Answer:
cosθ = [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
Given
sinθ = - [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
This is a 5- 12- 13 right triangle
with opposite = 5, adjacent = 12 , hypotenuse = 13
since θ is in 4th quadrant then cosθ > 0
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex]
The trigonometric ratio of cos θ in quadrant IV is 12/13.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
Sin θ = -5/13, and
θ lies in the quadrant IV.
By trigonometric ratio,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
⇒ [tex]sin \theta = -\frac{5}{13}[/tex]
Here opposite side = 5 and
hypotenuse side = 13
The adjacent side can be calculated by using the Pythagoras theorem,
[tex]Hypotenuse^{2} = opposite^{2} +adjacent^{2}[/tex]
⇒ [tex]adjacent = \sqrt{hypotenuse^{2} -opposite^{2} }[/tex]
⇒ [tex]adjacent = \sqrt{13^{2} -5^{2} }[/tex]
⇒ [tex]adjacent = \sqrt{169 -25 }[/tex]
⇒ [tex]adjacent = \sqrt{144}[/tex]
⇒ [tex]adjacent = 12[/tex]
Thus [tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex]
⇒ [tex]cos \theta = \frac{12}{13}[/tex]
θ lies in the quadrant IV, so cos θ > 0.
Hence we can conclude that the trigonometric ratio of cos θ in quadrant IV is 12/13.
Learn more about trigonometry here
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Derrick is a middle distance runner for his college indoor track team. One day his coach suggests a workout in which Derrick runs 3 repetitions of 7 2/3 laps at full speed with a two-minute rest between each repitition. How many laps does he run in this workout?
Answer:uttt
Step-by-step explanation:
PQR is a triangle. PR= 23cm, PQ= 22cm and angle QPR= 48 degrees. Calculate length of QR.
Answer:
The length of QR is approximately 18.3 cm
Step-by-step explanation:
The given parameters are;
The length of the side PR = 23 cm
The length of the side PQ = 22 cm
The measure of the angle QPR = 48°
By cosine rule, we have;
[tex]\overline{QR}^2 = \overline{PR}^2 + \overline{PQ}^2 - 2 \times \overline{PR} \times \overline{PQ} \times cos(\angle QPR)[/tex]
Plugging in the values gives;
[tex]\overline{QR}^2 = 23^2 + 22^2 - 2 \times 23 \times 22\times cos(48^{\circ}) \approx 335.84[/tex]
[tex]\therefore \overline{QR} \approx \sqrt{335.84} \approx 18.3[/tex]
The length of QR ≈ 18.3 cm
The result of the expression 8 * 5 ** 0 is *
a. 8
b. 1
c. 0
d. 40
HELP ME PLEASE [WILL GIVE BRAINLIEST TO BEST ANSWER WITH BEST EXPLAINATION]
Hi there!
[tex]\large\boxed{\text{33 in}^2}[/tex]
Find the total area by breaking the figure into two rectangles, one trapezoid, and one triangle.
Rectangles:
A = l × w
A = 2.75 × 4 = 11 in²
Solve for the other rectangle's length by subtracting from the total:
12 - 2 - 3 - 4 = 3
A = 3 × 3 = 9 in²
Total rectangle area: 11 + 9 = 20 in²
Trapezoid:
A = 1/2(b1 + b2)h
A = 1/2(4.25 + 2.75)3 = 21/2 = 10.5 in²
Triangle:
A = 1/2(bh)
A = 1/2(2.5 · 2) = 2.5 in²
Add up all of the areas:
20 + 10.5 + 2.5 = 33 in²
Please help with work shown (only if possible)
Answer:
The cylindrical one
Step-by-step explanation:
We know that the container does not have anything inside it, and we only want the surface, so we will figure out the surface area. The less surface area the package has, the less plastic is used.
The surface area for a cylinder is 2πrh +2πr². Plugging 5 in for r (the radius) and 19 in for the height, we get
2π(5)(19) + 2π(5)² = 753.98
The surface area for a rectangular prism is 2(wl + hl +hw), with 10 being the width, 12 being the length, and 19 being the height in this example, resulting in
2(10*12 + 19 * 12 + 10 * 19) = 1076
The surface area for the cylinder will clearly have less surface area/plastic
Given mlln, find the value of x.
(x+27)
(2x-7)
Answer:
x=34
Step-by-step explanation:
The angles are corresponding angles so they are equal if m is parallel to n
x+27 = 2x -7
Subtract x from each side
x+27 -x =2x-x-7
27 = x-7
Add 7 to each side
27+7 = x-7+7
34 =x
Mike and Sarah are packing boxes at a factory. Mike packs 30 boxes each hour. Sarah packs 15 boxes each hour. How many boxes will each person have packed after an 8 hour shift?
