Answer:
After a Week(7 days)
[tex]Purse \:A: \$2200\\Purse B: \$0.64[/tex]
After 2 Weeks(14 days)
[tex]Purse \:A: \$3600\\Purse B: \$81.92[/tex]
After 3 Weeks(21 days)
[tex]Purse \:A: \$5000\\Purse B: \$10485.76[/tex]
After 30 days
[tex]Purse \:A: \$6800\\Purse B: \$5368709.12[/tex]
Therefore, Purse B contains more money after 30 days.
Step-by-step explanation:
Purse A
The amount of money($1000) in purse A for each consecutive day grows with $200. The sequence is written as:
1000,1200,1400,...
This is an arithmetic sequence with the first term being $1000 and the common difference $200.
Therefore, for any number of day, n, the amount of money in the purse,
[tex]T_n=1000+200(n-1)[/tex]
Purse B
1 Penny=$0.01
The amount of money(1 Penny) in purse B for each consecutive day doubles. The sequence is written as:
0.01,0.02,0.04,...
This is a geometric sequence with the first term being $0.01 and the common ratio 2.
Therefore, for any number of day, n, the amount of money in purse B,
[tex]T_n=0.01(2)^{n-1}[/tex]
After a Week(7 days)
[tex]Purse \:A: T_7=1000+200(7-1)=\$2200\\Purse B: T_7=0.01(2)^{7-1}=\$0.64[/tex]
After 2 Weeks(14 days)
[tex]Purse \:A: T_{14}=1000+200(14-1)=\$3600\\Purse B: T_{14}=0.01(2)^{14-1}=\$81.92[/tex]
After 3 Weeks(21 days)
[tex]Purse \:A: T_{21}=1000+200(21-1)=\$5000\\Purse B: T_{21}=0.01(2)^{21-1}=\$10485.76[/tex]
After 30 days
[tex]Purse \:A: T_{30}=1000+200(30-1)=\$6800\\Purse B: T_{30}=0.01(2)^{30-1}=\$5368709.12[/tex]
Final answer:
After calculating daily increases for Purses A and B over several time frames, it's evident that Purse B, which doubles its amount every day, holds a vastly greater sum after 30 days, illustrating the power of compound interest.
Explanation:
Calculating Growth in Purses A and B
Let's start by determining the amount in each purse after one week (7 days) and after two weeks (14 days). Purse A gains $200 more each day, starting with $1,000 on day 1. Purse B's amount doubles every day, beginning with 1 penny on day 1.
For Purse A, we can calculate the total after one week as:
$1,000 + (6 days × $200/day) = $1,000 + $1,200 = $2,200
After two weeks (14 days):
$1,000 + (13 days × $200/day) = $1,000 + $2,600 = $3,600
For Purse B, since the amount doubles each day, we use the power of 2 to represent the growth:
After one week (7 days):
1 penny × [tex]2^6[/tex] = 64 pennies (because we don't count the first day)
After two weeks (14 days):
1 penny × [tex]2^13[/tex]= 8,192 pennies, or $81.92
After three weeks (21 days) for Purse A we get:
$1,000 + (20 days × $200/day) = $1,000 + $4,000 = $5,000
And for Purse B:
1 penny × [tex]2^{20}[/tex] = 1,048,576 pennies, or $10,485.76
Now, let's see which purse contains more money after 30 days:
Purse A: $1,000 + (29 days × $200/day) = $1,000 + $5,800 = $6,800
Purse B: [tex]1 penny \times 2^{29} = 536,870,912 \ pennies \, \ or\ \$\ 5,368,709.12[/tex]
After 30 days, Purse B contains significantly more money due to the power of compound interest.
Scott is making a snack mix using almonds and raisins. For every 2 cups of almonds in the snack mix, there are 3 cups of raisins. Ariel is making a snack mix that has 3 cups of almonds for every 5 cups of sunflower seeds. If Scott and Ariel each use 6 cups of almonds to make a batch of snack mix, who will make a larger batch?
Answer:
Ariel will make a bigger batch.
Step-by-step explanation:
Scott- Every 2 cups Almonds = 3 cups raisins
so 6 cups almonds = 9 cups raisins
6+9= 15
Scott's batch- 15 cups
Ariel- Every 3 cups Almonds = 5 cups sunflower seeds
so 6 cups almonds = 10 cups sunflower seeds
6+10= 16
Ariel's batch- 16 cups
16 > 15 so Ariel's is bigger.
