Answers
Answer: option a.
Step-by-step explanation:
By definition, we know that:
[tex]cos^2(\theta)=1-sen^2(\theta)\\\\tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute [tex]sin(\theta)=\frac{6}{11}[/tex] into the first equation, solve for the cosine and simplify. Then, you obtain:
[tex]cos(\theta)=\±\sqrt{1-(\frac{6}{11})^2}\\\\cos(\theta)=\±\sqrt{\frac{85}{121}}\\\\ cos(\theta)=\±\frac{\sqrt{85}}{11}[/tex]
As [tex]sec\theta<0[/tex] then [tex]cos\theta<0[/tex]:
[tex]cos(\theta)=-\frac{\sqrt{85}}{11}[/tex]
Now we can find [tex]tan\theta[/tex]:
[tex]tan\theta=\frac{\frac{6}{11}}{-\frac{\sqrt{85}}{11}}\\\\tan\theta=-\frac{6\sqrt{85}}{85}[/tex]
Answer:
a
Step-by-step explanation:
Related Questions
ABC paint company needs to paint the outside of the building shown. They will also need to paint the roof. What is the surface area that needs to be painted?
3,100 ft 2
4,600 ft 2
4,100 ft 2
4,300 ft 2
see image
Answers
Answer:
3100ft
Step-by-step explanation:
There are 2 sides to the prism that have an area of 50ft * 10ft or 500ft. The total of those will be 500ft * 2 or 1000ft. There are 2 more sides to the prism that have an area of 30ft * 10ft or 300ft. The total would be 300ft * 2 or 600ft. Then the last two sides to the prism have an area of 50ft * 30ft or 1500ft. Since we're imagining this prism to be a house, you can't paint the floor (well, I guess you could but I think they want us to leave that part out because you can't pick the house up to paint the bottom that would be ridiculous). So the surface area is each area added, or 1000ft + 600ft + 1500ft = 3100ft.
Answer:
3,100 ft^2
Step-by-step explanation:
jamal feeds 14.4 pounds of dog food to the 24 dogs at a shelter. each dog gets the same amount of food. six of the dogs eat only 0.4 pound of food each. how much food is left in the bowls of these six dogs in all?
A . 0.2lbs
B. 0.6lbs
C. 1.2lbs
D. 12lbs
Answers
Answer:
1.2 pounds
Step-by-step explanation:
As mentioned in the question,
14.4 pounds of foods is distributed among 24 dogs.
Therefore, each dog gets: [tex]\frac{14.4 (pounds)}{24} = 0.6 pounds[/tex]
6 dogs eat only 0.4 pounds, so the amount left: ( 0.6 - 0.4 ) = 0.2 pounds
Hence, the total food left in the bowls of six dogs = 6 * 0.2 = 1.2 pounds
20 PTS!!!! What is the probability that a randomly selected person is on the swim team? Express the probability as a percent rounded to the nearest tenth of a percent. Enter your answer in the box.
Answers
There are 67 total people and 28 people on the swim team.
The probability of picking someone on the swim team would be 28/67 which is equal to 41.8%
Answer:
The probability that a randomly selected person is on the swim team is 41.79%
Step-by-step explanation:
ProbabilityProbability means possibility of occurrence. It is a branch of mathematics which deals with the occurrence of particular event out of total random events.The favorable event will be 28
The total no of event will be 67
So The probability will be = [tex]\frac{no of favorable events}{Total no of event}[/tex]
= [tex]\frac{28}{67}[/tex]
= 41.79%
Thus the probability that a randomly selected person is on the swim team is 41.79% .
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Ben missed math class because he was sick. He has 10 math problems he needs to complete for homework and submit by 4pm. Ben does not know how to solve the math problems and does not want to get a bad grade. How can Ben use his self advocacy skills to help himself?
Answers
Answer: Ben could ask his peers or a trusted adult for help, or Ben could use reliable sources to help him with any questions he might have. Ben could also try his best, if he doesn't get a good grade at least he doesn't have a missing assignment.
