Answer:
[tex]\cos\left(\theta\right)=\frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
Given that [tex]\sin\left(-\theta\right)=-\frac{1}{4}[/tex] and [tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex]
Using those values we need to find value of [tex]\cos\left(\theta\right)[/tex]
So let's begin with equation of [tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex] and simplify it to get value of [tex]\cos\left(\theta\right)[/tex]
[tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex]
[tex]\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{\sqrt{15}}{15}[/tex]
[tex]\sin\left(\theta\right)=\frac{\sqrt{15}}{15}\cos\left(\theta\right)[/tex]
[tex]\sin\left(\theta\right)\cdot\frac{15}{\sqrt{15}}=\cos\left(\theta\right)[/tex]
[tex]\cos\left(\theta\right)=\sin\left(\theta\right)\cdot\frac{15}{\sqrt{15}}[/tex]
[tex]\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot\frac{15}{\sqrt{15}}[/tex] {since [tex]\sin\left(-\theta\right)=-\sin\left(\theta\right)[/tex] }
[tex]\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot\sqrt{15}[/tex]
[tex]\cos\left(\theta\right)=-\left(-\frac{1}{4}\right)\cdot\sqrt{15}[/tex]
[tex]\cos\left(\theta\right)=\frac{\sqrt{15}}{4}[/tex]
Answer:
[tex]\cos \theta = \frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
The sine function is an odd function, that is:
[tex]\sin (-\theta) = - \sin \theta[/tex]
Then,
[tex]\sin \theta = \frac{1}{4}[/tex]
The cosine function is computed by the following relation:
[tex]\cos \theta = \frac{\sin \theta}{\tan \theta}[/tex]
[tex]\cos \theta = \frac{\frac{1}{4} }{\frac{\sqrt{15}}{15} }[/tex]
[tex]\cos \theta = \frac{\frac{1}{4} }{\frac{1}{\sqrt{15}} }[/tex]
[tex]\cos \theta = \frac{\sqrt{15}}{4}[/tex]
Simplify the expression 2+3i/4+3i
Please help
Answer:
17+6i
-----------
25
Step-by-step explanation:
2+3i
---------
4+3i
We want to multiply by the complex conjugate of the denominator
4+3i has a complex conjugate of 4-3i
2+3i 4-3i
--------- * --------------
4+3i 4-3i
Lets multiply the numerator
(2+3i) ( 4-3i)
2*4 +4*3i -3i*2 - 3i*3i =
8 +12i -6i - 9i^2
Remember i^2 = -1
8 +6i -9(-1)
17 +6i
Lets multiply the denominator
(4+3i) ( 4-3i)
4*4 +4*3i -3i*4 - 3i*3i =
16 +12i -12i - 9i^2
Remember i^2 = -1
16 -9(-1)
25
Putting numerator over denominator
17+6i
-----------
25
From which language does the underlined phrase originate? When the house guests arrived, Granny said, "Mi casa es su casa." A. French B. Italian C. Spanish D. Algonquian Please select the best answer from the choices provided A B C D
The correct answer is option C - Spanish.
From which language does the underlined phrase originate? When the house guests arrived, Granny said, "Mi casa es su casa."
"mi casa es su casa" is a common Spanish expression which means - "welcome" or "make yourself at home" Mi casa es su casa literally means "my house is your house".
35 pts!! Please help this will help me graduate!!!
Consider this system of equations:
-3x + 5y = 22 (equation 1)
20y − 11 = 12x (equation 2)
This system of linear equations represents ___lines.
(A. coincidental B. Intersecting C. parallel)
The system of equation 1 and the equation 20y = 12x + 88 represents___ lines.
(A. coincidental B. Intersecting C. parallel)
Answer:
This system of linear equations represents parallel lines.
The system of equation 1 and the equation 20y = 12x + 88 represents coincidental lines
Step-by-step explanation:
-3x + 5y = 22 (equation 1)
Lets solve the equation for y
Add 3x on both sides
5y= 3x+22
Now divide by 5 on both sides
[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]
Slope of equation 1 is [tex]\frac{3}{5}[/tex]
20y − 11 = 12x (equation 2)
solve for y
Add 11 on both sides
20y = 12x + 11
Divide by 20 on both sides
[tex]y=\frac{12x}{20}+ \frac{11}{20}[/tex]
simplify the fraction
[tex]y=\frac{3x}{5}+ \frac{11}{20}[/tex]
Slope of equation 2 is [tex]\frac{3}{5}[/tex]
Slope of equation 1 and equation 2 are same , so the lines are parallel
This system of linear equations represents parallel lines.
-3x + 5y = 22 (equation 1) and 20y = 12x + 88
Solve both equations for y
-3x + 5y = 22 (equation 1)
[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]
Slope of equation 1 is [tex]\frac{3}{5}[/tex] and y intercept is 22/5
20y = 12x + 88
Divide by 20 on both sides and simplify the fraction
[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]
Slope of 20y=12x+88 is [tex]\frac{3}{5}[/tex] and y intercept is 22/5
Slope and y intercepts are same so the lines are coincidental
The system of equation 1 and the equation 20y = 12x + 88 represents coincidental lines
What is the difference in height between an albatross flying at 100 m above the surface of the ocean and a shark swimming 30 m below surface? What is the distance between them if the shark is right below the albatross
Answer:
130 m
Step-by-step explanation:
Let surface of ocean be at 0 feet (sea level)
Albatross is 100 m ABOVE surface of ocean, andShark is 30 m BELOW the surface of oceanThe distance from albatross to surface is 100 and the distance from surface to shark is 30 m. The total distance between them is [tex]100+30=130[/tex]
Distance between shark and albatross is 130 m
Answer:
130 m
Step-by-step explanation:
Can someone please explain this question?
Answer:
The limit does not exist
Step-by-step explanation:
lim as we approach from below 7
x+5 when x=7
7+5
12
lim as we approach from above 7
5x-25 when x=7
5*7 -25
35-25
10
The limit does not exist since these numbers are not the same
Answer:
Limit [tex]7^{-}[/tex] (left hand side limit) is 12
Limit [tex]7^{+}[/tex] (right hand side limit) is 10
Limit at 7 DOES NOT EXIST
Step-by-step explanation:
Limit [tex]7^{-}[/tex] means the limit from left side of 7Limit [tex]7^{+}[/tex] means the limit from left side of 7Limit at 7 will exist and would be equal IF BOTH SIDE limits are EQUAL, or else LIMIT DOESN'T EXIST!Limit [tex]7^{-}[/tex]:
When we want to find limit of left side of 7, we take the first part of the function shown (since its defined for [tex]x\leq7[/tex]).
We check values very close to 7 but less than it:
checking 6.98: [tex]6.98+5=11.98[/tex]checking 6.99: [tex]6.99+5=11.99[/tex]So the limit is approaching 12.
Thus, left hand side limit is 12.
Limit [tex]7^{+}[/tex]:
When we want to find limit of right side of 7, we take the second part of the function shown (since its defined for [tex]x>7[/tex]).
We check values very close to 7 but greater than it:
checking 7.02: [tex]5(7.02)-25=10.1[/tex]checking 7.01: [tex]5(7.01)-25=10.05[/tex]So the limit is approaching 10.
Thus, right hand side limit is 10.
Limit at 7:
If both right hand side limit and left hand side limit equal, then the limit at that specific number exists and is equal to it.
Since we see that the left hand limit (12) and the right hand limit (10) ARE NOT EQUAL, so we conclude that the limit at 7 for the function given DOES NOT EXIST.
There are 40 flavors of ice cream at the local ice cream store. 37.5% of the flavors contain chocolate. Which proportion could be used to calculate the total number of ice cream flavors that contain chocolate?
AD _____ EC
Choose the relationship symbol to make a true statement.
