In right triangle PQR, P and Q are complementary angles. The value of sin Q is 9/
41
. What is the value of cos P?
Will be given brainley
Option: A is the correct answer.
The value of cos P is:
A) [tex]\dfrac{9}{41}[/tex]
Step-by-step explanation:We know that if two angles A and B are complementary then,
[tex]A+B=90[/tex]
i.e.
[tex]B=90-A[/tex]
Here we have angle P and angle Q are complementary i.e.
[tex]P=90-Q[/tex]
Also, we are given,
[tex]\sin Q=\dfrac{9}{41}[/tex]
We are asked to find:
[tex]\cos P[/tex]
It could also be written as:
[tex]\cos P=\cos (90-Q)\\\\i.e.\\\\\cos P=\sin Q\\\\i.e.\\\\\cos P=\dfrac{9}{41}[/tex]
A machine is made of two parts, gizmos and widgets. the probability that a gizmo is defective is 0.20, and the probability that a widget is defective is .25. if a machine is assembled with one gizmo and one widget, what is the probability that the machine will not have any defective parts?
Express the polynomial −g + 3g + 2g2 in standard form and then classify it.
Answers plz?
Which quadrilateral will always have 4-fold reflections symmetry
Answer:
square
Step-by-step explanation:
i got it right in edge
What is the difference between log(x/y) and log(x)/log(y)?
The difference between log(x/y) and log(x)/log(y) is that the first expression can be written as log x - log y, which is not equal to the second term.
What is a logarithm function?The opposite of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, the logarithm of 1000 in base 10 is 3, or log₁₀ = 3.
Given:
log(x/y) and log(x) / log(y),
The formula for log(x / y) can be written as shown below,
log(x / y) = log x - log y
As you can see the term is not equal to log(x) / log(y), hence they are different,
The values of the function would differ as in this expression log(x/y) you would first divide x by y and then will take the log of the result,
In the expression log(x) / log(y), you will take the log first individually and then divide the answer.
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Marisha plots her flower garden on a computer. She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x−8)2+(y+10)2=25.
What is the diameter, in meters, of the circular area that gets watered by the sprinkler?
2.5 m
5 m
10 m
20 m
If the radius of the circle will be 5, then the diameter of the circle is 10 m. Then the correct option is C.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
Marisha plots her flower garden on a computer.
She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x − 8)² + (y + 10)² = 25.
Then the equation can be written as
(x − 8)² + (y + 10)² = 5²
The radius of the circle will be 5
Then the diameter of the circle is given as
d = 2r
d = 2 x 5
d = 10 m
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Find the area of the circle if the square has an area of 900 in2. Give your answer in terms of pi
Final answer:
The area of the inscribed circle within a square with an area of 900 in² is 225π in².
Explanation:
The subject here is circle geometry, which is a part of Mathematics. Given that the area of the square is 900 in², we want to find the area of the inscribed circle. The side length a of the square can be found by taking the square root of the area, so a = √{900} = 30 inches. The diameter of the circle is the same as the side of the square, which means the radius r is half of that, so r = 30 / 2 = 15 inches. The formula for the area of a circle is A = πr², and substituting in our value of r, we get:
A = π * (15 in)² = 225π in²
What is the perimeter of this tile.
Imagine if you wrapped a rope tightly around the earth at the equator. how much longer would you have to make the rope if you wanted it to be exactly one foot above the surface all the way around?
Which is a possible number of real roots for a cubic function? Select all that apply.
0
1
2
3
4
what even is this,
I have another Brainliest
What are the x and y intercepts of the line? 2x - 3y = 12
A bicycle shop rents bicycles for $3.50 per hour and helmets for $6 per day. Ashley has $20 to spend to rent a helmet and a bicycle for some number of hours. For how many hours can she rent the bicycle?
Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 2.
What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?
−3
−1.5
1.5
3
Find the measure of the complement and the supplement of the angle.
Matthew ran 3/8 mile and then walked 7/10 mile. Which pair of fractions can he use to find how far he went in all? (A 15/40 and 28/40 (B 35/40 and 21/40 (C 35/40 and 37/40 (D 30/80 and 70/80 *Please Help*
Answer:
Before we could add these numbers, 3/8 and 7/10 need a common denominator. Both 8 and 10 go into 40.
8 goes into 40 five times
3/8= (3*5)/40 = 15/40
10 goes into 40 four times
7/10= (7*4)/40= 28/40
ANSWER: A) 15/40 and 28/40
Hope this helps! :)
Step-by-step explanation:
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .? PLEASE HELP ME, ALSO CAN YOU EXPLAIN HOW YOU GOT THE ANSWER SO I CAN FIGURE IT OUT ON MY OWN THE NEXT TIME.
What is the value of X?
Sin64 degree= cos x
Enter your answer in the box.
Answer:
x = 26° is the answer.
Step-by-step explanation:
We have to find the value of x from the given equation.
sin 64° = cos x
since sin 64° = 0.8987
Therefore cos x = 0.8987
[tex]x = cos^{-1}(0.8987) = 26[/tex]
x = 26°
5. The two trapezoids are similar. Which is a correct proportion for corresponding sides?
A. BA FG
— = —
FE BC
B. BA CD
— = —
FE GD
C. BA AD
— = —
FE GD
D. BA AD
— = —
FE FG
What is the sum of the series?
