At what points will the line y = x intersect the unit circle x2 y2 = 1? smaller value and larger value
[tex]The two equations given arey = x …. (1)x2 + y2 = 1 …. (2)Substitute equation (1) in (2)x2 + x2 = 12x2 = 1x2 = ½x = √1/2x = ±0.707As the square can be positive or negative we get x1 = 0.707 and x2 = -0.707From equation (1) we know that y = xy1= x1= 0.707y2= x2 = -0.707Therefore, the line y = x intersects the unit circle x2 + y2 = 1 at (0.707, 0.707) and (-0.707, -0.707).[/tex]
What is intersect?A junction is a place where two lines come together or cross. In the illustration above, "point K is the intersection of line segments PQ and AB" is what we would state. The phrase "the line segment PQ crosses AB at position K" is another option.
Keep in mind that two line segments do not always need to intersect. In the illustration above, move point B higher until the intersection of the two line segments disappears. However, keep in mind that lines (as opposed to line segments) continue indefinitely in both directions, thus unless they are absolutely parallel, they will always cross someplace.
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the sum of two angles of a triangle is 6/5 of a right angle, and one of these two angles is 30 larger than the ohter
The measure of two angles are 39 degree and 69 degree. By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree, so the final angle is 72 degree. Therefore, the largest angle in the triangle is 72 degree.
Describe the Triangle Angle Sum property?According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
Given:
[tex]The\;sum\;of\;two\;angles\;in\;a\;triangle\;is\;\frac{6}{5}\;of\;a\;right\;angle\;is,\;\frac{6}{5} \times 90^{\circ} = 108^{\circ}[/tex]
[tex]let\;x\;is\;the\;measure\;of\;the\;first\;angle[/tex]
[tex]one\;of\;these\;two\;angles\;is\;30\;larger\;than\;the\;other,\;is\;x+30=108[/tex]
We know that sum of two angles is 108
[tex]x+x+30=108^{\circ}[/tex]
[tex]2x+30=108[/tex]
[tex]2x=108-30[/tex]
[tex]2x=78[/tex]
[tex]x=39^{\circ}[/tex]
Second angle y is,
[tex]y=x+30[/tex]
[tex]y=39+30[/tex]
[tex]y=69^{\circ}[/tex]
By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree,
Third angle z is,
[tex]x+y+z=180[/tex]
[tex]39+69+z=180[/tex]
[tex]108+z=180[/tex]
[tex]z=180-108[/tex]
[tex]z=72^{\circ}[/tex]
[tex]By\;comparing\;the\;angles\;39^{\circ},\;69^{\circ}\;and\;72^{\circ}, 72^{\circ}\; is\;greater[/tex]
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According to this graph, what can be said about the global surface temperature trend from 1910 to 1950?
On average, it fell about 0.2 degrees between 1910 and 1950
On average, it rose about 0.3 degrees between 1910 and 1950
On average, it rose about 0.5 degrees between 1910 and 1950
On average, it rose about 0.8 degrees between 1910 and 1950
According to this graph, the global surface temperature trend from 1910 to 1950: C. on average, it rose about 0.5 degrees between 1910 and 1950.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
By critically observing the graph of the average global surface temperature during the 20th century, we can logically deduce the following data points and statements:
The average global surface temperature appears to have increased by 1.4 degrees (1.4°).During the period from 1850 to 1910, the average global surface temperature was significantly lower.On average, the global surface temperature rose about 0.5 degrees (0.5°) between 1910 and 1950.Read more on temperature graph here: https://brainly.com/question/3856090
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Answer:
Step-by-step explanation:
I took the quiz! :)
Given g(x)=-5x-4, solve for x when g(x)=1.
Answer:
Your answer is 2
Step-by-step explanation:
If g(x) = -5x - 4 and g(x) = 1 then -5x - 4 = 1.
Given this, we can now solve for x by adding 4 to both sides and then dividing both sides by -5 to isolate the value of x.
-5x-4=1
-5x-4+4=1+4
-5x=5
5 5
5 5
x=-1
A machine that originally cost $15,600 has a value of $7500 at the end of 3 years. the same machine has a value of $2800 at the end of 8 years. find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years. a. -$3200 per year c. $-5400 per year b. -$2700 per year d. $2700 per year
A) The rate for the first 3 years :
15,600 - 7500 = 8100
8100/3 years = 2,700 per year depreciation.
B) The rate between 3 and 8 years:
7500 - 2800 = 4700
4700 / 5 year = 940 per year depreciation.
C) the value of the machine depreciated at a higher rate in the first 3 years. After the first 3 years, the depreciation rate decreased.
