Using a trigonometric identity, considering the given value of the tangent of theta, the secant of the same angle is given by:
[tex]\sec{\theta} = \pm \sqrt{\frac{11}{8}}[/tex]
How is the tangent related to the secant?According to the following identity:
[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]
In this problem, the tangent squared is given as follows:
[tex]\tan^2{\theta} = \frac{3}{8}[/tex]
Hence the secant is given by:
[tex]\sec^{2}{\theta} = 1 + \tan^2{\theta}[/tex]
[tex]\sec^{2}{\theta} = 1 + \frac{3}{8}[/tex]
[tex]\sec^{2}{\theta} = \frac{11}{8}[/tex]
[tex]\sec{\theta} = \pm \sqrt{\frac{11}{8}}[/tex]
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Answer:
Plus-or-minus StartRoot eleven-eighths EndFraction
Step-by-step explanation:
The answer above is correct.
How do I do number 7 I wasn’t taught this
The perimeter of the polygon will be (2x + 2xy + y + xz). Then the correct option is D.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The figure is given below.
The sides of the polygon are given as x, y, xz, x, xy, and xy.
Then the perimeter of the polygon will be
The perimeter of the polygon is given as the sum of all the sides of the polygon.
Then the perimeter will be
P = x + y + xz + x + xy + xy
P = 2x + y + 2xy + xz
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A company needs a faster computer to enhance its e-business capabilities. the computer can be purchased for $1890 or rented for $900 plus $90 per month. what is the maximum number of months the computer could be kept so that it is cheaper to rent than to buy?
The maximum number of months the computer could be kept so that it is cheaper to rent than to buy is 10 months.
What is the maximum number of months?The first step is to determine the month in which the two options would have the same cost. The equation that can be used to determine this value is:
$1890 = $900 + 90t
90t = 1890 - 900
90t = 990
t = 990 / 90
t = 11 months
The maximum number of months = 11 months - 1 = 10 months
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Whats the definition of PI
Answer:
is the ratio of the circumference of any circle to the diameter of that circle.
Step-by-step explanation:
A television is on sale for $75 off. The price of the television with the sale is $300. If you use the equation n−75=300 to solve this problem, what does n represent?
Answer:
The original price
Step-by-step explanation:
I got it right
A
2.
-3
-2
-3
The midpoint of AB = ([?],[])
=PLEASE HELP I WILL MARK BRAINLIEST
Explanation:
The x coordinates of points A and B are 2 and -2 respectively. Add them up and divide by 2 and we would get (A+B)/2 = (2+(-2))/2 = 0/2 = 0.
The x coordinate of the midpoint is 0.
The y coordinate of the midpoint follows the same idea, but we focus on the y coordinates of course. You should find the y coordinate of the midpoint is 0.
The midpoint is at (0,0) as the diagram shows.
help Mary ann and carlos are each saving for new scooters. Their savings are shown. Let x represent the number of hours each person works y represent the total earnings in dollars
after how many hours of work will mary ann and carlos have saved the same amount?
Answer:
4 hoursStep-by-step explanation:
Use a couple of ordered pairs on the graph and get the equation of the line:
(0, 2), (1, 10)The y-intercept is 2 and the slope is 10 - 2 = 8
The line is
y = 8x + 2Solve the system of equations by substitution to find the intersection
y = 6x + 10y = 8x + 26x + 10 = 8x + 28x - 6x = 10 - 22x = 8x = 4They will work 4 hours to get same amount of saving
Answer:
4 hours
Step-by-step explanation:
First, create a linear equation for Carlos using the graph.
Two points on the line: (0, 2) and (1, 10)
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{10-2}{1-0}=8[/tex]
Use the point-slope equation with the found slope and one of the points:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=8(x-0)[/tex]
[tex]\implies y=8x+2[/tex]
Now equate the equations for Mary Ann and Carlos, and solve for x:
[tex]\implies 6x+10=8x+2[/tex]
[tex]\implies 8=2x[/tex]
[tex]\implies x=4[/tex]
Therefore, Mary Ann and Carlos have saved the same amount after 4 hours work.
can you help me its worth 50
B. X is less than or equal to -4
Can anyone help me figure out what shape this is? 10th grade geometry
Answer:
I think option C is correct or it can be. B OPTION
As if we join B to C it will form a diagonal BC which will cut the shape into two right angled triangle
Step-by-step explanation:
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20Lexi is hiking a trail that is 7.5 miles long. She stops to take a break after hiking 3.8 miles of the trail. Which equation can be used to find how many miles, m, Lexi has left to hike?
