Answer:
[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \tan\theta=\frac{6}{5}\text{ and } \cos\theta <0[/tex]
And we want to find the value of sin(2θ).
First, recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the hypotenuse is:
[tex]h=\sqrt{6^2+5^2}=\sqrt{61}[/tex]
Next, note that tangent is positive and cosine is negative. Tangent is positive in QI and QIII. Cosine is negative in QII and QIII.
Hence, we can conclude that θ must be in QIII.
In QIII, sine is negative, cosine is negative, and tangent is positive.
And with respect to θ, our opposite side is 6, adjacent side is 5, and the hypotenuse is √(61).
We can rewrite our expression as:
[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]
Using the above information, substitute:
[tex]\displaystyle =2\left(-\frac{6}{\sqrt{61}}\right)\left(-\frac{5}{\sqrt{61}}\right)[/tex]
Simplify. Hence:
[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]
The area of the right triangle shown is 30 ft squared. The segment XY has a length of 5 ft. Find the length of the hypotenuse.
Answer:
Hypotenuse is 13 ft.
Step-by-step explanation:
A=(1/2)bh
30=(1/2)(5)(h)
30=2.5h
h=12 so ZY = 12ft
Then
[tex]a^{2} +b^{2} =c^{2} \\5^{2} +12^{2} =c^{2} \\25+144=c^{2} \\169=c^{2}\\13=c[/tex]
Find the value of x to the nearest tenth.
46°
Х
20°
Answer:
x = 14.7
Step-by-step explanation:
law of sines:
sin 20°/7 = sin 46°/x
x ·sin(20°) = 7 ·sin(46°)
x = 7 ·sin(46°) / sin(20°)
x = 14.722
the bearing of point x from point is 148 find the bearing of y from x solve it
Explain two different ways that you can solve the exponential equation 3^x+2=8 .
Answer:
solving a quadratic equation by factoring
using the quadratic formula
Step-by-step explanation:
If x= 3, then the length of AB is
Answer:
7
Step-by-step explanation:
AB = 3x-2
Let x=3
AB = 3*3 -2
= 9-2
=7
the average of nine number is 16. the average of 4 of these number is 11. what is the average of the other five number ?
Answer:
11
Step-by-step explanation:
We know formula to find average is,
Average=
Numberofnumbers
Sumofnumbers
Since the average of 10, so the sum of numbers is 5×10=50
As the fifth number is given 6, so rest 4 numbers will be = 50−6=44
Average of first four numbers will be Average=
4
44
=11
please help me answer this
Answer:
1) glazed = 48 people
Chocolate = 72 people
Jelly = 24 people
Coconut = 16 people
2)9th grade = 219 students
10th grade = 167 students
11th grade = 147 students
12th grade = 151 students
Step-by-step explanation:
We are solving the examples;
1) We are told that there are 20 students in Kayla's first period class.
No. that preferred glazed donuts = 6
No. that preferred chocolate donuts = 9
No. that preferred jelly donut = 3
Number that preferred coconut donut = 2
Now,there are a total of 160 students in the entire grade. So to find the Number of students in this entire grade that will each prefer the types of donuts listed above, we will solve as;
For glazed donuts; 6/20 × 160 = 48 people
For chocolate donuts; 9/20 × 160 = 72 people
For jelly donut; 3/20 × 160 = 24 people
For coconut donut; 2/20 × 160 = 16 people
2) Total number of students is;
9th grade = 300 students
10th grade = 275 students
11th grade = 250 students
12th grade = 280 students
73% of 9th grade prefer valorant. Thus;
73% × 300 ≈ 219 students
61% of 10th grade prefer valorant. Thus;
61% × 275 ≈ 167 students
59% of 11th grade prefer valorant. Thus;
59% × 250 ≈ 147 students
54% of 12th grade prefer valorant. Thus;
54% × 280 ≈ 151 students
Determine whether the side lengths could represent a right triangle.
14, 21, 25
Answer:
No
Step-by-step explanation:
Using the given values, 25 is the largest value, so if this were a right triangle, it would be the hypotenuse.
Using Pythagoras' theorem: For this triangle to be a right triangle, √(21² + 14²) must be equal to 25.
√(21² + 14²) = 25.239 (5sf) ≠ 25
Hence the triangle formed is not right.
i dont get these questions on math help i give brainliest
Answer:
here a link to your answer
Step-by-step explanation:
https://brainly.com/question/20419046
plus the answer is b
Find the value of x.
Answer:
d. 16 feet
Step-by-step explanation:
x² + 12² = 20²
x² + 144 = 400
x² + 144 - 144 = 400 - 144
x² = 256
√x² = √256
x = 16
Use the grouping method to factor this polynomial completely.