Step-by-step explanation:
A rectangular fish pond is 21 ft2 in area. If the owner can surround the pond with a 20-foot fence, what are the dimensions of the pond?
3.5 ft by 6 ft
4 ft by 6 ft
3 ft by 7 ft
3.5 ft by 7 ft
Answers
Answer:
3 ft by 7 ft
Step-by-step explanation:
Try the solutions and find the one that works.
3.5 × 6 — area OK, perimeter = 19 ft
4 × 6 — area = 24 ft², perimeter OK
3 × 7 — area OK, perimeter OK
3.5 × 7 — area 24.5 ft², perimeter 21 ft
___
The perimeter is the sum of the four side lengths; the area is the product of two adjacent side lengths.
There were 4 apple trees planted and 3 pecan trees. 2 peach trees for 3 pecan trees. If there 24 peach trees, how many apple trees would you have?
Answers
➷ 4 : 3
? : 3 : 2
The overall ratio is:
4 : 3 : 2 for apple trees to pecan trees, to peach trees.
24/2 = 12
12 x 4 = 48
There would be 48 apple trees.
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The ratio of any number should be taken in its simplest form only. If there were 24 peach trees, then 48 apple trees you would have.
If 4 apple trees are planted then 3 pecan trees are planted.
If 2 peach trees are planted then 3 pecan trees are planted.
Therefore, the ratio will be:
Apple Trees Pecan Trees
4 3
Peach Trees Pecan Trees
2 3
Thus, the ratio is 4:3:2.
Two values are equal to 24 peach trees.
One value is equal to the 12 trees.
The value of an apple is 4, therefore the number of apple trees will be 48 trees.
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How many ways can 8 players be chosen from 10 players
Answers
Use the table of values below to select the correct statement.
A.
The function f is linear and is growing by equal differences over equal intervals. The growth rate is 6.
B.
The function f is exponential and is growing by equal factors over equal intervals. The growth factor is 245%.
C.
The function f is exponential and is growing by equal factors over equal intervals. The growth factor is 600%.
D.
The function f is linear and is growing by equal differences over equal intervals. The growth rate is 3.5.
Answers
Answer:
do u know the answer??
i think it is The function f is exponential and is growing by equal factors over equal intervals. The growth factor is 245%.
Step-by-step explanation:
The function f is exponential and is growing by equal factors over equal intervals. The growth factor is 245% option (B) is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have a table in which the x, and f(x) data are shown.
As we can see the value of f(x) is increasing rapidly for every x.
The exponential function is:
y = a(1+r)×
After plugging all points and finding the value of a and r
y = 6.9402(2.4495)×
The exponential growth factor = 1 + r = 2.4495 ≈ 2.45 or 245%
Thus, the function f is exponential and is growing by equal factors over equal intervals. The growth factor is 245% option (B) is correct.
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FIND THE DEGREE MEASURE OF ANGLE DPR.
Answers
[tex]\widehat{DPR}=\frac{1}{2}(\stackrel\frown{ET}-\stackrel\frown{DR}) = \frac{1}{2} (118 - 26) = \frac{92}{2} = 46°[/tex]
Write the augmented matrix corresponding to the system of equations. 3x + 4y − 5z = 8 x + 2z = −3 4x − 3y = 6 Incorrect: Your answer is incorrect.
Answers
3x+4y-5z=8
1x+0y+2z=-3
4x-3y+0z=6
|`3 4 (-5)`||`x`| |`8`|
| 1 0 2 | |y |=|-3 |
|.4 (-3) 0 .||.z.| |.6.|
a pipe cleaner 20cm long. it is bent into a rectangle. use a quadratic model to calculate the dimensions that give the maximum area.
Answers
Answer:
5 cm by 5 cm
Step-by-step explanation:
The perimeter of this rectangle is 20 cm, and the relevant formula is
P = 20 cm = 2W + 2L. Then W + L = 10 cm, or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized. Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
The dimensions that give the maximum area is 5 cm by 5 cm.
Given:
The perimeter of this rectangle is 20 cm, and formula for perimeter is
P= 2(W+L)
P = 20 cm = 2W + 2L.