Pretty please help me
Answer:
see explanation
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2y + 50 + y + 10 = 180
3y + 60 = 180 ( subtract 60 from both sides )
3y = 120 ( divide both sides by 3 )
y = 40
2y = 2 × 40 = 80
y + 10 = 40 + 10 = 50
Answer:
y = 40
2y = 80
y + 10 = 50
Step-by-step explanation:
The sum of the angles of a triangle is 180°
Using values given,
2y + (y + 10) + 50 = 180
2y + y + 10 + 50 = 180
3y + 60 = 180
3y = 180-60 = 120
y = 120/3 = 40
2y = 80
y + 10 = 40 + 10 = 50
evaluate write your answer as a whole number or as a simplified fraction
Answer: The answer is 27
Step-by-step explanation: 6 x 6 x 6 = 216. 216 is the numerator. 2 x 2 x 2 = 8. 8 is the denominator.
216 / 8 = 216 '/. 8 = 27
A small model car is 12 inches long and the actual car is 132 inches long. what is the scale factor of the model to the actual car?
Help please
Answer: 11
Step-by-step explanation: 132/12 = 11
You divide the actual car length by the model and you get the scale factor.
The scale factor of the model to the actual car is 1/11 inches.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
A small model car is 12 inches long and the actual car is 132 inches long.
To find the scale factor:
When both the original dimensions and the new dimensions are known, the scale factor may be determined.
The following is a basic formula to determine a figure's scale factor:
Scale factor = Dimension of the new model ÷ Dimension of the actual car
Scale factor = 12 / 132
Scale factor = 1/11
Therefore, the scale factor is 1/11 inches.
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What is a polynomial function in standard form with zeros 1,-1, 2, and 4?
○_A. y = x¹ − 6x³ + 7x² + 6x − 8
O B. y = x² - 6x³ + 9x² + 6x-8
OC. y = x³ + 7x² + 6x - 8
OD. y = x - x³ + x²+x-8
The equation using the polynomial function is a x⁴ - 6x³ + 7x² + 6x - 8.
According to the statement
We have to find that the equation using the polynomial function.
So, For this purpose, we know that the
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation
From the given information:
The standard form with zeros 1,-1, 2, and 4:
Polynomial with Zeros 1, - 1, 2 and 4 can be expressed thus :
x = 1 : x - 1
x = - 1 :x + 1
x = 2 :x - 2
x = 4 :x - 4
Hence, we have :
(x - 1)(x + 1)(x - 2)(x - 4) = 0
We can then expand ;
(x - 1)(x + 1) = x² + x - x - 1 = x² - 1
(x² - 1)(x - 2) = x³ - 2x²-x + 2
(x³ - 2x² - x + 2)(x - 4)
x⁴ - 4x³ - 2x³ + 8x² - x² + 4x + 2x - 8
x⁴ - 6x³ + 7x² + 6x - 8.
So, The equation using the polynomial function is a x⁴ - 6x³ + 7x² + 6x - 8.
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he larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, find the numbers.
Answer:
51 and 12
Step-by-step explanation:
Solve➲ Let a be the bigger number
➲ Let b be the smaller number
[tex]a = 3b + 15\\a = 3 \cdot b + 15\\a + b = 63\\\bold{Solve:b}\\3b + 15 + b = 63\\3b + b = 4b\\4b + 15 = 63\\4b = 63 - 15\\4b = 48\\b = 12\\\\\bold{Solve:a}\\a = 3b + 15 \rightarrow a = 3 \cdot 12 + 15 = 51[/tex]
Thus,
b = 12, a = 51
_______________________________
Wrapping up:
➲ Hope this helps.
➲ Address concerns if needed.
➲ Have a great day!
Question 1 (Multiple Choice Worth 5 points)
(01.06 LC)
Which statement shows that money is a "measure of value?"
This bill is worth twenty dollars.
My phone is worth eight hundred dollars.
The dollar I just found in my drawer is still worth a dollar.
The more features it has, the more it is worth.
Answer: My phone is worth eight hundred dollars.
Step-by-step explanation:
The correct statements are:
This bill is worth twenty dollars.
My phone is worth eight hundred dollars.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given statements:
This bill is worth twenty dollars.
My phone is worth eight hundred dollars.
The dollar I just found in my drawer is still worth a dollar.
The more features it has, the more it is worth.
From the given statements:
This bill is worth twenty dollars.
Here, the measure of the value is n = $20.
My phone is worth eight hundred dollars.
Here, the measure of the value is m = $800.
Therefore, the correct explanation is given above.
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0.1x+ 3x/5+ 20/ 5 =0.5
Answer:
x = -5
Step-by-step explanation:
Im not very sure but here it is. =D
Tell me if it helps you.
The word geometry comes from the Greek words geo, which means "earth," and metron, which means "a measuring
of." Given this information, how do you think the study of geometry developed?
The study of geometry developed from. measuring the Earth.
What is geometry about?Geometry has its roots in issues that people face on a daily basis. According to the conventional myth, which was preserved in Herodotus' History (5th century bce), the Egyptians invented surveying to restore property values following the yearly Nile flood.
One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.
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evaluate the expression if a=3/4, b=-8, c=-2, and d=3
Answer: 206
Step-by-step explanation:
a=3/4, b=-8, c=-2, d=3
-b[a+(c-d)^2]=
-(-8)[3/4+(-2-3)^2]=
8[3/4+(-5)^2]=
8[3/4+25]=
8*3/4 + 200=
24/4 + 200=
6+200=206
is y=-3/2x+10/3 parallel to y=-2/3x+11/3?
Answer:
nope
Step-by-step explanation:
parallel or not just depend on the coefficient of the first degree
3/2 ≠ 2/3 so not
The depth of a local lake averages 38 ft, which is represented as |−38|. In February, it measured 6 ft deep, or |−6|, and in July, it was 25 ft deep, or |−25|. What is the difference between the depths in February and July?
32 feet
31 feet
19 feet
13 feet
The difference between the depths in February and July is 19 feet.
To find the difference between the depths in February and July, we need to subtract the depth in February from the depth in July.
The depth in February is given as |−6|, which is 6 feet, and the depth in July is given as |−25|, which is 25 feet.
Difference = Depth in July - Depth in February
Difference = 25 feet - 6 feet
Difference = 19 feet
Therefore, the difference between the depths in February and July is 19 feet.In February, the depth of the lake is given as |−6|, which represents the absolute value of -6. The absolute value of a number disregards its sign, so |−6| is equal to 6 feet.
In July, the depth of the lake is given as |−25|, which represents the absolute value of -25. Again, disregarding the sign, |−25| is equal to 25 feet.
To find the difference between the depths in February and July, we subtract the depth in February from the depth in July:
Difference = Depth in July - Depth in February
Difference = 25 feet - 6 feet
Difference = 19 feet
Therefore, the difference between the depths in February and July is 19 feet. This means that the lake experienced a change of 19 feet in depth between those two time points.
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6.25% of what number is 7?
Answer:
Step-by-step explanation:
0.4375
Answer:
6.25%of 112 is 7
Step-by-step explanation:
hope it helps you
if right mark me the brainliestA cat runs 3/5 of a mile in 2/10 of an hour. How many miles did the cat run in 1 hour?
The cat ran 3 miles in one hour
How to calculate the number of miles ?
A car runs 3/5 of a mile in 2/10
The number of miles ran in one hour can be calculated as follows
3/5= 2/10
x= 1
Cross multiply
2/10x= 3/5
x= 3/5 ÷ 2/10
= 3/5 × 10/2
= 3
Hence the car ran 3 miles in 1 hour
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Some friends are playing a music trivia game that has 4 topics: rock, rap, country, and pop. Each player spins a spinner with 9 equal sections to get
the topic of their question. The friends answer a total of 54 questions, of which 20 are rock questions. 16 are rap questions, and 7 are country
questions.
How many sections of the spinner are most likely labeled pop? Enter the answer in the box.
Answer:
3
Step-by-step explanation:
I need help please !!
Step-by-step explanation:
A has no solution.
15x - 45 = 15x + 75
-45 = 75
is false for every value of x.
in other words, when you add to the same thing different amounts, the result cannot be identical ever.
B has a solution
-45x - 45 = -75x + 75
-120x = 120
-x = 1
x = -1
C has a solution
45x - 45 = -15x + 75
60x = 120
x = 2
D has a solution
15x - 45 = 75x + 75
-120 = 60x
-2 = x
Please help me find the type of angles !!!!!!
You are running a left-tailed 2-sample z-test at the 0.05 level of significance and you find a test statistic of z=-1.87. shoudl you reject or not reject the null?
Using the critical value, we should reject the null.
What is a test statistic?A test statistic is a quantity derived from a sample that is used in statistical hypothesis testing. A hypothesis test is usually specified in terms of a test statistic, which is a numerical summary of a data set that reduces the data to a single value that can be used to perform the hypothesis test. In general, a test statistic is chosen or defined in such a way that it quantifies, within observed data, behaviors that distinguish the null hypothesis from the alternative hypothesis, where such an alternative is prescribed, or that characterize the null hypothesis if no alternative hypothesis is explicitly stated.So,
Test = 2.85Critical value = Z(0.05) = 1.645RR: Reject if the Z test > 1.645Z test = 2.85 > 1.645 ⇒ RejectTherefore, using the critical value, we should reject the null.
