Answer:
3(r + 5)(r - 5)
Step-by-step explanation:
Both 3 and 75 are divisible by 3, so we take out a 3.
3(r^2 - 25)
Next, we can factor r^2 - 25. It's a difference of squares.
3(r + 5)(r - 5)
Brainliest, please :)
Which function is graphed below?
The function that represents the given trigonometric graph is; f(x) = cos (x)
How to Interpret Trigonometric Graphs?From the given trigonometric Graph, we can see the following;
When x = 0, y = 1
When x = π/2, y = 0
When x = π, y = -1
When x = 2π, y = 1
Now, according to trigonometric functions in radians, we know that;
cos 0 = 1
cos π/2 = 0
cos π = -1
cos 2π = 1
These values correspond with what we have in the given trigonometric graph and as such we can say that the function that is graphed is;
f(x) = cos (x)
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Koos spent 3/7 of his monthly pocket money during the first week. The following week he spends two- thirds of what he had spent the previous week. The fraction of the pocket money that is still left is.
Answer: 2/7
Step-by-step explanation:
The total amount of pocket money he has is 7/7.
He spent 3/7 of his pocket money during the first week.
He then spends 2/3 of what he spent the previous week, 2/3 * 3/7 which is 2/7.
What he has left is 7/7 - 3/7 - 2/7 = 2/7.
Find the measure of D, and the perimeter and area of parallelogram ABCD.
A
16cm
30⁰
25cm
8cm
OLD = 150°, P = 82 centimeters, A = 200 square centimeters
O D = 60°, P = 41 centimeters, A = 200 square centimeters
O D = 160°, P = 82 centimeters, A = 400 square centimeters
OLD = 60°, P = 41 centimeters, A = 400 square centimeters
The measure of D, perimeter and area of a parallelogram are 150°, 82cm and 200 square centimeters respectively. Option A
How to determine the area and perimeter
For the parallelogram ABCD, it can be deduced that
Line AB and CD are parallel and AD is a transversal so the angles A and D is co-interior , Co-interior angles are said to be supplementary whose sum is 180 degrees
A + D = 180°
30° + D = 180°
D = 180° - 30°
D = 150°
Perimeter = 2 ( a + b)
a = 16cm, b = 25cm
Perimeter = 2 ( 16 + 25) = 2 ( 41)
Perimeter = 82 cm
Area = b × h
base = 25cm , h = 8cm
Area = 25 × 8
Area = 200 square centimeters
Thus, the measure of D, perimeter and area of a parallelogram are 150°, 82cm and 200 square centimeters respectively. Option A
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Find a Cartesian equation for the curve.
r = 3 sec(θ)
Identify the curve.
▢ ellipse
▢ line
▢ hyperbola
▢ limaçon
▢ circle
[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]
[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]
[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]
9 and 1/9 subtracted by 1 and 4/5
Answer:
7 14/45
Step-by-step explanation:
9 1/9 - 1 4/5
82/9 - 9/5
410/45 - 81/45
329/45
7 14/45
Answer:
●7.31
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Nicole sold 15 tickets to the school play and Andrew sold 24 tickets. what is the ratio of the number of tickets Nicole sold to the number of tickets Andrew sold
Answer:
5:8
Step-by-step explanation:
Nichole sold 15 while Andrew sold 24, so the ratio is 15:24. Simplify the ratio by dividing both sides by 3, and we’ll get 5:8.
Chris bought a new car for 12,500 he made 3,000 down payment and financed the rest for 14.5% for 36 months for 3 years how much less would his total be for same loan 24 months 2 years
The difference in total loan repayments between the two mortgage payment option is 771.12
The requirement here is to determine the difference between total loan repayments when the period of loan is 36 months and the total repayments when the period of loan is 24 months instead.
Note the loan amount is the excess of purchase price over the down payment required.
loan amount=12,500-3,000
loan amount=9,500
The monthly payment in each case can be determined using the present value formula of an ordinary annuity.