Then W + L = 10 cm,
or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized.
On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
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A football stadium holds 52,000 fans. A college student is doing research and determines that on any given game day, the home team has five times as many fans as the visiting team. In order to help the student in his research, he represents the number of home team tickets as H and the visiting team’s tickets as V.
Which system of equations does the college student use to determine how many tickets each team gets?
Answers
Answer:
Option d
Step-by-step explanation:
We know that 52,000 fans can fit into the stadium.
Then the amount of tickets that can be sold must equal 52,000.
If we call H the number of tickets for the home team and call V the number of tickets for the visiting team, then:
[tex]H + V = 52,000[/tex]
Then, we know that the local team has 5 times more fans than the visiting team. So we can write that:
[tex]H = 5V\\H-5V = 0[/tex]
Finally, the system of equations sought is:
[tex]H - 5V = 0\\H + V = 52 000[/tex]
A printer 8s typesetting a book and he needs pn piece of type for each digit in the page number of the book and each piece of type can be used only once for example page 3 and page 33 will require 3 piece of type how many twos will he need to number pages 1 through 232?
Answers
Answer:
Step-by-step explanation:
Simplify the given equation. please don't solve for x! it says SIMPLIFY!
17x - 6 + 3x - 5 = x + 11 + 4x
Answers
Answer:
x= 22/15
Step-by-step explanation:
20x-11=5x+11
20x-5x=11+11
15x=22
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A cylinder has diameter 34 m and height 27 m. A label at bottom states drawing not to scale.
Find the volume of the cylinder. Use 3.14 for
π
PLEASE WRITE YOUR ANSWER IN STEPS CLEAR, I WILL GVE 100 POINTS ASAP AND BRAINLIEST
Answers
The volume of the cylinder is 25295.26 cubic meters.
Explanation:To find the volume of a cylinder, we can use the formula V = π * r^2 * h, where r is the radius and h is the height. Given that the diameter is 34 m, the radius is half of that, which is 17 m. The height is given as 27 m.
Plugging in the values into the formula, we get V = 3.14 * (17^2) * 27. Evaluating this expression, we find that the volume of the cylinder is 25295.26 cubic meters.
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The volume of a cylinder is 25295.26 cubic meters.
Explanation:To find the volume of a cylinder, use the formula V = πr^2h, where V represents the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, the diameter of the cylinder is given as 34 m, so the radius is half of the diameter, or 17 m.
The height of the cylinder is given as 27 m. Substitute these values into the formula to calculate the volume.
V = 3.14 × (17^2) × 27
= 25295.26 cubic meters.
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What is the value of x?
Answers
Answer:
x = 35
Step-by-step explanation:
Since they are vertical angles, the angles are congruent and therefore you can set them equal to each other.
4x + 20 = 3x + 55
Have x on one side of the equation by subtracting 3x from both sides.
x + 20 = 55
Subtract 20 from both sides of the equation.
x = 35
Which of the following equations represents a line that is paraellel to Y=5x-4 and passes through the point (3, 4)?
A. Y=5x-7
B. Y=5x+19
C. Y=-1/5x-4
D. Y=5x-11
Answers
choice D is the correct solution
PARALLEL slopes always have the same slope no matter what because they are parallel
The equation of the line that is parallel to y = 5x-4 and passes through the point (3, 4) is y = 5x - 11 because it has the same slope, 5, as the given line depicting parallelism and it passes through the specified point.
Explanation:In Mathematics, two lines are parallel if their slopes are equal. In this case, the given line is y = 5x - 4, and its slope is 5. To find an equation of a line that is parallel to this line and passes through a specific point, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes.
Replace m with 5 (the slope of the given line), and (x1, y1) with (3, 4) (the point through which the line passes), and we have y - 4 = 5(x - 3). Distributing and simplifying, we get y = 5x - 15 + 4 = 5x -11. Therefore, the equation of the line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
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Graph the following equation
[tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex]
If you can. Also, what is the Oblique Asymptote.