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Which answer graphs the parent function f(x) = |x|, and the translated function g(x) = |x − 2| + 1 on the same grid?
Using translation concepts, the graphs of f(x) = |x| and g(x) = |x - 2| + 1 are given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
For this problem, the parent and translated functions are given, respectively, by:
f(x) = |x|.g(x) = |x - 2| + 1.The translations are given as follows:
x -> x - 2, meaning that the function was shifted 2 units right.g(x) = f(x) + 1, meaning that the function was shifted 1 unit up.Considering these two translations, the functions are plotted in the graph given at the end of the answer, with:
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a company's charge for electricity is ¢6.434 per kilowatt-hour. in addition, each monthly bill contains a customer charge of $7.81. if last year's bills ranged from a low of $51.74 to a high of $192.28, over what range did usage vary (in kilowatt-hours)?
The range did usage vary over from 823.81 to 2461.97 kilowatt-hours.
What is kilowatt-hour?Kilowatt-hours are units of energy that represent one kilowatt of electricity for one hour (SI symbol: kWh or kWh; typically abbreviated as kWh). It is 3.6 megajoules in terms of standard units (MJ). For electrical energy supplied to customers by electric utilities, kilowatt-hours are a typical billing unit. The abbreviation "kWh," which is derived from the letters kilowatt and hour, stands in for the kilowatt-hour and is a commonly used abbreviation. In addition to being often used in commercial, academic, and scientific publications as well as in the media, it is also frequently employed by electric utility companies to bill consumers for energy delivered to them. One kilowatt (kW) sustained for one hour (multiplied by one) is equivalent to one kilowatt-hour, a composite unit of energy.
$64.34=6434 cents
$192.28=19228 cents
So 6434 cents correspond to 6434/7.81
=823.81 kilo watt hours
19228 cents=19228/7.81
=2461.97 kilowatt-hours
So Range is 823.81 to 2461.97 kilowatt-hours.
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3)927
Show your work
Answer:
What is the question?
Step-by-step explanation:
Decide weather T he statement is true or false
Answer:
True, True, False, False, True
Step-by-step explanation:
X, Y, and Z are on the same line.
Point W is on line I, not line M.
YW and YD aren't on the same line.
YX and YZ are on the same line.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Is the number 6.2 x 10^(-3) greater than 1 or smaller than 1?
Tom keeps all of his marbles in a bag. 5 red marbles. 4 blue marbles. and three yellow are in the bag. if he randomly chooses one marble what is the probability it is blue?
If Tom choose one marble then the probability that it will blue is 1/3.
According to the given question.
Total number of red marbles in a bag = 5
Total number of blue marbles in a bag = 4
Total number of yellow marbles in a bag = 3
So, the total number of marbles in a bag = 5 + 4 + 3 = 12
As we know that, the probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.
Therefore, if Tom choose one marble then the probability that it will blue
= 4/12
= 1/3
Hence, if Tom choose one marble then the probability that it will blue is 1/3.
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Knowledge Check
Question 10
Keith purchased a prepaid phone card for $50.75. Calls cost 8 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x
minutes of calls is given by the following
C=50.75-0.08x
How much credit is left on the card after Keith uses it for 30 minutes of calls
The credit that is left on the card after Keith uses it for 30 minutes of calls is $48.35.
How to calculate the cost?From the information given, Keith purchased a prepaid phone card for $50.75. Calls cost 8 cents a minute using this card
The equation was given as C=50.75-0.08x
Therefore, the credit that is left on the card after Keith uses it for 30 minutes of calls will be:
C=50.75-0.08x
C = 50.75 - 0.08(30)
C = 50.75 - 2.40
C = $48.35
The credit is $48.35.
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Explain the difference between partitioning a directed line segment MN in a 2:7 ratio
versus a 7:2 ratio. Include a specific example as part of your explanation.
The difference between partitioning a directed line segment MN in a 2:7 ratio versus a 7:2ratio because of following
To understand this let us take the line segment MN which is of a length is divided into 9 equal parts. Here, we are dividing it into nine parts because the proportions 2 and 7 make a sum of 9.
When we divide the line segment MN in the ratio 2:7, the first two parts out of the nine from the left side are separated from the rest 7. This means that the first proportion from the left hand side of the line is smaller than the other.
Now, when we divide the line segment MN in the ratio7:2, the first seven parts out of the nine from the left side are separated from the rest two. This means that the first proportion from the left hand side of the line is larger than the other.
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