<
=
>
Answer:
AD>EC
Step-by-step explanation: If you look at the two traingles, angle AD is a bit larger than angle EC, this is due to the degrees of the angles, EC-> 25,
AD-> 30, this makes the triangle of AD, greater than EC.
Explain how mental math can be used to estimate a 15% tip on a taxi ride that costs $23.25 Find the tip using that method. Halp pllz!
Answer:
$3.4875
Step-by-step explanation:
AS the ride is completed and according the rule the person have to give a tip on the total taxi ride
according to the given
tip given 15%
Total ride cost = $23.25
To find is the total tip given in dollars
Solution:
Total tip in dollars = 15 % of total ride cost
Putting the values of the given
Total tip in dollars = 15 % of 23.25
it can be written as
= [tex]\frac{15*23.25}{100}[/tex]
=[tex]\frac{348.75}{100}[/tex]
=$ 3.4875
So the total tip would be $3.4875
Answer:
3.50 cent
Step-by-step explanation:
I take 10% and 20% of the number. For this ride, that would be about $2.33 and 4.66.
Then I estimate what is about half way between those two numbers. It looks like about $3.50 would be about 15%.
Need help with Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
To know if a dilation is an expansion ( bigger) r a contraction ( smaller) ignore the negative sign.
If the number is larger than 1, it is an expansion, if the number is smaller than 1 it is a contraction.
-4 is an expansion
2.5 is an expansion
2/3 is a contraction
-3/4 is a contraction
Write the quadratic equation in standard form for the following equations
(7,4);(-2,1);(1,9)
Answer:
[tex]y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}[/tex]
Step-by-step explanation:
We need to write a quadratic equation so we can use standard quadratic equation:
[tex]y=ax^2+bx+c[/tex]
Plug the given points to get three equations.
for (7,4), we plug x=7 and y=4
[tex]4=a(7)^2+b(7)+c[/tex]
[tex]4=49a+7b+c[/tex] ...(i)
similarly using other two points, we get:
[tex]1=4a-2b+c[/tex] ...(ii)
[tex]9=a+b+c[/tex] ...(iii)
Now we solve those three equations by any method like substitution, or matrices or by any method and get:
[tex]a=-\frac{7}{18},\ b=\frac{41}{18},\ c=\frac{64}{9}[/tex]
Now plug these values into [tex]y=ax^2+bx+c[/tex], we get final equation as:
[tex]y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}[/tex]
Anna wants to buy season passes to two theme parks. If one season pass costs $54.99 and Anna has $100 to spend on both passes, the second pass has to cost no more than what amount?
Answer:
54.01
If it’s an less than problem then
49.01<54.01<100
Step-by-step explanation:
100-54.99
= 54.01
It takes layla 2/5 hour to swim 1/2 mile what is the unit rate of miles that layla can swim per hour
Answer:
1 1/4 mph
Step-by-step explanation:
Distance = rate x time
1/2 mile = R x 2/5 hour
1/2=2/5R
/2/5 /2/5
R=1/2 x 5/2
R=1 1/4
I hope this helps :)
In your neighborhood, 7/25 of your neighbors have dogs. This is equivalent to what decimal?
See the attached picture:
The fraction 7/25 translates to the decimal 0.28 in mathematics.
Explanation:In the question, we are to translate the fraction 7/25 to a decimal. This is a straightforward conversion in the field of mathematics. To convert this fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number), yielding 7 ÷ 25 = 0.28. Therefore, the fraction 7/25 is equivalent to the decimal number 0.28 when rounded to two decimal places.
Learn more about Fraction to Decimal Conversion here:https://brainly.com/question/31738948
#SPJ3
What is the equation of the line:
Answer:
Final answer is y=3x-2.
Step-by-step explanation:
We have been given a graph and using that graph we need to find the equation of line.
Equation of line is given by formula y=mx+b
Where b is the y-intercept.
We see that graph crosses y-axis at (0,-2) so that means b=-2
Now plug b=-2 into formula y=mx+b. We get:
y=mx-2 ...(i)
Now find any point from the graph say (1,1) and plug into (i) to find value of slope m
1=m*1-2
1=m-2
1+2=m
3=m
Now plug m=3 into (i). We get:
y=3x-2
Hence final answer is y=3x-2.
Solve the system by substitution. Show your work. 4 pts 2) -2x - 3 y = -2 y = 2x + 6
Solve the system by elimination. Show your work. 4 pts
3) -x - 18 y = -3
7x - 9 y = 21
please help
I need this before midnight 12/19/2018
Answer:
2. x=-2 y= 2
3. x=3 y=0
Step-by-step explanation:
-2x - 3 y = -2
y = 2x + 6
The first step is to get x and y on the same side
Take the second equation and subtract 2x from each side
-2x+ y = 2x-2x + 6
-2x+y = 6
Multiply this by -1
-1(-2x+y) =-1*6
2x -y =-6
Add this to the first equation to eliminate x
-2x - 3 y = -2
2x -y =-6
--------------------
-4y = -8
Divide by -4
-4y/-4 = -8/-4
y =2
Now we need to find x
y = 2x + 6
Substituting in y=2
2 = 2x+6
Subtract 6 from each side
2-6 = 2x+6-6
-4 = 2x
Divide by 2
-4/2 = 2x/2
-2 =x
3) -x - 18 y = -3
7x - 9 y = 21
We will eliminate by by multiplying the second equation by -2
-2(7x - 9 y) = -2*21
-14x + 18y = -42
Now we will add this to the first equation
-x - 18 y = -3
-14x + 18y = -42
-------------------------
-15x = -45
Divide by -15
-15x/-15 = -45/-15
x =3
We still need to solve for y
-x -18y = -3
Substituting in x =3
-3 -18y = -3
Add 3 to each side
-3+3 -18y =-3+3
-18y =0
Divide by -18
y= 0
Three electrical appliances each have power ratings of 1 7/8 watts, and 2 other appliances each have power ratings of 4 3/4 watts.What is the total power used by these appliances?
Answer:
11 3/8 watts
Step-by-step explanation:
1 7/8 converts to 1.875
4 3/4 converts to 4.75
4.75 * 2 = 9.5
9.5 + 1.875 = 11.375
11.375 converts to 91/8 or 11 3/8
Given the inequality: m − 11 ≤ 16 or 15 − 2m < −7 Solve for j and graph the solution on a number line. Must show your work to receive full credit. (Equation is the second question in the attached photo)
Answer:
m ≤ 27 or m > 11
m is all real number since we have the or
Step-by-step explanation:
m − 11 ≤ 16 or 15 − 2m < −7
Lets solve the one on the left first
m − 11 ≤ 16
Add 11 to each side
m-11+11 ≤ 16 +11
m ≤ 27
Now lets solve the one on the right
15 − 2m < −7
Subtract 15 from each side
15 −15- 2m < −7 -15
-2m < -22
Divide by -2, remembering to flip the inequality
-2m/-2 > -22/-2
m > 11
Which letter on the number line represents the solution to -2.5r = -20? A) Point P B) Point Q Eliminate C) Point R D) Point S
Answer:
Point R = 8
Step-by-step explanation:
-2.5 r = -20
The solution to this equation is represented by a number line
In the given equation we have only the variable 'r'
We will get the value of 'r' while solving the above equation
That 'r' value is the solution point R on number line
[tex]-2.5r = -20[/tex]
divide by -2.5 on both sides
[tex]r=\frac{-20}{-2.5}[/tex]
r= 8 is our solution
Which expression, when simplified, is equal to 7p? A) 9p – 2pq – 7p – 5p + 2pq B) 9p – 2pq – 7p + 5p – 2pq C) 9p + 2pq – 7p + 5p – 2pq D) 9p + 2pq + 7p + 5p – 2pq E) 9p + 2pq – 7p + 5p + 2pq
Answer:C
Step-by-step explanation:
2pq - 2pq is zero. B and E have no zero pq coefficient.
p(9-7+5) = 7p
Answer:
c
Step-by-step explanation:
i did the test lol
Justing has 20 pencils, 25 erasers, and 40 paper clips. He organize them into groups with the same number of items and each group. All the items in. Group will be the same type. How many items can he put in each group?
Answer:
The answer is 17 items in 5 groups.
Step-by-step explanation:
If we have 20 pencils + 25 erasers + 40 paper clips; that´s a total of 85 items.
Then we just divide all the items into 5 groups so we can have the same amount of items in each group.
85 items ÷ 5 groups = 17 items each.
17 x 5 = 85.
7) Days People 1 26 2 30 3 34 4 38 5 42 6 46 The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On which day would you expect that number to be reached? A) 8 B) 9 C) 10 D)
Answer:The answer is mostly C) 10
Step-by-step explanation:
It's C because when you go to day 9, you count after 58 by adding 4 more, which equals 62 and then, since day 10) is 68 people that means that the answer is C.
Answer: c 10
Step-by-step explanation:
Since each day 4 more people sign up, on day 7, 50 will have signed up; on day 8, 54 people; day 9, 58 people; and day 10, 62 people
A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? Item 22 A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon?
The relationship between the weight of a person on Earth and the
person's weight on the Moon is a proportional relationship.
The weight of a 93 pounds person on the Moon is 15.5 pounds.Reasons:
The weight of the person on Earth = 120 pounds
Weight of the person on the Moon = 20 pounds
Required:
The weight of a person that weighs 93 pounds on Earth on the Moon
Solution:
Let x represent the factor (acceleration due to gravity) on Earth, let y
represent the factor on the Moon, and let m, represent the mass of the
person, we have;
x·m = 120
y·m = 20
Therefore;
[tex]\displaystyle \mathbf{\frac{x \cdot m}{y \cdot m}} = \mathrm{\frac{x}{y} } = \frac{120}{20} = 6[/tex]
For the person that weighs 93 pounds on Earth, we have;
[tex]\displaystyle \mathrm{\frac{x}{y} } = \mathbf{\frac{93}{Weight \ on \ the \ Moon}} = 6[/tex]
Which gives;
[tex]\displaystyle Weight \ of\ the \ person\ on \ the\ Moon = \frac{93}{6} = 15.5[/tex]
The weight of the person on the Moon = 15.5 pounds
Learn more about proportional relationships here:
https://brainly.com/question/8348898
1
8
of the boys at a high school tried out for the football team,
1
6
tried out for the baseball team, and
1
12
tried out for the football team and baseball team. What fraction of those who tried out for football also tried out for baseball?
Answer:
78
Step-by-step explanation:
112-18-16=78
Answer:
Correct answer is 2/3.
Step-by-step explanation:
It takes 28 minutes to play 8 songs on a radio.Every song is played for the same length of time.How does it take to play 1 song?Express your answer as a mixed number or a decimal
Answer:
you would divide 28 by 8 and get 3.5. so around 3:30 per song
Step-by-step explanation:
Answer:
Step-by-step explanation:28÷8=3.5 , each song is 3 and a half minutes long
Sarah drove 40 miles per hour . In 3 hours sarah drove 120 miles . Which is a vaild proportion to represent the problem?
Answer:
Step-by-step explanation:
1/40=3/120
One side of a kite is 5 cm less than 2 times the length of another. If the perimeter is 14 cm, find the length of each side of the kite.
A) 5 cm, 5 cm
B) 4.2 cm, 3.4 cm
C) 6.3 cm, 7.7 cm
D) 4 cm, 3 cm
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose one side of the kite is x
One side of a kite is 5 cm less than 2 times the length of another.
So, another side of the kite will be = [tex]2x-5[/tex]
So, the all 4 sides of the kite will be x, x , 2x-5 and 2x-5
The perimeter of the kite will be = [tex]x+x+2x-5+2x-5=6x-10[/tex]
As per given in question, perimeter is 14, so
[tex]6x-10=14[/tex]
Adding 10 in both sides
[tex]6x=24[/tex]
Dividing 6 in both sides
[tex]x=4[/tex]
So, another side is [tex]2*4-5=3[/tex]
So, the sides are 4 cms and 3 cms : Answer D
Hope it will help :)
Answer:
D) 4 cm, 3 cm
Step-by-step explanation:
Since we know that kite is made of two sets of equal sides.
Let x be the length of one of equal sides and y be length of another side of equal sides.
We have been given that one side of a kite is 5 cm less than 2 times the length of another. We can represent this information as:
[tex]x+5=2y...(1)[/tex]
We are also told that the perimeter is 14 cm. We can represent this information as:
[tex]2(x+y)=14...(2)[/tex]
From equation (1) we will get,
[tex]x=2y-5[/tex]
Substituting this value in equation (2) we will get,
[tex]2(2y-5+y)=14[/tex]
[tex]2(3y-5)=14[/tex]
[tex]6y-10=14[/tex]
[tex]6y-10+10=14+10[/tex]
[tex]6y=24[/tex]
[tex]y=\frac{24}{6}[/tex]
[tex]y=4[/tex]
Therefore, length of one side of kite is 4 cm.
Upon substituting y=4 in equation (1) we will get,
[tex]x+5=2*4[/tex]
[tex]x+5=8[/tex]
[tex]x+5-5=8-5[/tex]
[tex]x=3[/tex]
Therefore, the length of another side of kite is 3 cm and option D is the correct choice.
Erica has 1 over 3 of a watermelon to share equally with 3 friends. How much will each person get
Answer:
1/9
Step-by-step explanation:
1/3 ÷ 3 is the set-up for the problem we are trying to solve.
Remember when we divide fractions we multiply by the reciprocal. So we have:
1/3 × 1/3 since the reciprocal of 3/1 is 1/3
Multiplying 1/3 x 1/3 we find the product is 1/9
Therefore, each person would receive 1/9 of the watermelon
Select the equation which graphs to a vertical line at -3.
A) y=-3
B) x=-3
C) y=-3x
D) x=-3y
Answer: B) x = -3
Every point on this line has one thing in common: the x coordinate is -3. This is why x is fixed at -3, so we simply say the equation is x = -3
Some example points on this line are (-3,10) and (-3,2)
The y coordinate can be anything you want, so that is why it doesn't show up at all (because it doesn't affect how x will turn out).
Sarah bought a shirt on sale for $35. The original price of the shirt was three times that amount Sarah also bought a pair of shoes on sale for $28 they original price of the shoes with five times that amount together how much money did the shirt and shoes cross before they went on sale.
Answer:
$245
Step-by-step explanation:
Orignal price for shirt was 105
Original price for shoe sizes was 140
105+140=245
Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is [tex]\frac{2}{5}[/tex]. Find the perimeter of the other polygon.
Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].
So if the perimeter of the larger polygon is
[tex]s_1+s_2+s_3=85[/tex]
then the perimeter of the smaller polygon would be
[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]
so its perimeter would be 34 meters.
Final answer:
The perimeter of the smaller similar polygon is 34 meters, calculated by setting up and solving the proportion 2/5 = P/85.
Explanation:
When dealing with similar polygons, the ratio of their corresponding side lengths is the same as the ratio of their perimeters. Given that the ratio of the sides is 2 to 5, and the perimeter of the larger polygon is 85 meters, we can set up a proportion to find the perimeter of the smaller polygon.
Let the perimeter of the smaller polygon be P. The proportion will be 2/5 = P/85. To find P, we cross-multiply and get: 2 * 85 = 5 * P. Simplifying, we find that P equals 34 meters. Hence, the perimeter of the smaller polygon is 34 meters.