Answers
Answer:
[tex]\text{A. }\frac{4\sqrt{14}}{{7}}[/tex]
Step-by-step explanation:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Therefore, we can form a right triangle with non-right angle [tex]\theta[/tex] and its opposite side [tex]\sqrt{7}[/tex] and its adjacent side [tex]5[/tex].
By definition, [tex]\csc \theta=\frac{1}{\sin\theta}[/tex].
In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle. To find the hypotenuse, use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
Solving, we get:
[tex]5^2+\sqrt{7}^2=c^2,\\25+7=c^2,\\c^2=32,\\c=\sqrt{32}=4\sqrt{2}[/tex]
Therefore, we have:
[tex]\csc \theta = \frac{1}{\sin \theta}=\frac{1}{\frac{\sqrt{7}}{4\sqrt{2}}},\\\\\csc \theta=1\cdot \frac{4\sqrt{2}}{\sqrt{7}},\\\\\csc \theta =\frac{4\sqrt{2}}{\sqrt{7}}\cdot \frac{\sqrt{7}}{\sqrt{7}}=\boxed{\text{A. }\frac{4\sqrt{14}}{{7}}}[/tex]
Answer: Choice A) [tex]\frac{4\sqrt{14}}{7}[/tex]
======================================================
Explanation:
Refer to the figure below. We start off drawing a right triangle that has opposite side sqrt(7) and adjacent side 5.
This is because tan = opposite/adjacent.
Use the pythagorean theorem to find the hypotenuse is sqrt(32) which simplifies like so
sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)
The last thing to do is to take the ratio of the hypotenuse over the opposite side. Recall that csc, aka cosecant, is the reciprocal of sine.
sin = opposite/hypotenuse
csc = hypotenuse/opposite
---------
So we get the following
[tex]\csc{\theta} = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc{\theta} = \frac{4\sqrt{2}}{\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2*7}}{\sqrt{7*7}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{\sqrt{49}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{7}\\\\[/tex]
So that's why the answer is choice A.
Related Questions
Name the property shown by the statement. (5 + m) + n = 5+ (m + n)
Answers
Answer:
Associative property of addition
3. Round off the following numbers to three decimal places:
a) 31,1104
b) 0,10989
Answers
B) 0.110
When rounding to three decimal places, you consider if the number to the right of the third decimal place is less than or greater than 5. If it's less than 5, then the digit in the third decimal place stays the same. If it is greater than or equal to 5, then you round the digit in the third decimal place up by one.
Answer:
311.104
010.989
Step-by-step explanation:
In a class of 40 students, a teacher surveyed everyone to see how many had a pet dog (D), a pet cat (C), or a pet bird (B). 28 students have a cat. Of those 28, 10 of them also have a bird. 19 students have a dog. Of those 19, 6 of them also have a cat and 2 of them also have a bird. Out of the 40 students, 2 of them have all three pets.
Draw a Venn Diagram to help you answer the questions.
Find P(B). Write your answer as a percent to the nearest tenth. Do NOT include the percent sign!
Answers
Answer:
This cant be an accurate question, i drew the diagram and before i got to the people who only have birds i already had over 40 people total
Step-by-step explanation:
In a wildlife park, there were 18 gray wolves. After three years, there were 27 gray wolves. What is the percent gain?
Answers
9/18=0.5 (9 as a percentage of original as a decimal)
0.5x100=50 (as a percentage)
50% increase
Answer:
50%.
Step-by-step explanation:
Gain as a fraction is (27-18) /18
= 9/18
= 1/2.
Percent gain = 1/2 * 100 = 50%.
Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the measure of angle b in the image below
Answers
Answer:
Relationship: supplementary
B = 110
Step-by-step explanation:
The two angles shown form straight line
Angles that form a straight line add up to equal 180. Angles that add up to 180 are known as supplementary angles
If the angles add up to equal 180 then b + 70 = 180
Subtract 70 from both sides
b = 110
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A used car dealer prices her cars so that she makes a minimum profit of 15% on each car sold. If she acquired a car
for $4,500, which inequality can be used to determine the acceptable selling prices, p, of that car?
