A rectangular note card has a perimeter of 18 inches and an area of 20 square inches. What are the dimensions of the note card?
Answers
4 x 5 = 20
5 + 5 + 4 + 4 = 18
hope I helped (:
Related Questions
What is the rate of change from x = π to x = 2π? (6 points) trig graph with points at 0, negative 4 and pi over 2, 0 and pi, 4 and 3 pi over 2, 0 and 2 pi, negative 4
PLEASE HELP!!!!!!
a. 8 over pi
b. pi over 8
c. negative 8 over pi
d. negative pi over 8
Answers
We are given points on trig graph as
[tex](0,-4)[/tex]
[tex](\frac{\pi}{2} ,0)[/tex]
[tex](\pi ,4)[/tex]
[tex](\frac{3\pi}{2} ,0)[/tex]
[tex](2\pi ,-4)[/tex]
now, we can find rate of change from x = π to x = 2π
so, we will select two points
[tex](\pi ,4)[/tex] and [tex](2\pi ,-4)[/tex]
we can also write as
[tex]a=\pi , f(a)=4[/tex]
[tex]b=2\pi , f(b)=-4[/tex]
now, we can use average rate of change formula
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]
now, we can plug values
and we get
[tex]A=\frac{-4-4}{2\pi -\pi}[/tex]
[tex]A=\frac{-8}{\pi }[/tex]
so, option-C.............Answer
1. What is the value of w? 7 3.5 7(sqrt)of 3 14
Answers
1. You have:
Cos(α)=Adjacent/Hypotenuse
α=30°
Adjacent=7√3
Hypotenuse=w
2. When you substitute this values into Cos(α)=Adjacent/Hypotenuse, you obtain:
Cos(α)=Adjacent/Hypotenuse
Cos(30°)=(7√3)/w
3. When you clear "w", you obtain:
wCos(30°)=7√3
w=(7√3)/Cos(30°)
4. Then, the result is:
w=14
The answer is the last option: 14
AB and AD are tangents of the circle with the center at C. The measure of BDC = 45o, and the circle has a diameter of 4. Which is the length of AB?
help needed!!
Answers
ABCD is a diamond.
Let's D' the intersection of the circle and DC.
m∠BCD'=2*m∠BDC=2*45=90°
m∠BCD=90°
The diagonals of ABCD are perpendicular==>ABCD is a diamond and AB=BC=CD=DA=2
What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –2/3(x – 6) and passes through the point (−2, −2)?
y = –2/3x –10/3
y = –2/3x +10/3
y = 3/2x – 1
y = 3/2x + 1
Answers
y - 4 = -2/3(x-6)
y - 4 = -2/3x + 4
y = -2/3x + 8
therefore the slope is -2/3 and intercept is +8
the perpendicular line passes through x = -2 and y = -2
then if the given graph has a slope of -2/3 the line that is perpendicular to that should have the reciprocal of the gradient and should be in the opposite direction. So m = +3/2
lets substitute x,y and m values for the new perpendicular line
y =mx + c
-2 = 3/2 * -2 +c
-2 = -3 +c
c = -2 +3
c = 1
Therefore the equation for the perpendicular line is
y = 3/2x + 1
Answer:
y = 3/2x + 1
Step-by-step explanation:
which ordered pairs lie on the graph of the exponential function f(x)=-3^2x+5
select each correct answer
(3,724)
(-2,76)
(0,4)
(1,-4)
(-2,76)
Answers
It must be -3^(2x) + 5 In that case 0,4 works. That gives (-3)^0 = -1
-1 + 5 = 4
Unfortunately so does 1,-4 because -3^2 = - 9
- 9 + 5 = - 4
If (-2,76) is the answer, then the question should be written (-3)^(2x) - 5
Until the ambiguity is gone, we're not sure.
