For questions 7-8: P is the center of a circle with diameter KR.7. If P(7,-5) and R(4,-2), find the coordinates of point K.8. What is the length of the radius to the nearest hundredth?
Answers
Answer:
7.) The coordinates of point K are (10,8)
8.) The length of the radius, to the nearest hundreth, is of 4.24 units.
Step-by-step explanation:
P is the center of a circle with diameter KR:
This means that P is the midpoint between K and R.
I will see that the points are:
[tex]P(x_P,y_P),K(x_K,y_K),R(x_R,y_R)[/tex]Since P is the midpoint:
[tex]x_P=\frac{x_K+x_R}{2},y_P=\frac{y_K+y_R}{2}[/tex]P(7,-5) and R(4,-2)
This means that:
[tex]x_P=7,y_P=-5,x_R=4,y_R=-2[/tex]7. If P(7,-5) and R(4,-2), find the coordinates of point K
[tex]x_P=\frac{x_K+x_R}{2}[/tex]Substituting:
[tex]7=\frac{x_K+4}{2}[/tex][tex]x_K+4=14[/tex][tex]x_K=10[/tex]Now we do the same for y:
[tex]y_P=\frac{y_K+y_R}{2}[/tex]Replacing with what we have
[tex]-5=\frac{y_K-2}{2}[/tex][tex]y_K-2=-10[/tex][tex]y_K=-8[/tex]The coordinates of point K are (10,8)
8. What is the length of the radius to the nearest hundredth?
The radius is half the diameter(distance between KR divided by 2). It can also be the distance between an endpoint of the circle and the centre(Distance between P and K, or between P and R).
I am going to calculate the distance between P and R.
P(7,-5) and R(4,-2). So
[tex]R=\sqrt{(7-4)^2+(-5-(-2))^2}=\sqrt{3^2+(-5+2)^2}=\sqrt{9+9}=\sqrt{18}=4.24[/tex]The length of the radius, to the nearest hundreth, is of 4.24 units.
Related Questions
In the parallelogram ABCD, MLA = 2x + 50 and m C = 3x + 40. The measure of LA is
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The measure of angle m∠A will be 70°,for the parallelogram ABCD
Parallelogram and its Properties:
Parallelogram is a special kind of quadrilateral, in which opposite sides are equal and parallel to each other.
Properties:
1. Opposite sides are parallel to each other.
2. Length of opposite sides are equal.
3.Diagonally opposite angles are equal.
4. Diagonals bisects each other.
5. Sum of any two adjacent angle is 180°
From figure,
ABCD is a parallelogram
m∠A = 2x + 50
m∠ C = 3x + 40
In a parallelogram ABCD we know opposite angles are equal to each other,
m∠A = m∠C
2x + 50 = 3x + 40
3x - 2x = 50 - 40
x = 10
Hence,
m∠A = 2x + 50
put the value of x we get,
m∠A = 2 * 10 + 50
= 20 + 50
= 70°
m∠A = 70°
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Two of the angles in a triangle measure 56° and 6° what is the measure of the third angle
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The sum of angle in a triangle is 180°
If two of the angles in a triangle is 56° and 6°
Let x be the third angle
56 + 6 + x = 180° (sum of angle in a triangle)
62° + x = 180°
subtract 62° from both-side of the equation
x = 180° - 62°
x = 118°
Hence, the third side is 118°
I need help simplifying this question (last answer that is cropped is 1 over 9 with exponent of 5
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To simplify this expression we need to follow this procedure:
It means that the correct answer is:
[tex]\frac{1}{9^5}[/tex]In parallelogram ABCD, which angle is congruent to
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In parallelogram ABCD, which angle is congruent to ?
Let us draw the parallelogram to better understand the problem.
As you can see from the above figure,
∠ABC and ∠CDA are congruent. (drawn in black color)
Also, ∠BCD and ∠DAB are congurent. (drawn in red color)
This means that the opposite angles are congruent in a parallelogram.
Therefore, the correct answer is option C
∠ABC and ∠CDA are congruent.
cost of iPhone $699 with a 15% discount what will be the total paid
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cost = $699
Discount = 15% = 15/100 = 0.15 (decimal form)
Multiply the cost by the discount in decimal form
699 x 0.15 = 104.85
Subtract the discount amount
699-104.85 = $594.15
if 5 ibs apples cost $2.99, how much would 3 ibs cost?
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We know that 5 lbs of apples cost $2.99
To know how much do 3 lbs of apple cost, you can use cross multiplication
If 5 lbs cost $2.99
Then 3 lbs cost $x
The proportion between the price and the number of apples is the same, you have to calculate it as:
[tex]\begin{gathered} \frac{2.99}{5}=\frac{x}{3} \\ (\frac{2.99}{5})\cdot3=x \\ x=1.794 \end{gathered}[/tex]3 lbs of apples cost $1.79
A restaurant sells tea for $1.50 plus $0.50 per refill. the restaurant brews enough tea for 4 refills per customer. The linear function that represents the total cost of, r , tea refill is C(r)=0.5r+1.5.