PV=monthly payment*(1-(1+r)^-N/r
36-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=36
9,500=X*(1-(1+0.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-0.6489543809903260)/0.0120833333333333
9,500=X*0.3510456190096740/0.0120833333333333
9,500=X*29.0520512283869000
X=9,500/29.0520512283869000
X=327.00
Total month repayments=327.00*36
Total month repayments=11,772.00
24-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=24
9,500=X*(1-(1+0.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-0.7495652524008220/0.0120833333333333
9,500=X*0.2504347475991780/0.0120833333333333
9,500=X*20.7256342840700000
X=9,500/20.7256342840700000
X=458.37
Total month repayments=458.37*24
Total month repayments=11,000.88
Difference in total payments=11,772.00-11,000.88
Difference in total payments=771.12
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Answer:
just 771.21
Step-by-step explanation:
to make it shorter credits to the og person who said the awnser 771.21
Students at a high school were polled to determine the type of music they preferred. There were students who completed the poll. Their responses are represented in the circle graph.
What percent of students preferred music?
A circle graph titled Music Preferences consists of a circle divided into 6 regions with labels and sizes as follows: rap, 945; alternative, 462; rock and roll, 275; country, 168; jazz, 15; other, 85.
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85
The percent of students that preferred alternative music is 23.7%
How to determine the percentage?The music type and the preference are given as:
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85
From the above table, we have:
Alternative = 462
Total = 945 + 462 + 275 + 168 + 15 + 85
Total = 1950
The percentage is then calculated as:
Percentage = Alternative/Total * 100%
This gives
Percentage = 462/1950 * 100%
Evaluate
Percentage = 23.7%
Hence, the percent of students that preferred alternative music is 23.7%
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Find the shortest distance from A to B in the diagram below. A. 505‾‾‾‾√ m B. 17 m C. 329‾‾‾√ m D. 10 m
The shortest distance from A to B in the diagram is 17 m.
How to find the shortest distance?The shortest distance from D to B can be found as follows:
using Pythagoras theorem,
c² = a² + b²
where
c is the hypotenusea and b are the other legsTherefore,
DB² = 15² + 8²
DB² = 225 + 64
DB² = 289
DB = √289
DB = 17 m
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Answer:
B, 17 m
Step-by-step explanation:
Founders 23
Factor x2 − 2x + 3. (1 point) (x − 3)(x − 1) (x + 3)(x + 1) (x − 3)(x + 1) Prime
Answer: for the factor one: The expression isn't factorable with rational numbers
Step-by-step explanation: Since the polynomial can be factored it isn't prime (i don't know if that is what you meant or not but I hope this helps and I got all of them correct )
The graph shows the solution to a system of inequalities:
pe
Which of the following inequalities is modeled by the graph?
O 2x + 5y = 14; x = 0
O2x + 5y s 14; x 20
O2x - 5y 14; x 20
O-2x - 5y 14; x = 0
Answer: option (2)
Step-by-step explanation:
The slanted line has a negative slope.
Eliminate options 3 and 4.Also, the line is shaded below.
Eliminate option 1.This leaves option (2) as the correct answer.
Calculate the geometric center of the grapg under the function
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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Here is this question im stuck on.
The polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0
Dividing polynomialsFrom the question, we are to divide the given polynomial P(x) by the divisor d(x)
From the given information,
P(x) = x³ + 8
d(x) = x + 2
The division operation is shown in the attachment below.
The quotient, Q(x) = x² -2x + 4
and the remainder, R(x) = 0
We area to express P(x) in the form
P(x) = d(x).Q(x) + R(x)
Thus, we get
x³ + 8 = (x+2)(x² -2x + 4) + 0
Hence, the polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0
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Use the drawing tool(s) to form the correct answer on the provided graph. Graph the solution to this system of inequalities in the coordinate plane. 3y> 2x+122x+y < -5
Thank you in advance!