Answer:
1,-4
0,4
3,-724
Step-by-step explanation:
A rectangular pool contains 920 cubic meters of water. the pool is .4 meter deep and 100 meters wide. How long is the pool?
Answers
To find the length of the pool, divide the volume (920 m³) by the product of the width (100 m) and depth (0.4 m), which gives a pool length of 23 meters.
Explanation:The question asks to find the length of the pool given the volume, width, and depth of the pool. The volume of a rectangular prism (which is the shape of the pool) can be found using the formula Volume = length × width × depth. We can rearrange this formula to solve for the length by dividing the volume by the product of the width and depth.
Therefore, the length of the pool is calculated as follows:
Volume = 920 cubic metersWidth = 100 metersDepth = 0.4 metersLength = Volume / (Width × Depth)Length = 920 m³ / (100 m × 0.4 m)Length = 920 m³ / 40 m²Length = 23 metersSo, the length of the pool is 23 meters.
What is the value of k?
Answers
Value of k = 10
Further explanationTriangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
There are two angles that can form:
Supplementary Angles: if both angles are added = 180 ° Complementary Angles: if both angles are added = 90 °From picture: ∠Y = Supplementary Angles:
115 ° + ∠Y = 180 °
∠Y = 180 ° - 115 °
∠Y = 65 °
As we know, the sum of angles in a triangle = 180 °
So from the picture, the sum of ∠Y + ∠X + ∠Z = 180 °
65 ° + 6k + 10 ° + 4k + 5 ° = 180 ° (combine like terms)
65 ° + 10 ° + 5 ° + 6k + 4k = 180 °
80 ° + 10 k = 180 °
10 k = 180 ° -80 °
10 k = 100 °
k = 10
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Answer:
The value of k is 10.
Step-by-step explanation:
Triangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
There are two angles that can form:
Supplementary Angles: if both angles are added = 180 °
Complementary Angles: if both angles are added = 90 °
From picture: ∠Y = Supplementary Angles:
115 ° + ∠Y = 180 °
∠Y = 180 ° - 115 °
∠Y = 65 °
As we know, the sum of all interior angles of a triangle = 180 °
So from the picture, the sum of ∠Y + ∠X + ∠Z = 180 °
65 ° + 6k + 10 ° + 4k + 5 ° = 180 ° (combine like terms)
65 ° + 10 ° + 5 ° + 6k + 4k = 180 °
80 ° + 10 k = 180 °
10 k = 180 ° -80 °
10 k = 100 °
k = 10
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If the circumference of a circle is 10 pie inches, what is the area, in square inches, of the circle?
Answers
therefore 2r=10, r=5
Area, A=pi r ^2=78.54 square inches
Paige’s back yard has an area of 95.9 square meters of the length of the yard is 14 meters what is the width
Answers
find the interest due on $5,000 at 11% for 3 years.
a. 136.36
b. 165.00
c. 1,363.63
d. 1,650.00
Answers
I hope I helped!
two cards are drawn without replacement from a standard deck of 52 playing cards. find the probability that both are odd numbers (aces are considered odd because they have a value of 1 or 11).
Answers
7 odd cards per suit, 4 suits = 7 * 4 = 28 odd cards
so 1st card being odd is a 28/52 = 7/13 probability
2nd card would be a 27/51 = 9/17 probability
7/13 x 9/17 = 63/221 probability of both
The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1- 1-12). What is the standard form of the equation for this line?
Answers
.. y -1 = (1/4)(x -12)
Multiply by 4 and subtract the left side to put into general form.
.. x -12 -4(y -1) = 0
.. x -4y -8 = 0
Add 8 to put into standard form
.. x -4y = 8
The sum of two angles in a triangle totals 117 degrees, what is the measure of the third angle
Answers
117 degrees + 3rd angle = 180
3rd angle = 180 -117
3rd angle = 63 degrees
Simplify the expression 6√2/√3
B. 6√3
C. 2√3
D. 2√6
Answers
I am going to say your answer is D. 2 squar6
1000p for an answer please
Answers
A town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet. What will the area of the park be?