SESE
O 1.15ps4,500
O 1.15p24,500
O P51.15(4,500)
O p21.15(4,500) W
Submit
Answers
How to do long division
Answers
Answer:
if you wanna do long division you have to simply just follow a procedure that is nice and easy so long division method is mainly need to find the square of a number with out using the prime factorization method the procedure is consisting of these of two steps
Obtain the number whose square root is to be computedplace bars every pair of digits starting with the unit digits .Also place a bar on one digit if any not forming a on the extreme left. each pair and the remaining one digit (if any) on the extreme left is called a period think of the largest number whose square is less than or equal to the first period . if this number as the divisor and the quotient put the question above the period and write the product of divisor and question just below the first period.subtract the product of divisor and quotient from the first period and bring down the next point to the right of the remainder this becomes the next dividend.double the question as it appears and enter It to the blank on the right for the next digits, as the next possible divisor.think of a digit to fill the blank in step 6 in such a way that the product of new divisor and its digit is equal to or just less than the new dividend obtained in the step 5 .subtract the product of the digits chosen in steps 7 and the new division from the dividend obtained in step 5 and bring down the next period to the right of the remainder of this becomes new dividend .repeat the steps 5 6 and 7 till all the periods have been taken up .obtain the quotient as a square root of the given number .Hope it helps
A cylinder has a diameter of 24 inches. If its height is half its radius, what is the volume of the cylinder in cubic inches?
A.
72π cu. in.
B.
864π cu. in.
C.
3,456π cu. in.
D.
6,912π cu. in.
Answers
Answer:
B. 864π cu. in.
Step-by-step explanation:
Given the following data;
Diameter = 24 inches
Radius, r = diameter/2 = 24/2 = 12 inches
Height, h = radius/2 = 12/2 = 6 inches
To find the volume of the cylinder in cubic inches;
First of all, we would determine the area of its circular base.
Area of circle = πr²
Area = π * 12²
Area = 144π in² (in terms of pie, π)
Next, we would find the volume of the cylinder;
Mathematically, the volume of a cylinder is given by the formula;
V = πr²h
Where;
V is the volume of a right circular cylinder.r represents the radius of the cylinder.h represents the height of the cylinder.Substituting into the formula, we have;
Volume = 144π * 6
Volume = 864π cu. in
Answer:
B. 864π cu. in.
Step-by-step explanation:
What is the inverse of the statement below?
x →y
A. -X
B. y = x
C. y = x
O D. -x=y
Help plz
Answers
Answer:
d -x=y the awnssr may not be correct but I tried so
9: A rectangular room is 14m long and 8m wide. Jessica is going to carpet the room with carpet that costs £17.50 per square metre. Work out the cost of carpeting the room.
Answers
Answer:
£1,960
Step-by-step explanation:
Find the area of the room using the formula, A = lw
Plug in the length and width, and solve:
A = lw
A = 14(8)
A = 112
So, the area of the room is 112 square meters. Find the cost of carpeting the room by multiplying this by the price, £17.50
112(17.5)
= 1960
So, the price will be £1,960
What is the equation of the line that is parallel to the line y = -1/3 x + 4 and passes through the point (6, 5)?
y = -1/3 x + 3
y = -1/3x + 7
y = 3x – 13
y = 3x + 5
Answers
Answer:
[tex]5)8 \sqrt[6]{?} [/tex]
allá paosgesusussj siisveveu días dbd dusv
some number was divided into 176.9. this quotient was then multiplied by 4 , after which the resulting product was added to 10.2 given this sum totalled -38.6, find the initial number
Answers
9514 1404 393
Answer:
-14.5
Step-by-step explanation:
Let the number be represented by x.
176.9/x . . . . the quotient of some number divided into 176.9
4(176.9/x) . . . . the quotient multiplied by 4
10.2 + 4(176.9/x) . . . . the product added to 10.2
And that totals -38.6:
-38.6 = 10.2 +4(176.9/x)
Solution
-48.8 = 4(176.9/x) . . . . subtract 10.2
-12.2 = 176.9/x . . . . . . . divide by 4
x = 176.9/(-12.2) . . . . . multiply by x/-12.2
x = -14.5 . . . . . . . . . . . finish the division
The initial number is -14.5.
points E, F and D are located on the circle C. The measure of arc ED is 108.