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C(r)=0.5r+1.5.
The domain of a function is the set of all input variables of the function. In this case "r"
The domain r is the number of tea refills.
Hi tutor,What is the connection between the slope of a tangent of a function at a given point, and it’s derivative evaluated at that point? If possible, can you please use a diagram and derivation steps to help explain?
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Given:
Derivative and sope of tangent
Required:
We want to define relation
Explanation:
The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line for example
and the slope of that tangent is the derivative of function at point P
Now to find equation of a tangent line
1) Find the first derivative of f(x).
2) Plug x value of the indicated point into f '(x) to find the slope at x.
3) Plug x value into f(x) to find the y coordinate of the tangent point.
4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.
need help asappppppp
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At first, we will find the volume of the cone and the volume of the sphere, then subtract them to find the answer
The rule of the volume of the cone is
[tex]V_c=\frac{1}{3}\times\pi\times r^2\times h[/tex]Since the height of the cone is 1 cm and its radius is 3 cm, then
h = 1 and r = 3
Substitute them in the rule above
[tex]\begin{gathered} V_c=\frac{1}{3}\times\pi\times(3)^2\times(1) \\ V_c=\frac{1}{3}\times\pi\times9\times1 \\ V_c=3\pi \end{gathered}[/tex]The formula of the volume of the sphere is
[tex]V_{sp}=\frac{4}{3}\times\pi\times r^3[/tex]Since the diameter of the sphere is 3 cm, then
[tex]\begin{gathered} r=\frac{1}{2}\times3 \\ r=\frac{3}{2} \\ r=1.5\operatorname{cm} \end{gathered}[/tex]Substitute it in the formula above
[tex]\begin{gathered} V_{sp}=\frac{4}{3}\times\pi\times(1.5)^3 \\ V_{sp}=4.5\pi \end{gathered}[/tex]Noe subtract them to find the answer
[tex]\begin{gathered} V=4.5\pi-3\pi \\ V=1.5\pi \end{gathered}[/tex]The amount of the extra soap is
[tex]1.5\pi cm^3[/tex]What is 10 meters long by 7 meters wide in square meters?
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1) Assuming this is a quadrilateral, then the area is width times length
So
A =10 x 7
A= 70 m²
It's an area of 70 m²
How to calculate the square foot
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Solution:
To find square feet, multiply the length measurement in feet by the width measurement in feet.
Hence, the standard formula to calculate square foot is;
[tex]length\times width[/tex]List the sale price of the item. Round to two decimal places when necessary. Original price: $25; Markdown: 12%.
Answers
Answer
Sale Price = $22
Explanation
Mark down percentage is given as
[tex]\text{Markdown percentage = }\frac{(Original\text{ Price) - (Sale Price)}}{(Original\text{ }Price)}\times100[/tex]For this question,
Markdown percentage = 12%
Original Price = $25
Sale Price = ?
[tex]\begin{gathered} \text{Markdown percentage = }\frac{(Original\text{ Price) - (Sale Price)}}{(Original\text{ }Price)}\times100 \\ 12=\frac{25-(\text{Sale Price)}}{25}\times100 \\ \text{Divide both sides by 100} \\ 0.12=\frac{25-(\text{Sale Price)}}{25} \\ \text{Cross multiply} \\ 25-(\text{Sale Price) = (0.12 }\times25) \end{gathered}[/tex]25 - (Sale Price) = 3
Sale Price = 25 - 3
Sale Price = $22
Hope this Helps!!!
2. Kylie wants to earn $100 a month. She rakes leaves for $7 an hour and cleans windows for $6 an hour. Kylie cannot work more than 30 hours a week. Write the system of inequalities that represents this situation. Be sure to define your variables.
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Let L be the amount of hours that Kylie works on raking leaves and W the amount of hours that she works on cleaning windows (on a week).
Since she cannot work more than 30 hours a week, and the total time spent working is L+W, then:
[tex]L+W<30[/tex]Since one month has 4 weeks, she should win $25 a week to earn $100 in a month. Since she gets paid $7 per hour for raking leaves, after L hours she would have won a total amount of 7L, and since she gets paid $6 for cleaning windows, she would have won 6W after W hours. The total amount of money earned would be 7L+6W, which should be greater than 25:
[tex]25\le7L+6W[/tex]Therefore, the system of inequalities that represents the situation, is:
[tex]\begin{gathered} L+W\le30 \\ 25\le7L+6W \end{gathered}[/tex]10.2 x 3.80
I am still confused on this question
Answers
Answer: 38.76
Step-by-step explanation:
All you have to do is move both decimals to the right and multiply, example, 10.2 = 102. & 3.80 = 380., then you multiply both numbers. In this case, 102 x 380 is 38760. After you multiply both numbers, you move the decimal to the left, so 38760. = 38.760 or 38.76.
I would like to work through how to determine whether this is even, odd or netiher.
