situation where he collects different amounts of royalties based on whether his music is played in commercials or movies. We can represent the number of commercials as c and the number of movies as m. Since he earns $50 per commercial, we can write the first equation as 50c, and since he earns $130 per movie, we can write the second equation as 130m. Carter earned a total of $1000 from 12 commercials and movies, which gives us two equations:
50c + 130m = 1000
c + m = 12
By solving this system of equations, we can determine the number of commercials and movies. Multiplying the second equation by 50 gives us 50c + 50m = 600, which we can subtract from the first equation to eliminate c and solve for m. Doing so, we get:
50c + 130m = 1000
-(50c + 50m = 600)
After subtracting, we are left with 80m = 400, from which we can solve for m to find that m = 5. Using the second original equation, we can now find out that c = 7.
So, Carter had his songs played in 7 commercials and 5 movies to earn a total of $1000 in royalties.
The surface area of this rectangular prism is __ square centimeters.
Answer:
216 sq. cm.
Step-by-step explanation:
If we fold the paper of the given dimensions then we will get a rectangular prism with dimension 10 cm by 6 cm by 3 cm.
Now, a rectangular prism has the total surface area given by
A = 2(LW + WH + HL)
where, L = length = 10 cm.
W = width = 6 cm. and
H = height = 3 cm.
Therefore, total surface area = A = 2(10 × 6 + 6 × 3 + 3 × 10) = 216 sq. cm. (Answer)
Answer:
216 sq. cm.
Step-by-step explanation:
The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y.
y = StartFraction 3 x 10 Superscript 8 Baseline Over x EndFraction
What are the wavelengths for X-rays with frequency 3 × 1018?
1 × 10–10 m
3 × 10–10 m
3 × 1026 m
9 × 1026 m
Answer: The wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]
Step-by-step explanation:
To calculate the wavelength of light, we use the equation:
[tex]\lambda=\frac{c}{\nu}[/tex]
where,
[tex]\lambda[/tex] = wavelength of the light
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\nu[/tex] = frequency of light = [tex]3\times 10^{18}s^{-1}[/tex]
Putting the values in above equation, we get:
[tex]\lambda=\frac{3\times 10^8m/s}{3\times 10^{19}s^{-1}}=1\times 10^{-10}m[/tex]
Hence, the wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]
Answer:
1 x 10 ^-10 m
Step-by-step explanation:
LOTS OF POINTS
The lengths of the sides of a triangle are in the extended ratio 8 : 9 : 10. The perimeter of the triangle is 81 cm. What are the lengths of the sides?
The lengths of the sides are 24cm, 27cm and 30cm.
Step-by-step explanation:
The ratio of lengths is 8:9:10
Perimeter = 81 cm
Let x be the length of side.
Therefore,
The length of sides is 8x, 9x and 10x.
Perimeter is the sum of 3 sides, therefore,
[tex]8x+9x+10x=81\\27x=81[/tex]
Dividing both sides by 27;
[tex]\frac{27x}{27}=\frac{81}{27}\\x=3[/tex]
Therefore, the lengths of sides are [tex]8(3), 9(3)\ and\ 10(3)[/tex]
The lengths of the sides are 24cm, 27cm and 30cm.
Keywords: triangles, perimeter
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The lengths of the sides of the triangle are 24 cm, 27 cm, and 30 cm.
Explanation:To find the lengths of the sides of the triangle, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter. Let's assume the common ratio between the sides is 'x'. So, the lengths of the sides can be written as 8x, 9x, and 10x. According to the problem, the perimeter of the triangle is 81 cm.
Therefore, 8x + 9x + 10x = 81.
Combining like terms, we get 27x = 81.
Dividing both sides by 27, we find that x = 3.
Substituting this value back into the lengths of the sides, we find that the lengths are 8x = 8(3) = 24 cm, 9x = 9(3) = 27 cm, and 10x = 10(3) = 30 cm.
what is the radical form?
Answer:
B
Step-by-step explanation:
Using the rules of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]t^{-\frac{2}{7} }[/tex]
= [tex]\frac{1}{t^{\frac{2}{7} } }[/tex]
= [tex]\frac{1}{\sqrt[7]{t^{2} } }[/tex]
HELP PLEASEEEEeeeeeeeeeeww
Answer: 5/10 (5 tenths)
Step-by-step explanation:
Since the value of 5 in 124.519 is 5 tenths, it can therefore be expressed as 5/10 in fraction form.