4x^3 + 8x^2 + 3x + 6
A. (4x^2 + 2)(x+3)
B. (4x^2 + 3)(x+2)
C. (4x^2 + 2)(x+ 2)
D. (4x^2 + 3)(x + 3)
Answer:
B. (4x^2 + 3)(x+2)
Luz catches 83% of the balls in the outfield. What fraction of the balls does she not catch?
Answer:
17/100
Step-by-step explanation:
Answer:
17/100
Step-by-step explanation:
I’ve done this
Helpppppp!!!!!!!!!!!!!
============================================================
Explanation:
As the diagram shows, we have a triangular face with a base of b = 18 and height of h = 13. The area of this triangular face is:
A = 0.5*b*h
A = 0.5*18*13
A = 117 square cm or cm^2
This represents the area of one face, but there are 4 identical copies of this triangular face assuming this tetrahedron is a regular polyhedron. So we have a total surface area of 4*117 = 468 cm^2 which points us to choice B
This is the amount of paint you'll need to cover the outer surface of the pyramid, or you can think of it as the amount of wrapping paper needed. This assumes there are no gaps or overlaps.
What is the domain and range of each relation?
Drag the answer into the box to match each relation.
i don’t get this !!
Answer:
they are talking about the congruent sides of the figures.
Step-by-step explanation:
both are the same triangle, just rotated a little differently... image you rotated them to look the same direction.... angles cd would look like the same angles as JL. same with CE and JM. just imagine the triangles are facing the same direction and then match up the same looking angle letters....
im sorry, it's hard to explain over writting..... :l
Harry solved a quadratic equation. His work is shown below.
In which step did Harry make an error?
(x - 5)² + 6 = 42
(x - 5)^2 = 36 Step 1
x- 5 = 6 step 2
x = 11 Step 3
Choose 1 answer:
Step 1
Step 2
Step 3
Answer:
x = 11 or x = -1
Step-by-step explanation:
(x-5)^2 = 36
(x-5) = 6 or (x-5)= -6
then x = 11 or x = -1
Answer:
Step 2
Step-by-step explanation:
PLEASE THIS IS TIMED I REALLY NEED HELP
PLEASE ONLY PUT CORRECT ANSWER!! :)
answers :
10^21
10^42
24^21
24^42
Answer:
the answer is ..........
c: 24^21
Solve 19=4x+3 .
x = __
Answer:
x = 4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
19=4x+3
-4x=3-19
-4x/-4= -16/-4
x=4
How much paper is needed to cover a square-based pyramid with sides that are 3 inches and faces that have a height of 5 inches?
Answer:You get 21 Square inches i believe
Step-by-step explanation:
Answer:20
Step-by-step explanation:
(SOMEONE HELP ME, NO LINKS)
What is the value of (5 2 -10) divided by 5 x 2 3?
Answer:
The answer of the question is C
24
Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 247 with 85% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places
Answer: [tex]0.791\leq p\leq0.909[/tex]
Step-by-step explanation:
The confidence interval for the population proportion is given by:-
[tex]\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], where [tex]\hat{p}[/tex]= sample proportion, n =sample space , z* = critical z-value.
As per given, we have
[tex]n = 247[/tex]
[tex]\hat{p}=0.85[/tex]
Critical value for 99.9% confidence = 2.576
The required confidence interval will be:
[tex]0.85-2.576\sqrt{\frac{0.85\times0.15}{247}}\leq p\leq 0.85+2.576\sqrt{\frac{0.85\times0.15}{247}}\\\\\Rightarrow\ 0.85-(0.058526)\leq p \leq0.85+(0.058526)\\\\\Rightarrow\ 0.791474\leq p\leq0.908526\approx0.791\leq p\leq0.909[/tex]
The required confidence interval: [tex]0.791\leq p\leq0.909[/tex]
The two quantities are in proportion. Find the missing value.
Answer:
297
Step-by-step explanation:
Since we have to make 9 as the whole, and 33 is the denominator to make 9, we need to multiply 9*33=297.
This makes no sense if you hear it. But trust me it is the right answer i think.
what does sides of equal length mean
Answer:
equilateral
Step-by-step explanation:
A shape is equilateral if all the sides are the same length. In geometry class, people learn about many shapes, such as triangles and squares. A square is equilateral, because all of its sides are the same length. ... The word equal should help you remember what equilateral means.
Answer:
An isosceles triangle has 2 sides of equal length . The dashes on the lines show they are equal in length. The angles at the base of the equal sides are equal.An equailateral triangle has 3 sides of equal length.
1-5. Find the coordinates of the center and the measure of the radius for a circle whose equation is, 1. (x-8)^2+(y+4)^2=12 2. (x+8)^2+(y-4)^2=81 3. X^2+(y-5)^2=9 4. (x+4)^2+(y+5)^2=64 5. (x-7)^2+(y-3)^2=144 6. Write the equation of a circle whose center is (0, -5) and radius is 7. 7. Write the equation of a circle whose center is (6, -1) and diameter is 12. 8. Write the equation of a circle whose center is (-2, 3) and radius is 4. 9. Find the radius of a circle whose center is (0,3) and a y-intercept of (0,7).