Answer:
Mike= 240 boxes
Sarah= 120 boxes
Step-by-step explanation:
Mike and Sarah are packing boxes at a company
Mike packs 30 boxes each hour, after an 8 hour shift the number of boxes he will pack is
= 30×8
= 240
Sarah packs 15 boxes each hour, afterr an 8 hour shift the number of boxes she will pack is
= 15×8
= 120
Hence after the 8 hours shift Mike will pack 240 boxes while Sarah will pack 120 boxes
Find the perimeter of a field with the following dimensions: Length: x² + 3x - 1 Width: 2x + 3
Answer:
B. 2x²+10x+4
Step-by-step explanation:
the perimeter =
2×(x²+3x-1+2x+3)
= 2×(x²+5x+2)
= 2x²+10x+4
State the amplitude and period of f(x) = 3cos9/5t
Answer:
The amplitude is 3 and the period is 10π/9.
Step-by-step explanation:
The standard cosine function is in the form:
[tex]y=a\cos(b(x-c))+d[/tex]
Where |a| is the amplitude, 2π/b is the period, c is the phase shift, and d is the vertical shift.
We have the function:
[tex]f(x)=\displaystyle 3\cos\frac{9}{5}t[/tex]
We can rewrite this as:
[tex]\displaystyle f(x)=(3)\cos\left(\frac{9}{5}\left(t-0\right)\right)-(0)[/tex]
Therefore, a = 3, b = 9/5, c = 0, and d = 0.
Hence, our amplitude is |3| = 3.
Our period will be:
[tex]\displaystyle \text{Period}=\frac{2\pi}{9/5}=2\pi \cdot \frac{5}{9}=\frac{10\pi}{9}[/tex]
Question 6
1 pts
6)
What expression is equivalent to (x - 5)(x + 5) ?
a) x2 - 10x + 25
b) b) x2 - 25
c) x2 + 25
d) x2 + 10x - 25
Answer:
-33x o hope this helps and the rest you just do the same
which one is the nth term if a1=15 and d= -3
Answer:
nth term = 18 - 3n
Step-by-step explanation:
nth term = a + (n - 1)d
a1 = 15
d = -3
nth term = a + (n - 1)d
= 15 + (n - 1)-3
= 15 + (-3n + 3)
= 15 - 3n + 3
= 18 - 3n
nth term = 18 - 3n
For instance, if you want to find the 10th term
nth term = 18 - 3n
10th term = 18 - 3(10)
= 18 - 30
= -12
10th term = -12
Solve for x.
Please help
Answer:
11
Step-by-step explanation:
59*2= 118
118+75= 193
360-193=167
167+20=187
187/17 = 11
Rationalize the denominator:
Please give step by step solution
Answer:
1 + i
Step-by-step explanation:
To rationalize multiply numerator and denominator by (2 + i )
[tex]\frac{3+i}{2-i}= \frac{3+i}{2-i} \times \frac{2+i}{2+i} = \frac{(3+i)(2+i)}{(2-i)(2+i)} = \frac{6+3i+2i-1}{4-(-1)} = \frac{5+5i}{5} = 1 + i[/tex]
(24 + 4) ÷ 2 = (24 ÷ 2) + ( __ ÷ 2)
i dont know this
Answer:
4
Step-by-step explanation:
(24+4) ÷ 2 = (24 ÷ 2) + (4 ÷ 2)
28÷2 = 14
Check:
24÷2 = 12
4÷2 = 2
12+2=14
Answer:
The answer is 4.
Step-by-step explanation:
(24 + 4) ÷ 2 = (24 ÷ 2) + (x ÷2)
=28 ÷ 2 = 12 + (x÷2)
14 = 12 + (x ÷ 2)
14 - 12 = x ÷ 2
2 = x ÷ 2
2 × 2 = x
x = 4
Please help I am so confused lol. I’ll mark you the brainiest
Answer:
Since the pentagon is regular, the line connecting the centre of the circle to the verticles (A,B,C,D,E) should inscribe an equal angle in them
You can see what I mean in the attachment
So to mark other points we follow the following steps
Connect OAWith OA as base, make angle of 72°. Say th new line is OB. Similarly, do for the rest of themThis is a cyclic pentagonStep-by-step explanation:
Hope this helps... Pls vote as brainliest
sorry but I need help AGAIN so sorry but help me plz
Answer:hfhfhfh
Step-by-step explanation:
hfhfhfh
ricardo have two snacks.One snack has the mass of 167 grams,and the other has 243 grams what is the difference in the mass of snacks
50 point HELP ASAP Question: A rectangle has sides measuring (3x + 8) units and (6x + 5) units.
Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?
Answer:
see below
Step-by-step explanation:
(3x + 8) units by (6x + 5) units.
A = l*w
= (3x+8)(6x+5)
Distribute
3x*(6x+5) + 8(6x+5)
18x^2 +15x + 48x +40
Combine terms
18x^2+63x+40 units^2
The degree is 2 ( the highest power of x)
This is a trinomial ( it has 3 terms)
Multiplication is closed for polynomial multiplication
We started with polynomials and we ended up with a polynomial.