Answer:
1/2
Step-by-step explanation:
Since 5 is in the tenths place it can be written as
5/10
1/2(in simplified form)
what is the distance between -3 and 2 on the number line?
Answer:
5
Step-by-step explanation:
You move 3 places to the right to get to zero. And two places to the right to get to 2. 3 plus 2 is 5.
Answer:
5Step-by-step explanation:
The formula of a distance between two points A and B:
d = |B - A|
We have A = -3 and B = 2.
Substitute:
d = |2 - (-3)| = |2 + 3| = |5| = 5
Jacinta buys 4 pounds of turkey and 2 pounds of
ham. She pays a total of $30, and the turkey costs
$1.50 less per pound than the ham. What would
be the combined cost of 1 pound of turkey and 1
pound of ham?$6
The combined cost for 1 pound of turkey and 1 pound of ham is $10.5
Step-by-step explanation:
Let,
Turkey = x
Ham = y
According to given statement;
4x+2y=30 Eqn 1
x = y-1.50 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]4(y-1.50)+2y=30\\4y-6+2y=30\\6y=30+6\\6y=36[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{36}{6}\\y=6[/tex]
Putting y=6 in Eqn 2
[tex]x=6-1.50\\x=4.5[/tex]
1 turkey costs $4.5 and 1 ham costs $6.
Combined cost of 1 pound of turkey and ham each = 4.5+6=$10.5
The combined cost for 1 pound of turkey and 1 pound of ham is $10.5
Keywords: linear equations, subtraction
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Ashby ate a lot for thanksgiving dinner.he decided to go on a long run. He ran 6 miles in 57 minutes.how long did it take him to run one mile?
Answer: 9.5
Step-by-step explanation: 57 divided by 6 is 9.5
Tj had 20 baseballs pitched to him he hit the ball 17 times what percentage of balls pitched did Tj hit?
Tj hit 85% of the balls pitched to him.
Step-by-step explanation:
Baseballs pitched to Tj = 20
Baseballs hit by Tj = 17
Percentage = [tex]\frac{baseballs\ hit\ by\ Tj}{baseballs\ pitched\ to\ Tj}*100\\[/tex]
Percentage= [tex]\frac{17}{20}*100[/tex]
Percentage=[tex]\frac{1700}{20} = 85\%\\[/tex]
Tj hit 85% of the balls pitched to him.
Keywords: percentage, division
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Plz Help Me!
cross multiplying write the proportion:
2/310,5/c
m/3,32/4
Answer:
Step-by-step explanation:
2/310=5/c
simplify 2/310 into 1/155
1/155=5/c
cross product
155*5=1*c
775=c
c=775
---------------------------------
m/3=32/4
simplify 32/4 into 8,
m/3=8,
m=8*3=24
m=24
How much dollars is 100,000 nickels
Answer:
$5000
Step-by-step explanation:
A nickel is worth 5 cents, or 0.05 dollars.
Multiply the number of nickels by the worth of a nickel in dollars.
100,000 * $0.05
= $5000
Therefore, 100,000 nickels is worth $5000.
Answer:
THE ANSWER IS $5000
Step-by-step explanation:
A NICKLE IS WORTH 5 CENTS, OR $0.05. SO YOU MULTIPLY THE 100,000 BY THE WORTH OF NICKLES IN A DOLLAR. SO YOU DO 100,000 X 0.05= $5000. SO 100,000 NICKLES IS WORTH $5000.
The ratio of incomes of two persons is 9:7. The difference in their weekly incomes is $200. What are their weekly incomes?
What’s the answer
Answer:
The weekly savings of first person = $900
The weekly savings of second person = $700.
Step-by-step explanation:
Let us assume the income of first person = $ m
Now, as the difference in the income is $200.
⇒ And the income of first person - income of first person = $200
⇒ Income of second person = m - $200
So, according to the question:
Ratio of Income of First person : Second Person's Income = 9: 7
or, m : ( m - 200) = 9: 7
[tex]\implies \frac{m}{m - 200 } = \frac{9}{7}[/tex]
[tex]7 \times m = (m - 200) \times 9\\\implies 7 m = 9m - 1800\\\implies 7m - 9m = -1800\\\implies -2m = -1800\\m = \frac{1800}{2} = 900[/tex]
or,m = $900
Hence, the weekly savings of first person = $900
and the weekly savings of second person = m - 200 = $900 - 200 = $700.