Answer:
1. (8,-4), sqrt(12) = 2×sqrt(3)
2. (-8,4), 9
3. (0,5), 3
4. (-4,-5), 8
5. (7,3), 12
6. x^2 + (y+5)^2 = 49
7. (x-6)^2 + (y+1)^2 = 144
8. (x+2)^2 + (y-3)^2 = 16
9. (0-0)^2 + (7-3)^2 = r^2
0 + 16 = r^2
=> r = 4
Step-by-step explanation:
remember, the general equating of a circle is
(x-h)^2 + (y-k)^2 = r^2
Find the value of the variables please please help me out I will mark you the brainly! Please please
Answer:
[tex]20 = \frac{Far \ arc - Near \ arc}{2}\\\\20 = \frac{160 - (2m +12)}{2}\\\\40 = 160 - (2m + 12)\\2m + 12 = 160 - 40\\2m = 120 -12\\2m = 108\\m = 54[/tex]
Answer:
m = 54
Step-by-step explanation:
The secant- secant angle 20° is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] (160 - 2m - 12) = 20° ( multiply both sides by 2 to clear the fraction )
- 2m + 148 = 40° ( subtract 148 from both sides )
- 2m = - 108 ( divide both sides by - 2 )
m = 54
The circumference of a circle is 16 ft.
The radius is ?
Answer:
8/pi or approximately 2.55 ft
Step-by-step explanation:
The formula for the circumference is
C = 2 * pi *r
16 = 2 * pi *r
Divide each side by 2 pi
16 / ( 2 pi) = 2 * pi * r/ ( 2 pi)
8 / pi = r
Using 3.14 for pi
8 / 3.14 = r
2.54777 = r
2.55 =r
Answer:
Radius ≈ 2.55 ft.
Step-by-step explanation:
GIVEN :-
Circumference of circle = 16 ft.TO FIND :-
Radius of the circleFORMULAE TO KNOW BEFORE SOLVING :-
For a circle with radius 'r' & circumference 'c' ,
[tex]r = \frac{c}{2\pi }[/tex]
SOLUTION :-
[tex]Radius = \frac{Circumference}{2\pi } = \frac{16}{2\pi } = \frac{8}{\pi } = 2.55 ft. (appx)[/tex]
What is the slope of the line??
Answer:
The slope is -1/2
Step-by-step explanation:
slope is found by putting the rise over run, which is -2/4 or -1/2
In parallelogram ABCD if m
Answer:
145 degrees
Step-by-step explanation:
All angles in a parallelogram always add up to 360 degrees when added together.
And all angles are the same as the angle adjacent to them.
Since we already know that angle DAB is 35, then the adjacent angle BCD, is also 35.
And since we know that all the angles add up to 360, we just gotta do the math.
35 + 35 = 70 and when you subtract 70 from 360 you get 290. Now all you have to do is divide 290 by 2, and you get 145, which is also the same as angle ABC since they are adjacent to each other.
someone help me please!!!!
hurry
Answer:
z = 30; obtuse isosceles triangle
Step-by-step explanation:
4z + z + 30 = 180
5z + 30 = 180
5z (+ 30 - 30) = 180 - 30
5z = 150
5z/5 = 150/5
z = 30
Since z = 30, and 30 = 30, two angles are congruent to each other and there is only one obtuse angle. Therefore, this is an obtuse isosceles triangle.
Answer:
30, obtuse isosceles
Step-by-step explanation:
Tow sides are the same making it an isosceles triangle. This requires two of the same sides and two of the same angles. This means that z is the sameas 30 degrees.
El agua de un manantial se conduce hasta unos depósitos cilíndricos que miden 12 m de radio de la base y 20 m de altura. Luego se embotella en bidones de 2.5 litros. ¿Cuántos envases se llenan con cada depósito?
Answer:
Con cada depósito se pueden llenar 3,617.28 envases.
Step-by-step explanation:
Dado que el agua de un manantial se conduce hasta unos depósitos cilíndricos que miden 12 m de radio de la base y 20 m de altura, y luego se embotella en bidones de 2.5 litros, para determinar cuántos envases se llenan con cada depósito se debe realizar el siguiente cálculo, sabiendo que el volumen de un cilindro se obtiene multiplicando pi por el radio del cilindro al cuadrado por su altura:
3.14 x (12x12) x 20 = X
3.14 x 144 x 20 = X
452.16 x 20 = X
9,043.2 = X
9,043.2 / 2.5 = X
3,617.28 = X
Por lo tanto, con cada depósito se pueden llenar 3,617.28 envases.