Ariel makes the larger batch of snack mix
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Equation for Scott :
Number of cups of Almonds = 2 cups
Number of cups of Raisins for 2 cups of almonds = 3 cups
Number of cups of almonds = 6 cups
Number of cups of raisins for 6 cups of almonds = 3 x 3
= 9 cups
So , total number of cups by Scott =
Number of cups of almonds + Number of cups of raisins for 6 cups of almonds
Total number of cups by Scott = 6 + 9 cups
The batch of snack mix by Scott has 15 cups
Equation for Ariel :
Number of cups of Almonds = 3 cups
Number of cups of sunflower seeds for 3 cups of almonds = 5 cups
Number of cups of almonds = 6 cups
Number of cups of raisins for 6 cups of almonds = 5 x 2
= 10 cups
So , total number of cups by Ariel =
Number of cups of almonds + Number of cups of sunflower seeds for 6 cups of almonds
Total number of cups by Ariel = 6 + 10 cups
The batch of snack mix by Ariel has 16 cups
Therefore , the batch mix of snack by Ariel is more than the batch mix of snack by Scott
Hence , Ariel makes the larger batch
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What is 2+2
I need help right nowwwwww
Answer:
4
Step-by-step explanation:
Answer:
21
(4)
Step-by-step explanation:
Incredibly, Enzo wins 555 tickets from every game, and Beatriz wins 111111 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. What is the minimum number of games that Enzo could have played
Answer:
55 games.
Step-by-step explanation:
We have been given that Enzo wins 5 tickets from every game, and Beatriz wins 11 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. We are asked to find the minimum number of games that Enzo could have played.
To solve our given problem, we need to find least common multiple of 1 and 55.
We know that least common multiple of two numbers is smallest umber, which is divisible by both numbers.
We know that 5 and 11 are prime numbers, so there LCM would be product of both numbers.
[tex]5\times 11=55[/tex]
Therefore, Enzo could have played 55 games at least.
Which is closest to the value of w in the triangle below?
Answer: B. 2.5 in
Step-by-step explanation:
From the given right angle triangle,
the hypotenuse of the right angle triangle is the unknown side.
With m∠32 as the reference angle,
the adjacent side of the right angle triangle is 4 in
the opposite side of the right angle triangle is w
To determine w, we would apply
the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan 32 = w/4
w = 4tan32 = 4 × 0.625
w = 2.5 in
Solve for p.
16 – 3p = 2/3p+5
Answer:
p=3
Step-by-step explanation:
16-3p=2/3p+5
16=3 2/3p+5
11=3 2/3p
3=p
Answer:
p = -33/7
Step-by-step explanation:
We first re-organize the equation.
3p - 2/3p = 5 - 16
9-2/3p = -11
7p/3 = -11
Then we cross multiply-
7p = -33
p = -33/7
Solve for x. -3x - 8 = 10
Steps to solve:
-3x - 8 = 10
~Add 8 to both sides
-3x - 8 + 8 = 10 + 8
~Simplify
-3x = 18
~Divide -3 to both sides
-3x/-3 = 18/-3
~Simplify
x = -6
Best of Luck!
The solution of the equation -3x - 8 = 10 is,
⇒ x = -6
The given algebraic equation is,
-3x - 8 = 10
Now since its degree is 1
Therefore it is nothing but a linear equation.
By simple operation we can solve it
Now to solve it proceed the following steps:
Add 8 both sides, we get
⇒ -3x - 8 + 8 = 10 + 8
⇒ -3x = 18
Divide by -3 both sides we get
⇒ x = 18/-3
⇒ x = 6
Hence,
The solution is x = -6
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A cube has side length
a. The side lengths are decreased to 30% of their original size. Write an expression in simplest form for the volume of the new cube in terms of
a.
Answer:
.027(a^3)
Step-by-step explanation:
The volume of a cube is s^3, where s is the sidelength
We plug in .3a for s, because the sidelength has been reduced to 30% of a.
We get (.3a)^3 = .027(a^3)
Answer:
.027(a^3)
Step-by-step explanation:
Can someone help find these angles??