Final answer:
To find the weekly incomes of two persons with a ratio of 9:7 and a difference of $200, represent their incomes as 9x and 7x. Solving for x, we get $100, so their incomes are $900 and $700 respectively.
Explanation:
The question asks us to solve for the weekly incomes of two persons given that the ratio of their incomes is 9:7 and the difference between their incomes is $200.
Let's represent the incomes of the two persons as 9x and 7x respectively, where x is a common multiplier. According to the information provided,
9x - 7x = $200
Solving for x:
(9x - 7x) = 2x
2x = $200
x = $200 / 2
x = $100
Now calculating each person's income:
Person A: 9x = 9 * $100 = $900
Person B: 7x = 7 * $100 = $700
Therefore, the weekly incomes of the two persons are $900 and $700 respectively.
If 4x=18, what is the value of 4(X-2)?
Answer:16
Step-by-step explanation:
If 4x=18 then 4x-2=16
What is the value of the expression below? (27^5/3) ^1/5
Answer:
The correct answer is 3.
Step-by-step explanation:
1. Let's resolve the expression below:
(27^5/3) ^1/5
( ∛ 27 ⁵ ) ^ 1/5 ⇒ ∛ 27 ⁵ = 27^5/3
( ∛ 3³ ⁵ ) ^ 1/5 ⇒ ∛ 3³ ⁵ = ∛ 27 ⁵
( 3 ⁵) ^ 1/5
⁵√ 3 ⁵ ⇒ ( 3 ⁵) ^ 1/5 = ⁵√ 3 ⁵
3
After making all the calculations and applying all the exponent rules, the final result is 3.
Answer:
B. 3
Step-by-step explanation:
Quiz 1
52 - 2y = 30
Complete the missing value in the solution to the equation
RHEILULIITTO
MONROE
TITANIU
What is the perimeter of the figure?
A, 68 1/2 yd
B. 68 5/14 yd
C. 67 1/2 yd
D. 67 5/14 yd
Triangle ABC has side lengths: V6, V2, and 2/2 units.
The measures of the angles of the triangle are
If the base of the triangle has a length of 16 then the measure of the base angle is
Answer:
90°, 60°, and 30°
60°.
Step-by-step explanation:
The triangle ABC has side lengths √6, √2, and 2√2 units.
It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.
Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is [tex]\theta[/tex], then
[tex]\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} } = \frac{1}{2}[/tex]
Hence, [tex]\theta[/tex] = 60°
Therefore, the three angles of the triangle are 90°, 60°, and 30°.
Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.
And in that case the base angle will remain 60°. (Answer)
[20 pts] evaluate the logarithm log(6)1/36, show work pls!
Answer:
[tex]\large\boxed{\log_6\dfrac{1}{36}=-2}[/tex]
Step-by-step explanation:
[tex]\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2[/tex]
[tex]\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}[/tex]
The solution of logarithmic function is, - 2
We have to given that,
Logarithmic function is,
⇒ log ₆ (1/36)
Now, We can apply the logarithmic rule to solve as,
⇒ log ₆ (1/36)
⇒ log ₆ (36)⁻¹
⇒ log ₆ (6)⁻²
⇒ - 2 log ₆ (6)
⇒ - 2 × 1
⇒ - 2
Therefore, The solution of logarithmic function is, - 2
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What is the 2010th letter in the following sequence: ABCDEDCBA.
Please answer ASAP. This is due tomorrow.
Answer:
B
Step-by-step explanation:
The sequence is ABCDEDCBABCDEDCBABCDEDCBA....
⇒The main sequence is the repitition of the sub-sequence ABCDEDCB
2010 when divided by 8 gives a quotient of 251 and a remainder of 2
251×8 = 2008
This means that after the sub-sequence ABCDEDCB is repeated for 251 times, it's last letter B is the [tex]2008^{th}[/tex] letter of the main sequence
Even after that, the sub-sequence ABCDEDCB keeps repeating and the [tex]2010^{th}[/tex] letter in the main sequence is the [tex]2^{nd}[/tex] letter of the sub-sequence ABCDEDCB, that is "B"
Final answer:
To find the 2010th letter in the repeating sequence ABCDEDCBA, divide 2010 by 9 and use the remainder to identify the letter's position in the pattern. The 2010th letter is C.
