Answers
⇒ n= 7*x +2
4n= 4*(7x+2)=28x+8=28x+7+1=7*(4x+1)+1
⇒ the remainder is 1
.. n = 7k +2
Then, multiplying by 4, you have
.. 4n = 28k +8
.. 4n = 7(4k +1) +1
The remainder is a) 1.
Related Questions
What is the area of the polygon??
Answers
lets divide the polygon into sections.
the longer rectangle at the bottom has a length of 24 by adding all the numbers
It also has a side width of 5, so 24x5=120.
Onto section 2, you can see the smaller rectangle on top has a length of 11
and width of 5, so 11x6=66. so in total 66+120=186. and that is the square units of this polygon
Hope this helped.
A dress that retails for 160 dollars was on sale 96 dollars by what percent was the dress discounted?
Answers
Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00. The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price. After purchasing the computer, how much does Hakim have left in his bank account? Show your work.
Answers
Each of the steps is shown in the attached work.
He will have $111 left is his account.
Given the arithmetic sequence an = −3 + 9(n − 1), what is the domain for n? all integers where n ≥ 1 all integers all integers where n ≥ 0 all integers where n > 1
Answers
Explanation:
Since this is a sequence, n represents the term number, which is the position in the sequence. We start counting terms of a sequence beginning with term #1, and continue using integers; this means the domain will be all integers greater than or equal to 1.
Each morning papa notes the birds feeding on his bird feeder. so far tis month he has seen 59 blue jays, 68 black crows, 12 red robins and 1 cardinal. if 300 birds list papa's birdfeeder, how many blue jays can we expect to see?
Answers
First, we need to determine the percent of blue jays that he typically sees.
59 + 68 + 12 + 1 = 140 He saw a total of 140 birds.
59 of them were blue jays. So 59 / 140 = 42% of the birds were blue jays.
Multiply 300 by 42% and we have an expected number of 126 blue jays.
A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 6 inches and a height of 5.2 inches. The tube is 14 inches long. Find the lateral surface area of the shipping tube.
Answers
The lateral surface area of the equilateral triangular prism shaped shipping tube is 252 square inches.
Explanation:The question pertains to the calculation of the lateral surface area of a triangular prism shaped shipping tube, more specifically an
equilateral triangular prism
. The lateral area of a triangular prism can be calculated using the formula: Perimeter of the base x length of the prism. Here, the base of the prism is an equilateral triangle, so the perimeter of the base will be 3 x the length of one edge, which in this case is 3 x 6 inches = 18 inches. The length of the prism is given to be 14 inches. Hence, by substituting these values into the formula, the lateral surface area = 18 inches x 14 inches =
252 square inches.
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What is the slant height x of the square pyramid? Enter your answer in the box, express your answer in radical form.
Answers
hypotenuse of the triangle.
Angle between the base of the triangle and the hypotenuse.
We want to find the height of the triangle.
For this, we use the following trigonometric relationship:
[tex]sine (60) = x / 8 [/tex]
From here, we clear the value of x.
We have then:
[tex]x = 8 * sine (60) x = 6.93 m[/tex]
Answer:
The inclined height of the pyramid is given by:
x = 6.93 m
Briyana has a $500 bond with a 6% coupon. Briyana purchased this bond for $460. What is the yield of this new bond?
A. 6%
B. 4.6%
C. 6.3%
D. 6.5%
Answers
To find the yield, we first need to multiply the value of the bond by the coupon percent. This is the amount paid to the bond holder.
500 x 0.06 = 30
So Briyana earned $30 on a bond that cost her $460.
30 / 460 x 100 = 6.5%
Answer:
The correct answer is: 6.5%
Step-by-step explanation:
The base of a regular pyramid is a hexagon. The figure shows a regular hexagon with center C. An apothem is shown as a dashed segment perpendicular to an edge and is labeled as a. A dashed line segment joins the center with the left vertex of the edge perpendicular to the apothem. This segment has a length of 8 centimeters. The angle formed by the edge and the segment measure 60 degrees. What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.
Answers
The area of the base of the pyramid which is a hexagon with given parameters is; 96√3
How to find the area of a Polygon?We are told that the base of the pyramid is a hexagon.
