The value of tan(m - p), where the value of sin(m) = -(4/5), and the value of cos(p) = -(15/17) using trigonometric identities is; [tex]tan(m - p) = \dfrac{36}{77}[/tex]
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions which are true for all values of the input variables.
The information in the question are;
[tex]sin(m) = -\dfrac{4}{5}[/tex][tex]cos(p) = -\dfrac{15}{17}[/tex]Therefore;
[tex]cos(m) = \sqrt{1- \left(-\dfrac{4}{5}\right)^2} =\pm\dfrac{3}{5}[/tex]
The location of m is in Quadrant III, therefore;
[tex]cos(m) =-\dfrac{3}{5}[/tex]
[tex]sin(p) = \sqrt{1- \left(-\dfrac{15}{17}\right)^2} =\pm\dfrac{8}{17}[/tex]
The angle p is located in Quadrant III, therefore;
[tex]sin(p) = -\dfrac{8}{17}[/tex]
180° ≤ Angle ∠m ≤ 270°; definition of angles in Quadrant III
180° ≤ Angle ∠p ≤ 270°; definition of angles in Quadrant III
Therefore;
270° - 270° ≤ |∠m - ∠p| ≤ 270° - 180°
0° ≤ |∠m - ∠p| ≤ 90°
The trigonometric identity for tan(m - p) is presented as follows;
[tex]tan(m - p) = \dfrac{tan(m) -tan(p)}{1+tan(m)\cdot tan(p)}[/tex]
[tex]tan(m - p) = \dfrac{\dfrac{sin(m) }{cos(m) } -\dfrac{sin(p) }{cos(p) } }{1+\dfrac{sin(m) }{cos(m) } \cdot \dfrac{sin(p) }{cos(p) } }[/tex]
Therefore;
[tex]tan(m - p) = \dfrac{\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) -\left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) }{1+\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) \times \left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) } }= \dfrac{36}{77}[/tex]
[tex]tan(m - p) = \dfrac{36}{77}[/tex]
Learn more about trigonometric identities and trigonometric functions here:
https://brainly.com/question/22591162
#SPJ1
Lamonte was comparing the price of grapefruit juice at two stores. The equation
y = 1.75x represents what Lamonte would pay in dollars and cents, y, for a bottles
of grapefruit juice at store A. Lamonte can buy 17 bottles of grapefruit juice at Store B
for a total cost of $36.38.
How much less is a bottle of grapefruit juice at Store A than
at Store B?
The bottle of grapefruit juice at store A is $6.63 less than the store B.
According to the question,
We have the following information:
The equation y = 1.75x represents what Lamonte would pay in dollars and cents, y, for a bottles of grapefruit juice at store A.
Cost of 17 bottles of grapefruit juice at store B = $36.38
Now, we will find the cost of 17 bottles at store A.
y = 1.75*17
y = $29.75
Now, the difference in their price = 36.38-29.75
Difference = $6.63
Hence, the bottle of grapefruit juice at store A is $6.63 less than the store B.
To know more about bottle of grapefruit juice here
https://brainly.com/question/28983587
#SPJ1
Answer: 0.39
Step-by-step explanation:
Store A
y= 1.75x
A bottle of grapefruit juice costs 1.75 at store A
Store B
36.38$/17 bottles = 2.14$ per bottle
A bottle of grapefruit juice costs 2.14$ at store B
Store B - Store A= 2.14$ - 1.75$
=0.39
Complete the square to transform the expression x^2 + 6x + 5 into the form a(x − h)^2 + k. (1 point)
(x + 3)2 + 4
(x + 6)2 − 4
(x + 3)2 − 4
(x + 6)2 + 4
a perfect square trinomial, namely [tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2[/tex]
where the middle-term is just a product of "2 times the square root of the terms on both sides".
so let's start by grouping the terms with a variable, and then adding the last term for the trinomial, keeping in mind the middle-term is just that product.
[tex]x^2+6x+5\implies (x^2+6x) ~~ +5\implies (x^2+6x+\square^2) ~~ +5 \\\\\\ \stackrel{middle-term}{6x}=2(\sqrt{x^2})(\sqrt{\square^2})\implies 6x=2x\square\implies \cfrac{6x}{2x}=\square\implies 3=\square[/tex]
ahhhaaa!!! so our missing term from our group is 3, meaning we need to use 3², however, let's remember, all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add 3², we also have to also subtract 3²
[tex](x^2+6x+3^2-3^2) ~~ +5\implies (x^2+6x+3^2)-3^2 +5\implies {\Large \begin{array}{llll} (x+3)^2-4 \end{array}}[/tex]
Find a b and c ??????
Answer:
a = 70 degrees
b = 20 degrees
c = 20 degrees
Step-by-step explanation:
First, we can find "c":
angleBCA = 90
angleBCA = angleBCD + c
90 = 70 + c
90 - 70 = c
20 = c
Knowing "c", we can find "a".
angleADC = 90
triangleADC = 180
triangleADC = angleADC + c + a
180 = 90 + 20 + a
180 = 110 + a
180 - 110 = a
70 = a
Knowing "a", we can find "b".
angle BCA = 90
triangleACB = 180
triangleACB = angleBCA + a + b
180 = 90 + 70 + b
180 = 160 + b
180 - 60 = b
20 = b
PLEASE HELPPP!!
The pair of points (-6, y) and (4,8) lie on a line with a slope of 5/2. Set up and solve for the missing y-value using the slope formula. Show all work to receive credit.
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Slope = 5/2
x1 = -6
y1 = y
x2 = 4
y2 = 8
5/2 = (8-y) / (4 - (-6))
5/2 = (8-y) / (4+6)
5/2 = (8-y) / 10
5 x 10 = 2 x (8-y)
50 = 16 - 2y
2y = 16 - 50
2y = -34
y = -17
A sample of 144 cans of coffee showed an average weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces. Construct a 68.26% confidence interval for the mean of the population.
The 68.26% confidence interval for the mean of the population, using the z-distribution, is given as follows:
(15.88 ounces, 16.12 ounces).
What is a z-distribution confidence interval?The bounds of a z-distribution confidence interval are presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given by:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value of the z-distribution.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population. -> as the z-distribution is used when the population standard deviation is known.The confidence level is of 68.26%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.6826}{2} = 0.8413[/tex], so the critical value is z = 1.
The values of the remaining parameters are given as follows:
[tex]\overline{x} = 16, \sigma = 1.4, n = 144[/tex]
Hence the lower bound of the interval is obtained as follows:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 16 - \frac{1.4}{\sqrt{144}} = 15.88[/tex]
The upper bound of the interval is obtained as follows:
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 16 + \frac{1.4}{\sqrt{144}} = 16.12[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Can you help with these vocabulary questions
King's Books sold 480 bookmarks last year, in comparison to 672 bookmarks this year. What is the percentage of the increase in the number of bookmarks sold annually?
Answer:
Step-by-step explanation:
percentage increase = (final - initial)/initial
increase = (672 - 480)/480
= 192/480
= 0.4 * 100 = 40% increase
There was a blizzard. Snow was falling at the rate of 3 inches per hour. If the snow keeps acclimating how long will 5 feet of snow to accumulate
The time taken for the 5 feet of snow to accumulate is 20 hours.
How to calculate the number of hours?In this case, Smsnow was falling at the rate of 3 inches per hour and if the snow keeps acclimating, we want to know how long will 5 feet of snow to accumulate.
Since 1 foot = 12 inches
5 feet = 5 × 12
= 60 inches
Therefore the time taken will be the division and this will be:
= 60 / 3
= 20
It'll take 20 hours.
Learn more about inches on:
brainly.com/question/876758
#SPJ1
Please answer. Thanks.
The missing statements/ reasons are:
Statement Reason
LN bisects ∠MLO Given
LM ≅ LO Given
∠MLN ≅ ∠NLO Def of angle bisector
LN ≅ LN Common side
ΔLMN ≅ ΔLON SAS postulate of triangle congruence
In this question, we have been given some information about triangles LMN and LON.
We need to prove ΔLMN ≅ ΔLON
LN bisects ∠MLO ....................(Given)
LM ≅ LO ...................(Given)
∠MLN ≅ ∠NLO ...................(Def of angle bisector)
LN ≅ LN ....................(Common side)
ΔLMN ≅ ΔLON ...................(SAS congruence postulate)
Therefore, the missing statements/ reasons are:
Statement Reason
LN bisects ∠MLO Given
LM ≅ LO Given
∠MLN ≅ ∠NLO Def of angle bisector
LN ≅ LN Common side
ΔLMN ≅ ΔLON SAS postulate of triangle congruence
Learn more about SAS postulate here:
https://brainly.com/question/13814326
#SPJ1
Determine which integer makes the inequality 8(n − 3) < 4(n + 7) true. S:{13} S:{24} S:{9} S:{52}
The inequality has a solution set of {-∞, 13} in order to make it equal
InequalityIn mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. An inequality shows the relationship between two values in an algebraic expression that are not equal.
In the given question
8(n - 3) < 4(n + 7)
Expand the bracket
8n - 24 < 4n + 28
8n - 4n < 28 + 24
n < 13
The solution set to make the inequality equal is {-∞, 13}
Learn more on inequality here;
https://brainly.com/question/25275758
#SPJ1
(3x + 8)°
(5x – 20)°
(5x + 4y)°
Find the value of each variable.
Answer:you have 2 lines that cross.
the left angle formed is equal to 3x + 8
the right angle formed is equal to 5x - 20.
the bottom angle formed is equal to 5x + 4y
since the lines are crossed, the opposite angles to each other are equal.
this means that:
3x + 8 = 5x - 20
solve for x to get x = 14 degrees.
the angle on the left side will be equal to 3(14) + 8 = 50 degrees.
the angle on the right side will be equal to 5(14) - 20 = 50 degrees.
this is at it should be since the angles are equal to each other.
since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.
since those 2 angles are equal, then each one must be equal to 130 degrees.
one of those angles is equal to 5x + 4y.
you get 5x + 4y = 130
since x was already found to be 14, replace x with 14 to get:
5(14) + 4y = 130
solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.
when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.
your answers are:
x = 14 degrees
y = 15 degrees
2 of the angles measure 50 degrees each.
2 of the angles measure 130 degrees each.
The value of a car depreciates over time. The table shows the value of a car over a
period of time.
2A- What kind of function does the scatter plot model? *
quadratic
exponential
none of these
The value of the car depreciates according to the scatter plot model that is attached , from the model we can infer that the model is exponential in nature.
So from the data that is plotted in the scatter plot we can see that
The graph is exponential.
We know that the depreciation is calculated by the formula as
A = A₀(1-r)ⁿ
So it is an exponential form of equation. therefore the scatter plot model will also predict an exponential equation.
A scatter plot is a type of plot or mathematical diagram that displays values for a group of data using two or more variables and Cartesian coordinates. A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.
If the points are somehow coded according to colour, shape, or size, another variable can be seen. A series of points is used to represent the data, with each point's position on the y line determined by the value of one variable and its position on the vertical axis by the value of the other.
To learn more about scatter plot visit:
https://brainly.com/question/29231735
#SPJ1
How many fifths equal 1/5
Answer: only 1
Step-by-step explanation:
Answer: One-fifth.
Step-by-step explanation:
2/5 is two-fifths, 3/5 is three-fifths, and so on.
1/10 is one-tenth, 2/10 is two-tenths, and so on.
Calculator
What is the area of this rectangle?
O 40 units²2
O 45 units²
O 50 units²
O 55 units²
-10-9-8-7-6-5-4
10-
9
8
8
9.10
Answer:
(c) 50 units²
Step-by-step explanation:
You want to know the area of the rectangle with vertices (-5, 5), (-1, 7), (4, -3), and (0, -5).
Distance formulaThe distance formula can be used to find the lengths of the sides. That formula is ...
d = √((x2 -x1)² +(y2 -y1)²)
The distance between the first two points is ...
d = √((-1 -(-5))² +(7 -5)²) = √(4² +2²) = √20
The distance between the next two points is ...
d = √((4 -(-1))² +(-3 -7)²) = √(5² +(-10)²) = √125
AreaThe area is the product of two adjacent side lengths:
A = LW
A = (√125)·(√20) = √(125·20) = √2500 = 50 . . . . square units
The area of the rectangle is 50 units².
To find the quotient Three-fourths divided by one-eighth,
Answer:
Step-by-step explanation:
1. Convert words to math
3/4/1/8=
3/4*8/1=
24/4=
6
3. Answer: 6
A washcloth is 9 inches long. If the area of the washcloth is 72 square inches, what is the width of the washcloth?
O A. 9 inches
OB. 7 inches
O C. 6 inches
O D. 8 inches
Step-by-step explanation:
Its is 8 inches as 72÷9 is 8
Need help finding the conclusion to this problem and the theorem that supports.
the theorems to choose from, base angles theorem, exterior angle theorem and, SAS
The thing that can be conluded about the diagram is that the ponds are the same length. This is according to the SAS theorem.
What is SAS theorem?According to the SAS theorem, if two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent.
If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. If two triangles meet one of the following criteria, they are congruent. All three corresponding side pairs are equal. Two corresponding side pairs and their corresponding angles are equal.
In this case, the triangle for the frog pond and duck pond are the same.
Learn more about triangles on:
https://brainly.com/question/1675117
#SPJ1
The purpose of post hoc tests following an Analysis of Variance is...
a.
...to address the question of which groups differ from one another.
b.
...to address the question of whether there are any differences at all between groups.
The purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.
Let us understand the post hoc tests:
Post hoc tests are an essential component of ANOVA. When at least three group means are tested for equality using ANOVA, statistically significant findings suggest that not all of the group means are equal. ANOVA results, on the other hand, do not specify which differences between pairs of means are significant. Use post hoc tests to investigate variations between various group averages while keeping the experiment-wise error rate under control.
There are a lot of post hoc tests that you can be used but the main purpose of the post hoc tests is always the same.
Thus, the purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.
To learn more about post hoc tests visit:
https://brainly.com/question/13179431
#SPJ1
Una barra de fierro tiene 3,5 metros de largo. en un punto de la barra se ubica una marca que dista 125cm de uno de los extremos.¿cuanto dista en dm del otro extremo?
Answer:
El otro extremo dista :
12.5 decímetros
Step-by-step explanation:
1 dm = 1 decímetro = 10 cm
1 m = 1 metros = 10 decímetros = 10 dm
3.5 metros = 3.5 * 10 = 35 decímetros
125 cm = 125/10 = 12.5 decímetros
Entonces:
35 dm - 12.5 dm = 22.5 dm
I need help with my math
Answer:
Page 1 of 3
1. twenty
2. 16,49
3. option3
4.32
5. 40 tickets show your work--10= 1.00 40=4.00
Page 2 of 3
7, 14, 21, 28, 35, 42, 49, 56, 63
Page 3 of 3 (left to right)
56, 0, 21, 63, 42, 35, 14, 28, 7, 77, 84, 56, 14, 49, 63, 28, 70, 42, 21, 35, 84, 7, 77, 0, 70
Step-by-step explanation:
learn your times tables
it will help you in high school and college
i need help with this
Check step-by-step explanation.
Step-by-step explanation:1. Form a table for the given equation.In order to form the table, we must take several values of x (any values you want to evaluate) and find it's correspondent y value. This is how you do it:
[tex]y=3x+12[/tex]
[tex]x=0, \\y=3(0)+12\\y=12[/tex]
As you may notice, we are just substituting the x value for the x variable into the equation and calculating y. Do this with several values and form a table (check attached image 1).
[tex]x=1, \\y=3(1)+12\\y=15[/tex]
[tex]x=2, \\y=3(2)+12\\y=18[/tex]
2. Draw the points.Using the calculated points, draw them in the cartesian plane. Remember that "x" means how many spaces you move horizontally, and "y" means vertical spaces.
Check attached image 2.
3. Interpret the information.Let's take point (2, 18) as an example. This point is generated when you substitute the x value of 2, meaning 2 hotdogs and the souvenir hat. Then, the functions gives a result of 18, which would be the cost of those 2 hotdogs in addition to the souvenir hat. Point (0, 12), on the other hand, means that you didn't buy any hotdogs but you still have to pay $12 for the souvenir hat.
Abby and Annie have the same number of coins Abby has sorted her coins into groups of 80 and he has sorted her coins into groups of 75 they each have less than 2000 coins how many coins do they have altogether
Altogether, Abby and Annie have 2,400 coins, using the Lowest Common Multiple of 75 and 80.
What is the lowest common multiple?The lowest common multiple (LCM) of two or more numbers is the common multiple shared by the numbers.
LCM of 75 and 80 can be obtained by multiplying common prime factors of 75 and 80, and then raising them to their respective highest power, i.e. 2^4 × 3^1 × 5^2, which gives 1200.
For instance, 1,200 can be divided by both 75 and 80 evenly without a remainder. And there is no other number less than 2,000 that 75 and 80 can divide evenly without a remainder.
Abby's coins = 1,200
Annie's coins = 1,200
Total coins = 2,400
Abby's 80 coins will have 15 groups (1,200/80)
Annie's 75 coins will have 16 groups (1,200/75)
Thus, using the LCM of 80 and 75, the total number of coins held by Abby and Annie is 2,400.
Learn more about the LCM at https://brainly.com/question/233244
#SPJ1
an object is traveling at the steady speed of 8 and 2/3 mph how long will it take the object to travel 5 and 1/5 miles
Answer:
36mins
Step-by-step explanation:
So, the time of travel to cover 5 1/5 miles at a speed of 8 2/3 mph is 36 minutes.
when diving a hummingbird can reach a speed of 40 miles per hour. What is this speed in miles per minute
The speed of the humming bird when converted to miles per minute is; 0.67 miles per minute
How to carry out unit conversions?In scientific problems, sometimes, it is necessary to change units from one to another as specifically needed.
The procedure for unit conversion is;
1. Identify the unit you have.
2. Identify the unit you desire or require.
3. Identify appropriate unit conversion factor(s).
4. Cancel units and carry out the math calculations.
5. Evaluate the result.
We are given the speed as 40 miles per hour. Now, the unit of conversion factor from mph to miles per minute is;
1 mile per hour = 1/60 miles per minute
Thus;
40 miles per hour = 40 * 1/60 = 0.67 miles per minute
Read more about Unit conversions at; https://brainly.com/question/141163
#SPJ1
examples of direct variation with nonzero numbers
A direct variation with nonzero numbers is if y varies directly as x, and y = 6 when x = 2,
What is direct variation?The relationship between two variables in which the variables have a constant ratio, k, where k is not equal to 0.
K is known as the constant. Assume the variables are x and y, and that y varies directly with x. We can say that the y/x ratio is equal to k, where k is not equal to zero.
This formula can also be written as y = kx where k is not equal to 0.
It's critical to understand that we can use these two ratios interchangeably depending on the problem at hand.
In the example given, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
Learn more about variation on:
https://brainly.com/question/2098610
#SPJ1
You started this year with $458 saved and
you continue to save $14 per month.
Write an equation to model this situation
(use m for months and s for savings).
Answer:
s = 14m + 458
Step-by-step explanation:
current amount = 458
14 per month
s = 14m + 458
9 feet is the same as how many meters? Hint: 1 ft≈ 0.305 m Learn with an example Round your answer to the nearest tenth. Submit (
9 feet is the same as = 2.74 m
Given
1 ft≈ 0.305 m
To find out 9 feet is the same as how many meters:
To convert a foot measurement to a meter measurement, multiply the length by the conversion ratio.
Since one foot is equal to 0.3048 meters, you can use this simple formula to convert:
meters = feet × 0.3048
= 9 * 0.3048
= 2.7432 m
The length in meters is equal to the feet multiplied by 0.3048.
Hence the answer is the 9 feet is the same as meters = 2.74m.
To learn more about conversion click here https://brainly.com/question/23718955
#SPJ9
(Scientific Notation LC)
Write 280,000,000 in scientific notation
Answer:
2.8 x 10º
Step-by-step explanation:
Because if you travel 10 spaces in the number 280,000,00.
x + 2x
Helpp, no link :/
Answer:
3x
Step-by-step explanation:
When the equation is like this and they both are being multiplied by x you can just add the coefficients
x+2x
1x+2x
3x
Hopes this helps please mark brainliest
Hello..!
Similar Terms:[tex] \sf{x + 2x = 3x}[/tex]
It is known that in similar terms "x" is an unknown quantity and that in this problem "x" is 1 and that we only have to add it to 2:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf2 + 1 = 3[/tex]
So the result is 3x
HELP!!! Simplify the expression
Answer: (3x^2)(y^3√y)
Step-by-step explanation:
1. To simplify the radical
> break the radicand (the number under the radical sign) into a product (the result of two numbers being multiplied together) of known factors.
2. Assume all numbers are real.