The circle below has center P.The point (x, y) is on the circle as shown.12-(a) Find the following.1110-unitsRadius: 0Center: 0987Value of a:(Choose one)(x,y)351Value of b:(Choose one)4a32(b) Use the Pythagorean Theorem to write an equationrelating the side lengths of the right triangle. Writeyour answer in terms of x and y (with no otherletters)+
Answers
Given:
Center of the circle = P
Let's determine the following:
a) Radius.
Here, the radius of the circle is the hypotenuse of the triangle.
Therefore, the radius of the circle is 3 units
b) Center:
To find the point at the center of the circle, let's locate the point P on the graph.
On the graph, the point P is at (x, y) ==> (9, 4)
Therefore, the center (h, k) is (9, 4)
c) Value of a:
To find the value of a, let's first find the value of b.
Value of b = 6 - 4 = 2
Apply Pythagorean Theorem to find the value of a:
[tex]c^2=a^2+b^2[/tex]Where:
c is the hypotenuse = 3
b = 2
Thus, we have:
[tex]\begin{gathered} 3^2=a^2+2^2 \\ \\ 9=a^2+4 \\ \\ \text{Subtract 4 from both sides:} \\ 9-4=a^2+4-4 \\ \\ 5=a^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{5}=\sqrt[]{a^2} \\ \\ 2.2=a \\ \\ a=2.2 \end{gathered}[/tex]Therefore, the value of a is 2.2 units
d) Value of b.
The value of b is 2 units
ANSWERS:
• Radius: , 3 units
,• Center: , (9, 4)
,• Value of a = , 2.2 units
,• Value of b = , 2 units
Related Questions
Which of the following is correct based on this picture? A. sinY=38/63B. none of these are correctC. tanY=38/63D. cosY=38/63
Answers
Answer
A. sin Y = 38/63
Explanation
Given:
What to find:
To find the correct trigonometric function of the given diagram.
Step-by-step solution:
Using the trigonometric function: SOH CAH TOA
[tex]\begin{gathered} SOH\text{ }is\text{ }sin\text{ }\theta=\frac{Opposite}{Hypotenuse} \\ \\ CAH\text{ }is\text{ }cos\text{ }\theta=\frac{Adjacent}{Hypotenuse} \\ \\ TOA\text{ }is\text{ }tan\text{ }\theta=\frac{Oppos\imaginaryI te}{Adjacent} \end{gathered}[/tex]From the diagram, θ = Y, Opposite = 38, Hypotenuse = 63
So the correct trigonometric function based on the given picture will be:
[tex]sin\text{ }Y=\frac{38}{63}[/tex]Thus, the correct answer is option A. sin Y = 38/63
To find the missing length below, would you use Law of Sines or Law of Cosines?Find the missing length. There are 2 answers, Law of _____ and missing side length.
Answers
Solve for a.69a = = √ [?]Pythagorean Theorem: a2 + b² = c²a
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1) In this problem, we need to find the leg "a". Note that in the Pythagorean Theorem the hypotenuse, the largest leg is opposed to the right angle.
2) So, we can write out the following:
[tex]\begin{gathered} 9^2=6^2+a^2 \\ 81=36+a^2 \\ 81-36=a^2 \\ a^2=45 \\ a=\sqrt{45} \end{gathered}[/tex]Note that we could simplify that, but since the question wants it all under the radical.
Where are you most likely to build up enough static charge to receive a shock? O A. In a rain forest B. On a concrete sidewalk on a dry day O c. On a nylon carpet in a dry area O d. On a nylon carpet in a hotel by the beach
Answers
Where are you most likely to build up enough static charge to receive a shock?
The correct answer is option C on a nylon carpet in a dry area
Explanation:
As nylon is a good conductor of electricity, the static electricity accumulatedin the body does ntot flow to the ground. Also, when we touch a metal object directly connected to the ground, a difference in electric charges creates a static electric discharge.iAs a reult ,we receive a shock.
Question number 2.7T: (Please help!)
Answers
The values of function F(5) is 35 and F(-10) is 4.
For F(5), x≥5
So, the appropriate function will be
[tex]F(x)=6x+5\\\\F(5)=6(5)+5\\\\F(5)=30+5\\\\F(5)=35[/tex]
For f(-10), x≤-8
So, the appropriate function will be
[tex]F(x)=4\\\\F(-10)=4[/tex]
Thus, the values of function F(5) is 35 and F(-10) is 4.