Now, from the given image we can find the base length of the right angle triangle from trigonometric ratio which is;
x/8 = cos 60°
x = 8 cos 60°
x = 4
Thus, length of side of hexagon is;
s = 4 * 2
s = 8
Formula for area of hexagon is given by;
A = ((3√3) * s²)/2
Where;
s is length of a side of hexagon
A = ((3√3) * 8²)/2
A = 96√3
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A JetSki depreciates at 11% of its original value each year. if the Jetski is $8000 at a time of purchase what is the value of a JetSki after five years ?
Answers
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Value after n years = 8000(1 - 0.11)^n = 8000(0.89)^n
so after 5 years the value is 8000(0.89)^5 = $4467 to the nearest dollar.
A rectangular note card has an area of 18 square inches. Its perimeter is 18 inches. What are the dimensions of the note card? inches by inches
Answers
Perimeter is 18 inches
2x + 2y = 18
Area is 18 square inches
xy= 18
2x + 2y = 18 ---------- (1)
xy= 18 ------------------ (2)
From (2):
xy = 18
x = 18/y ------- sub into (1)
2(18/y) + 2y = 18
multiply by y through
36 + 2y^2 = 18y
2y^2 - 18y + 36 = 0
Divide by 2 through
y^2 - 9y + 18 = 0
(y - 3)(y - 6) = 0
y = 3 or y =6
If y = 3 --- sub into (2)
3x = 18
x = 6
If y = 6 .----- sub into (2)
6x = 18
x = 3
So the two dimension is 3 and 6 inches.
The dimension of the rectangle will be 6 inches by 3 inches.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
A rectangular note card has an area of 18 square inches. Its perimeter is 18 inches. Then the equations are given as,
18 = 2(L + W)
9 = L + W ...1
L x W = 18 ...2
From equations 1 and 2, then we have
L x (9 - L) = 18
L² - 9L + 18 = 0
L² - 6L - 3L + 18 = 0
L(L - 6) - 3(L - 6) = 0
(L - 6)(L - 3) = 0
L = 3, 6
Then the width of the rectangle will be calculated as,
W = 9 - 3 = 6
W = 9 - 6 = 3
Then the dimension of the rectangle will be 6 inches by 3 inches.
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Which of the following is the image of C after a rotation of 180° about the origin?
(-5, 2)
(-5, -2)
(-2, 5)
Answers
Answer:
Option A.(-5, 2).
Step-by-step explanation:
Picture attached in the question we know the coordinates of the point C are (5, -2). Now we rotate C with a rotation of 180° about the origin.
As we can see a line connecting C and a new point C'. This line shows the rotation of the poit by 180°.
Therefore the new coordinates of C will be C'(-5, 2).
Option A is the correct option.
Match the following items. In the figure below, several reflections are illustrated. Note one line of symmetry is m and one is l. Pay close attention to the line of reflection being indicated by R l and R m.
Answers
This means that the line of symmetry is line I.
[tex]R_m[/tex]
This means that the line of symmetry is line m.
1. [tex]R_I:T[/tex]
This matches with Q.
In this number, the line of symmetry is I. If you reflect T across line I, you will get point Q. This is because they are right across from each other with line I between them, and they are both the same distance from line I.
2. [tex]R_I:S[/tex]
This matches with S.
Point S lies on the line of symmetry; thus, S reflects itself.
3. [tex]R_I:Z[/tex]
This is similar to number 1. If you reflect Z across line I, you will get point X because they are directly across each other with line I between them and they have the same distance from the line of symmetry.
4. [tex]R_m:S[/tex]
This time, S isn't on the line of symmetry. The line of symmetry is the vertical line m. Point Y matches with point S because they are directly across each other with line m between them. They are also the same distance apart from line m.
5. [tex]R_I:B[/tex]
This is very similar to number 1. This matches with F. The point directly across the line of symmetry is F.
6. [tex]R_I:F[/tex]
This is the exact same as number 5! With the same line of symmetry, B matched with F. Thus, F must match with B!
Here are the matches:
3-X
5-F
6-B
4-Y
1-Q
2-S
In this set, the points reflect across the indicated lines of symmetry. Matches are as follows: 3 corresponds to X, 5 to F, 6 to B, 4 to Y, 1 to Q, and 2 to S.
R_I
This means that the line of symmetry is line I
R_m
This means that the line of symmetry is line m.
1. R_I:T
This matches with Q.
In this number, the line of symmetry is I. If you reflect T across line I, you will get point Q. This is because they are right across from each other with line I between them, and they are both the same distance from line I.
2. R_I:S
This matches with S.
Point S lies on the line of symmetry; thus, S reflects itself.
3. R_I:Z
This is similar to number 1. If you reflect Z across line I, you will get point X because they are directly across each other with line I between them and they have the same distance from the line of symmetry.
4. R_m:S
This time, S isn't on the line of symmetry. The line of symmetry is the vertical line m. Point Y matches with point S because they are directly across each other with line m between them. They are also the same distance apart from line m.
5. R_I:B
This is very similar to number 1. This matches with F. The point directly across the line of symmetry is F.
6. R_I:F
This is the exact same as number 5! With the same line of symmetry, B matched with F. Thus, F must match with B!
Here are the matches:
3-X
5-F
6-B
4-Y
1-Q
2-S
Multiply.
638 × 49
_____
Answers
Is that what you're looking for?
Help plz and explain. ..........
Answers
in the picture. If you need any clarification, just ask in the comments.
Which of the following equations can be used to solve for the radius (r)
Answers
Answer:
The last option is the correct answer: [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Step-by-step explanation:
The area of a circle is given by :
[tex]A=\pi r^{2}[/tex] ; where r is the radius.
Now, lets find the radius.
[tex]\frac{A}{\pi } =r^{2}[/tex]
[tex]\sqrt{\frac{A}{\pi}} =r[/tex]
or [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Therefore, the last option is the correct answer.
△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ? reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x
Answers
Reflections can be across the x-axis meaning that the result of the image is going to be (x,y) to (x,-y), and across the y-axis where the preimage (x,y) would be reflect to result in the image of (-x,y).
Another to kinds of reflection are across the line y=x where preimage (x,y) results in the new point (y,x) and the reflection across the line y=-x where the transformation results in the preimage (-y,-x).
Is given that the triangle ABC was reflected to create the new triangle A'B'C'. The coordinates of the vertices of the triangle ABC are A(3,1), B(1,5), and C(6,9), the new vertices after the reflection of the preimage are A'(-1,-3), B'(-5,-1), and C'(-9,-6).
After the previous said, the transformation occur was a reflection across the line y=-x. You can check this answer by selecting a point, and then looking at the rule for this kind of reflection.
How to find the derivative of a fraction without using the quotient rule?
Answers
(u/v)'=(u*v^(-1))'=u'*v^(-1)+u*(-1)*v^(-2)*v'=u'/v-u*v'/v²=(u'v-uv')/v²
Final answer:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule.
Explanation:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule. Here's an example:
Let's differentiate the function f(x) = (3x + 2) / (2x + 1).
First, identify the numerator and the denominator. In this case, the numerator is 3x + 2 and the denominator is 2x + 1.Apply the product rule by differentiating the numerator and the denominator separately. The derivative of the numerator is 3, and the derivative of the denominator is 2.Next, apply the chain rule by multiplying the derivative of the numerator by the denominator, and subtracting the derivative of the denominator multiplied by the numerator. In this case, the derivative of f(x) is (3 * (2x + 1) - (2 * (3x + 2))) / ((2x + 1)^2).Simplifying further, the derivative of f(x) is (6x + 3 - 6x - 4) / ((2x + 1)^2) = -1 / ((2x + 1)^2).
what is the slope? 0 or undefined
Answers
It is undefined when the line is vertical.
Select the locations on the number line to plot the points 4 1/ 3 and −1 1/3 .
Answers
4 1/ 3
−1 1/3
the answer in the attached figure
Answer:
The locations of given number are shown on the below number line.
Step-by-step explanation:
The given numbers are
[tex]4\dfrac{1}{3} and -1\dfrac{1}{3}[/tex]
We need to plot these points on the given number line.
In the given number write the integers -4,-3,-2,-1,0,1,2,3,4 on points indicated and two sub point between two consecutive points divides the line in three equal parts.
[tex]4\dfrac{1}{3}=4+\dfrac{1}{3}[/tex]
It means [tex]4\dfrac{1}{3}[/tex] lies next to 4 on right side.
[tex]-1\dfrac{1}{3}=-(1+\dfrac{1}{3})=-1-\dfrac{1}{3}[/tex]
It means [tex]-1\dfrac{1}{3}[/tex] lies next to -1 on left side.
Therefore, the locations of given number are shown on the below number line.
If you take Coleman's test grade and divide by 2 and add 27, you get 67. Write and solve an equation to find Coleman's test grade.