Answer:
7.5 - 3.8 = m
Step-by-step explanation:
Find the area of the region which is inside the polar curve r=5sin(θ) but outside r=4. Round your answer to four decimal places
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be
Then the intersection point will be given as
[tex]\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214[/tex]
Then by the integration, we have
[tex]\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\[/tex]
[tex]\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\[/tex]
On solving, we have
[tex]\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75[/tex]
Thus, the area of the region is 3.75 square units.
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The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.
Answer:
centre : (4;-5)
radius : 2
What is the reference angle for a 240° angle? 30° 60° 180° 270° Mark this and return
The reference angle for a 240° angle is 60°
How to calculate reference anglesA reference angle is the angel that is found on the first quadrant of a a circle.
The angle that is being measured is in the third quadrant of a circle, we will subtract 180° from the given angle.
Therefore, the reference angle for a 240° is =
240-180= 60°
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The diameter of a circle is 38 in. Find its area to the nearest whole number.
Answer:
1134
Step-by-step explanation:
Formula for diameter=2 x r
(π is 3.14)
Formula for area= π x r^2
So all you basically have to do is go backwords with the first one then plug the radius into the second one normally
38/2=19
Now just plug it into your second equation
π x 19^2=1134.11494795
And lastly round that to 1134, easy! :)
What are the factors of 6x2 37x−60? 3x−4 and 2x 15 3x 4 and 2x−15 2(x−2) and 3(x 5) 2(x 2) and 3(x−5)
The factors of the given quadratic expression are (3x+4) and (2x-15)
Factorizing a quadratic expressionFrom the question, we are to determine the factors of 6x²+37x-60
The given quadratic expression can be factored as shown below
6x² + 37x -60
This becomes
6x² -45x + 8x -60
3x(2x-15) +4(2x-15)
Then,
(3x+4)(2x-15)
Hence, the factors of the given quadratic expression are (3x+4) and (2x-15). The correct option is the second option (3x+4) and (2x-15)
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Answer:
(3x+4) and (2x-15)
Step-by-step explanation:
solve the system of equatioins 2x+3y=40 and -2x+2y=20
Answer:
x = 2 ; y = 12
Step-by-step explanation:
2x + 3y = 40
+ -2x +2y = 20
You solve for one of the variables by cancelling out one and making one the subject.
2x + 3y = 40.
+ -2x +2y = 20
5y = 60
5y/5 = 60/5
y = 12
Next, you solve for X by replacing the value of y in any of the equations.
2x + 3y = 40
2x + 3(12) = 40
2x + 36 = 40
2x = 40 - 36
2x = 4
2x/2 = 4/2
x = 2
To prove the equations are set, replace the values of X and Y in one of the equations.
2x + 3y = 40
2(2) + 3(12) = 40
4 + 36 = 40
40 = 40
I really need help with this. I don’t understand it at all. It was due yesterday and I need to finish it. Please help.
Help me find the Scale factor of these two rectangles!
Answer:
scale factor of 1/3 from the big rectangle to the small rectangle
Step-by-step explanation:
Hope this helps! Please mark me as brainliest:)
8x - 10
25
B
E
18
15
с
D
Solve for x
Step-by-step explanation:
the upper (smaller) triangle and the complete triangle are similar.
that means the angles in both triangles are the same. and the lengths of all corresponding pairs of sides correlate with the same scaling factor.
therefore,
(8x - 10) / (8x - 10 + 18) = 25 / (25 + 15)
(8x - 10) / (8x + 8) = 25 / 40 = 5/8
8(8x - 10) = 5(8x + 8)
64x - 80 = 40x + 40
24x = 120
x = 5
B(3a,2b)
PLEASE HELP
a
E
What is the
coordinate for
midpoint E?
A(-3a,-2b) D(a,-2b)
C(5a,-2b)
A
B
C
(4a, 0)
(0,0)
(0,46)
Answer:
Step-by-step explanation:
The coordinates of E(4a, 0).
What is mid point?A midpoint is a point in the middle of the line connecting two points that lies between them. The midpoint is a point that lies in the middle of the line and is equidistant from the two points if a line is drawn to connect them.
The midpoint between two points whose coordinates are known to us can be found using the midpoint formula. If we know the coordinates of the other endpoint and the midpoint, we can also use the midpoint formula to determine the coordinates of the endpoint.
Given coordinates
A(-3a, -2b), D(a, -2b), C(5a, -2b) and B(3a, 2b)
to find the coordinates of E,
and E is midpoint of B and C
for coordinates of midpoint is (x, y) = [(x₂ + x₁)/2, (y₂ + y₁)/2]
here B = (3a, 2b) = (x₁, y₁)
and C = (5a, -2b) = (x₂, y₂)
x = (5a + 3a)/2 = 8a/2 = 4a
y = (-2b + 2b)/2 = 0/2 = 0
E(4a, 0)
Hence coordinates of E are (4a, 0).
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What is the amplitude of the function graphed below?
Answer:
I believe one is the answer your looking for
Step-by-step explanation:
helpppp which expression is equivalent to
The equivalent expression of the provided expression g²h√(5g) is √(5g⁵h²). Then the correct option is B.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
→ g²h√(5g)
Then the function can be written as
→ √(5g⁵h²)
Then the equivalent expression of the provided expression g²h√(5g) is √(5g⁵h²).
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is this a quadratic function 2x+13=13
Answer:
Step-by-step explanation:
Simplifying
2x + 13 = 0
Reorder the terms:
13 + 2x = 0
Solving
13 + 2x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13
Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13
Combine like terms: 0 + -13 = -13
2x = -13
Divide each side by '2'.
x = -6.5
Simplifying
x = -6.5
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The coordinates of parallelogram UVWZ are U(a, 0), W(c-a, b), and Z(c,0). Find the coordinates of V without using any new variables
A• (0, b)
B• (c, b)
C• (a, b)
D• (b, 0)
Answer: Choice A.
(0, b)
==================================================
Explanation:
Pick any random 3 numbers you want for a,b,c.
a = 1b = 2c = 3The points U, W and Z become
U = (a,0) = (1,0)W = (c-a, b) = (3-1, 2) = (2,2)Z = (c, 0) = (3, 0)Or in short,
U = (1,0)W = (2,2)Z = (3, 0)Plot each of those points on the same xy grid.
Next, using a different color, plot each of the answer choices.
A is at (0,b) = (0, 2)B is at (c,b) = (3,2)C is at (a,b) = (1,2)D is at (b,0) = (2,0)You should find that point A helps form a parallelogram, while the other answer choices don't lead to a parallelogram.
See the screenshot below. I used GeoGebra to make the diagram. Desmos is another useful tool as well.
Which of the following fractions equal to 1/4
A. 12/60
B. 48/12
C. 36/108
D. 26/104
E. 17/50
Answer:
D
Step-by-step explanation:
A no = 1/5
B no = 4
C no = 1/3
D yes
E no = 17/50
26/104
Step-by-step explanation:the correct option is 26/104 because if 26 divides 26/104 it will give 1/4 because
26÷26= 1
104÷26=4
therefore, the correct option is 26/104
What is the equation of the line shown in this graph?
(3,-3) (-2,-3)
X
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MODELING REAL LIFE A green roof is like a traditional roof but covered with plants. Plants used for a green roof cost $0.75
per square foot. The roof shown is 40 feet long. How much does it cost to cover both sides of the roof?
8 ft
15f15 ft
It costs $
Justify your answer
The area of the rectangular roof (both sides of the roof) = 1,360 ft²
Cost to cover both sides = $1,020
What is the Area of a Rectangle?The area of a rectangle = (length)(width)
Length of one side of the roof = 40 ftWidth of one side of the roof = √(15² + 8²) = 17Area of both sides of the roof = 2(area of rectangle) = 2(40×17) = 1,360 ft²
Cost to cover both sides = 1,360 × 0.75 = $1,020
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Based on the information marked in the diagram, ABC and DEF must be
congruent.
A. True
B. False
Could someone please answer the following question?
Answer:
See below
Step-by-step explanation:
4 sin^2 -1 =0
sin^2 = 1/4 Take sqrt of both sides
sin = ± 1/2 < ===== this is likely where he went wrong (forgot + - )
answer: pi/6 5pi/6 7 pi/6 11pi/6
if michaels score is 87, the class average is 82, and the standard deviation is 4. what is michaels z-score?
Answer:
Z = 1.25
Step-by-step explanation:
[tex]\displaystyle Z=\frac{\text{Observed Value}-\text{Mean of the Sample}}{\text{Standard Deviation of the Sample}}\\\\Z=\frac{x-\mu}{\sigma}\\ \\Z=\frac{87-82}{4}\\ \\Z=\frac{5}{4}\\ \\Z=1.25[/tex]
Hence, Michael's z-score is 1.25, which means that he scored 1.25 standard deviations above the class average.