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Solve by graphing. If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initally. When will the amount left be 2 grams? Round to the nearest tenth of a day. Be sure to label your answer.
Answers
The exercise describes an exponential decay, you can express this using the general form:
[tex]y=ab^x[/tex]Where
a is the initial amount
b is the decay factor
x is the time intervals
y is the amount after x time intervals
The half-life of a substance indicates the time it takes for the amount to decrease by half.
If the initial amount is a=5 grams, the half-life indicates that after x=20 days, the amount will be
y= 5/2 = 2.5 grams.
You can replace these values on the formula above to obtain an expression where the decay factor will be the only unknown:
[tex]\begin{gathered} y=ab^x \\ 2.5=5b^{20} \end{gathered}[/tex]To solve for b, first, divide both sides of the equation by 5:
[tex]\begin{gathered} \frac{2.5}{5}=\frac{5b^{20}}{5} \\ 0.5=b^{20} \end{gathered}[/tex]Then apply the square root with index 20 to both sides of the equal sign no reach the value of b:
[tex]\begin{gathered} \sqrt[20]{0.5}=\sqrt[20]{b^{20}} \\ b=0.97 \end{gathered}[/tex]Now that you know the value of the decay factor, you can determine how much time it will take for the substance to decrease to 2grams.
The expression for the exponential decay in this case is:
[tex]y=5\cdot0.97^x[/tex]For y=2grams:
[tex]2=5\cdot0.97^x[/tex]Now, you have to solve the expression for x:
-Divide both sides by 5:
[tex]\begin{gathered} \frac{2}{5}=\frac{5\cdot0.97^x}{5} \\ 0.4=0.97^x \end{gathered}[/tex]-Apply the logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (0.4)=\log (0.97^x) \\ \log (0.4)=x\log (0.97) \end{gathered}[/tex]-Divide both sides by the logarithm of 0.97 to determine the value of x:
[tex]\begin{gathered} \frac{\log(0.4)}{\log(0.97)}=\frac{x\log (0.97)}{\log (0.97)} \\ x=30.08\approx30.1 \end{gathered}[/tex]It will take approximately 30.10 days to have 2 grams of substance left.
897 mL to liters ? L
Answers
We have to convert 897 mL to L.
We have to take into account the following equivalency between the two units:
[tex]1L=1000mL[/tex]If we write this as a unit factor, we have:
[tex]\frac{1L}{1000mL}=1[/tex]So we can use this factor to multiply the quantity and change the units without changing the actual measure:
[tex]897mL\cdot(\frac{1L}{1000mL})=\frac{897}{1000}L=0.897L[/tex]NOTE: this unit factors can be used to change multiple units in the same operation.
Answer: 0.897 liters
QUESTIONS 13,14 I NEED HELP dont understand ssorry for the caps didnt mean to
Answers
Answer
• 13. vertical angles.
,• 14. corresponding angles
Explanation
Assuming r and s are parallel lines, and that the line u (marked with stars) is a transversal cutting r and s, then the angles formed (a, b, and c) acquire some special properties.
• 13
Regarding ∠a and ∠b are vertical angles, which means they have the same measure.
• 14
Regarding ∠a and ∠c they are corresponding angles, which means they have the same measure.
A flagpole 3m tall casts a shadow5m long at the same time a nearby hill casts a shadow62m long. How Tall is the hill.
Answers
Explanation:
We are given information about the height of a flagpole and its shadow, and we also have information about the shadow of a hill.
This information is represented in the following diagram:
Where the symbol '?' represents what we are trying to find:
How tall is the hill
We will call this h for reference:
Since these shadows are happening at the same time, the ratio between these values must be the same, this is to say that
3/5 must be equal to h/62:
[tex]\frac{3}{5}=\frac{h}{62}[/tex]From this equation, we solve to find h:
[tex]\begin{gathered} \frac{3}{5}\times62=h \\ \end{gathered}[/tex]Solving the operations the result is:
[tex]\begin{gathered} 0.6\times62=h \\ \downarrow \\ 37.2=h \end{gathered}[/tex]The hill is 37.2 m tall.
Answer:
37.2 m
Astrid works in the oil and gas industry near Fort McMurray, Alberta. She earns $28.30/h and makes double time for hours worked beyond 40 each week. Calculate Astrid’s gross income for 45.25 hours worked last week.