Answers
To find Coleman's test grade, set up the equation x/2 + 27 = 67, solve for x by first subtracting 27 and then multiplying by 2 to get x = 80.
Explanation:The student is asking to find Coleman's test grade given that if you take Coleman's test grade, divide by 2, and add 27, the result is 67. To solve for Coleman's test grade, we can set up an equation where Coleman's test grade is represented by x. The equation based on the provided information would be x/2 + 27 = 67. We can solve for x by first subtracting 27 from both sides of the equation to get x/2 = 40, and then multiplying both sides by 2 to find x. Therefore, x = 80, which means Coleman's test grade is 80.
To find Coleman's test grade, we can set up an equation: (x/2) + 27 = 67. By solving this equation, we find that Coleman's test grade is 80.
Explanation:To find Coleman's test grade, we can set up an equation using the information given. Let's represent Coleman's test grade as 'x'. We have the equation: (x/2) + 27 = 67.
To solve this equation, we need to isolate 'x'. We can start by subtracting 27 from both sides of the equation: (x/2) = 40.
Next, we need to get rid of the fraction by multiplying both sides of the equation by 2: x = 80.
So Coleman's test grade is 80.
Which transformations will produce similar, but not congruent, figures?
Triangle PQR is reflected across the x-axis and then rotated 90° clockwise to form triangle P"Q"R" .
Triangle PQR is rotated 90° clockwise and then reflected across the y-axis to form triangle P"Q"R" .
Triangle PQR is rotated 180° counterclockwise and then translated 11 units left to form triangle P"Q"R" .
Triangle PQR is reflected across the y-axis and then dilated by a scale factor of 6 to form triangle P"Q"R" .
Answers
The reason why is because any time you have a dilation with a scale factor other than 1, then the resulting figure is either bigger or smaller compared to the original. If two figures of the same shape are different sizes, then they cannot be congruent. The other transformations of rotation, reflection and translation are what we call rigid transformations. They preserve the size leading to keeping the figures congruent.
Answer:
hello the answer is choice D
Step-by-step explanation:
TIMER CAN SOMEBODY HELP ME???
Answers
here we have arc length is
s=r*theta(in radians)
so we have
s=(4.5cm)(pi/2)= 9pi/4 = 7.1cm
hope this helps. any questions please just ask. thank you kindly
The cost of annual tution at a university increased from $10,500 to $11,300. what is the percent increase in tution to the nearest tenth of a percent? solution and answer
Answers
800/10,500 x 100 = 7.6%
If cost of annual tution at a university increased from $10,500 to $11,300.Then 7.61% increase in tution to the nearest tenth of a percent
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
The cost of annual tution at a university increased from $10,500 to $11,300.
We need to find what percentage increase in tution.
Firstly we have to check how much increased.
11300-10500
800
Hence 800 is increase.
We have to check what is 800 percentage in 10500
percent increase=change/original
origianal=10500
change=800
800/10500=8/105=0.0761
By the definition of percentage we know percent means parts out of 100
0.0761×100=7.61%
Hence 7.61% is the increase in tution to the nearest tenth of a percent.
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What are the solutions of the quadratic equation?
x2 + 11x = –24 (Multiple Choice)
◘ -3, -8
◘ -3, 8
◘ 3, -8
◘ 3, 8
Answers
Then, ( x + 11/2 )^2 = -24 + 121/4;
( x + 11/2 )^2 + 96/4 - 121/4 = 0;
( x + 11/2 )^2 - 25 / 4 = 0;
( x + 11/2 )^2 - (5/2)^2 = 0;
( x + 11/2 - 5/2)·( x + 11/2 + 5/2 ) = 0;
( x + 6/2 )·( x + 16/2 ) = 0;
( x + 3 )· ( x + 8 ) = 0;
x = - 3 or x = -8;
The first choice is the correct answer.
x^2 + 11x = -24
Move everything to the left hand side of the equation. To do this, add 24 to each side.
x^2 + 11x + 24 = 0
Now figure out a combination of two numbers that when added equals 11 but when multiplied equals 24. The answer is 8 and 3.
(x + 8)(x + 3) = 0
You can check the result by doing FOIL.
There are two values for which the equation works: x = -8 and x = -3.