What is the measure of angle ECD ?
Answers
Anthony is building a rectangular shaped swimming pool with a perimeter of 80 feet. Determine a function A(w) that models the area of the top surface of the swimming pool in terms of width W. A(w)= For w>0
Answers
Answer:
[tex]A(w) = 40w - w^2[/tex]
Step-by-step explanation:
Given
[tex]P = 80[/tex] --- perimeter
Required
Define the area in terms of width
The perimeter of the pool is:
[tex]P =2(l + w)[/tex]
Where:
[tex]l\to length[/tex]
[tex]w\to width[/tex]
So:
[tex]80 =2(l + w)[/tex]
Divide by 2
[tex]40 =l + w[/tex]
Make l the subject
[tex]l = 40-w[/tex]
The area is then calculated as;
[tex]A(w) = l * w[/tex]
Substitute: [tex]l = 40-w[/tex]
[tex]A(w) = (40 - w) * w[/tex]
[tex]A(w) = 40w - w^2[/tex]
Given The following right triangle, what is the ratio of Cos(b)
A) 5/13
B) 5/12
C) 13/5
D) 12/13
Answers
Answer:
A. 5/13
Step-by-step explanation:
Cos = Adjacent/Hypotenuse
Adjacent of B = 5
Hypotenuse = 13
Hence CosB = 5/13
100 POINTS!!!!
What is the value of 2 + (-2/3) ^2 ÷1/3 ?
16
3 1/3
-2
0
Answers
Answer:
10/3
Step-by-step explanation:
remember about right order
What is the x-value of point A?
1
6
4
ТА
2
-6
-4
-2
-8
х
-2
-4
-6
please help and hurry!!
Answers
Please click the photo and there are two questions to solve .Please help me guys
Answers
Answer:
Step-by-step explanation:
Distance formula:
[tex]\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}[/tex]
Distance for AB
[tex]\sqrt{(4-2)^2+(1-(-5))^2}=\sqrt{4+36}=\sqrt{40}\\[/tex]
Distance for AC
[tex]\sqrt{(8-2)^2+(-3-(-5))^2}=\sqrt{36+4}=\sqrt{40}[/tex]
2.
same formula solve when positive
[tex]5=\sqrt{(6-3)^2+(y-2)^2}\\25=9+(y-2)^2\\16=(y-2)^2\\4=y-2\\6=y[/tex]
Now when it's negative
[tex]5=\sqrt{(6-3)^2+(y-2)^2}\\25=9+(y-2)^2\\16=(y-2)^2\\-4=y-2\\y=-2[/tex]
so y can equal 6 or -2
Two friends Vicky and Love start a business together. They decided to share their capitals depending upon the variable
expenditure. The capital of the two
partners together is given by polynomial 6x+10x -35, which is the product of
their individual share factors.
On the basis of the above information,
answer the following questions.
i) The total expenditure of Vicky and Love
when x = 10 is (in )
(a) 375 (b) 475
(c) 575 (d) 675
(ii) The shares of the Vicky and Love
individually is
(a) 2x +7, 3x -
5
(b) 3x -5, 2x +7
(c) Both (a) and (b)
(d) None of the above
(iii) The value of x, when their shares are
equal
(a) 12 (b) 10
(c) 8 (d) 6
(iv) The value of x, when their total share is
equal tob0
7
(a)- (b) 3
(c) Both (a) and (b) (d) None of these
(v) The sum of their expenditure is
(a) 5r -2 (b)5x+2 (c) 4x-2 (d) 4x+2
Answers
You bought 6 bars of home made soap from eBay, and weighed them on an electronic scale. They weighed 4.003, 4.006, 4.012, 4.008, 4.004, and 4.009 ounces. What is the average weight of the bars? *DON'T ROUND*
1. 4.010 ounces.
2. 4.007 ounces.
3. 24.042 ounces.
Answers
The average weight of the soap bars is 4.007 ounces. Therefore, option 2 is the correct answer.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, the weight of 6 home made soaps are 4.003, 4.006, 4.012, 4.008, 4.004, and 4.009 ounces.
