Step-by-step explanation:
1.
the length of the terminal side from (0, 0) to (4, -7) is the radius of the circle, while
x = 4 = cos(theta)×radius
y = -7 = sin(theta)×radius
so,
sin(theta) = -7/radius
radius² = (4 - 0)² + (-7 - 0)² = 4² + 7² = 16 + 49 = 65
radius = sqrt(65)
sin(theta) = -7/ sqrt(65) = -0.868243142...
FYI
theta = -60.2551187...°
or 299.7448813...°
2.
tan(theta) = 3/2
so,
sin(theta)/cos(theta) = 3/2
2×sin(theta) = 3×cos(theta)
square both sides
4×sin²(theta) = 9×cos²(theta)
completing the square
4×sin²(theta) + 9×sin²(theta) = 9×cos²(theta) + 9×sin²(theta)
13×sin²(theta) = 9×(cos²(theta) + sin²(theta)) = 9
sin²(theta) = 9/13
sin(theta) = 3/sqrt(13)
to make it a rational denominator we multiply by
sqrt(13)/ sqrt(13)
and we get
sin(theta) = 3×sqrt(13)/13
3.
because the sum of all angles in a triangle is 180°.
one angle is theta.
then we have the 90° angle at the origin (or center of the circle).
and that leaves 180 - 90 - theta = 90 - theta for the third angle.
this triangle can be flipped with putting 90 - theta in place of theta.
the flipped triangle is equivalent to the original triangle (all angles and side lengths are identical between the 2 triangles).
the baseline (radius) is the same length in both triangles.
in that flipped triangle the side formerly sin(theta) is now cos(90-theta) and cos(theta) is now sin(90-theta).
Choose the letter of the word or phrase that best completes each statement.
a. ratio
b. proportion
c. means
d. extremes
e. similar
f. scale factor
g. AA Similarity Post.
h. SSS Similarity Theorem
i. SAS Similarity Theorem
j. midsegment
k. dilation
I. enlargement
m . reduction
A(n) ____?____ is a comparison of two quantities using division.
A ratio is a comparison of two quantities using division.
Ratio is defined as the comparison of two quantities. It is the relationship between two quantities, normally expressed as the quotient of one divided by the other. The ratio between quantities a and b can be expressed using the ":" symbol, a : b or as a fraction, a/b.
example:
1. There are 3 girls for every 5 boys in a class.
Then, the ratio of girls to boys can be written as
3 : 5 or 3/5.
2. In a basket filled with 30 pieces of two kinds of fruits, apples and oranges, 20 are apples and the rest are oranges.
Then, the ratio of apples to oranges can be written as
20 : 10 or 20/10.
When simplified,
2 : 1 or 2/1.
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A plastic pipe 5m long is divided into ten equal parts. What is the length of each part?
Answer:
each part will be half a meter or fifty centimeters
Step-by-step explanation:
divide the total length by ten to find the individual part.
6^5x1/6^5 =_______.
What
Answer:
1
Step-by-step explanation:
6^5x1/6^5
6^5 = 6*6*6*6*6 = 7776
7776x1/6^5 7776x1 = 7776
7776/7776= 1
-QS is a diameter of ®V . Find the measure.
m PQR
The measure of m∠RQS and m∠PQR is the line QS bisects ∠PQR and m∠PQS=63° are 63 and 126 degrees.
What is an angle bisector?The line or line segment that divides an angle into two equal pieces is known as the bisector of an angle, also known as the internal angle bisector. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
If line QS bisects ∠PQR, then;
<PQS = <RQS
WE have Given the following parameter;
m∠PQS=63°
Hence <PQS = <RQS = 63 degrees
Also,
<PQR = <PQS + <RQS
<PQR = 63 + 63
<PQR = = 126 degrees
The measure of m∠RQS and m∠PQR is the line QS bisects ∠PQR and m∠PQS=63° are 63 and 126 degrees respectively
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HABITS
9 of Mind
Make Sense of Problems Explain how using
basic facts can help you find 10 x 20 x 30 x 40 mentally. I need to get my homework done
The result of the multiplication is 24,000.
How to multiply any number with 10?Multiplication is simply repeated addition, and it is a crucial skill to master.
What occurred if we multiply by ten? 4 * 10 equals 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + What does this add up to? It adds up to 40. Take a look at that. We have a 4 and a 0 just at end.While multiplying whole digits by ten, surely add a 0 to a end of the number to get the answer. 5 * 10 equals a 5 with a 0 just at end: 50. 3 * 10 equals 30 (a 3 with such a 0 at the end).For the given multiplication;
= 10 x 20 x 30 x 40
This could be written in the terms of 10.
= 10 x 2 x 10 x 3 x 10 x 4 x 10
Simply count the 10 and put the same number of zero after 1 and multiply remaining.
= 2 x 3 x 4 x 10000
= 24 x 10,000
Now, put the same number of zero after the number 24.
= 240,000
Therefore, the given multiplication is solved using simple mental maths.
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The correct question is -
Explain how using basic facts can help you find 10 x 20 x 30 x 40 mentally.
Use the Distance Formula to find the distance between the pair of points.
M(1,-2), N(9,13)
Using the distance formula, the distance between the points M(1,-2) and N(9,13) is 17 units
Given,
The points = M(1,-2) and N(9,13)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
[tex]=\sqrt{(9-1)^{2}+(12--3)^{2} } \\=\sqrt{8^{2}+15^{2} } \\=\sqrt{64+225}\\ =\sqrt{289}[/tex]
=17 units
Hence, Using the distance formula, the distance between the points M(1,-2) and N(9,13) is 17 units
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A Florida orange juice plant started producing a juice blend, it must be within 0.78 fluid ounces of the advertised 32 fluid ounces on the label. If x represents the volume, write an equation to model the maximum and minimum volumes and determine the minimum volume in a bottle.
|x - 32| = 0.78
|x + 32| = 0.78
|x - 0.78| = 32
|x + 0.78| = 32
The equation to model the maximum and minimum volumes is given by |x - 32| = 0.78
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the volume of the orange juice in the bottle. it must be within 0.78 fluid ounces of the advertised 32 fluid ounces, hence:
|x - 32| = 0.78
The equation to model the maximum and minimum volumes is given by |x - 32| = 0.78
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When jorge arranges his pennies into a rectangle with two equal rows, three equal rows, or five equal rows, he has one leftover penny. when he arranges his pennies into a rectangle with four equal rows, he has three leftover pennies. how many pennies could jorge have?
Using common multiple, Jorge could have 31 pennies.
A common multiple is defined as a whole number, a shared multiple of each set of numbers. The common multiples of two or more prime numbers is the multiples of their product.
"when Jorge arranges his pennies into a rectangle with two equal rows, three equal rows, or five equal rows, he has one leftover penny"
Find the common multiples of 2, 3, and 5, and add 1.
Since 2, 3, and 5 are prime numbers, their common multiples are the multiples of their product.
Common multiples : 30, 60, 90, . . .
n = possible number of Jorge's pennies = 31 or 61 or 91 . . .
"when he arranges his pennies into a rectangle with four equal rows, he has three leftover pennies"
Find the common multiples of 4 and add 3.
multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, . . .
n = possible number of Jorge's pennies = 7, 11, 15, 19, 23, 27, 31, 35, . . .
31 ÷ 2 = 15 r 1
31 ÷ 3 = 10 r 1
31 ÷ 5 = 6 r 1
31 ÷ 4 = 7 r 3
Hence, Jorge could have 31 pennies.
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can you use the multiplication property of inequality to solve 8m>-1/10?can you use the division of property to solve -9/2 >3/2?explain your reasoning
a) Yes, by multiplying both sides by 1/8.
b) The inequality is false, thus, there is nothing to solve.
can you use the multiplication property of inequality to solve 8m>-1/10?Yes, you can.
There is a property that says that if you perform the same operation (multiplicating by 1/8 in this case) in both sides, then the truth value of the inequality does not change.
8m > -1/10
So, if we multiply both sides by 1/8, we will get:
8m/m > -1/(10*8)
m > -1/80
The inequality is solved.
can you use the division of property to solve -9/2 >3/2?There is nothing to really solve here, as you can see, the inequality says that a negative number is larger than a positive number, so the inequality is clearly false, and thus, there is nothing to solve.
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NEED HELP ON THIS PLEASE!!!
i think its the last one
Write an equation of each line in slope-intercept form.slope 1/2 , through (2,3)
y = 1/2x + 2 is an equation in slope-intercept form for the slope 1/2 , through (2,3).
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
As we have slope and x and y we can write the given data in point-slope form, that is,
y - 3 = 1/2(x - 2)
And now we can distribute to convert it to slope-intercept form
y - 3 = 1/2(x - 2)
y = 1/2x -1 + 3
y = 1/2x + 2
So, y = 1/2x + 2 is in lope-intercept form for the slope 1/2 , through (2,3)
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Are these two like terms or not like terms
is 4 2/5 greater than the square root of 19
Answer:yes
Step-by-step explanation:
because 4 2/5 is 4.4
and the square root of 19 is 4.358
Answer:
yes, 4 2/5 > √19
Step-by-step explanation:
You want to know if 4 2/5 is greater than √19.
ComparisonThere are several ways you can determine the relationship between these numbers. If you have a calculator, you can simply subtract one from the other. The sign of the result will tell you which is greater:
4 2/5 -√19 ≈ 0.0411 > 0 . . . . . . 4 2/5 is larger
Even without a calculator, you can square both numbers. Squaring positive numbers does not change their order, so ...
(4 2/5)² = 19.36 . . . . . . . . . . . . 4 2/5 is larger than √19
(√19)² = 19
Your calculator can tell you the decimal value of the two numbers, so you can compare their values yourself (as opposed to using subtraction).
4 2/5 = 4.400 . . . . . . . . . . . 4 2/5 is larger than √19
√19 ≈ 4.359
<95141404393>
Lin ordered 250 pens and 250 pencils to sell for a theatre club fundraiser. the pens cost 11 cents more than the pencils. if lin's total order costs $42.50, find the cost of each pen and pencil.
Using algebraic expression and equation, each pen costs 14 cents while each pencil costs 3 cents.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that the pens cost 11 cents more than the pencils, we can express this as:
x = 11 + y
where x = cost of each pen (cents)
y = cost of each pencil (cents)
If Lin ordered 250 pens and 250 pencils and the total order costs $42.50, we can express that as:
250x + 250y = $42.50
Substitute the value of x in this equation and solve for y.
250x + 250y = $42.50
250(11 + y) + 250y = 4250 cents
2750 + 250y + 250y = 4250
500y = 1500
y = 3
cost of each pencil = 3 cents
x = 11 + y
x = 11 + 3
x = 14
cost of each pen = 14 cents
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iddddkkkkk pleasse help
The statement which is given in option (b) is correct. Further, 25 glasses can be filled out from the 2 containers of fruit juice each held 64 ounces.
Given that, 2(64)-5g = 3 and we have to conclude the best situation from the four options given which satisfy this equation.
2(64)-5g = 3 means, the result of taking out 5 times g from the product of 2 and 64 equals to 3 in the end.
So, out of the four statement given option (b) shows the current statement i.e., Daniel had 2 containers of fruit juice. Each container held 64 ounces. How many ounces did Daniel pour in each glass, g, if he had 3 ounces left when he finished pouring?
Therefore, option (b) is correct.
Let's proceed to solve this question further, we get
The number of glasses g will be simply equal to
2(64)-5g = 3
128-5g = 3
128-3 = 5g
125 = 5g
125/5 = g
25 = g
So, There will be 25 glasses can be filled out from the 2 containers of fruit juice each held 64 ounces.
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Solve for x.
33 ÷ x = 3
Answer: 99
you do 33x3=99
33/99=3
Step-by-step explanation: hope this helps!!
1. A point is 5 units to the left of the y-axis
and 8 units up from the x-axis. Which
quadrant contains the point?
(-5,8) would be in quadrant 1
Write the following expression using the fewest possible terms.
(−3x − 12) + (16 + 8x)
A. 5x + 4
B. 5x + (−4)
C. 11x + 28
D. 11x + (−4)
The simplified expression of (−3x − 12) + (16 + 8x) is 5x + 4 (option A).
What is the simplified expression?A mathematical expression is when numbers and variables are combined together using mathematical symbols. A mathematical expression does not have an equal to sign.
To simplify an expression means to use the fewest possible terms. In order to simplify the expression, the BODMAS rule would be made use of. The BODMAS rule provides the procedure for solving mathematical expressions. According to the rule, terms in the bracket would be solved first.
Addition is the process of determining the sum of numbers. The sign used to represent addition is +. Subtraction is the process of calculating the difference between two or more numbers. The sign used to represent subtraction is -.
(−3x − 12) + (16 + 8x)
The first step is to combine similar terms together: (-3x + 8x) (-12 + 16)
Add similar terms together: 5x + 4
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What is the standard form of the following equation?
y = -2/5x + 4
Use integers for A, B, and C. Enter your answer in the box.
____ x +
____ y =
____
The standard form of the given equation is y = -2/5(x + 10).
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
y = -2/5x + 4
We know that the given equation is of parabola.
Thus, converting it to the standard form of parabola,
y = a(x-h)^2 + k
where (h, k) is the vertex .
Now we have,
y = -2/5x + 4
Thus, multiplying both the side the given equation by 5 we get,
5y = (-2/5x + 4)*5
Expanding the brackets we get,
5y = -2*5/5x + 4*5
Solving we get
5y = -2x + 20
Now factoring R.H.S we get,
5y = -2x + 2*10
Taking common we get,
5y = -2(x + 10)
Dividing both the side by 5 we get,
5y/5 = -2(x + 10)/5
Solving we get,
y = -2/5(x + 10)
thus is the required standard form of the given equation.