How do you prove cotx/(cscx-sinx)=secx
Answers
Carol makes 9 1/3 cups of snack mix. She put all snack mix into plastic bags. She puts 2/3 cup of the snack mix in each bag. How many plastic bags does Carol need?
Answers
Hope this helps
Esther and Jim plan to add a pond to their property. The area of the pond is 11 square meters. What is the radius?
Answers
@ajaylounsber Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month?,
Answers
PLEASE HELP
8.08, part 2
11. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).
A) y squared over 45 minus x squared over 36 = 1
B) y squared over 81 minus x squared over 36 = 1
C) y squared over 36 minus x squared over 81 = 1
D) y squared over 36 minus x squared over 45 = 1
12. Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 1 divided by 4. x.
A) y squared over 16 minus x squared over 64 = 1
B) y squared over 16 minus x squared over 256 = 1
C) y squared over 256 minus x squared over 16 = 1
D) y squared over 64 minus x squared over 4 = 1
13. Eliminate the parameter.
x = t - 3, y = t2 + 5
A) y = x2 + 6x + 14
B) y = x2 - 14
C) y = x2 - 6x - 14
D) y = x2 + 14
14. Find the rectangular coordinates of the point with the polar coordinates.
ordered pair 3 comma 2 pi divided by 3
A) ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
B) ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
C) ordered pair negative 3 divided by 2 comma 3 divided by 2
D) ordered pair 3 divided by 2 comma negative 3 divided by 2
15. Find all polar coordinates of point P where P = negative pi divided by 6 .
A) (1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ)
B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ)
C) (1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π)
D) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)
16. Determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.
A) (4 square root 2 , 135°), (-4 square root 2 , 315°)
B) (4 square root 2 , 45°), (-4 square root 2 , 225°)
C) (4 square root 2 , 315°), (-4 square root 2 , 135°)
D) (4 square root 2 , 225°), (-4 square root 2 , 45°)
17. The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.
a circular graph with an inner loop on the left
[-5, 5] by [-5, 5] (5 points)
A) r = 3 + 2 cos θ
B) r = 2 + 3 cos θ
C) r = 2 + 2 cos θ
D) r = 4 + cos θ
18. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -2 + 3 cos θ
A) No symmetry
B) y-axis only
C) x-axis only
D) Origin only
19. A railroad tunnel is shaped like a semiellipse, as shown below.
A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.
The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.
20. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 2 cos 3θ
Answers
Answer:
11. Equation of hyperbola having vertices at (0, ±6) and foci at (0, ±9).
is given by [tex]\frac{y^2}{a^2}- \frac{x^2}{b^2}=1[/tex]
also b²= c²-a²
b²=81-36
b²=45
So, Equation becomes , [tex]\frac{y^2}{36}- \frac{x^2}{45}=1[/tex]
Option (D) is correct.
12.Vertices (0, ± 4), Asymptotes = ±1/4.x
equation of asymptote is given by, [tex]x = \pm y \frac{b}{a}[/tex]
[tex]\frac{4}{b}=\frac{1}{4}[/tex]
So a=4 and b=16,
So , equation becomes [tex]\frac{y^2}{16}- \frac{x^2}{256}=1[/tex]
Option (B) is correct.
13. x= t-3, and y = t²+ 5
Replace t by x+3, we get
y= (x+3)² +5
y=x²+ 6x +14
Option (A) is correct.
14. Polar coordinates is given by (r,∅)
Polar coordinates of point is (3, 2π/3)
So, r =3, ∅ =2π/3
x= r cos∅ and y = r sin∅
x=3 Cos (2π/3) and y= 3 Sin (2π/3)
x= -3/2 and y=3√3/2
Option (A) is correct.
14. Polar coordinate is given by (r,∅)
Here , r=1, and ∅ = -π/6
x= r Cos ∅ and y =r Sin∅
x= 1 Cos (-π/6) and y= 1 Sin (-π/6)
x =√3/2 and y =1/2
Option (B) which is B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ) is correct.
16. Two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.
is option (B) which is B) (4 square root 2 , 45°), (-4 square root 2 , 225°).
17. A circular graph with inner loop on the left of a limacon curve is given by
r = a + b Cos∅.
In this case a> b.
So , Option (D) r = 4 + cos θ as well as (A) r = 3 + 2 cos θ looks correct.
18. Equation of limacon curve is given by r = -2 + 3 cos θ, here , a<b
So it is symmetric about y-axis only.Option (B) is correct.