if sin theta=1/root 3, then find the value of (tan theta + 1/cos theta)^2 + (tan theta - 1/cos theta)^2
Answer:
4
Step-by-step explanation:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{3} }\\ \\Therefore, opposite= 1, hypotenuse=\sqrt{3}. \ using \ Pythagoras:\\\\Hypotenuse^2=Adjacent^2+Opposite^2\\\\(\sqrt{3})^2 =Adjacent^2+1^2\\\\3=Adjacent^2+1\\\\Adjacent^2=3-1=2\\\\Adjacent=\sqrt{2}[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}=\frac{\sqrt{2} }{\sqrt{3}}\\ \\tan(\theta)=\frac{opposite}{adjacent } = \frac{1}{\sqrt{2}} \\\\Therefore:\\\\(tan(\theta)+\frac{1}{cos(\theta)})^2+ (tan(\theta)-\frac{1}{cos(\theta)})^2=( \frac{1}{\sqrt{2}}+\frac{1}{ \frac{\sqrt{2} }{\sqrt{3}}} )^2+( \frac{1}{\sqrt{2}}-\frac{1}{ \frac{\sqrt{2} }{\sqrt{3}}} )^2\\\\=( \frac{1}{\sqrt{2}}+ \frac{\sqrt{3} }{\sqrt{2}} )^2+( \frac{1}{\sqrt{2}}- \frac{\sqrt{3} }{\sqrt{2}} )^2[/tex]
[tex]=(\frac{1+\sqrt{3} }{\sqrt{2} } )^2+(\frac{1-\sqrt{3} }{\sqrt{2} } )^2=\frac{1+2\sqrt{3}+3 }{2} +\frac{1-2\sqrt{3}+3 }{2} =\frac{1+1+2\sqrt{3}-2\sqrt{3}+3+3 }{2} =\frac{8}{2}=4[/tex]
Please help me on this question
Answer:
2+7=9
450/9 = 50
2( 50) = 100 no concentrate
7(50) or 450 - 100 = 350 ml water
How many significant digits are in
17.090?
Answer: 4
Step-by-step explanation:
Answer:
there are 5 significant digits
what value of x makes the equation true
2 (6x-1) = -38
Answer:
[tex] \boxed{\bold{\boxed{ \sf{x = - 3}}}}[/tex]Step-by-step explanation:
[tex] \sf{2(6x - 1) = - 38}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{12x - 2 = - 38}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{12x = - 38 + 2}[/tex]
Calculate
⇒[tex] \sf{12x = - 36}[/tex]
Divide both sides of the equation by 12
⇒[tex] \sf{ \frac{12x}{12} = \frac{ - 36}{12} }[/tex]
Calculate
⇒[tex] \sf{x = - 3}[/tex]
Hope I helped!
Best regards!!
Eduardo counted ten seconds (y) between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles (x) away. What is the equation of the variation?
Answer:
The equation for the variation is:
[tex]\frac{Miles}{thunder\,\,time } =0.2\,\frac{mi}{s}[/tex]
Step-by-step explanation:
The relationship is given by the quotient between the two variables: (1) distance of the storm, and (2) the number of seconds to hear the thunder. That is:
[tex]\frac{Miles}{thunder\,\,time } =\frac{2}{10} =0.2\,\frac{mi}{s}[/tex]
help asap please:) i don’t know
Answer:
Step-by-step explanation:
area of triangle = 1/2 × b × h
here,
b = 37 m
h = 30 m
so area = 1/2 × b × h
= 1/2 × 37 × 30
= 555 m^2
hope this helps
plz mark as brainliest!!!!!!!
Find the length of UT¯¯¯¯¯¯¯+CV¯¯¯¯¯¯¯¯. A. 53 B. 4x + 35 C. 65 D. 59
Answer:
UT + CV = 4x + 33
Step-by-step explanation:
Given:
TW = 14
WU = 2x + 2
VW = 2x + 5
WC = 12
Find:
UT + CV
Computation:
UT = TW + WU
UT = 14 + 2x + 2 = 16 + 2x
CV = VW + WC
CV = 2x + 5 + 12 = 2x + 17
UT + CV
16 + 2x + 2x + 17
UT + CV = 4x + 33
Which simplified fraction is equal to 0.53 repeat ? A.24/46 B.8/15 C.42/90 D.5/9
Answer:
To see how these fractions are equal, I divided the numerators by the denominators. For instance, you could have 4 over 5 (4/5) and divide 4 by 5 (4/5) to get 0.8. Now you'll do the same thing for the fractions given
24/45=0.533...
8/15=0.533...
48/90=0.533...
5/9=0.5556
As you can see, the only fraction that doesn't equal 0.53, or the outlier, is 5/9 or 0.5556
Step-by-step explanation:
A fraction is a way to describe a part of a whole. The fraction that equals 0.53 is (8/15).
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The value of the given fractions is equal to,
A.)
[tex]\dfrac{24}{46} = 0.5217[/tex]
B.)
[tex]\dfrac{8}{15} = 0.5333[/tex]
C.)
[tex]\dfrac{42}{90} = 0.4666[/tex]
D.)
[tex]\dfrac{24}{46} = 0.55556[/tex]
Hence, the fraction that equals 0.53 is (8/15).
Learn more about Fraction:
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Write the slope intercept form for a line that goes through the points (5,6) and
(6,9).
Answer:
[tex]\huge\boxed{Slope = 3}[/tex]
Step-by-step explanation:
The coordinates are (5,6) and (6,9)
Slope = Rise / run
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{9-6}{6-5}[/tex]
Slope = [tex]\frac{3}{1}[/tex]
Slope = 3
Answer:
[tex]slope = 3[/tex]
Hope this helps you
brainliest plz
a recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt. The recipe can be scaled up to make multiple loaves of bread. Complete the table that shows the quantities to use for multiple loaves of bread.
Answer:
Step-by-step explanation:
A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water and 1 teaspoon of salt.
Therefore, if we add 2 loaves of bread then double of ingredients will be required for the recipe.
In the same way if 4 loaves of bread have been added, 4 times ingredients will be required.
If 3 cups of flour are added then 3 times of other ingredients will be required.
So the table will be,
Number of loaves Cups of flour Tablespoons of water Teaspoons of salt
1 2 12 1
2 4 24 2
4 8 48 4
3 6 36 3
What is the ratios 15cm: 5m lowest term?
The probability of spinning an even number on a spinner is 0.4. What is the probability of not spinning an even number, expressed as a percent?
Answer:
60%
Step-by-step explanation:
There are only even and odd numbers. If a number is not even, it is odd. If the probability of spinning an even number is 0.4, or 40%, then just subtract that by the whole spinner, which is equivalent to 100%:
100% - 40%
= 60%
This means that the odds of spinning an odd number is 60%
Hope this helps! Tell me if I'm wrong please!
Answer:
60%
Step-by-step explanation:
Gabe is mapping out important family events. He uses negative numbers to represent time before he was born and positive numbers to represent time after he was born. For example, Gabe's mom was given a special coin in year -20−20minus, 20, and Gabe's sister was born in year 555. What does year 000 represent? Choose 1 answer: Choose 1 answer:
Answer:
Year 0 is represent the year that Gabe was born
Step-by-step explanation:
Gabe is mapping out important family events. He uses negative numbers to represent time before he was born and positive numbers to represent time after he was born. For example, Gabe's mom was given a special coin in year -20, and Gabe's sister was born in year 5. What does year 0 represent?
Answer: Positive numbers represent things that happen after Gabe was born while negative numbers represent things that happened before Gabe was born. The first example in the question meant that Gabe's mom was given a special coin 20 years before he was born while the second example in the question meant that Gabe's sister was born 5 years after he was born.
Year 0 is represent the year that Gabe was born.
Which of the following is not the same as 1.69 meters? 0.0169 km 0.169 dkm 169 cm 1,690 mm
Answer:
0.0169 km.
Step-by-step explanation:
km - kilometers (One kilometer is equal to 1000 meters.)
dkm - dekameters (One dekameter is equal to 10 meters.)
cm - centimeters (One centimeter is equal to 0.01 meters.)
mm - millimeters (One millimeter is equal to 0.1 meters.)
Used a calc to check each of the values to see if they equal 1.69m and km was the one that wasn't equal. Instead it was 16.9.
Answer:
1.69 meter
Step-by-step explanation:
Which exponential function is represented by the table below? x –2 0 2 4 y 16 4 1 14 A. 4⋅2x B. 14⋅4x C. 4⋅(12)x D. 4⋅(14)x
The exponential function represented by the table is given as follows:
[tex]y = 4\left(\frac{1}{2}\right)^x[/tex]
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.Considering the table:
When x = 0, y = 4, hence a = 4.When x changes by 2, y changes by 1/4, hence b = 1/2.Then the equation is:
[tex]y = 4\left(\frac{1}{2}\right)^x[/tex]
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The altitude of a right square prism is of length 12 and its base has a side of length 8. What is the lateral surface area of this prism?
A. 484 units²
B. 48 units²
C. 192 units²
D. 384 units²
Answer:
D. 384 units²
Step-by-step explanation:
Hey there!
Well a right square prism's bases are squares meaning the area of the base is 64 units².
Meaning 128 "which is the sum of 64+64" needs to be taken out of the SA to find the LSA.
Now we only have 4 sides to find the area of,
h = 12
l/w = 8
A = (12*8) * 4
A = 96 * 4
LSA = 384 units²
Hope this helps :)
The lateral surface area of the given prism of length 12 and its base has a side of length 8 is 384 [tex]units^{2}[/tex]
What is Lateral surface area?The lateral surface area of an object is the total area of its sides excluding its top and the bottom.
What is a right square prism?A right square prism is a prism having four sides as rectangle and two sides as squares as its bases.
How to find the lateral surface area of right square prism?The lateral surface area of right square prism is equal to the area of the four rectangles only. So the formula is as follows:
Lateral surface area=4(length*breadth)
The altitude which is given to us of 12 will be the breadth of the rectangles and the length of base of 8 will be the length of the rectangles. So,
Lateral surface area of right prism=4(12*8)
=4*96
=384
Hence the lateral surface area of right prism of altitude of length 12 and base has a side of length 8 is 384[tex]units^{2}[/tex]
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Consider a rectangle whose length, L, is 4 more than twice its width, w. a. Write an expression for L in terms of w. b. Show that the perimeter, P, is equal to = 6 + 8. c. Given the perimeter is 20, find the length and width of the rectangle using your answer to part b.
Answer:
Step-by-step explanation:
a)L=2w+4
b)P=2L+2w
sub L=2w+4,
P=2(2w+4)+2w
P=4w+8+2w
P=6w+8
c) 20=6w+8
12=6w
2=w
L=2(2)+4
=8
Hence,
L=8 and w=2
how would i find y i need helppp
Answer:
C
Step-by-step explanation:
sin30° = y/6
sin30° = 1/2
y/6 = 1/2
y = 3
a number plus 12 is 36. write an equation and use equation to solve
Answer:
24
Step-by-step explanation
36-12=24
Its as simple as that.
A number plus 12 is 36. The equation for the given calculation is 36 - 12 = 24.
What is the arithmetic equation?Arithmetic is the fundamental branch of mathematics that covers number operations. Addition, subtraction, multiplication, and division are the operations involved.
The difference between each consecutive term in an arithmetic series is constant. The series 3, 5, 7, 9..., for example, is arithmetic because the difference between consecutive terms is always two.
Because the difference between subsequent words is always negative five, the sequence 21, 16, 11, 6... is also arithmetic.
Let the number added to 12 is x
Then,
12 + x = 36
x = 36 - 12 = 24
Therefore, the equation for the given calculation is 36 - 12 = 24.
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Rachel is making nachos for a party. The recipe calls for 2/3 cup of cheese for each plate of nachos. Part A: How many full plates of nachos can Rachel make with 5 cups of cheese? Part B: How many more cups of cheese would Rachel need to make 9 plates of nachos?
Part A:
We need to divide
5 ÷ 2/3
5/1 ÷ 2/3
5/1 * 3/2
15/2 or 7 1/2 plates of nachos.
Part B:
If Rachel can make 7 1/2 plates of nachos with 5 cups of cheese we need to multiply and subtract.
ma2/3 * 9 = 18/3 or 6 cups of cheese to make 9 plates
6 - 5 = 1 more cup of cheese she needs to make 9 plates
Best of Luck!
This agency preserves and promotes public confidence in the U.S. Financial system by insuring deposits in banks and thrift institutions for at least $250,000.
Which one is greater 10 squared or 22/7
Answer:
(22/7)²
576/49
is your answer hope it's help u
HELP ME Four students each wrote an equation. Which two students wrote equations that have no solution?
Answer:
Beto and Mark
Step-by-step explanation:
When you simplify Beto's equation, you get 0=5 which is inncorrect. 5 does not equal 0 so there are no solutions. When you simplify Mark's equation, you get 6=2 which is also inncorrect. 6 can not equal 2. If you solve the other 2 equations you get answers that can work.
4)
Jason is on a diet. His goal is to lose 5.9 pounds per month. How much weight will he have lost after 3.3 months?
Answer:
if he lost 5.9 in 3.3 months he we would lost weight.
5.9* 3.3 19.47lbs
In the expression 2x - 8 what is x referred to as?
1. coefficient
2. variable
3. constant
Which is NOT an equation?
1. 5 - 4x
2. 6x - 5 = 8
3. x/3 + 9 = -1
Answer:
Step-by-step explanation:
A) 2x - 8
x is called variable
Option 2
B) 5 - 4x is not a equation
Option 1
b. 2(3x - 5) = 2x + 6
Answer:
x = 4
Step-by-step explanation:
Given
2(3x - 5) = 2x + 6 ( divide both sides by 2 )
3x - 5 = x + 3 ( subtract x from both sides )
2x - 5 = 3 ( add 5 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Answer:
x = 4
Step-by-step explanation:
2(3x - 5) = 2x + 6
expand- 2(3x-5):6x+10
6x-10= 2x+6
Add 10 to both sides
6x-10+10=2x+6+10
simplify
6x=2x+16
subtract 2x from both sides
6x-2x=2x+16-2x
simplify
4x=16
divide both sides by 4
4x/4=16/4
x=4
I really need help with this problem, I don't know how to do it. Please help if you can.
2/3 +y =1/4
Answer:
see below
Step-by-step explanation:
2/3 +y =1/4
Subtract 2/3 from each side
2/3-2/3 +y =1/4-2/3
y = 1/4 -2/3
Get a common denominator
y = 1/4 (3/3) - 2/3 *4/4
= 3/12 - 8/12
=-5/12
or if
2/(y+3) = 1/4
Using cross products
y+3 = 2*4
y+3 = 8
y =8-3
y = 5
Answer:
y = -5/12
Step-by-step explanation:
2/3 + y = 1/4
y = 1/4 - 2/3
y = 3 - 8/ 12
y = -5/12
What constitutes a function
Answer:
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output...
B=(5,6)is a set. From this set make all possible ordered pairs.
5,6 and6,5
Step-by-step explanation:
there is only two ordered pairs of 5,6that is itself and 6,5
Answer:
the two possible orders are 5,6 and 6, 5
Plzzz help me im having alot of trouble understanding this question does some one understand if you do plz help fast!!!
1/2 - 3(1/2 + 1)²
(1 + 1/3)² - 2/9
Answer:
1/2 - 3(1/2 + 1)²
simplify the expression (1/2 + 1)
1/2 - 3•(3/2)²
using PEMDAS, we see we have to evaluate the exponent first
(3/2)² = 9/4
rewrite the equation
1/2 - 3 • (9/4)
multiply 3 by (9/4)
1/2 - (27/4)
subtract
-25/4
(1 + 1/3)² - 2/9
simplify the expression (1 + 1/3)
(4/3)² - 2/9
using PEMDAS, we see we have to evaluate the exponent first
(4/3)² = 16/9
rewrite the equation
(16/9) - (2/9)
subtract
14/9