A)13,800 ft2
B)27,600 ft2
C)6,900 ft2
D)6,612.5 ft2
Answers
The answer would be 6,900 ft2. The equation to find the area is "a=1/2bx"
a= area b=base h=height. Hope this helps :D
Given that, a town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet.
We know that area of a triangle = [tex] \frac{1}{2} [/tex] x base x height
Given that base of triangle is 120 feet and height is 115 feet. From the given data, we calculate the area of the triangular park.
Area = [tex] \frac{1}{2}*120 *115 = 6900 [/tex]
Hence , Area of triangular park is 6900 square feet.
Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. His total annual cost is a function of the number of books that he purchases in a year.
Let b represent the number of books he purchases in a year. Which function, C(b), represents his yearly cost?
C(b) = 10b + 2.75
C(b)= 2.75b + 10
C(b) = 12.75b
C(b) = 2.75b + 20
Answers
Each book = $2.75
Number of books = b
Total cost of the books = 2.75b
C(b) = 2.75b + 10 (Answer B)
Answer:
B)C(b)= 2.75b + 10
Step-by-step explanation:
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△ABC∼△DEF , △ABC has a height of 6 meters, and △DEF has a height of 10 meters.
What is the ratio of the area of △ABC to the area of △DEF ?
Enter your answer, in simplest form, in the boxes.
:
Answers
height of DEF = H = 10m
Since they are similar, their bases must be in the same proportion: base of ABC = b = 6/10B = 3/5B
Since a = 1/2 bh = 1/2 (3/5B)(6) = 9/5B
A = 1/2 BH = 1/2 (B)(10) = 5B
So ratio of a:A = 9/5B:5B = 9/5:25/5 = 9:25
Final answer:
The ratio of the areas of two similar triangles with heights of 6 and 10 meters is 9/25.
Explanation:
To find the ratio of the areas of two similar triangles, △ABC and △DEF, with heights 6 meters and 10 meters respectively, we use the knowledge that the areas of similar triangles are proportional to the squares of the corresponding linear dimensions, such as their heights. For these triangles, the ratio of their heights is 6/10 or 3/5. Thus, the ratio of their areas is (3/5)2 or 9/25.
How to find the intersection of a linear and exponential function?
Answers
The graph attached shows the point of intersection of a linear and exponential function.
What is a function? What is a linear function? What is an exponential function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.A linear function is given by the function → y = ax + b.An exponential function is given by the function → y = eˣGiven is a linear function and a exponential function.
We can write the equations as -
y = ax + b
y = eˣ
For the points of intersection -
ax + b = eˣ
Refer to the graph attached. It shows the point of intersection of a linear and exponential function.
Therefore, the graph attached shows the point of intersection of a linear and exponential function.
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Analyze the following statement: Marcus notices that he runs faster in the mornings rather than the evenings. Is the statement an example of correlation or causation?
A. Correlation, because time of day doesn't cause a person to run faster or slower B. Causation, because Marcus has noticed this over several trials
C. No relationship, because time of day has nothing to do with how fast a person runs
D.There is not enough information to make a conclusion
Answers
The answer is option A "Correlation, because time of day doesn't cause a person to run faster or slower." It's completely logic that the time of day doesn't affect the persons speed it's how fit the person that person is would effect his or her speed. Correlation is two data sets that are close together and are connected on a graph.
Hope this helps!
Answer:
A. Correlation, because time of day doesn't cause a person to run faster or slower
Step-by-step explanation:
Marcus notices that he runs faster in the mornings rather than the evenings.This is a correlation because it tells us about the relationship of Marcus's running speed with respect to the time of day. The causation is not possible because there is no definite mention for the increase in speed.
Hence, option A is the answer.
What ray is a common side of ∠EOB and ∠BOA?