4+12+36+108+...+8748
8908
10,204
13,120
17,816
Final answer:
The sum of the series 4+12+36+108+...+8748 is found by observing that it is a geometric progression with a common ratio of 3. By comparing the last term to the options, and understanding the rapidly increasing nature of geometric series, the sum is slightly larger than the last term, which only matches the option 8908.
Explanation:
To find the sum of the geometric series 4+12+36+108+...+8748, we first need to identify the common ratio (r) of the series. Each term is obtained by multiplying the previous term by the constant r. In this case, r = 12 / 4 = 36 / 12 = 108 / 36 = 3. The series is therefore a geometric progression with the first term a = 4 and common ratio r = 3.
We can then use the formula for the sum of the first n terms of a geometric series, which is Sn = a(1-rn) / (1-r), where r ≠ 1. However, we need the number of terms (n). To find n, we use the formula for the nth term of a geometric sequence, which is an = a * rn-1. We can solve for n considering the last term given: 8748 = 4 * 3n-1.
However, instead of manually finding the value of n and then the sum, let us approach the problem with the available options. The sum of a geometric series increases very rapidly due to the exponential nature of each subsequent term. Comparing the last term with the provided options, we can infer that the sum has to be a little bit greater than the last term of the series, 8748.
By inspection of the options, the only number that is slightly greater than 8748 is 8908. Therefore, to the quickest approximation and without going through detailed calculations, the sum of the series is 8908.
Consider the two functions shown here. What is the rate of change of each function?
Function 2: y = ½ x + 7
1.The graph shows the distance a car travels at a constant speed. What is the speed of the car?
2.Write an equation that represents the speed of the car.Question 2 options:
Sara bought a soft drink for 4 dollors and 9 candy bars. she spent a total of 49 dollors. how much did each candy bar cost
Help me on this please
The quality-control department of Starr Communications, a manufacturer of video-game DVDs, has determined from records that 1.5% of DVDs sold have video defects, 0.8% have audio defects, and 0.4% have both audio and video defects. What is the probability that a DVD purchased by a customer a. will have a video or audio defect? b. Will not have a video or audio defect?
Final answer:
The probability that a DVD will have a video or audio defect is 1.9%, calculated using the principle of inclusion-exclusion. The probability that a DVD will not have any defect is 98.1%, obtained by subtracting the probability of having a defect from 100%.
Explanation:
To solve the probability that a DVD purchased by a customer will have a video or audio defect or not, we can use the principle of inclusion-exclusion for probabilities.
According to the given data:
P(video defect) = 1.5%P(audio defect) = 0.8%P(both video and audio defects) = 0.4%Part a: The probability that a DVD will have a video or audio defect (at least one type of defect) is calculated by adding the probabilities of each defect and subtracting the probability of both defects occurring, as these are counted twice.
P(either type of defect) = P(video defect) + P(audio defect) - P(both defects)
P(either type of defect) = 1.5% + 0.8% - 0.4% = 1.9%
Part b: To find the probability that a DVD will not have any defect, we subtract the probability of either defect from 100%.
P(no defect) = 100% - P(either type of defect)
P(no defect) = 100% - 1.9% = 98.1%
Therefore, the probability that a DVD will have a video or audio defect is 1.9%, and the probability that a DVD will not have any defect is 98.1%.
Why would ww2 make it easier for African nations to gain independence
After the WW2, Britain had become weaker and its powers had started to decrease. It had lost many of its soldiers and revenues in the world war. Also it needed to focus on the development of its own country now.
so, the rebels in the colonial Africa became stronger than Britishers. So Africans were able to fight back for their freedom and land. Hence, after a while colonial powers left completely from certain parts of Africa.
Consider the proof.
Given: In △ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)
Statement
Reason
1. In △ABC, BD ⊥ AC 1. given
2. In △ADB, c2 = x2 + h2 2. Pythagorean thm.
3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. In △ADB, cos(A) = 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(A) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(A) 9. commutative property
What is the missing reason in Step 8?
a. Pythagorean theorem
b. definition of cosine
c. substitution
d. properties of multiplication
The Law of Cosines is used to find the remaining parts of a triangle when the triangle is not a right triangle and when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known.
The law of cosine states if a,b,c are the three sides of any triangle then [tex] a^{2} =b^{2} +c^{2} -2bccosA [/tex]
In the above proof in statement 8 the x in statement 5 is replaced by c cos A from statement 6.
Among the given options ,option C holds true as the reason for statement 8.
What is the value represented by the letter A on the box plot of data?
{5, 20, 40, 50, 50, 85}
Enter your answer in the box.
The first terms of (x + y)5 is y5.
TRUE
FALSE
Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)
A f(x) = –16x2
B f(x) = – x2
C f(x) = x2
D f(x) = 16x2
Equation of parabola with focus at (0,-4) and directrix is y=4 .
As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is (x,y).
Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
→x²+y²+8 y +16 = y² - 8 y+16
→ x² = -8 y - 8 y= -16 y [ Cancelling y² and 16 from L.H.S and R.H.S ]
So , equation of parabola is , x²= - 16 y or f(x)= -x²/16
The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .
Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]
[tex]d=\sqrt{x^2+(y+4)^2[/tex]
Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]
[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]
[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]
[tex]x^2=-8y-8y[/tex]
[tex]x^2=-16y[/tex]
[tex]y=\dfrac{-x^2}{16}[/tex]
So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
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