Kelly wants to buy 3 boxes of cereal.She wants to use the coupon that says buy one get on half off. If each box of cereal costs 4.75 how much will she pay in total
Answer:
$11.88
Step-by-step explanation:
Given that Kelly would get one box of cereal half off if she buys one, then we must take that into account.
Box 1: $4.75
Box 2: $4.75 ÷ 2 = $2.38
Box 3: $4.75
Now we simply add the totals:
4.75 + 2.38 + 4.75 = $11.88
A gemstone is cut in the shape of a triangular pyramid.The area of the base of the pyramid is 42 square millimeters.the height of the pyramid is 4 millimeters.what is the volume of the gemstone.
Answer:
The volume of this pyramid is 56 millimeters³
Step-by-step explanation:
The volume for a triangular pyramid is given by the following formula:
volume = (1/3)*(base area)*h
In order to solve this problem we must take the given data for the pyramid and apply it to the formula above. We have:
volume = (1/3)*42*4
volume = 14*4
volume = 56 millimeters³
The volume of this pyramid is 56 millimeters³
Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
Answer:
x^3 - 3x^2 + 5x - 15
x^2(x-3) +5(x-3)
(x^2 + 5)(x - 3) <==Answer
Step-by-step explanation:
When determining which x-values would make an expression undefinéd, you do not need to
include the factors you canceled out.
True
False
Answer:false
Step-by-step explanation: Then you would get rid of the x
PLEASE HELP WILL GIVE 1ST RIGHT ANSWER AS BRAINIEST The radius of a circle is x+6 and its diameter is 3x+5. What is the circumference of the circle, in terms of pi? (Do not include the variable x in your answer.)
Answer:
The circumference of the circle = 26π unit.
Step-by-step explanation:
Given:
Radius of the circle, r = "x+6"
Diameter of the circle, d = "3(x)+5"
We have to find the circumference of the circle in terms of pi.
Formula to be used:
Circumference of a circle = 2πr or πd
As we know that:
Radius = Half of diameter
So,
⇒ [tex]radius=\frac{diameter}{2}[/tex]
⇒ [tex]x+6=\frac{3x+5}{2}[/tex]
⇒ [tex]2\times (x+6)=\frac{3x+5}{2}\times 2[/tex]
⇒ [tex]2x+12=3x+5[/tex]
⇒ [tex]12-5=3x-2x[/tex] ...Arranging variables and constants.
⇒ [tex]7=x[/tex]
Plugging x = 7 we will find the radius and the diameter.
⇒ Radius = "x+6" = "7+6" = 13
⇒ Diameter = "3(x)+5" = 3(7)+5 =26
Lets find the circumference of the circle.
⇒ Circumference = [tex]2\pi r= 2\pi (13) = 26 \pi[/tex] Or
⇒ Circumference = [tex]\pi d=\pi (26)=26\pi[/tex]
The circumference of the circle = 26π unit.
7.5 liters of a certain solution contain 37 grams of salt. What is the density of salt in the solution? Round your answer, if necessary, to the nearest tenth.
Answer:
The density of salt solution is [tex]4.94\times 10^{-3}\ g/cm^3[/tex].
Step-by-step explanation:
Given that,
Volume of certain solution, V = 7.5 litres
Mass of salt in solution, m = 37 grams
We know that, [tex]1\ L=1000\ cm^3[/tex]
We need to find the density of salt in the solution. The density of salt is given by mass per unit volume. The formula can be written as:
[tex]d=\dfrac{m}{V}\\\\d=\dfrac{37\ g}{7.5\times 10^3\ cm^3}\\\\d=4.94\times 10^{-3}\ g/cm^3[/tex]
So, the density of salt solution is [tex]4.94\times 10^{-3}\ g/cm^3[/tex].
Answer:4.9
Step-by-step explanation:
N n N n N n N n N n n N N Suppose that you were to draw a random sample of one letter from the set of letters above. Two possible events are A = the chosen letter is upper-case and B = the chosen letter is underlined. Find P(A or B). Round your answer to three (3) decimal places.
Answer:
10/13 = 76.92%
Step-by-step explanation:
The question is missing some information because the underline is missing.