Thus, the standard form of the given equation is y = -2/5(x + 10).
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c) Work out the value of 8² + √100
Answer:
74.
Step-by-step explanation:
8² + √100
= 64 + 10
= 74.
Express 0.55555... as a fraction in
simplest form.
Answer:
11/20
Step-by-step explanation:
A salad dressing is made by mixing lemon juice and vinegar in the ratio 4:3 Vicky makes 700 ml of the salad dressing. How much lemon juice does she use? Give your answer in millilitres (ml).
Answer:
400 ml of lemon juice
Step-by-step explanation:
We know that there are 700 ml of salad dressing, and the ratio of lemon juice to vinegar is 4:3. We know that therefore, there are 7 equal parts. To find how many ml are in one part, we divide 700 by 7, which gives us 100. Then we can multiply that answer by 4 to find how many ml of lemon juice and 3 to find how many ml of vinegar.
100 x 4 = 400
Therefore, Vicky uses 400 ml of lemon juice.
I need help ASAP pls someone help and hurry
The solution to given equation 2(5 - 10x) + 8x = -19x + 52 is x = 2
In this question, we have been given an equation:
2(5 - 10x) + 8x = -19x + 52
We need to solve given equation for x.
2(5 - 10x) + 8x = -19x + 52 ................(Given equation)
10 - 20x + 8x = -19x + 52 ................(Evaluate the bracket )
10 - 12x + 19x = 52 ...............(Add 19x on each side)
10 + 7x = 52
7x = 52 - 10 ...............(Subtract 10 from each side)
7x = 42
x = 42/7 ..............(Divide each side by 7)
x = 6
Therefore, the solution to given equation 2(5 - 10x) + 8x = -19x + 52 is x = 2
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I need help with this question
168>= 7x+4y
I need to solve for Y
Two expressions with an equal sign in between is Equation, The given equation is 168>= 7x+4y, when we solve it for y we get y<=42-7x/4..
What is Equation?
Two expressions with an equal sign in between is called as Equation.
The given equation is
168>= 7x+4y
Now we need to make y as independent variable.
Subtract 7x on both the sides
168-7x>=7x-7x+4y
168-7x>=4y
Now divide both side by 4.
42-7x/4>=y
Therefore the value of y is 42-7x/4, y<=42-7x/4.
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3) What is the perimeter of the figure
below?
Please show how you solved it.
Answer:
Multiply 2 by 9, and then 2 by 11, and add it up all together. 18+22=40
Step-by-step explanation:
a video posted on the internet is becoming very popular, and the total number of views is increasing by 30% every hour. if the video currently has 11,882 views, how many views will it have in 3 hours
Answer:26105 rounded
Step-by-step explanation: if not rounded 26104.754
8x + 5 = 29; x = 3
how does that work?
Answer:
You substitute the x with the number.
8(3)+5=29 so 8*3 is 24 + 5 is 29
Step-by-step explanation:
11. (01.07 MC)
What is the value of x if log₂√x-1-2? (5 points)
82
O 65
O 19
O-8
Answer: 65
Step-by-step explanation:
Answer:
82
Step-by-step explanation:
65 because the other guy said it and im taking the test rn and i put that as my answer. and im answering this now cause i know i wont get back to it
omg jk its 82
wow im glad i actually tried to solve it..
but yeah
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
x=82
thats the best i can do to explain cause im lazy
Good luck
Sherman bought a new house. Over a 5 month period, he has paid $350 to his neighborhood homeowners association in monthly fees. Which representation shows the relationship between x, the number of months, and y, the fees Sherman has paid to the homeowners association?
The proportional relationship between the fees paid and the number of months is given by:
y = 70x.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
In the case of an inverse relationship, we have that:
y = k/x.
k is the constant of proportionality for both cases.
For this problem, the time and the fees are direct proportional, that is, the fee increases as the number of months increase.
Over a 5 month period, he has paid $350 to his neighborhood homeowners association in monthly fees, hence the constant is found as follows:
k = 350/5 = 70.
Hence the proportional relationship between the fees paid and the number of months is given by:
y = 70x.
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Answer:
Step-by-step explanation:
y]yyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Translate the sentence into an inequality.
The difference of twice a number and 5 is less than 30.
Use the variable y for the unknown number.
the inequality is
2y-5<30
Answer:
I think it's 2y - 5 < 30
Step-by-step explanation:
