Answers
Answer:
[tex] \frac{pr}{ \sin(q) } = \frac{rq}{ \sin(p) } = \frac{pq}{ \sin(r) } [/tex]
Answer:
a) R = 47.28 R = 312.73 b) 6.67
Step-by-step explanation:
a)
Use the sine rule to calculate angle PRQ
[tex]\frac{sinQ}{q} = \frac{sinR}{r}[/tex]
[tex]\frac{sin40}{7} = \frac{sinR}{8}[/tex]
[tex]0.091827 = \frac{sinR}{8}[/tex]
[tex]sinR = 0.73461[/tex]
[tex]sininverse(0.73461) = R[/tex]
[tex]R = 47.28[/tex]
2nd angle for PRQ is 360 - 47.28 = 312.73
b) Use the cosine rule to find side p
p² = r² + q² - 2rqcosP
To find the angle of p we will simply subtract angle R and angle Q from 180.
180 - 47.28 - 40 = 92.72
p² = 8² + 7² + 2(8)(7)cos(92.72)
p² = 107.685
p = √107.685
p = 10.38
Let's suppose that the shortest distance of R from PQ is [tex]x[/tex].
look at the diagram I gave
since the line I made makes a right angled triangle, we can use SOH CAH TOA
for the angle 40, [tex]x[/tex] is opposite and 10.38 is hypotenuse
which means we will have to use SOH
sin40 = O/H
sin40 = [tex]x\\[/tex]/10.38
0.6428 = [tex]x[/tex]/10.38
0.6428 × 10.38 = [tex]x[/tex]
[tex]x[/tex] = 6.67
Related Questions
In a game, players roll a number cube. the faces of the cube are numbered from 1 to 6. for the player to win a prize, the number cube must land with the top face showing the number 3. what is the probability of the complement of this event occurring?
Answers
The probability of the complement of this event occurring is 5/6.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
Sample space: {1,2,3,4,5,6}
Total number of outcomes=6
Complement of an Event: All outcomes that are NOT the event
In this case:
So, possible outcomes in the complement event:{1,2,4,5,6}
Number of possible outcomes=5
Formula:
Probability = (Number of possible outcomes)/(Total number of outcomes)
= 5/6
So, the probability of the complement of this event occurring is 5/6.
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An iPhone marked for $268 wa old for $334 due to it great
popularity to cutomer. By what percent did the price go up?
(Round to the nearet tenth)
Answers
In linear equation, 24.6 percent did the price go up .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Increased price= Selling Price - Original Price
Percent Increased = Increased price / Original Price × 100%
The increase of price: 334 – 268 = $66
The original price: $268
Thus, the Percent Increase: 66 ÷ 268 = 0.246 = 24.6
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The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the
number of minutes. What does the slope mean for this situation?
Answers
Answer:
A
Step-by-step explanation:
So x is the number of minutes, this means that for each minute, 3.00$ is spent at the taxi therefore, the rate of change of the cost of the taxi ride is $3.00 per minute.
the expression quantity three fourths times t minus 5 plus two fifths times t end quantity minus quantity five eighths times t plus 17 end quantity
Answers
The expression is 11(t/40-2)
From the question, we have
3/4t-5+2/5t-(5/8t+17)
=2t/5+3t/4-5t/8-22
=2t/5+t/8-22
=11t/40-22
=11(t/40-2)
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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select all the expressions that are enwall to 89.75 */* 10
A.897.5 */* 100
B.8.975 */* 10^2
C.8.975 */* 10^0
D.8,975 */* 1,000
E.89,750 */* 10^3
help pls!
Answers
Answer: A.897.5 */* 100
Step-by-step explanation:
Write an equation in slope-intercept form of the line that passes through (6, 11). and
(2, 25/3).
Answers
y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (6, 11) and (2, 25/3).
m=25/3-11/2-6
=-8/3/-4
=8/12=2/3
Now we have to find y intercept by considering (6,11)
y=2/3x+c
11=2/3(6)+c
11=4+c
11-4=c
7=c
The slope intercept form of line is y=2/3x+7
Hence y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3).
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On a certain hot summer's day, 586 people used the public swimming pool. The daily prices are for children$1.75 and $2.00 for adults. The receipts for admission totaled $1,078.75 How many children and how many adults swam at the public pool that day?
Answers
Answer: 373 children and 213 adults
Step-by-step explanation:
Children can be represented by x and adults can be represented by y.
x+y=586
1.75x+2y= $1078.75
x=586-y <-- substitute into 1.75x+2y=1078.75.
1.75(586-y) +2y=1078.75
1025.5 - 1.75y+2y =1078.75
0.25y = 53.25
y=213 adults
x + 213 = 586
x= 373 children
Check:
1.75(373) +2(213)=1078.75
1078.75=1078.75
todd prefers to drink mug root beer which contains 160 calories per 12 ounces. if he drinks a 44 ounce mug root beer, how many calories will he consume? round to the nearest whole number
Answers
Answer:
Step-by-step explanation:
62 60 ÷ 4 = x 4 = x 4 So 60 ÷ 4 =
Answers
The answer is 15.
From the question, we have
60 ÷ 4 = 15
The answer is 15.
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
Complete question:
Solve: 60 ÷ 4
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How do i find range?________________________________________________________________.How do i find median?______________________________________________________________________________________.How do i find Mean?____________________________________________________________________________________________________________________. Measures of center
Answers
The range of a list or set is the difference between the smallest and largest numbers. To find the range, arrange all of the numbers in ascending order. Subtract (deduct) the lowest number from the highest. The answer provides the list's range.
What is the median?The median is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers)
In two simple steps, you can calculate the mean or average of a data set: Add up all of the values to find the sum. Subtract the sum from the total number of values in the data set.
The mode, median, and mean are the three main measures of central tendency. Each of these measures describes a different indication of the distribution's typical or central value.
The mean (average) and the median are the two most commonly used measures of the data's "center."
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Complete the equation of this circle:
A
(x - [?])²+(y -[_])²=[ ]
Enter
Answers
[tex]{ \sf{the \: equation \: of \: circle}}[/tex]
[tex]{ \red{ \sf{ {(x - h)}^{2} + {(y - k)}^{2} = {a}^{2}}}} [/tex]
Is the area of a triangle always 1 2BH?.
Answers
By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).
Some properties of rectangle are ?The opposite sides are parallel and equally spaced apart, and each internal angle is 90 degrees.360 degrees are equal to the total of all internal angles.Both of the diagonals are identical in length and parallel to one another.A rectangle's perimeter is equal to 2a+2b units if its sides are of lengths a and b.A rectangle with sides that are a and b long has an area that is equal to ab sin 90 square units.Diagonally is the diameter of the circumference of a rectangle.To Prove:- Area of a triangle= 1/2 (base×height)
Diagonals of a rectangle divide it into two parts of equal areas.
Let ABCD be a rectangle.
In ΔABC and ΔADC,
AC=AC
By Alternate Interior Angles:
∠BAC=∠CAD
∠BCA=∠CDA
Hence, ΔABC≅ΔACD
∴ar(ΔABC) =ar(ΔACD)
Let ΔABC,
We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.
In rectangle ADBE,
we get,
ar(ΔABE)=ar(ΔADB)
Similarly, in rectangle ADCF,
ar(ΔADC)=ar(ΔACF)
Now, area of rectangle BCFE, from axiom,
=(length)⋅(breadth)
=AB⋅BC
=AD⋅BC
Also,
ar(BCFE)
=ar(ADBE)+ar(ADCF)
=2⋅ar(ΔADC)+2⋅ar(ΔADB)
=2(ar(ΔADC)+ar(ΔADC)
=2(ar(ΔABC))
From (1) and (2),
2(ar(ΔABC))=AD⋅BC
ar(ΔABC)=1/2AD⋅BC
ar(ΔABC)=1/2(base)⋅(height)
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What's the answer to question 1
Answers
Answer:
x ≥ - 2
Step-by-step explanation:
4x ≥ - 8 ( divide both sides by 4 )
x ≥ - 2
Answer
x ≥ 2
----------------------------------------------------------------
4x ≥ 8
[tex]x \geq \frac{8}{4}[/tex]
x ≥ 2
Ethan buys a video game on sale. If the video game usually costs $39. 99, and it was on sale for 20% off, how much did ethan pay? round to the nearest cent.
Answers
Answer:
$31.99
Step-by-step explanation:
20 : 100 = x : 39.99
x = 39.99 * 20 / 100
x = 39.99 * 0.2 = 7.998
final price
39.99 - 7.998 = $31.992
Find the take-home percent of gross pay: Gross pay: $627 Total Deductions: $185
Answers
Gross pay = $627 (I’m assuming this is the payment that is meant to be received if payed in full without counting any deductions.)
Total Deductions = $185 (The money that will not be received.)
$627 - $185 = $442 (This is the money that will be received.)
The person only receives **$422** Of **$627**.
Translate that into maths:
$422 / $627 (Of means a division line if you make it into a fraction)
If you enter that into a calculator you get: 0.7049…
Now this isn’t a percentage, to get a percentage you must times by 100.
—> (So the full equation would have been $422/$627 **multiplied by** 100.)
If you enter this on your calculator you get: 70.49…
—> This is your percentage.
**Unless** it specifies to leave the percentage as an amount of “significant figures/ decimal places” then you can leave it like this (70.49%).
omg this is the right one this is hard or i am dum
Answers
Answer: This is the numerator!
Step-by-step explanation:
The fraction line is well, the line.
The denominator is the number on the bottom.
And the numerator is the number on top!
This means that 3 is the numerator!
Answer: its the numerator because its on top
what is the number that goes in the blank
30/36 = ?/12
I NEED HELP ASAP WITH THESE
Answers
Answer:
10/12
Step-by-step explanation:
36 divided by 3 is 12 so you would have to divide 30 by 3 to make it equivalent and you would get 10/12.
Hope this helped!
HELP ASAP Question 2: Luna is riding her skateboard. She went a distance of 10 miles at a rate of 5 miles per hour. Using the distance formula, d = rt, solve for Luna's time in minutes. (1 hour = 60 minutes)
120 minutes
30 minutes
2 minutes
5 minutes
Answers
By using the distance formula, we can see that Luna's time in minutes is 120 minutes.
How to find the time in minutes?We know that she went a distance of 10 miles at a rate of 5 miles per hour.
Remember the linear relation:
distance = rate*time
Then if we define t as the time:
10 mi = (5mi/h)*t
(10 mi)/(5mi/h) = t
2 h = t
And we want the time in minutes, remember that:
1 hour = 60 min
Then:
2 hours = 2*(60 min) = 120 min
The correct option is the first one.
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A recipe uses 2 cups of sugar to make 32 brownies. how many X cups of sugar are needed for 72 brownies?
Answers
Answer:
4.5
Step-by-step explanation:
Find the value of x, please show your work
Answers
Answer:
x = 80
Step-by-step explanation:
This shape is a pentagon, and all of the angles in a pentagon always add up to 540. So, using this, we can create an equation, 3x + 300 = 540. we can then use the reverse order of operations to solve this, first subtracting 300 from both sides. this gets us the equation 3x = 240. We then divide 3 from both sides to get x alone and get x = 80.
Answer:
x = 80°
Step-by-step explanation:
You want the value of x given a pentagon with two angles marked with expressions in x.
Sum of anglesThe sum of interior angles in an n-gon is 180° × (n -2). For the 5-sided figure shown, the sum of angles is 180° × 3 = 540°.
Using this value, we have ...
(x +40°) +125° +(x +5°) +(x +50°) +80° = 540°
3x +300° = 540° . . . . . . simplify
x +100° = 180° . . . . . . . divide by 3
x = 80° . . . . . . . . . . . . subtract 100°
The value of x is 80°.
Can anyone teach me how to do this? Kinda stuck
Answers
Answer:
to me it look like a reflection
Step-by-step explanation:
note in photo
Graph each inequality.
27. y ≥x+7
28. y> 2|x+3| - 3
29. 4x-3y < 2
30. y≤ - 1/2|x+2|-3
Answers
The graph for each inequality is attached below.
We are given four inequalities. The first inequality is y ≥ x + 7. The second inequality is y > 2|x+3| - 3. The third inequality is 4x - 3y < 2. The fourth inequality is y ≤ (-1/2)|x + 2| - 3. In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. An inequality compares two values to determine if one is less than, larger than, or simply not equal to the other. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. A graph of every inequality is attached below.
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.
let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 16 tons of sugar.
Answers
The equation is C = 6500 + 175S
The total cost to transport 16 tons of sugar is $9300
From the question, we have
C = total cost
S represent the amount of sugar (in tons) transported.
C = 6500 + 175S
total cost to transport 16 tons of sugar = 6500 + 175(16)
= 6500 + 2800
= $9300
The total cost to transport 16 tons of sugar is $9300.
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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You took out a loan for $5000, with a 7.5% interest rate, over a period of 2 years. What is the accumulated interest?
Answers should be in $1,000.00 form (include $, comma, and period when necessary)
Answers
The accumulated interest on the loan given, equals to $778.125.
What is an accumulated interest?Also known as compound interest, means the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
Amount payable equals to:
= P(1+i/100)*n
= $5,000*(1 + 7.5%)^2
= $5,000 * 1.155625
= $5,778.125
The computation of the accumulated Interest goes as:
= Amount payable on loan - Loan Amount
= $5,778.125 - $5,000
= $778.125
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Find measure angle ACB
i need it step by step
please help :/
Answers
A regular polygon has an interior angle of 157.5°. Calculate the number of sides of the polygon.
Answers
Answer:
16
Step-by-step explanation:
(n-2)*180=total of the interior angles
(n-2)*180=157.5n
180n-360=157.5n
22.5n-360=0
22.5n=360
n=16
The table shows the amount of money in your bank account over a period of 5 weeks. You plan to keep saving at the same rate until you have $800 in the account. Which equation could you use to find the number of weeks, n, it would take to reach your goal?.
Answers
The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given table,
Amount of money in 0 weeks = $100
Amount of money in 1st week = $135
In 2nd week = $170, in 3rd week = $205
So there is a $35 increment each week.
Let's say it takes "n" number of weeks to reach the goal.
So, 35n + 100 = 800
Hence the answer is The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800".
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Greatest Common Factor (96,144)
Answers
The greatest common factor of 96 and 144 is 48
How to determine the greatest common factor of 96 and 144Information given in the question
144
96
Greatest common factor can be found by listing the factors of the numbers required and choosing the common factors, the biggest number among them is the greatest common factor
listing the factors
144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
the common factors = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48,
the greatest among the factors is 48
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Batteries are sold in packets and boxes.
There are 4 batteries in a packet.
There are 10 batteries in a box.
Sarah buys P packets of batteries and B boxes
of batteries.
She buys a total of 7 batteries.
Write down a formula for T in terms of P and B.
Answers
The formula for P and B is 4P + 10B = 7
Given,
The number of batteries in a packet = 4 batteries
The number of batteries in a box = 10 batteries
Sarah bought P packets and B boxes of batteries
The total number of batteries Sarah bought = 7 batteries
We have to write an expression;
Here,
4 batteries in a packet.
Sarah bought P packets of battery.
So, she bought 4P batteries
Then,
10 batteries in a box
Sarah bought B boxes of battery
So, she bought 10B batteries
That is,
Sarah bought a total of 4P + 10B batteries which is 7 batteries
Therefore,
The formula for P and B is 4P + 10B = 7
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Find the 70 term of the arithmetic sequence 18, 34, 50
Answers
The 70th term of the arithmetic sequence is 1,122
Given,
In the question:
The Arithmetic Sequence is given as:
18, 34, 50 ,...
To find the 70th term of the sequence.
Now, According to the question:
First term is = 18
Second term is = 34
Common difference(d) = second term - first term
d = 34 - 18
d = 16
Write the general term through the pattern ;
[tex]a_n[/tex] = 16n + 2
We have to find the 70th term
Put the value of n = 70 in above general term:
[tex]a_7_0[/tex] = 16 x 70 + 2
[tex]a_7_0[/tex] = 1,122
Hence, The 70th term of the arithmetic sequence is 1,122.
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