Answers
which of the following is the best definition of three-dimensional drawing? A. a three-dimensional drawing represents, on a three-dimensional plane, the length and width of a solid figure.B. a three-dimensional drawing uses graph paper to show the length and width of a solid figure in such a way that it looks realistic.C. a three-dimensional drawing represents on a two-dimensional plane the length, width, and depth of a three-dimensional figure.D. a three-dimensional drawing uses at least one vanishing point to create the illusion of width.
Answers
30 Points! Please Help!
At the end of May, Janet told Sam that she has read 10 books this year and reads 2 books each month. Sam wants to catch up to Janet. He tracks his book reading with a table on his door. Using his table below, what month will Sam have read the same amount of books as Janet?
Month Books
June 3
July 6
August 9
Answers
the answer to this question is march
please help me thank you I will give you brainly
Answers
You are considering buying one of two brands of barbecue grills. Brand F costs $650 and will last for about fifteen years. Brand G costs $200 and will last for about five years, so you will need to buy three of them over the years to equal one Brand F grill. In either case, you plan to pay for the grill with your credit card, which has an interest rate of 13.01%, compounded monthly. You will pay off a Brand F grill in five years of monthly payments, and you will pay off a Brand G grill in three years of monthly payments. Assuming that you have no other purchases on your credit card, over a fifteen-year period, which kind of grill will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.) a. Brand G will end up costing $159.48 less than Brand F. b. Brand G will end up costing $50.00 less than Brand F. c. Brand F will end up costing $134.28 less than Brand G. d. Brand F will end up costing $91.08 less than Brand G.
Answers
Answer:
hes saysing its "a" the first brand g
Step-by-step explanation:
Brand G will end up costing $159.48 less than Brand F.
The correct option is a.
To determine which grill is cheaper over a fifteen-year period, we need to compare the total cost of buying and paying off each grill.
Brand F: The grill costs $650, and we will pay it off in five years of monthly payments, which is 60 payments.
The monthly payment required to pay off a $650 loan with a 13.01% annual interest rate, compounded monthly, over five years is:
PMT = (r x P) / (1 - (1 + r)⁻ⁿ
= (0.1301/12 x 650) / (1 - (1 + 0.1301/12)⁻⁶⁰
= $14.79
Therefore, the total cost of a Brand F grill, including interest, is:
Total Cost = 650 + 60(14.79) = $1537.4
Brand G: The grill costs $200, but we will need to buy three of them over fifteen years.
Each grill will be paid off in three years of monthly payments, which is 36 payments.
The monthly payment required to pay off a $200 loan with a 13.01% annual interest rate, compounded monthly, over three years is:
PMT = (0.1301/12 x 200) / (1 - (1 + 0.1301/12)⁻³⁶
= $6.74
Therefore, the total cost of three Brand G grills, including interest, is:
Total Cost = 3 * (200 + 36 * 6.74) = $1327.92
The difference in cost is: $159.48.
Therefore, over a fifteen-year period, buying three Brand G grills instead of one Brand F grill will save you $159.48.
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What is the differecne of the following polynomials? (6x^2 - 3x^3) - (2x^3 + 4x^2 -5)
Answers
[tex](6x^2 - 3x^3) - (2x^3 + 4x^2 -5)\\\\=6x^2-3x^3-2x^3-4x^2-(-5)\\\\=6x^2-3x^3-2x^3-4x^2+5\qquad\text{combine like terms}\\\\=(-3x^3-2x^3)+(6x^2-4x^2)+5\\\\=\boxed{-5x^3+2x^2+5}[/tex]
If x + 3 is a factor x^2 + kx + 2k, where k is a constant, what is the value of k?
Answers
(-3)^2 + (-3k) + 2k = 0
9 - 3k + 2k =0
9 - k = 0
9 = k
Check
=====
x^2 + 9x + 18 = 0
(x + 3)(x + 6) = 0
These are the two factors. As expected from the givens one of them is (x + 3)
According to the national center for health statistics in 1990 28% of babies in the United States were born to parents who were not married. Throughout the 1990s this increased by approximately 0.6% per year. If this trend continues, in which year will 43% of babies be born out of wedlock?
Answers
If the trend continues, 43% of babies will be born out of wedlock in the year 2015.
Explanation:To find the year in which 43% of babies will be born out of wedlock, we can use the information given. In 1990, 28% of babies were born to unmarried parents. And throughout the 1990s, there was an increase of approximately 0.6% per year. So, we can set up an equation: 28 + 0.6x = 43, where x represents the number of years after 1990.
To solve for x, we can subtract 28 from both sides of the equation: 0.6x = 15. Then, divide both sides by 0.6 to isolate x: x = 15 ÷ 0.6. Using a calculator, we find that x is approximately 25. Therefore, if the trend continues, 43% of babies will be born out of wedlock in the year 1990 + 25 = 2015.
Final answer:
If the trend continues, 43% of babies will be born out of wedlock in the year 2015.
Explanation:
To find the year when 43% of babies will be born out of wedlock, we need to calculate how many years it will take for the percentage to reach 43% based on an initial value of 28% and an annual increase of approximately 0.6%.
Calculate the difference between the target percentage and the initial percentage: 43% - 28% = 15%Divide the difference by the annual increase rate to find the number of years: 15% ÷ 0.6% = 25 yearsAdd the number of years to the initial year (1990) to determine the year when 43% of babies will be born out of wedlock: 1990 + 25 = 2015Therefore, if the trend continues, 43 of babies will be born out of wedlock in 2015.
According to these three facts, which statements are true?
Circle M has center (1, 10) and radius 12.
Circle N is a translation of circle M, 1 unit left.
Circle N is a dilation of circle M with a scale factor of 3.
Select each correct answer. (can be more than one)
The radius of circle N is 12.
Circle N and circle M have equal diameters.
The center of circle N is (0, 10).
Circle M and circle N are similar.
Answers
Answer:
The center of circle N is (0, 10).
Circle M and circle N are similar.
Step-by-step explanation:
It is given circle N is translation of circle M 1 unit left .The radius of circle M is (1,10) when it is translated 1 units left the circle N will have the center (0,10).The y value will remain same while the x coordinated is reduced by 1 that is 1-1=0.The center of circle N is (0, 10)
As the circle N is a dilation of circle M by scale factor 3 so the radius of the two circle will not be same and hence the diameter will also be different.
In translation we have a similar figure ,So circle M and N will be similar.
If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=4/5 and cos b=5/13
Answers
We have then:
sin a = 4/5
a = Asin (4/5)
a = 53.13 degrees.
cos b = 5/13
b = Acos5 / 13
b = 67.38 degrees.
We now calculate cos (a + b). To do this, we replace the previously found values:
cos ((53.13) + (67.38)) = - 0.507688738
Answer:
-0.507688738
Note: there is another way to solve the problem using trigonometric identities.
Answer:
cos(a+b)≈0.507
Step-by-step explanation:
Hi there, in Quadrant I both sine and cosine functions are positive.
This cos (a+b) being a Classical Trigonometrical Identity, the product of the sum between two cosines equals the product of two cosines minus the product of two sines.
But we need to find the value of a and b, so that we can go on. Calculate the arccosine and arcsine function respectively is mandatory
[tex]cos(a+b)=cosa*cosb-sena*senb\\ cos(a+b)=cosa*\frac{5}{13} -\frac{4}{5}*senb\\ a=arcsin(\frac{5}{13})\\a=22.61\\b=arccos(\frac{4}{5})\\b=36.86\\ 5/13=0.38\\4/5=0.8\\cos(a+b)=cos(22.61)*cos(36.86) -sen(22.61)*sen(36.86)\\ cos (a+b)=0.507[/tex]