Answers
Answer:
Graphic attached
Step-by-step explanation:
The oblique asymptote of the function has the shape of a line of the form
[tex]y = mx + b[/tex]
We need to find the slope m and the intercept b.
The oblique asymptote is found by these two limits:
[tex]m = \lim_{x \to \infty}\frac{f(x)}{x}\\\\b = \lim_{x \to \infty}[f(x) - mx][/tex]
If [tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex] then:
[tex]m = \lim_{x \to \infty} \frac{\frac{(2x+3)(x-6)}{(x+2)(x-1)}}{x}\\\\m = \lim_{x \to \infty} \frac{2x^2-9x-18}{x^3 +x^2 -2x}\\\\m = 0[/tex]
The slope is 0. Therefore the function has no oblique asymptote.
Horizontal asymptote:
[tex]y = 2[/tex]
Vertical asymptote
[tex]x = -2\\x = 1[/tex]
Which pay is equivalent to 16 $ per hour A) 48 for 3 hours B)120 for 12 hours C) 60 for 5 hours D) 96 for 9 hours
Answers
Answer:
The answer is A. 48 divided by 3 equals 16. Therefore, if you earn $48 for 3 hours, then you are earning $16 per hour.
Step-by-step explanation:
Hey there!
The correct answer is A. $48 for 3 hours
I figured this out by multiplying 16 by 3 which equals 48
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
Mark needs 2 3/4 cups of sugar to make cookies he has 1 7/8 cups of sugar how much more sugar does mark need
Answers
so, we have the denominators of 4 and 8, thus our LCD will just be 8, but let's firstly convert the mixed fractions to improper fractions and find their difference.
[tex]\bf \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}}~\hfill \stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{11}{4}-\cfrac{15}{8}\implies \stackrel{\textit{using LCD of 8}}{\cfrac{(2)11~~-~~(1)15}{8}}\implies \cfrac{22-15}{8}\implies \cfrac{7}{8}[/tex]
There are 11 more goats than sheep in the farm. Together there are 137 animals in the farm. How many goats and how many sheep are there?
Answers
Answer:
The number of goats in the farm is [tex]74[/tex]
The number of sheep in the farm is [tex]63[/tex]
Step-by-step explanation:
Let
x----> the number of goats in the farm
y----> the number of sheep
we know that
[tex]x+y=137[/tex] ----> equation A
[tex]x=y+11[/tex] -----> equation B
substitute the equation B in equation A and solve for y
[tex](y+11)+y=137[/tex]
[tex]2y=137-11[/tex]
[tex]2y=126[/tex]
[tex]y=126/2=63[/tex]
Find the value of x
[tex]x=63+11=74[/tex]
therefore
The number of goats in the farm is [tex]74[/tex]
The number of sheep in the farm is [tex]63[/tex]
To the nearest hundredth, what is the value of x?
Use a trigonometric ratio to compute a distance
Question 3 options:
62.25
100.25
101.12
128.32
Answers
➷ cos38 = 79/x
x = 79/cos38
x = 100.2524
The correct option would be 100.25
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Answer:
100.25
Step-by-step explanation:
Using the cosine ration in the right triangle, then
cos38° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{79}{x}[/tex]
Multiply both sides by x
x × cos38° = 79 ( divide both sides by cos38° )
x = [tex]\frac{79}{cos38}[/tex] ≈ 100.25
Which polynomial represents a sum of cubes?
x^3 - 64
8x^3 + 125
16x^3 + 1
27x^3 + 4
Answers
Answer:
8x³ + 125
Step-by-step explanation:
Cubes: look for the exponent 3 and for perfect cubes such as 1, 8, 27, ...
8x^3 + 125 is a sum, and 8 is a perfect cube (the cube of 2), and x^3 is a cube, and 125 is a cube.
Thus, the correct answer is 8x^3 + 125 (which is equivalent to
(2x)³ + 5³).