The solution to the system of inequalities is (-3.375, 1.75)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x+12
2x+y < -5
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(-3.375, 1.75)
Hence, the solution to the system of inequalities is (-3.375, 1.75)
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14) 8 people from a group of 15
O a.) 5435
Ob.) 6345
O c.) 6435
Od.) 6543
Answer: 6435
Step-by-step explanation:
[tex]\binom{15}{8}=6435[/tex]
3. Your new job requires you to calculate the material
costs for manufactured goods. One of goods you
manufacture is a fabric sample in the shape of a circle.
Given the formula A = πr^2, find the
area (A) of the fabric sample whose radius (r) is
7.6 x 10^7 m. Round your answer to the nearest thousandth. (Use 3.14 for π)
A= _____________ m^2
The area of the circular manufactured good is given by:
[tex]A = 1.8146 \times 10^{16} \text{m}^2[/tex]
What is the area of a circle?The area of a circle of radius r is:
[tex]A = \pi r^2[/tex].
In this problem, the radius in meters is:
[tex]r = 7.6 \times 10^7[/tex]
Hence the area in m² is:
[tex]A = \pi (7.6 \times 10^7)^2 = 181.46 \times 10^{14} = 1.8146 \times 10^{16} \text{m}^2[/tex]
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What are the sums? Complete the equations. 12 +15= -12+(-15) = help 36 points
A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
12 + 15= 27
-12 + (-15)= -12 -15
= -27
☆...hope this helps...☆
_♡_mashi_♡_
Please help me with this problem literally so desperate right now.
Answer: 13 inches by 2 inches
Step-by-step explanation:
26 can be made by:
1 x 26
2 x 13
There are only 2 possibilities for the dimensions.
2 x 3 + 7 is 13, which fits the requirements.
Which means, the length is 13 and the width is 2.
2. Merchandise from the vendor carries an invoice of July 1 and is received on July 4. Terms are 2/10 net 30 EOM, and the invoice is for $5,000. What amount should be remitted if the retailer pays the bill on July 13?
The retailer would remit $4,900 to the vendor on July 13.
What is invoice date?
The invoice date is the date written on this which is the same as the date the goods were shipped to customer, in this case, invoice date is July 1.
Invoice receipt date?
This is the date the customer received the invoice as well as the goods sent by the vendor, which is July 4 in this case.
2/10 means that a discount of 2% is available if the customer pays within the first 10 days, which starts counting from July 4, not July 1, because the customer actually received the invoice on July 4.
From July 4 to July 13 is a period of 10 days, which means that the 2% cash discount that customer would be entitled if payment is made within the first 10 days is still available
discount=2%*$5000
discount=$100
The retailer would remit the invoice price of $5,000 minus the discount.
amount remitted=$5000-$100
amount remitted=$4,900
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Does this table represent a function? Why or why not
Answer:
No
Step-by-step explanation:
This table does not represent a function. The domain(x) can have only one range(y) in order for a set of data to represent a function. However, the domain value 2 has the range of both 1 and 4. Therefore, the table does not represent a function.
you deposit 2000 in an account earning 3% interest compounded monthly.
a. how much will you have in the account in 20 years
b. how much interest will you earn
Answer:
a. 3641.51
b. 1641.51
Step-by-step explanation:
The future value formula will tell you the amount in the account in 20 years.
FormulaFV = P(1 +r/n)^(nt)
Principal P is compounded n times per year at annual rate r for t years.
ApplicationThe future value of the account with P=2000, r=0.03, n=12, and t=20 will be ...
FV = 2000(1 +0.03/12)^(12·20) = 2000(1.0025^240) ≈ 3641.50999
a.The account value in 20 years will be 3641.51.
b.The first 2000 of account value is the principal, so the interest is ...
interest = 3641.51 -2000
interest = 1641.51
__
Additional comment
Many calculators and all spreadsheets have built-in capability for making this calculation.
Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?
A (16,+infinity)
B (-16,+infinity)
C (-infinity, 16)
D (-infinity,-16)
The solution set that represent the solution to the inequality is (16,+infinity)
Solving linear equationThe mathematical representation of the statement given is expressed as shown below;
4 1/2 x - 9 1/2 >62.5
Convert to improper fraction to have:
9/2 x - 19/2 > 62.5
Find the LCM
9x-19/2 > 62.5
9x-19 > 125
9x > 125 + 19
9x > 144
x > 16
Hence the solution set that represent the solution to the inequality is (16,+infinity)
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I need this answered please and thank you! ASAP
Answer:
Greetings!