We know that, average = Sum of all the observations/Number of observations
Here, the average = (4.003+4.006+4.012+4.008+4.004+4.009)/6
= 24.042/6
= 4.007 ounces
Therefore, option 2 is the correct answer.
To learn more about an average visit:
https://brainly.com/question/11195029.
#SPJ3
can somebody help me with this question !
Answers
Answer:
No please! Mr excuse me I am not your type bye
m2 = 10x + 2 and m2) = 9x + 8.
Find x.
U
Solve for x.
Answers
Answer:
x=m2/10 − 1/5
x=m2/9 − 8/9
Step-by-step explanation:
Fred drew the pentagon below how should fred fold the pentagon to determine
Answers
The question is incomplete. The complete question is :
Fred drew the pentagon below how should Fred fold the pentagon to determine if ∠ C is congruent to ∠ D ?
Solution :
Given Fred drew a pentagon as shown below :
In mathematics, congruent angles are defined as the angles having the same measure or the same angle.
A angles of a regular pentagon always have the same measures and each angle is equal to 108 degrees.
In the context, Fred drew a pentagon and if he folds the pentagon along the vertical axis, the side BC aligns with the side DE and thus it makes the ∠ C congruent to ∠ D.
Mrs.Tate is 5 feet 3 inches tall. Her daughter is 4 feet 8 inches tall. How much taller is Mrs.Tate than her daughter?
A) 5 inches
B) 7 inches
C) 1 foot 5 inches
D) 1 foot 7 inches
Answers
========================================================
Explanation:
1 foot = 12 inches
5 feet = 60 inches (multiply both sides by 5)
5 ft, 3 in = 63 inches (add 3 inches to both sides)
Through similar steps, you should find that 4 ft 8 in converts to 56 inches
The difference is 63-56 = 7 inches
Find 3v - 4w if v = -3i and w=-i + 5j. Use < > for
vector notation.
Answers
Answer:
[tex]<-5, 20>[/tex]
Step-by-step explanation:
What we're given:
[tex]\vec{v}=-3i[/tex] [tex]\vec{w}=-i+5j[/tex]The vector [tex]3v-4w[/tex] is then [tex]3(-3i)-4(-i+5j)=-9i+4i-20j=-5i+20j\implies \boxed{<-5, 20>}[/tex]
(1) At the local nursery, 1/2 of the plants for sale are flowers and another 1/10 of them are
bushes. What fraction of the plants for sale are either flowers or bushes?
Answers
Answer:
6/10
Step-by-step explanation:
Look at is a whole. Half the plants are flowers, and just a few are bushes. That leaves other plants that are neither.
We can find a total amount of plants that are either flowers or bushes by combining the two.
Because 1/2 and 1/10 are not currently combinable, you must find a common denominator. This common denominator is 10. If you multiply 2 by 5, you'll get 10.
[tex]\frac{1}{2} +\frac{1}{10}[/tex]
[tex]\frac{5}{1} (\frac{1}{2} )+\frac{1}{10}[/tex]
[tex]\frac{5}{10} +\frac{1}{10}[/tex]
[tex]\frac{6}{10}[/tex]
This means that 6/10 of the whole number of plants are either flowers or bushes. You could also say it means that 4/10 of the plants are something other than flowers or bushes.
I hope this helped :)
Check whether (0, -2) is solution of the equation x - 2y = 4 or not
Answers
Answer:
Step-by-step explanation:
Plugin x = 0 & y = -2 in the LHS of the equation. After substituting, if you get the RHS, then this point is the solution of the equation.
x - 2y = 0 - 2*(-2)
= 0 + 4
= 4 = RHS.
(0,-2) is solution of the equation.
With three people living together, how will the rent and other expenses be split?
Answers
Answer:
Everything will be split in threes. You can do this by either multiplying the cost by 1/3 or dividing by 3.
Step-by-step explanation:
3x + 14 < 38
Please show work
Answers
3x + 14 < 38
Subtract 14 from both sides:
3x < 24
Divide both sides by 3:
X < 8
4. If you color the perfect squares on a multiplication table, you will be coloring a_______ line.
A. Diagonal
B. Vertical
C. Horizontal
D. Zig-zag
Please helpppp
Answers
Answer:
A. Diagonal line
Answer:
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Step-by-step explanation: