Answer:
1
Step-by-step explanation:
First, convert all the secants and cosecants to cosine and sine, respectively. Recall that [tex]csc(x)=1/sin(x)[/tex] and [tex]sec(x)=1/cos(x)[/tex].
Thus:
[tex]\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}[/tex]
[tex]=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }[/tex]
Let's do the first part first: (Recall how to divide fractions)
[tex]\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}[/tex]
For the second term:
[tex]\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}[/tex]
So, all together: (same denominator; combine terms)
[tex]\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}[/tex]
Note the numerator; it can be derived from the Pythagorean Identity:
[tex]sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)[/tex]
Thus, we can substitute the numerator:
[tex]\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1[/tex]
Everything simplifies to 1.
Find the value of x that will make L||M. 7x+9 & 8x+2 x=? please help!
Answer:
x = 7
Step-by-step explanation:
=> 7x+9 = 8x+2 (Corresponding angles are equal)
=> 8x-7x+2 = 9 (Subtracting 7x to both sides)
=> x = 9-2 (Subtracting 2 to both sides)
=> x = 7
Which expression is equivalent to (3a)-27
3a2
0
o
o
Answer:
Step-by-step explanation:
(3a) - 27 = 3a - 3^3 = 3(a - 3^2)
Next time, please share all of the answer choices. Thanks.
Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 – 16) feet and (–x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?
Answer:
P = 2x² + 8x - 30
P = 12 (if x = 3)
Step-by-step explanation:
Perimeter Formula: 2l + 2w
Step 1: Find perimeter
2(2x² - 16) + 2(-x² + 4x + 1)
4x² - 32 - 2x² + 8x + 2
2x² + 8x - 30
Step 2: Plug in x = 3
2(3)² + 8(3) -30
18 + 24 - 30
42 - 30
12
state whether it represents a function
Answer:
See below.
Step-by-step explanation:
To be a function the graph must pass the vertical line test. If any of the vertical lines which can be drawn intersects the graph more than once then it's not function.
So Graph 1 is not a function because a vertical line passes through the 2 points in quadrant 1, whereas Graph 2 is a function because any vertical line you can draw only passes through the graph once.
Graph 3 - not a function.
Graph 4 - not a function.
Graph 5 - not a function.
Graph 6 is a function.
Abigail was skateboarding home when the wheel axle of her skateboard broke. She had already traveled two-thirds of the way home and had to walk the rest of the way. Walking the rest of the way home took her twice as long as it took her to ride her skateboard. How many times faster is Abigail on her skateboard than she is walking?
Answer:
4 times faster
Step-by-step explanation:
From the above question, we have the following information
Let us represent the Distance traveled by Abigail as Y
On her skateboard she travelled two thirds of the way = 2/3Y
She walks the rest of the way home = Y - 2/3Y = 1/3Y
The time she used to walk home is twice the time she used to ride her skate board
Hence, let us represent the time she used to ride her skateboard as S
So, Time she used to walk home = 2 × S = 2S
The question is asking us, how fast ,this is = Speed
The formula for Speed = Distance/ Time
Speed for her skate board = 2/3Y/S = 2Y/3S
Speed as she walks = 1/3Y / 2S = Y/ 6S
How many times faster is Abigail on her skateboard than she is walking is calculated as :
Speed of Abigail while skating ÷ Speed of Abigail while walking
= 2Y/3S ÷ Y/6S
= 2Y/3S × 6S/Y
= 4
Therefore, Abigail was 4 times faster on her skateboard than she is walking.
*ANSWER ASAP PLS* How can someone live smarter to reduce his/her carbon footprint? a.) remove insulation b.) live in a smart community c.) buy inefficient appliances d.) use incandescent bulbs
Answer:
remove insulation ,,,eat low on the food chain
Step-by-step explanation:
u can reduce it by 8 pounds
Answer:
remove insulation
I need help with number 5
Answer:
A
Step-by-step explanation:
62 +65=127
C+127=180
C=180-127=53°
so x=53°
53-y=11
y=53-11=42
Answer: A
Step-by-step explanation:
Since ΔCDE and ΔGHI are congruent triangles, they are equal to each other. This means x-y=11. We want to find y, but we first need to find x. We can do that by finding x° on ΔGHI.
We know that the sum of the angles is 180° in a triangle. We are given 2 angles from ΔCDE. We can use those to find x°.
62+65+x=180 [combine like terms]
127+x=180 [subtract 127 on both sides]
x=53
Now that we have x, we can find y by plugging in.
53-y=11 [subtract both sides by 53]
-y=-42 [divide both sides by -1]
y=42
simplify the expression [tex]-\frac{4x+7}{2} -\frac{3x-2}{2}[/tex]
Answer:
-(4x + 7)/2 - (3x - 2)/2 = (-4x - 7 - 3x + 2)/2 = (-7x - 5)/2
A t-shirt increased in price by 1/7. After the increase it was priced at £56. What was the original price of the t-shirt?
Answer:
£48
Step-by-step explanation:
56 ÷ 7 = £8
56 - 8 = £48
Please let me know if my answer is correct.
Answer:
48
Step-by-step explanation:
What is the value of Fraction 1 over 2x3 + 3.4y when x = 2 and y = 5?
18
20
21
37
Answer:
C.21
Step-by-step explanation:
The value of 1/ (2x³ + 3.4y) is 1/33.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Fraction = 1/ (2x³ + 3.4y)
We have the value x= 2 and y=5.
So, 1/ (2x³ + 3.4y)
= 1/ (2(2)³ + 3.4(5))
= 1/ (2(8) + 17)
= 1/ (16+17)
= 1/ 33
Hence, the value is 1/33.
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Suppose a cube is given.
How many non-congruent triangles can be formed by connecting 3 of the vertices of the cube?
Answer:
The number of non-congruent triangles that can be formed from the vertices of a cube are 3 triangles
Step-by-step explanation:
The number of non congruent triangles that can be formed by connecting 3 of thee vertices of the cube is found as follows;
The available different lengths of segments joining two vertices of a cube of side length s = 2 are;
2, 2·√2, and 2·√3
Therefore, since there are only three different side lengths we have the possible triangle dimensions given as follows
Distinct triangle one = 2, 2, 2·√2
Distinct triangle two = 2·√2, 2·√2, 2·√2
Distinct triangle three = 2, 2·√3, 2·√2
Therefore, there are ₃C₃ = 3 ways of forming three non-congruent triangles from the vertices of a cube.
1. A line passes through (1, -5) and (-3, 7).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in slope-intercept form.
А
16
y-5=
1
(x + 1); y ==x+
3
3
3
B y- 5= 3(x + 1); y = 3x + 8
C y + 5 = -3(x - 1); y = -3x - 2
D
8
y-1 =
1 = $(x + 5): y = x+
3
Answer:
Step-by-step explanation:
The slope is -3
You can now substitute (1,-5) for x and y
-5= -3+b
b=-2
So in slope intercept form the answer is y=-3x-2
In point slope form the answer is 3x+y=-2
PLEASE HELP!!!
What is the distance, in units, between P=(−6,8) and Q=(9,8)?
Answer:
15
Step-by-step explanation:
A triangle with vertices at A(20, -30), B(10.-15), and C(5,-20) has been dilated with a center of dilation at the origin.
The image of B, point B', has the coordinates (2, -3). What is the scale factor of the dilation?
10
o
5
е
10
Answer:
scale factor = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Consider the ratio of corresponding coordinates of the image to original, that is
scale factor = [tex]\frac{2}{10}[/tex] = [tex]\frac{-3}{-15}[/tex] = [tex]\frac{1}{5}[/tex]
Sarah's car travels 28 miles on on gallon of gas. Greta's car travel 18 kilometers on one liter of gas. Which car gets better gas mileage?
Answer:
Gretas car gets better gas mileage
Step-by-step explanation:
18 km= 18,000 miles
18,000>28
So, Gretas car gets better gas mileage
Hope this help!
The local dairy farm has 3.7×10^3 cows and each cow produces 2.6×10^3 gallons of milk each year. How many gallons are produced at this farm each year? Write in standard form
Answer:
96.2*10^5 gallons
Step-by-step explanation:
gallons of milk produced by 1 cow = 2.6×10^3
No. of cows with local dairy farm = 3.7×10^3
Total of gallons of milk produced by farm = gallons of milk produced by 1 cow * No. of cows with local dairy farm = 2.6×10^3 * 3.7×10^3 = 9.62*10^6
we have to write it in standard form = 96.2*10^5 gallons
i can be also written as = 9,620,000 Gallons.
9.62 Million Gallons of milk is produced by local dairy farm Yearly.
Which of the following applies the law of cosines correctly and could be solved to find m∠Q? ANSWERS: A) 302 = 182 + 172 – 2(18)(17) ⋅ cos Q B) 182 = 302 + 172 – 2(30)(17) ⋅ cos Q C) 302 = 182 + 172 – cos Q D) 182 = 302 + 172 – cos Q
Answer:
Step-by-step explanation:
Law of cosines: c^2 = a^2 + b^2 − 2ab cos(C)
Used to find: the angles of a triangle when we know all three sides
We are looking for: Angle Q. The side opposite Angle Q (30) can be c. Line segments RQ and QS are a(17) and b(18).
30^2 = 18^2 + 17^2 - 2(17)(18) cos (q)
If sin α + cos α = 1.2, find sin α · cos α THANKS! (:
Using trigonometric relations, it is found that:
[tex]\sin{\alpha}\cos{\alpha} = 0.22[/tex]
We are given that:
[tex]\sin{\alpha} + \cos{\alpha} = 1.2[/tex]
Hence:
[tex]\sin{\alpha} = 1.2 - \cos{\alpha}[/tex]
The basic relation is:
[tex]\sin^{2}{\alpha} + \cos^{2}{\alpha} = 1[/tex]
Hence:
[tex](1.2 - \cos{\alpha})^2 + \cos^{2}{\alpha} = 1[/tex]
[tex]2\cos^{2}{\alpha} - 2.4\cos^{\alpha} + 0.44 = 0[/tex]
Which is a quadratic equation, with coefficients [tex]a = 2, b = -2.4, c = 0.44[/tex].
Using a quadratic equation calculator, and considering that the cosine has to assume a value between 0 and 1, it is found that the solutions are:
[tex]\cos{\alpha} = 0.9742, \cos{\alpha} = 0.2258[/tex]
Since [tex]\sin{\alpha} = 1.2 - \cos{\alpha}[/tex], there are two solution pairs:
[tex](\sin{\alpha}, \cos{\alpha}) = (0.9742, 0.2258)[/tex]
[tex](\sin{\alpha}, \cos{\alpha}) = (0.2258, 0.9742)[/tex]
They result in the same multiplication result, hence:
[tex]\sin{\alpha}\cos{\alpha} = 0.9742(0.2258) = 0.22[/tex]
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A grandfather's age in years is the same as his granddaughter's age in months. Together, they are 91 years old. How old is the grandfather?
Answer: Grandfather is 84 the granddaughter is 7 years old(84 months
Step-by-step explanation:
We know the grandfather and the granddaughters age is a whole number meaning there are no decimals. the nearest number that is whole and lower than 91 is 84. 84 / 12 = 7 we can do this because 84 months is equivalent to 91 years ||| 84 + 7 = 91 therefore that is the answer
Answer:
The age of grandfather is 84 years
The age of granddaughter is 7 months.
Step-by-step explanation:
Given information
Grandfather's age in years is same as granddaughter's age in months.
Let, the age of granddaughter is [tex]x[/tex] in months
Then the age of grandfather will be [tex]12x[/tex] in years
Now , according to the given information
[tex]x+12x=91[/tex]
On solving the above equation
We get,
[tex]13x=91\\x=7[/tex]
Hence ,
The age of grandfather is 84 years
The age of granddaughter is 7 months.
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HELP PLS. solve the triangle shown in the figure. LC=90 degrees, BC=7.50mi, AC=11.43mi
Answer: C
Step by step:
Use the pythagoras' theorem ( c² = a² + b² ) to find the length of AB.Use trigonometry to find the 2 missing angles of the triangle.That's all!
Answer:
C.
Step-by-step explanation:
Pls help C: Summer Homework (ASAP)
Answer:
3/2f = 2e
Step-by-step explanation:
The equation is Written has this (3/2f = 2e)
Answer:
[tex]\frac{2}{3} f=2e[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *9=6[/tex] ~ this is an example of the answer being used to be multiplied by [tex]f[/tex] to get the result which is listed through [tex]e[/tex]. This example is Batch B, cups of flour was 9. 9 multiplied by [tex]\frac{2}{3}[/tex] will lead us to 6 which is the number of eggs used in Batch B.
Hope this helps!
Help Please I'm Out Of Time ;(
A wooden roller coaster at a theme park has a height restriction: passengers must be at least 45 inches tall.
A. Write an inequality to represent the height restriction.
B. Using complete sentences, describe how to graph your inequality on a number line.
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~~`
[tex]h \geq 48 inches tall[/tex]
In order to ride on the ride an individual must be at least 48 inches tall.
This means that the individual must be equal to 48 inches tall.
[tex]h = 48[/tex]
and the individual could be greater than 48 inches tall.
[tex]h > 48[/tex]
So the individual could be greater than and equal to 48 inches tall.
[tex]h \geq 48[/tex]
Hope this helped you. Brainliest would be nice!
Solve the inequality 3x - 5 < 4.
Answer:
I got x<3
Step-by-step explanation:
Answer:
x < 3
Step-by-step explanation:
Add 5 to both sides. Then: 3x < 9 and x < 3.
The solution is the area to the left of x = 3 (but not touching x = 3).
Which expressions have a quotient that is undefined? Select three that apply. a.0/3 b.0/0 c.−8/0 d.−0/2 e.−0/1 f.11/0
Answer:
B, C, and F
Step-by-step explanation:
There's a certain universal property that we must all understand whenever we apply division: we can never divide by 0. This would be considered undefined.
Look at the answer choices.
- B says 0/0, which is dividing by 0, so this is one of our answers.
- C says -8/0, which is also dividing by 0, so this is another one of our answers.
- Finally, F says 11/0, which is dividing by 0, so this is our last answer.
Thus, the answers are B, C, and F.
~ an aesthetics lover
Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza with t toppings, her total cost can be found using this expression: 0.90(2.25d + 1.40t + 6). What is the total cost for Lindy and her friends to order 4 drinks and a medium pizza with 3 toppings?
Answer:
$17.28.
Step-by-step explanation:
In the expression, d represents the number of drinks she orders and t represents the number of toppings.
In this case, she orders 4 drinks and 3 toppings, so d = 4 and t = 3.
0.90(2.25d + 1.40t + 6)
= 0.9(2.25 * 4 + 1.4 * 3 + 6)
= 0.9(9 + 4.2 + 6)
= 0.9 * 19.2
= 17.28
So, the total cost for Lindy and her friends will be $17.28.
Hope this helps!
PLEASE HELP!!! Find each measure. m<1, m<2, m<3
Number 1: To find number 1 use hypotenuse theory. 180-(69+31) is the equation. After you solve it you get m<1 as 80.
Number 2: Since you already found m<1 find the other angle across from it.
Equation is: 180-80, which equals to 100.
Then once you have two angles use the theory again: 180-(100+45)=35.
Therefore m<2=35.
Number 3: Still using m<1, 180-100=80. Now you have to angles you get the equation:
180-(80+47), which equals to 53. Therefore m<3=53
Answers: m<1=80; m<2=35; m<3=53
Answer:
1= 80
2= 35
3= 33
Step-by-step explanation:
First start by solving for angle 1. A triangle is always equal to 180 degrees so if you know triangle 1 has an angle equal to 69 degrees and another angle equal to 31 degrees then all you would need to do is add them up (this equals 100) and subtract that sum from 180 to find the difference (it's 80.)
Now that you know angle 1 is equal to 80 you can solve angle 2 and 3. When there are intersecting lines, the angles across from each other are always equal. So, it is safe to assume that the angle across from angle 1 is also 80 degrees. This will help us figure out the other angles in triangles 2 and 3. These four intersecting angles will equal 360, therefore because angle 1 and the angle across from it equal 80 degrees, then what we can do is add up 80+80 (which equals 160) then subtract that from 360 (which equals 200.) Because the two undetermined center angles are equal to each other, we can simply divide 200 by 2 to get 100.
Now that we know that triangle 2 has angles equal to 45 and 100 degrees, and triangle 3 has angles equal to 47 and 100 degrees, we can figure out what angles 2 and 3 are. To find angle 2 we will add 45 and 100 to get 145, then we'll subtract it from 180 like before to get 35. To find angle 3 we will add 47 and 100 to get 147, then we'll subtract it from 180 like before to get 33.
The volume of the sphere is
500
- cubic units.
What is the value of x?
C 0
4 units
0 5 units
08 units
0 10 units
Save and Exit
Na
Submit
Mark this and retum
Answer:
[tex]n + 4 - 9 - 5n[/tex]
if one number is five more than another number, and the smaller number is half of the larger, what are the two numbers
Answer:
smaller number = 5
larger number = 10
Step-by-step explanation:
Let
smaller number = x
larger number = x+5
"the smaller number is half of the larger" means
x+5 = 2x
Solve for x
5 = 2x -x = x
Therefore
smaller number = 5
larger number = 10
Answer:
The larger number is 10 and the smaller is 5 less, or 5.
Step-by-step explanation:
Represent the larger and the smaller numbers by L and S.
Then L = S + 5, and S = L/2
Substituting L/2 for S in the first equation, we get L = (L/2) + 5
Multiplying both sides by 2, we get 2L = L + 10, or L = 10.
The larger number is 10 and the smaller is 5 less, or 5.
What is the complement of an angle that measures 24° 13' 49”
Answer:
65°46'11"
Step-by-step explanation:
What is the complement of an angle that measures 24° 13' 49” ?
Complementary Angles = they add up to 90°
90° - 24° 13' 49” =
= 89°59'60" - 24° 13' 49”
= 65°46'11"
Answer:
65°46'11'' OR 65.76972222°
Step-by-step explanation:
Explanation above is better than mine
Classify the following triangle. Check all that apply.
7
9
11.4
A. Equilateral
O B. Isosceles
O C. Acute
O D. Scalene
O E. Right
O F. Obtuse
Answer:
Scalene and right
The given triangle is the right-angle triangle.
What is a right-angled triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular.
The given triangle has one angle equal to 90 degrees and the line is perpendicular to the base.
Hence, the given triangle is the right-angle triangle.
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