John wrote 1/5 of a paper in 1/4 of an hour how long did it take him to write an entire paper?\
Answers
Answer:
[tex]1\frac{1}{4}\ hours[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{(1/4)}{(1/5)}\frac{hour}{paper}=\frac{x}{1}\frac{hour}{paper} \\ \\x=5/4\ hours[/tex]
covert to mixed number
[tex]5/4\ hours=1\frac{1}{4}\ hours[/tex]
(Q4) Which values of a and b in the exponential function y = a (bx) would result in the following graph?
Answers
Answer: second option.
Step-by-step explanation:
By definition, you know that:
[tex]b^0=1[/tex]
You can see in the graph that the interception with the y-axis is at -1.
Therefore, in that point: x=0 and y=-2
Substitute into the function and solve for a:
[tex]-1=a(b)^0\\-1=a(1)\\a=-1[/tex]
Now, choose any point of the function and substitute this point and the value of a into the function and solve for b. Then you obtain:
Point (2,-4)
[tex]-4=-1(b)^2\\\frac{-4}{-1}=b^2\\b=\sqrt{4}\\b=2[/tex]
Answer:
Its B
Step-by-step explanation:
Because it is
On edge
A circle has a radius of 4/9 units and is centered at (-6.2,5.8). Write an equation of this circle
Answers
Answer:
[tex](x+6.2)^2 + (y-5.8)^2 = \frac{16}{81}[/tex]
Step-by-step explanation:
The vertex form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h,k) is the center of the circle and r is the radius. This circle has center (-6.2, 5.8) and r= 4/9. Substitute h = -6.2, k = 5.8 and r = 4/9 into the vertex form. Then simplify for the equation.
[tex](x-h)^2 + (y-k)^2 = r^2\\(x--6.2)^2 + (y-5.8)^2 = \frac{4}{9}^2\\ (x+6.2)^2 + (y-5.8)^2 = \frac{16}{81}[/tex]
The circumference of a circular rug is 24.8 meters. What is the area of the rug? Use 3.1 for pi
Answers
Answer:
49.6 square meters
Step-by-step explanation:
first, circumference is 2*pi*r, so we want to find r. so we take 2*pi*r=24.8 and solve for r which is 4.
Now, area is pi*r^2 so pi*4^2 = pi*16 = 49.6
First, let’s find the radius of the rug. The radius is equal to the circumference divided by 2pi, or 2 * 3.1, which is 6.2, in this case.
24.8/6.2
4
The radius is 4. The area of a circle is pi times the radius squared.
3.1 * 4^2
3.1 * 16
49.6
So, the area of the rug is 49.6 square meters.
The landscaper charges a rate of $40 per hour to plant trees.Amelia paid a total of $725 for the trees and for the landscaper to plant them. How many hours did it take the land scaper to plant the trees?
Answers
23.5 hours is the anser yeteressdfdsfsjufrhhmrgijfjfxkjvnrtjeigrjiegre
Find the area of the parallelogram. HELP ASAP!!
Answers
Answer:
A) 300 cm2
Step-by-step explanation:
First you have to find height
use Pythagorean theorem: a2 + b2 = c2
[tex]h^{2}+ 8^{2} = 17^{2}[/tex]
h2 + 64 =289
h2 = 289-64
h2 = 225
h= 15
now the area
A = a * h
A = 20 * 15
A = 300 cm2
Answer:
[tex]\large\boxed{A=300\ cm^2}[/tex]
Step-by-step explanation:
The formula of an area of a parallelogram:
[tex]A=bh[/tex]
b - base
h - height
Use the Pythagorean theorem to calculate a height h:
[tex]h^2+8^2=17^2[/tex]
[tex]h^2+64=289[/tex] subtract 64 from both sides
[tex]h^2=225\to h=\sqrt{225}\\\\h=15\ cm[/tex]
Calculate the area:
[tex]A=(20)(15)=300[/tex]
graphing a line given its slope and y-intercept
graph the line - 3 / 2 and y-intercept -2
the fraction is negative
Answers
Answer:
see below for a graph
Step-by-step explanation:
One point can be plotted at the y-intercept: (0, -2). Since the slope tells you the line drops 3 units for each 2 units to the right, the point (2, -5) will be another point on the line. The graph will go through those two points.