If we make table based on if the letter upper case (A) or lower case(a), and if the letter underlined(B) vs not underlined(b) the data will be:
A a
B 4 3 7
b 3 3 6
total 7 6
There are total of 13 letter there. The calculation will be:
P(A or B) = P(A) + P (B) - P(A and B) = (7 + 7 -4) / 13= 10/13 = 76.92%
Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective
which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse ?
Answer:
Step-by-step explanation:
Please share the answer choices next time.
The simplest diagram of a 30-60-90 triangle indicates leg lengths of 1 and √3 and hypotenuse 2. Thus, the desired ratio is √3/2. This is the sine of 60° and also the cosine of 30°
Answer: 3\3 :6 , \3:2 and 3 :2/3
Step-by-step explanation:
A fish tank is 2 metres long, 50 centimetres wide and 20 centimetres high. How many litres of water will it hold if it is filled to the top ?
Answer:
It will hold 200 Litres of water
Step-by-step explanation:
To find the number of litres of water the fish tank can hold, we will follow the steps below;
Write down the formula for calculating its volume
V = l×w×h
where v = volume of the tank
w=width of the tank
l = length of the tank
From the question given;
w= 50 cm = 0.5 m
height h = 20 cm = 0.2 m
l = 2 m
V= l×w×h
= 2×0.5×0.2
=0.2 m³
we can now change it to liters
V = 0.2 m³ × 1000 = 200 L
It will hold 200 Litres of water
You decide to take a guitar lessons. Each half-hour lesson costs $20. How much will you budget to pay for a half-hour lesson each week for 26 weeks?
Answer:
520
Step-by-step explanation:
If you pay for a half an hour lesson that is 20 dollars.
So if you do that for a total of 26 weeks you would multiply 20 dollars by 26 weeks.
20*26=520
Therefore she spends 520 dollars for half hour lessons that cost 20 for 26 weeks
can someone write this in standard form? 1/7(14x+7)-5
Answer:
No because it is mathematically incorrect.
The expression simplifies to [tex]\( 2x - 4 \)[/tex] in standard form after distributing and combining like terms.
Let's break it down step by step:
1. Start with the given expression: [tex]\( \frac{1}{7}(14x+7) - 5 \)[/tex]
2. Distribute [tex]\( \frac{1}{7} \)[/tex] across the parentheses:
[tex]\[ \frac{1}{7} \cdot 14x + \frac{1}{7} \cdot 7 \][/tex]
3. Simplify each term after distributing:
[tex]\[ \frac{1}{7} \cdot 14x = 2x \][/tex]
[tex]\[ \frac{1}{7} \cdot 7 = 1 \][/tex]
4. Now, rewrite the expression with the distributed terms:
[tex]\[ 2x + 1 - 5 \][/tex]
5. Combine like terms (1 and -5):
[tex]\[ 2x + (1 - 5) \][/tex]
6. Simplify the terms inside the parentheses:
[tex]\[ 2x + (-4) \][/tex]
7. Simplify further:
[tex]\[ 2x - 4 \][/tex]
So, the expression [tex]\( \frac{1}{7}(14x+7) - 5 \)[/tex] in standard form simplifies to [tex]\( 2x - 4 \).[/tex]
Why do cats bang their head against humans?!!..
Im sorry but why are you putting this on here?
Answers:
They probably bump their heads against humans because they want someone to pet them or they like humans.
Explanation:hope I get brainliest!:D
Order the numbers from greatest to least based on their absolute value. |− 2 5 |, |0.5|, |− 3 4 |, |0.35| A) |0.5| > |0.35| > |− 2 5 | > |− 3 4 | B) |− 3 4 | > |− 2 5 | > |0.35| > |0.5| C) |0.5| > |− 2 5 | > |− 3 4 | > |0.35|, D) |− 3 4 | > |0.5| > |− 2 5 | > |0.35|
Answer:|−3 4 | > |0.5| > |− 2 5 | > |0.35|
Hope this is helpful!
The Drama Club is showing a video of their recent play. The first showing begins at 3:45 p.m. The second showing is scheduled at 6:25 p.m. with a 1 2 −hour break between the showings. How long is the video in hours and minutes? The video is hours and minutes. Complete the explanation of how you can use a number line to find the answer. You can work backward from the start time of the second showing at : . You count back 1 2 hour, which is minutes, for the break between showings to : . The second showing started 20 minutes late. Will the second showing be over by 8:45 p.m.? Complete the explanation why your answer is reasonable. The second showing started at : p.m. The movie lasts hours minutes, so it ends at :55 p.m. So, the second showing be over by 8:45 p.m.
Answer:
a) The movie is 2 hours and 10 minutes long.
b) Check Explanation
c) The second showing starts at 6:45 p.m. The movie lasts 2 hours and 10 minutes, so it ends at 8:55 p.m. So, the second showing will not be over by 8:45 p.m.
Step-by-step explanation:
The first showing starts at 3:45 pm, the second showing starts at 6:25 pm and there's a break of (1/2) hour between the showings,
To now find how long the video was.
The length of the film.is the difference between the times 6:25 pm and 3:45 pm while also removing the (1/2) hour break time too.
The time between 3:45 pm and 6:25 pm is 2 hours, 40 minutes. Now removing the (1/2) hour break from this time, we are left with 2 hours, 10 minutes.
Hence, the movie is 2 hours and 10 minutes long.
b) To use the number line, we would convert the times into hours, that way, it works.
The time 3:45 is 3.75 on the number line, the time, 6:25 is 6.4167 on the number line. And the (1/2) hour break is a length of 0.5 on the number line.
Working backwards from 6.4167, we go back a length of 0.5 and land on 5.9167.
We can then calculate the length of time between 3.75 and 5.9167
5.9167 - 3.75 = 2.16667 hours
Which directly translates to 2 hours and 10 minutes as obtained in (a)
c) The second showing started 20 minutes late. Will the second showing be over by 8:45 p.m.? Complete the explanation why your answer is reasonable.
The second showing is known to initially start at 6:25 pm, but now, there's a delay of 20 minutes, which pushes the start time to 6:45 pm and the movie lasts for 2 hours and 10 minutes as calculated in (a).
So, 2 hours and 10 minutes from 6:45 pm gives 8:55 pm. So, the second showing will end by 8:55 pm if it starts 20 minutes late.
And the second showing will not be over by 8:45 pm.
Hope this Helps!!!
A circle with diameter of StartFraction 7 over 2 EndFraction centimeters. The radius is cm. The circumference in terms of π is π cm. Using 3.14 for π, the approximate circumference of the circle is cm.
Answer:
1 is 7/4
2 is 7/2
3 is 11.0
Step-by-step explanation:
they all the right answer thank me later
Answer:
the guy above is right on edge 2021
Step-by-step explanation:
i got the question right because of them
When the temperature stays the same, the volume of gas is inversely proportional to the pressure of the gas. If a balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 38 cubic inches.
Answer:
84 pounds per square inch
Step-by-step explanation:
Extracting the key information from the question:
*** Volume of a gas is inversely proportional to pressure of the gas.
*** A balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch.
*** Volume is then decreased to 38 cubic inches. we are required to find the new pressure of the gas.
Since volume is inversely proportional to pressure, then:
V = k × (1/p)
V = k/p
V = volume, p= pressure, k = mathematical constant
Since, V = 228 cubic inches, P = 14 pounds per square inches, k = ?
Substituting appropriately, we have:
228/1 = k/14
cross multiply
K = 228 × 14 = 3192
Using the same formula, we can calculate the new pressure of the gas since we know our mathematical constant and the volume it was decreased to.
V = k/p
Here, volume = 38, k = 3192
We now have:
38/1 = 3192/p
Cross multiply
38 × p = 3192
p = 3192/38
p = 84 pounds per square inch.
The new pressure of the gas after decrement of the volume= 84 pounds per square inch
When the temperature stays the same, the new pressure of the gas if the volume is decreased is 84 pounds per square inch.
Given the following data:
Pressure A = 14 pounds per square inchVolume A = 228 cubic inchesVolume B = 38 cubic inchesTo find the new pressure of the gas if the volume is decreased:
Translating the word problem into a mathematical expression, we have;
[tex]V \alpha \frac{1}{P} \\\\V = \frac{k}{P}[/tex]
Where:
P is the pressure.V is the volume.First of all, we would determine the constant of proportionality.