Find the unknown angle and explain how plzzz
In a straight line, like the one presented before you, there is 180 degrees. So that means 115 degrees + x is gonna equal 180.
So that means, x is gonna be 180 - 115. So x is 65 degrees
On a grocery store shelf, there are 16 loaves of white bread and 24 loaves of wheat bread. A shopper randomly selects a loaf of bread.
What is the PROBABILITY it is WHEAT
Round to the NEAREST PERCENT!
Answer:
60%
Step-by-step explanation:
16 loaves of white bread and 24 loaves of wheat bread. = 40 loaves of bread
P( wheat) = number of wheat/ total
= 24/40
=.6
=60%
Figure ABCD is a parallelogram.
What are the measures of angles B and D?
A
B
O ZB = 55°; ZD = 55°
(2n + 15)
O ZB = 55°, ZD = 125°
O ZB = 97°, 2D = 97°
O ZB = 83° 2D = 97°
(3n - 5)
Answer:
<B=55°, <D=55°
Step-by-step explanation:
in a parallelogram, opposite angles are congruent. so:
3n-5=2n+15
n-5=15
n=20
now that we know n is 20, we can substitute that into either <B or <D to figure out what their measures are (since they are congruent, they'll both have the same angle measure)
m<D=3n-5
m<D=3(20)-5
m<D=60-5
m<D=55
therefore, both <B and <D equal 55°.
From the figure of the parallelogram we know that the value of its angle must be <B=55°, <D=125°
What is a parallelogram?Parallelograms are geometric figures that have only four sides, the opposite sides being parallel. This means that the opposite sides of a parallelogram are line segments belonging to lines that do not touch at any point.
In a parallelogram, opposite angles are congruent. so:
[tex]3n-5=2n+15\\n-5=15\\n=20[/tex]
now that we know n is 20, we can substitute that into either <B , so we have:
[tex]m < B=3n-5\\m < B=3(20)-5\\m < B=60-5\\m < B=55[/tex]
So caculating the D, we have:
[tex]D=180-B\\D=180-55\\D=125[/tex]
See more about parallelogram at brainly.com/question/1563728
Global warming is known as the gradual increase in _________________ of the atmosphere.
a
precipitation
b
sun spots
c
temperature
d
ocean currents
Answer:
Global Warming is the gradual increase in the overall temperature of the Earth’s atmosphere.
c
Answer:
c temperature
Step-by-step explanation:
it is a gradual increase in the overall temperature generally attributed to the greenhouse effect caused by increased levels of carbon dioxide
Which angle is congruent to 5?
Answer:
Angle #4
Step-by-step explanation:
4 & 5 are equal, and opposite.
1 & 2 are also congruent by this standard.
pls helpppp me
i shall give brainliest
Answer:
B
Step-by-step explanation:
A) -4
B) results in a non-terminating, non-repeating decimal, which is irrational
C) 2
D) 4
What is the determinant of k=[6 8]
[0 3]
-18
-8
10
18
SATELLITE DISH Suppose the receiver in a parabolic dish antenna is 2 feet
from the vertex and is located at the focus. Assume that the vertex is at the
origin and that the dish is pointed upward. Find an equation that models a
cross section of the dish.
a. x2 = -8y
b. x2 = 2y
c. x2 = 8y
d. y2 = 8x
Answer:
D) [tex]x^{2} =8y[/tex]
Step-by-step explanation:
Because the receiver of the parabolic dish antenna is 2 feet above the vertex, the parabola must be vertical. Therefore, we will use the equation [tex](x-h)^2=4p(y-k)[/tex] where [tex](h,k)[/tex] is the vertex of the parabola and [tex](h,k+p)[/tex] is the focus point. Since we are given that the receiver is 2 feet above the vertex which is located at the focus point and the vertex is [tex](0,0)[/tex] at the origin, then the focus point is [tex](0,0+p)[/tex] where [tex]p=2[/tex]. Therefore, the equation that models a cross section of the dish is [tex]x^{2} = 8y[/tex].
Melanie wants to create a pattern using a transformation that will change the orientation of a figure but not the orientation of verticals. Which transformation should she use?
Answer:
Melanie can translate the figure, rotate the figure, or reflect the figure. The figure would still be congruent.
Step-by-step explanation:
Hope that helps.... sorry if it doesn't..
What is the amplitude of this function f (x)?
f(x) = 3 cos (2x) + 5
Enter your answer in the box.
The amplitude of this function is 3.
What is the slope intercept form here!!!
Answer:
y=x
Step-by-step explanation:
How many teams haven't apperared in a super bowl
A. 2
B. 5
C.4
D. None
Answer:
c. 4
Step-by-step explanation:
I'm correct if I'm rwong
