The simpler form of the expression [tex]\rm \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex] is [tex]\\\rm sec\theta[/tex].
It is given that the expression [tex]\rm \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex]
It is required to find the simpler form from the given options.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have the expression:
[tex]\rm= \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex]
We know:
[tex]\rm cos\theta = \frac{1}{sec\theta} \\\\\rm tan\theta = \frac{sin\theta}{cos\theta}[/tex]
By using these trigonometry formulas, we get:
[tex]\rm= \frac{sin\theta sec\theta}{cos\theta tan\theta}\\\\\rm= \frac{sin\theta }{(cos\theta) (cos\theta) \frac{sin\theta }{cos\theta} }\\\\\rm= \frac{1}{cos\theta} \\\\\rm = sec\theta[/tex]
Thus, the simpler form of the expression [tex]\rm \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex] is [tex]\\\rm sec\theta[/tex].
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Answer:
option A: sec Ø
Step-by-step explanation:
Find the distance FG between the points F(6,7) and G(8,9)
Answer:
2.828
Step-by-step explanation:
Part 2:
2.4.3: Denver to Chicago
A plane flew at a constant speed between Denver and Chicago. It took the plane 1.5 hours to fly 915 miles.
Answer:
Whats the question?
Step-by-step explanation:
−5(x−10)=−50 i need help answering it
[tex] - 5(x - 10) = - 50[/tex]
[tex] - 5x + 50 = - 50[/tex]
[tex] - 5x = - 50 - 50[/tex]
[tex] - 5x = - 100[/tex]
[tex] \frac{ - 5x}{ - 5} = \frac{ - 100}{ - 5} [/tex]
[tex]x = 20[/tex]
Jim made $143 for 11 hours of work at the same rate how many hours would he have to work to make $91
Answer:
Step-by-step explanation:
The equation is
Salary = 11 * x Where x is the number of hours.
salary = 143
hours = 11
x = ?
143 = 11x Divide both sides by 11
143/11 = 11x/11
13 = x
So to get 143 he works for 13 dollars / hour
salary = 13 * x
salary = 91
13 x = 91
13x/13 = 91/13
x = 7
He must work 7 hours to get 91 dollars.
Jim made 143 dollar for 11 hours of work at the same rate how many hours would he have to work to make 91 dollar
✺ Explanation -:Given:
Jim made $143 for 11 hours of work.To Find:
Hours he have to work to make $91.Solution:
We can solve this question using two methods Unitary Method and Method of proportion.
Unitary Method -
For $143 he work 11 hours
For $1 he work [tex]\dfrac{11}{143}[/tex] hrs
For $91 he works [tex]\dfrac{\cancel{11}} {\cancel{143}\: \: \cancel{13}}[/tex] × [tex]\cancel{91}\: \: 7 [/tex]hrs
= 7 hours
He must work 7 hours to get $91.
[tex] \ {\rule{50mm}{3pt}}[/tex]
Method of proportion -
He work 'x' hours for $91. (x as no. of hrs)
[tex] \left[\begin{array}{c | c}\ \bf{Salary} & \bf{Number \: of \: hrs} \\ \sf{143 \: dollar} & \sf{11hrs} \\ \sf{91 \: dollar}& \sf{x}\end{array} \right][/tex]
143 : 91 :: 11 : x
Product of mean = Product of extreme
143 × x = 91 × 11
→ x = [tex]\dfrac{91 × 11}{143}[/tex] = 7hrs
He must work 7 hours to get $91.
[tex] \ {\rule{90mm}{3pt}}[/tex]
I need help ASAP, with numbers 3-6 above. Please help.
Answer:
3. 2 6 30 6. 8:5
3 9 45
Step-by-step explanation:
If a club has 20 members and 4 officers how many choices are there for secretary
A. 20
B. 18
C.19
note: The secretary is the third officer to be elected.
What is the solution to the equation?
A. x = 144
B. x = 30
C. x = 18
D. x = 4
Answer:
D
Step-by-step explanation:
1/24x = 1/6
Multiply 1/6 by the reciprocal of 1/24 which is 24/1
Therefore;
X = 1/6 × 24/1
X = 4
A clay model of a new car is 7 in. Long. The actual car is 21 ft long. Part 1: What proportion can you use to find the scale used to make the model? Part 2: What is the scale of the model? Select BOTH answers. * 2 points Option 1 1 in. : 3 ft. 1 in. : 1 ft. Option 3 Option 2 3 in. : 1 ft.
Answer:
3ft:1in
Step-by-step explanation:
Given the clay model of a new car = 7in
If the actual car is 21ft, first we will have to convert 21ft to inches
Ift = 12in
21ft = x
x = 21×12.
x = 252in
21ft = 252in
This means that the clay model (7in) has to be scaled up to 252in. This is known as enlargement.
To know the scale of the model, we will take the ratio of the actual car to the clay as shown
Scale = actual car model/clay car model
Scale = 252/7
Scale = 36/1
We can also use the exact units of both measurement used in question
Scale = 21ft/7in
Scale = 3ft/1in
Hence the scale of the model is 3ft:1in
Joe's fitness club charges $40 a month for a membership. Mike's fitness club charges $20 for a membership per month and a $100 starting fee. After how many months will the total amount paid to the two clubs be the same?
Answer:
5 months
Step-by-step explanation:
Create an Equation:
m=months
Joe- 40m
Mike- 20m +100
Make each equation equivalent:
40m=20m+100
Solve:
40m-20m=100
20m=100
m=5
If you plug it back in, the equation is satisfied:
40(5)=20(5)+100
200=100+100
200=200
Which derivation correctly uses the cosine sum identity to prove the cosine double angle identity
Answer: A
Step-by-step explanation: took the test
The derivation that correctly uses the cosine sum identity to prove the cosine double angle identity is A; cos²(x) - sin(x)²
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Let revise the identities of double an angle
sin(2x) = 2 sin(x) cos(x)
cos(2x) = cos²(x) - sin²(x)
cos(2x) = 2 cos²(x) - 1
cos(2x) = 1 - 2 sin²(x)
The equation
∵ cos(2x) = cos(x + x)
cos(x)cos(x) - sin(x)sin(x)
cos²(x) - sin(x)²
The identity is cosine double angle identity for cosine difference
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Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub. What is the area of the cover? Use Pi = 3. 14 and round the answer to the nearest square foot.
Answer:
38 square feet
Step-by-step explanation:
How do we find the area of a circle?
❖ The area of a circle is πr², where r = radius. For this case, we're going
to approximate pi as 3.14.
How do we find the radius given diameter?
❖ We are given the diameter of Claire's hot tub as 7 feet. The diameter
is 2x the radius, so we divide 7 by 2 to get the radius, which is 3.5
feet.
Solving
[tex]3.14*3.5^2[/tex] [tex]3.14 *12.25[/tex] [tex]38.465[/tex] 38.465 ≈ 38Therefore, the answer is 38 square feet. Have a lovely rest of your day/night, and good luck with your assignments! ♡
Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the coefficient 'k' in the factored form?
6x3 + 4x2 − 6x − 4 = 2(x + k)(x − k)(3x + 2)
k=
1
2*(x+1)*(x-1)*(3x+2)
hope this helps
Which is the best description of the equivalency of the two expressions?
Expression 1
5x2 - 2x-4+6x+3
Expression 2
6x2 - 6x+6-x^2+10x-7
The two expressions are not equivalent because when x=2, the two expressions do not have the same value
O The two expressions are not equivalent because when they are simplified, they do not have the same coefficients
for the x2 and x terms.
O They are equivalent because the sum of the constants is the same in both expressions.
O They are equivalent because when x = 2, the two expressions have the same value.
PLEASE HELP IM ON A TIMER I WILL GIVE BRAINLIEST
Answer: D
Step-by-step explanation:
Equivalent when u use x=2
Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch's 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo's margin of error, rounded to the nearest whole number? (The formula is 1.96 straight x left parenthesis StdDev right parenthesis divided by square root of straight N)
Answer:
The answer is "20".
Step-by-step explanation:
Given value:
[tex]\to Z_{critical}= 1.96\\\\\to {StdDev} = standard\ deviation = 50 \\\\\to n= 25\\\\[/tex]
formula:
[tex]\bold{Margin error}= Z_{critical} \times \frac{\text{StdDev}}{\sqrt{n}}\\[/tex]
[tex]= 1.96 \times \frac{ 50 }{\sqrt{25}}\\\\= 1.96 \times \frac{ 50 }{\sqrt{5 \times 5}}\\\\= 1.96 \times \frac{ 50 }{{5}}\\\\= 1.96 \times 10 \\\\= 19.6 \\\\= 20[/tex]
Graham uses a 10 by 10 grid to model a decreasing pattern. He cuts off a section representing a percent of the current area so that the remaining area represents the next term in the pattern, rounded to nearest whole centimeter. The area after each cut is shown on the graph. A graph shows number of cuts labeled 1 to 10 on the horizontal axis and remaining area (square centimeters) on the vertical axis. A line decreases from 0 to 10. After each cut, what percentage of the previous area is the the remaining area? 10% 20% 80% 100%.
After each cut, by observing the graph, the remaining area is 80% of the previous area.
It is given that
Actual area = 100cm²
What is the percentage?The percentage is the value per hundred.
According to the graph,
Area after the first cut =80cm² (80% of the previous are)
Area after the second cut = 64 cm²(80% of 80)
Area after third cut = 51.2 cm²(80% of 64)
So we can observe that area after each cut is 80% of the previous area.
Therefore, after each cut, the remaining area is 80% of the previous area.
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After each cut, by observing the graph, the remaining area is 80% of the previous area.
It is given that
Actual area = 100cm²
What is the percentage?
The percentage is the value per hundred.
According to the graph,
Area after the first cut =80cm² (80% of the previous are)
Area after the second cut = 64 cm²(80% of 80)
Area after third cut = 51.2 cm²(80% of 64)
So we can observe that area after each cut is 80% of the previous area.
Therefore, after each cut, the remaining area is 80% of the previous area.
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There are 40 monkeys and 60% of the monkeys are in the trees. How many monkeys are in the trees?
Show your work: Write an equation, solve and explain your thinking
Answer:
24 monkeys are in the tree
Step-by-step explanation:
We solve it by writing [tex]\frac{60}{100}[/tex] times [tex]\frac{40}{1}[/tex]
Why is it over 100? Because every percent is out of 100!
[tex]\frac{60}{100}[/tex] X [tex]\frac{40}{1}[/tex] (your equation)
60 times 40 = 2400 and 100 times 1 = 100, We get, [tex]\frac{2400}{100}[/tex],
Lastly, we simplify the fraction by 100 on each side:
[tex]\frac{2400}{100}[/tex] / [tex]\frac{100}{100}[/tex]
you get 24
2i-3n=8
i+2n=-3
solve for i and n
Answer:
n= -2/7 i= 3 4/7
Step-by-step explanation:
i=3-2n
2(3-2n)-3n=8
6-4n-3n=8
6-7n=8
6-8=7n
-2=7n
-2/7=n
=3-2(-2/7)
3+4/7
i=3 4/7
What is the area of this figure?
Answer:
70 m^2
Step-by-step explanation:
I did this quickly, so please check the numbers.
Divide the figure into 3 recdtangles and one triangle. Calculate the area of each and take the sum.
I realize after looking at the image that one could have made only two rectangles and gotten the same result.
The area of a right triangle is 336 square inches. The height of the right triangle is 48 inches. What is the length of the hypotenuse of the right triangle?
Is the figure shown in the xy-coordinate plane a parallelogram? Why or why not? Use the given coordinates to justify your answer.
The figure shown would represent a parallelogram if opposite sides are parallel and congruent
It is true that the figure is a parallelogram
How to determine if the figure is a parallelogram
The coordinates of the figure are given as:
O = (0,0)
P = (a,b)
S = (a + c,b)
T = (c,0)
Vertices O and T are on the same horizontal level, because they have the same y-coordinate
The above is also applicable to vertices P and S
By observation, we have the following distances:
PS = c
OT = c
This means that the opposite sides are parallel and congruent
Hence, the figure is a parallelogram
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PLS HELP GIVING BRAINLIEST TO FIRST PERSON
Answer:
Solve for x
by simplifying both sides of the equation, then isolating the variable. x=ordw
Step-by-step explanation:
or it could be word
Answer:
x=57
Step-by-step explanation:
I think i already answered this question, but i will rewrite it again! since the angles 'x' and '2x+9' add up to become a supplement angle or a straight line.
We can establish the relation which says that the sum of these two angles is equal to 180.
[tex]x + 2x + 9 = 180[/tex]
[tex]3x + 9 = 180[/tex]
[tex]3x = 180 - 9[/tex]
[tex]3x = 171[/tex]
[tex]x = \frac{171}{3} = 57[/tex]
Use the algebra tiles to model x 1. Then choose the answer that describes the correct tiles. One blue x tile and one orange tile one orange x tile and one blue – tile one blue x tile and one blue – tile one orange x tile and one orange tile.
The correct statement which describe about the algerbric tile one orange x tile and one orange + tile.
What are algerbra tiles?
Algebra tiles are square and rectangle shaped tiles or tiles that represent numbers and variables.
Given
Use the algebra tiles to model x + 1.
Algebra tiles are square and rectangle-shaped tiles that represent numbers and variables.
Using algebra tiles provides a more visual way for us to solve our problems.
The correct statement which describe about the algerbric tile one orange x tile and one orange + tile.
Hence, the correct statement which describe about the algerbric tile one orange x tile and one orange + tile.
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Which of these is a unit of density?
[tex]\longrightarrow \textsf{The unit of density is\;} [/tex][tex]\sf kg/m^3[/tex]
Solution :-[tex]\green{ \underline { \boxed{ \sf{Density = \frac{Mass}{Volume}}}}}[/tex]
[tex]\longrightarrow[/tex]The unit of mass is kg and unit of Volume is m³ . Since density is division of mass by volume , the corresponding units will also get divided and unit of density would come out to be kg/m³
Some basic derived Units :-
area => m²volume cubic meter => m3speed meter per second => m/sacceleration => m/s²mass density meter => kg/m3specific volume cubic meter per kilogram m³/kgThe answer has to be a fraction, number 10!!! Urgent!!!
Answer:
x = 0
Step-by-step explanation:
Calculate the product
Any expression multiplied by 0 equales 0
Solution
X = 0
Hope this helps!
For which interval is the function constant?
(-infinity, 0)
(6, infinity)
(2, 6)
(0, 2)
Answer:
the answer is (2,6)
Step-by-step explanation:
What is the slope of the equation y=5/4x - 7/4
Answer:
The equation of a line is given by y = mx + c; where m is the slope.
The given equation is y = 5/4 x - 7/4.
Therefore, the slope is 5/4.
The area of a triangle 36 ×39×15
Answer:
a=21060[tex]in^{3}[/tex]
Step-by-step explanation:
A= B*W*H
A=36*39*15
A=1404*15
A=21060
PLEASE HELP 30 POINTS
Line A is represented by the equation, y=1/4x +5
(a) Write in slope-intercept form the equation of a line that is parallel to Line A and passes through the point, (8, -2). Show your work
(b) Write in slope-intercept form the equation of a line that is perpendicular to Line A and passes through the point, (4,1). Show your work.
Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
(a)
Parallel lines have the same slope but different y-intercepts.
m = 1/4x
y = 1/4x + b
-2 = 1/4(8) + b
-2 = 2 + b
b = -4
y = 1/4x - 4
(b)
Perpendicular lines have the negative reciprocal slope.
m = -4
y = -4x + b
1 = -4(4) + b
1 = -16 + b
b = 17
y = -4x + 17
Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope but different y-intercepts
Perpendicular lines have the negative reciprocal slope.
I need this for my homework!: Describe the steps you can use to find an average of
fractional amounts.
Thanks! ＜；
Step-by-step explanation:
for example 1)8,9,12,8,7,11,3,9,5
we need to find average
first add all the numbers =72
we divide by how many number we havein data base which is 9 (mean count how many numbers we have)
72/9=8
the ratio at which x axis divides the point (2, - 8) and (-3, 6).
Pls tell me the answer as fast as possible...
We are having math surprise test today...
Answer:
The answer is Math. M a t h
Step-by-step explanation:
Good luck!