[tex]k = VP\\\\k = 228 \times 14[/tex]
k = 3,192
To find the new pressure:
[tex]P = \frac{k}{V} \\\\P = \frac{3192}{38}[/tex]
New pressure, P = 84 pounds per square inch
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There are 9⋅54 sheep spread across 18⋅52 square miles of land. Find the average number of sheep per square mile. Round your answer to the nearest whole number.
Answer:
There is an average of approximately 1 sheep per square mile.
Step-by-step explanation:
Given there are 9.54 sheep spread across 18.52 square miles of land.
The average number of sheep per square mile is given as
A = 9.54/18.52
Without using a calculator, this is by inspection, about 9/18 = 0.5.
Using a calculator, we have
A = 9.54/18.52 = 0.51511879
Approximately 1 sheep per square mile.
If the Interest earned is 119.88 and the the interest rate is 3.6 and the time is 3 years what is the principal
Answer:
that is the solution to the question
Final answer:
To calculate the principal with an interest of $119.88, an interest rate of 3.6%, and a time of 3 years, use the simple interest formula. By rearranging the formula and doing the math, the principal amount is found to be $1,110.
Explanation:
To find the principal amount when you know the interest earned, the interest rate, and the time, you can use the formula for simple interest which is Interest = Principal × rate × time. Our goal is to rearrange the formula to solve for the principal.
Given that the Interest earned is $119.88, the interest rate is 3.6% (or 0.036 when converted to a decimal), and the time is 3 years, we can plug these values into the formula:
Interest = Principal × rate × time
$119.88 = Principal × 0.036 × 3
$119.88 = Principal × 0.108
To find the Principal, divide the interest earned by the product of the rate and time:
Principal = $119.88 / 0.108
Principal = $1,110
The principal amount is $1,110.
Identify the zeros of the polynomial function N(x)=1/2 (x-1)(x+3).
a:x+-3
b:x=-1
c:x=1
d:x=3
Answer:
a:x=-3
c:x=1
Step-by-step explanation:
The zeros of a function are the values of x for which the value of the function f(x) becomes zero.
In this problem, we have the following function:
[tex]f(x)=\frac{1}{2}(x-1)(x+3)[/tex]
Here we want to find the zeros of the function, i.e. the values of x for which
[tex]f(x)=0[/tex]
In order to make f(x) equal to zero, either one of the factors [tex](x-1)[/tex] or [tex](x+3)[/tex] must be equal to zero.
Therefore, the two zeros can be found by requiring that:
1)
[tex]x-1=0\\\rightarrow x=+1[/tex]
2)
[tex]x+3=0\\\rightarrow x=-3[/tex]
So the correct options are
a:x=-3
c:x=1
P(x)equals=R(x)minus−C(x). Given R(x)equals=59 x minus 0.3 x squared59x−0.3x2 and Upper C left parenthesis x right parenthesis equals 3 x plus 14C(x)=3x+14
Answer:
[tex]P(x)=-0.3x^2+56x-14[/tex]
Step-by-step explanation:
The given functions are
[tex]R(x)=59x-0.3x^2[/tex]
[tex]C(x)=3x+14[/tex]
It is given that
[tex]P(x)=R(x)-C(x)[/tex]
Substitute the values of given functions in the above equation.
[tex]P(x)=59x-0.3x^2-(3x+14)[/tex]
[tex]P(x)=59x-0.3x^2-3x-14[/tex]
Combine like terms.
[tex]P(x)=-0.3x^2+(59x-3x)-14[/tex]
[tex]P(x)=-0.3x^2+56x-14[/tex]
Therefore, the required function is [tex]P(x)=-0.3x^2+56x-14[/tex] .
In the figure below, the two adjacent polygons are regular. What is the measure of ∠ABC?
Answer:
= 150°
Step-by-step explanation:
Since the polygons are regular, certain mathematical assumptions would help us here.
A square is a quadrilateral with all it's 4 sides equal and all it's angles equal.
Sum of angles of a regular quadrilateral = 360.
Therefore, a single angle = 360/4
= 90°.
The Triangle is adjacent to the side of the square. We will thus assume it's an Equilateral triangle.
For an equilateral triangle, all it's 3 angles = 180.
A single angle = 180/3
= 60°.
With this,
Angle ABC = 90° + 60=
= 150°