Explanation:
The sequence ABCDEDCBA consists of 9 letters. To find the 2010th letter in this pattern, we need to divide 2010 by the number of letters in the sequence. Dividing 2010 by 9 gives us 223 with a remainder of 7. This tells us that the 2010th letter is the same as the 7th letter of the sequence, because after every full repetition of 9 letters, the pattern starts over.
Let's map out the sequence: A(1), B(2), C(3), D(4), E(5), D(6), C(7), B(8), A(9). Using this mapping, the 7th letter corresponds to the letter C.
The 2010th letter in the sequence ABCDEDCBA is C.
The area of a rectangle is 99 ft^2, and the length of the rectangle is 7 more than double the width. Find the dimensions of the rectangle.
Answer:
width =5.5ft
length =18
Step-by-step explanation:
w=x
L=2x+7
area=w*L
99 = x(2x+7)
[tex]99=2x^{2} +7x[/tex]
[tex]2x^{2} +7x-99=0[/tex]
[tex]2x^{2} +18x-11x-99=0[/tex]
2x(x+9)-11(x+9)=0
(2x-11)(x+9)=0
2x-11=0
2x=11
x=11/2
x=5.5
L=2x+7=2*5.5+7=11+7=18
Simplify using the distributive property:
2a + 4(a+5) - 7
Answer:
6a + 13
Step-by-step explanation:
Given
2a + 4(a + 5) - 7 ← distribute parenthesis
= 2a + 4a + 20 - 7 ← collect like terms
= 6a + 13
Answer: 6a + 13
Step-by-step explanation: here you go: 2a + 4*(a+5) - 7
first we simplify the brackets (distributive property, you multiply 4 "a" times plus 5 times): 2a + 4a + 20 - 7
then you add those that multiply the variable separately from those that don't: 6a + 13
Ben starts commision as a real estate agent last month his total sales for all the houses he sold $950,000.If ben earns a 3% rate of commision what was his gross income kast month
Ben's gross income was $28,500.
Step-by-step explanation:
Sales for the month = $950000
Commission rate = 3%
Amount of commission = 3% of sales for the month
Amount of commission = [tex]\frac{3}{100}*950000[/tex]
Amount of commission = [tex]\frac{2850000}{100}[/tex]
Amount of commission = $28500
Ben's gross income was $28,500.
Keywords: percentage, division
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Calculate the unknown angles
Answer:
see explanation
Step-by-step explanation:
Since the 2 lines are parallel, then
d = 55° ( corresponding angles are congruent )
e = 55° (vertical to d and congruent )
e and f are same side interior angles and are supplementary, thus
e + f = 180°, that is
55° + f = 180° ( subtract 55° from both sides )
f = 125°
c = 125° ( alternate to f and congruent )
Hence
c = 125°, d = 55°, e = 55°, f = 125°
Please help!!
Write an exponential function (in terms of x) to model the following situation.
A population of 110,000 grows 5% per year for 16 years.
How much will the popluation be after 16 years?
Answer:
The population will be 240,116
Step-by-step explanation:
Exponential growth can be represented by the expression:
[tex]P(t) = P_i\,(1+r)^t[/tex]
where:
[tex]P(t)[/tex] is the population at time (t)
[tex]P_i[/tex] is the initial value of the population
"r" is the annual rate of growth (written in decimal form)
and "t" is the time in years.
Therefore in this situation, P(16) is what we want to find [the population after 16 years]
the initial population [tex]P_i[/tex] is 110,000
the rate of growth is 0.05 [decimal form of 5%]
and t is 16 years.
Replacing all these in the given functional form gives:
[tex]P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116[/tex]
An exponential function to model a population of 110,000 that grows at 5% per year for 16 years is P(t) = 110,000 ∙ (1.05)^t. After 16 years, using this exponential function, the population would be approximately 242,884.
Explanation:To model the population growth using an exponential function, we can use the formula P(t) = P0 ∙ (1 + r)t, where P(t) is the population after t years, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population P0 is 110,000, the growth rate r is 5% (or 0.05), and the time t is 16 years.
The exponential growth function would be:
P(16) = 110,000 ∙ (1 + 0.05)16
To find the projected population after 16 years, we'll calculate:
P(16) = 110,000 ∙ (1.05)16
P(16) = 110,000 ∙ 2.20804
P(16) = 242,884.4
After rounding, the population would be approximately 242,884 after 16 years.