The answer for the first figure is attached but the second diagram is not clear.
Also use the image i attached horizontally.
and also it TD subject not Mathematics.
A boat travels 50 miles downstream in 2 hours and it takes 5 hours to travel back upstream. What is the speed of the boat if it were in still water and what is the speed of the river current?
The 50 mile distance traveled downstream and back that takes 2 hours and 5 hours respectively gives;
The speed of the boat in still water = 17.5 mphThe river current flows at 7.5 mphHow can the boat speed be calculated?Let v represent the speed of the boat and let u represent the speed of the river current.
Distance the boat travels downstream = 50 miles
Time taken to travel downstream by the boat = 2 hours
Time taken to travel back upstream = 5 hours
[tex]velocity = \frac{distance}{time} [/tex]
Therefore;
Which gives;
[tex]v + u = \frac{50}{2} = 25...(1)[/tex]
v + u = 25[tex]v - u = \frac{50}{5} = 10...(2)[/tex]
v - u = 10Adding equation (1) to equation (2) gives;
(v + u) + (v - u) = 2•v = 25 + 10 = 35
2•v = 35
v = 35 ÷ 2 = 17.5
The speed of the boat, v = 17.5 mphu = 25 - v
Which gives;
u = 25 - 17.5 = 7.5
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F(x)=x^3*125 complex zeros
Answer: 0
Step-by-step explanation:
[tex]125x^3 =0\\\\x^3 =0\\\\x=0[/tex]
question in the picture below
The doubling time after 4 and 7 years is 400 months and 700 months respectively
How to determine the doubling timeThe formula for finding doubling time is given as;
Doubling time = [tex]t \frac{In 2}{In 1 + \frac{r}{100} }[/tex]
Where t = time = 4 and 7 years
r = rate
For 4 years, we have
Doubling time = [tex]4 * \frac{In 2}{In ( 1 + \frac{0.7}{100}) }[/tex]
⇒ [tex]4 * \frac{In 2}{In 1. 0074}[/tex]
⇒ [tex]4 * \frac{0. 6931}{0. 0074}[/tex]
⇒ [tex]4[/tex] × [tex]93. 66[/tex]
⇒ 374. 65
⇒ 400 months in the nearest hundredth
For 7 years
⇒ [tex]7[/tex] × [tex]93. 66[/tex]
⇒ [tex]655. 62[/tex]
⇒ 700 months in the nearest hundredth
Thus, the doubling time after 4 and 7 years is 400 months and 700 months respectively
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Simplify the problem
Answer:
B. 2√3+4
Step-by-step explanation:
3√3+4−√3
=2√3+4 (Decimal: 7.464102)
Find the measure of side a.
A = _ m
An Annuity Immediate Has 32 Initial Quarterly Payments Of 20 Followed By A Perpetuity Of Quarterly Payments Of 25 Starting In The 9th Year. Find The Present Value At A Nominal Rate Of 16%
The present value of the nominal rate of the annuity will be $535.
How to calculate the annuity?Annuity amount = 20
Number of annuities = 32
APR = 16%
PV of annuities = 357
Number of years to perpetuity = 8
Quarterly perpetuity = 25
PV of perpetuity at 9th year = 625
PV of perpetuity today = 178
Total PV = 357 + 178 = 535
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Evaluate the expression. 2+6+ – 4 4 /5 ÷ – 3 Write your answer as a fraction or as a whole or mixed number.
Answer:
9 3/5
Step-by-step explanation:
2+6+-4 4/5 ÷ -3
PEMDAS! First is multiplicationSo, solve the bold
2+6+ -4 4/5 ÷ -3
So,
2+6+ 1 3/5
Next is Addition(IN ORDER OF THE EQUATION), So solve the bold,
2+6+ 1 3/5
So, the answer is
9 3/5