Answers
We have that the first 40h are paid at $28.30 each hour, so this first 40h give $1132
[tex]28.30\cdot40=1132[/tex]Now the other 5.25 hours that are beyond 40h the last week are paid at the double of a normal hour this means are paid at $56.60 ($28.30 x 2). Now the 5.25h give 297.15
[tex]56.60\cdot5.25=297.15[/tex]So the total is $1429,15. The answer is $1429,15
7.If you raised $15 byday 2 and by day 7 youhad $75. What is therate of change?
Answers
We have the following:
the rate of change is equal to a slope, therefore we can calculate it as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{75-15}{7-2}=\frac{60}{5}=12[/tex]The rate of change is $12/day
On your own paper, solve the system of equations using substitution and identify the solution.4=16 +=2
Answers
Answer: (4,-2)
Explanation:
Given:
4x=16
x+y=2
We solve for x in 4x=16.
4x=16
Then, divide both sides by 4.
4x/4=16/4
Calculate
x=4
Substitute x=4 into x+y=2.
x+y=2
4+y=2
Simplify and rearrange
y=2-4
Calculate
y=-2
Therefore, x=4 and y=-2.
What is the distance between points (-8,5) and (7,-3)? (Hint. Use the distance formula)
Answers
SOLUTION:
We are to find the distance between points (-8,5) and (7,-3).
[tex]\begin{gathered} \sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{where x}_1=-8,x_2=7,y_1=5andy_2=-3_{} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{(7-(-8))^2+(-3-5)^2} \\ \\ \sqrt[]{(7+8)^2+(-8)^2} \\ \\ \sqrt[]{15^2_{}+(-8)^2} \\ \\ \sqrt[]{225+64} \\ \\ \sqrt[]{289} \\ 17\text{ units} \end{gathered}[/tex]CONCLUSION:
The distance between points (-8,5) and (7,-3) is 17 units.
x^2+3x-6 Find the Discriminat and state how many solutions and type of zero
Answers
Solution
Discriminant
- The formula for the discriminant of a quadratic equation is:
[tex]\begin{gathered} \text{ Given,} \\ ax^2+bx+c \\ \\ \text{ The Discriminant is:} \\ D=b^2-4ac \end{gathered}[/tex]- Applying the formula, we have:
[tex]\begin{gathered} a=1,b=3,c=-6 \\ \\ \therefore D=3^2-4(1)(-6) \\ D=9+24 \\ D=33 \end{gathered}[/tex]- Discriminant is 33
How many solutions
- If the discriminant is > 0, then, the Quadratic equation has 2 solution.
- If the discriminant is = 0, then, the Quadratic equation has 1 solution
- If the discriminant is < 0, then, the Quadratic equation has no real solutions.
- The discriminant is 33 > 0, thus, the Quadratic equation has 2 solutions
Type of zero
- Since there are 2 solutions, then, it has real solutions
Final Answer
OPTION B
Simplify the expression⅜b - ¾b
Answers
-3b / 8
Explanations:The given expression is:
[tex]\frac{3}{8}b\text{ - }\frac{3}{4}b[/tex]Which can be re-written as:
[tex]\frac{3b}{8}-\frac{3b}{4}[/tex]Note that the LCM of 8 and 4 is 8
Therefore, the expression can be simplified as:
[tex]\begin{gathered} \frac{3b-2(3b)}{8} \\ \frac{3b-6b}{8} \\ \frac{-3b}{8} \end{gathered}[/tex]The simplified expression is -3b/8
Task:Dilate the extra gum package by a scale factor of 8.Will the small pack of gum cover the whole billboard given thedimensions? Explain your answer in complete sentences.
Answers
No, because the length of the billboard is larger than the dilated gum cover length.
If we dilate the gum package by a scale factor of 8:
Original = 3 x 2.5 in
3 x8 = 24 (length)
2.5x8 = 20 (width)
New measures: 24 x 20 ( Lenght by width)
Since the billboard is 48x14, the small pack of gum can't cover the billboard.
24<48
The length of the gum cover can't cover the length of the billboard.
Which function's graph is shown below? ད་ལྟ་བ་དང་ o = A. Y = COS X O B. y = -cos x C. y = sin x OD. y = -sin
Answers
Given:
Consider the given graph in figure.
To find:
Select the correct option that shows the given function's graph.
Explanation:
Here, graph is in the form of,
[tex]y=acos(bx)[/tex]Where, a is amplitude and the period of a cosine function is the length of the shortest interval on the x axis over which the graph repeats.
[tex]\text{ period =}\frac{2\pi}{|b|}[/tex]Here, at x = 0, the y value is 1. so, the graph starts at (0, 1) which indicates the graph of
[tex]y=cosx[/tex]Consider the below graph:
So, the correct option is (A) y = cosx.
Final answer:
Hence, the required correct option is (A) y = cos
how much is 1 + 1 bc i’ve been failing high school
Answers
Explanation
to add two natural numbers, just move n units the initial to the rigth in the numeric line, so
fo
3,400 mL. 34 L I need help which one is bigger
Answers
Answer: 34L is bigger than 3400mL
Given data
3, 400 mL and 34L
Firstly, we need to convert mL to L for unit consistency
1000mL = 1L
3, 400Ml = xL
Cross multiply
1000 * x = 1 x 3400
1000x = 3400
Divide both sides by 1000
1000x / 1000 = 3400/ 1000
x = 3.4 L
Therefore, 3400mL = 3.4L
34L is bigger than 3400mL
At a local bakery, at a local bakery Ariel Bots for oatmeal cookies four $1.20 Mia bought 9 mil cookies for $2.70 Becky bought 12 oatmeal cookies for $3.60 Larry purchased 15 oatmeal cookies $4.5. Graph the data on the graph
Answers
EXPLANATION
Drawing given set data ni a graph, will give us:
As we can see in graph, this is a proportional relationship given by a straight line.
Recall the perimeter of a figure is the distance around figure
Answers
To find the perimeter of the triangle you have to add the length of its sides:
[tex]\begin{gathered} P=a+b+c \\ P=\frac{4}{17}+\frac{5}{17}+\frac{8}{17} \\ P=\frac{4+5+8}{17} \\ P=\frac{17}{17} \\ P=1 \end{gathered}[/tex]The perimeter of the triangle is 1 inch
h(x) = x² – 5 – x; Find h(8)
Answers
hello
to solve this question, we simply need to substitute 8 as the value of x in the expression
[tex]\begin{gathered} h(x)=x^2-5-x \\ h(8)=8^2-5-8 \\ h(8)=64-5-8 \\ h(8)=51 \end{gathered}[/tex]from the calculation above, the value of h(8) is equal to 51
what is the solution to the equation below? (round your answer to two decimal places.) 3•6^x= 15.57
Answers
Simplify the given expression as shown below
[tex]\begin{gathered} 3*6^x=15.57 \\ \Rightarrow6^x=\frac{15.57}{3}=5.19 \\ \Rightarrow xln(6)=ln(5.19) \end{gathered}[/tex][tex]\Rightarrow x=\frac{ln(5.19)}{ln(6)}\approx0.92[/tex]Thus, the answer is x=0.92, option D.The graph of F(x), shown below, has the same shape as the graph of G(x) = x4, but it is shifted to the right 1 unit. What is its equation?
Answers
Given:-
The graph of x power 4.
To find the equation when the graph is shifted right 1 unit.
So the equation in vertex form is,
[tex]y=a(x-h)^2+k[/tex]Substituting the values. we get,
[tex]g(x)=1(x-1)^4+0[/tex]Since the graph is shifted right side the value will be in negative. so we get,
[tex]g(x)=(x-1)^4[/tex]Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother's score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire's mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance? Claire did better because her Z-score is greater than her mother's. Claire's mother did better because her z-score is greater than Claire's. Claire did better because her z-score is closer to the mean than her mother's. Claire's mother did better because her z-score is closer to the mean than Claire's.
Answers
The z score tells us the number of standard deviations that a given value is from the mean. Recall, standard deviation tells us the spread of the values from the mean
For Claire, the mean score was 510 but she scored 690 which was higher than the mean score
The z score would be
(690 - 510)/110 = 1.63
For Claire's mother, the mean score was 490 but she scored 680 which was higher than the mean score
The z score would be
(680 - 490)/100 = 1.9
We can see that her mother had a higher z score. Compared to the average score, she had a better performance. Therefore, the correct option is
Claire's mother did better because her z-score is greater than Claire's.
Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal placesgiven in the dataRate of Fatal Alcohol ImpairedCar Crashes per 100 MillionVehicle Miles of Travel0.29 0.45 0.69 0.53 0.600.37 0.59 0.43 0.61 0.300.54 0.43 0.70 0.40 0.760.38 0.72 0.43 0.60 0.73Copy DataPrevAnswer 2 PointsKeypadKeyboard ShortcutsSeparate multiple answers with commas, if necessary.Selecting a button will replace the entered answer value(s) with the button value. If the button is not selected, the entered answer is used.Mean:Median:Mode:O No mode
Answers
The mean of the given data set is 0.528, the median of the given data set is 0.535 and the mode of the given data set is 0.43.
The given data set is:
0.29, 0.45, 0.69, 0.53, 0.60, 0.37, 0.59, 0.43, 0.61, 0.30, 0.54, 0.43, 0.70, 0.40, 0.76, 0.38, 0.72, 0.43, 0.60, 0.73.
Arranging the given data set in ascending order:
0.29, 0.30, 0.37, 0.38, 0.40, 0.43, 0.43, 0.43, 0.45, 0.53, 0.54, 0.59, 0.60, 0.60, 0.61, 0.69, 0.70, 0.72, 0.73, 0.76.
The mean of the data is given by;
Mean = (Sum of the numbers)/(total numbers)
=(0.29 + 0.30 + 0.37 + 0.38 + 0.40 + 0.43 + 0.43 + 0.43 + 0.45 + 0.53 + 0.54 + 0.59 + 0.60 + 0.60 + 0.61 + 0.69 + 0.70 + 0.72 + 0.73 + 0.76) / 20
= 10.55 / 20
= 0.5275 ≈ 0.528
Median = (0.53 + 0.54) / 2
= 0.535
Mode = 0.43 (0.43 repeated most time)
Thus, the mean of the given data set is 0.528, the median of the given data set is 0.535 and the mode of the given data set is 0.43.
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use the diagrams to answer the following questions Number 6
Answers
Explanation:
86 is the far arc and 18 is near intercepted arc
x = 1/2(far arc - near arc)
[tex]\begin{gathered} x\text{ = }\frac{1}{2}(86-18) \\ \text{ =34} \end{gathered}[/tex]Answer: x = 34
Would you be able to assist me in answering these questions ?
Answers
A direct variation is a relationship between 2 variables in which the changes are proportionate. The variables are related by a constant. This is also called a slope. Thus, the graph would always be a straight line. Therefore,
c) Direct variation models are always a type of linear models
a) The straight line always pass through the origin(0, 0)
b) A polynomial is an expression containing variables and coefficients. The variable can be in the form x^n where n can be any positive integer. This means that n can be 1,2,3,4.....If n is 1, the polynomial expression is linear. Thus, it can be a direct variation model. Therefore,
Direct variation models are sometimes a type of polynomial models
d) An exponential model is not linear. The form of a linear model is
y = ax
where a is the constant of pro
An exponential model is y = ab^x
The models are not the same. Thus,
Direct variation models are never a type of exponential model
List all the possible rational roots, then find all the roots of the function
Answers
Take into account that for a polynomial function, the possible roots are given by the following quotient:
roots = p/q
where p is the constant of the function (and its factors) and q is the coefficient of the term with the greates degree (variable with greatest exponent) or its factors.
Then, based on the previous explanation, you have:
p = -9
q = 5
factors -9: -1, 1, -3, 3, -9, 9
factors 5: -1, 1, -5, 5
Hence, the possible factors are:
±1, ±3, ±9, ±1/5, ±3/5, ±9/5
and the roots:
roots = {i(√15)/5 , -i(√15)/5, √3, -√3}
The roots can be also obtained by using quadratic formula for x^2, and then, by applying square root to the result to obtain x.
A dog alte 5 feet away from its owner's 50-foot tall house. What equation could be used to find the angle of elevation? 60 8 tan = BO CON 60 bine BO 50 ban () = b
Answers
Answer:
The equation that could be used to find the angle of elevation is;
[tex]\tan \theta=\frac{50}{5}[/tex]Explanation:
Given that the dog sits 5 ft away from its owner's 50 ft tall house.
it can be represented with the drawing below;
Using Trigonometry;
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the diagram;
opposite = 50 ft
adjacent = 5 ft
so, we have;
[tex]\tan \theta=\frac{50}{5}[/tex]Therefore, the equation that could be used to find the angle of elevation is;
[tex]\tan \theta=\frac{50}{5}[/tex]