Answers
We are given a function and are asked to determine if it's even, odd or neither. Our approach is to employ the negative test and modify the function to ascertain its status. This will be depicted below.
[tex]h(x)=-6x^3+x^2+8x+8[/tex]This is our original function, next, we find h(-x)
[tex]\begin{gathered} h(x)=-6x^3+x^2+8x+8 \\ h(-x)=-6(-_{}x)^3+(-x)^2+8(-x)+8 \\ h(-x)=6x^3+x^2-8x+8 \\ h(-x)=6x^3+x^2-8x+8 \\ h(-x)=-(-6x^3-x^2+8x-8) \end{gathered}[/tex]Looking at the function h(x) and h(-x), we have to put the polynomial in the correct degree. The input of the negative sign before the h(-x) function is to check if the function will maintain the same format with the original function, h(x). The disparity is what tells us if it is even, odd or neither of the two.
Now we know h(-x), we now use a certain set of conditions to test if function is even, odd or neither.
[tex]\begin{gathered} \text{if h(x)=h(-x), then function is even} \\ \text{if h(-x)=-h(x), then function is odd} \\ \text{if it is neither of the above, function is neither even nor odd.} \end{gathered}[/tex]In this case, based on the above criteria, the function is neither even nor odd.
I was on vacation for this unit and having a hard time
Answers
1.a
We can rewrite the given information in an algebraic expression as follows:
[tex]\frac{3}{8}x=6[/tex]where x represents the number of 3/8-inch thick books. Solving for x:
[tex]x=\frac{6}{\frac{3}{8}}[/tex]We can rearrange the operation:
[tex]x=\frac{6}{3}\cdot8[/tex][tex]x=\frac{48}{3}[/tex][tex]x=16[/tex]Then, we need 16 3/8-inch books to make a stack 6 inches tall.
1.b
To solve this exercise, we can use the same procedure as in 1.a.
0. Writing the information in an algebraic expression.
[tex]\frac{1}{2}x=2\cdot\frac{3}{4}[/tex]where x represents the groups of 1/2 pound.
We can convert the mixed number into an improper fraction:
[tex]2\cdot\frac{3}{4}=\frac{2\cdot4+3}{4}=\frac{8+3}{4}=\frac{11}{4}[/tex]2. Rewriting the operation:
[tex]\frac{1}{2}x=\frac{11}{4}[/tex][tex]x=\frac{\frac{11}{4}}{\frac{1}{2}}[/tex][tex]x=\frac{11\cdot2}{4\cdot1}[/tex][tex]x=\frac{22}{4}[/tex][tex]x=5.5[/tex]We have 5.5 groups of 1/2 pounds in 2 (3/4) pounds.
Answer:
• 1.a 16
,• 2.b 5.5
Hi, i need help with question 1 of my Precalculus homework.
Answers
The interval notation uses the form (x1,x2) and it depends on whether the interval includes or does not includes the limits. if the interval includes the limit then we use the notation [x1,x2].
a. Since neither of the endpoints is included in the inequality the interval notation should be
[tex]-1b. The inequality includes all numbers greater or equal to 5, the interval notation should be [tex]x\ge5=\lbrack5,\infty)[/tex]c. The inequality includes all numbers that are less to 4 but does not include number -4, the interval notation should be
[tex]-4>x=(-\infty,-4)[/tex]d. The solution for the inequality includes two solutions, then we write both separately and unite them together. The interval notation should be
[tex]-4\le x<-1or0e. The interval notation should be between numbers 5 and 100 [tex]\lbrack5,100\rbrack[/tex]f. The numbers should be all less than pi, but it does not include pi
[tex](-\infty,\pi)[/tex]g. all numbers greater or equal to 3
[tex]\lbrack3,\infty)[/tex]h. All numbers less or equal to -2
[tex](-\infty,-2\rbrack[/tex]i. All numbers greater than 0, but it does not include 0
[tex](0,\infty)[/tex]j. all numbers less than e but it does not include e
[tex](-\infty,e)[/tex]Find the equation of the line with Slope = 5 and passing through (-7,-34). Write your equation in the form y=mx+b .
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[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-34})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-34)}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-7)}) \implies y +34= 5 (x +7) \\\\\\ y+34=5x+35\implies {\Large \begin{array}{llll} y=5x+1 \end{array}}[/tex]
These dot plots show the ages (in years) for a sample of sea turtles and a sample of sharks. Sea Turtles 00 000 to 0000 000 : 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Sharks 000000 : OO 00000 0000 000 OO o 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Age (in years) What are the differences between the centers and spreads of these distributions? Select two choices: one for the centers and one for the spreads. O A. Centers: The sea turtles have a lower median age than the sharks. B. Spreads: The ages of the sea turtles are more spread out. O C. Centers: The sea turtles have a greater median age than the sharks. O D. Spreads: The ages of the sharks are more spread out
Answers
Options C and D.
The median age of the Sea turtles is 55 while the median age of the sharks is 30, thus validating OPTION C
We can get the ranges of the two distributions to be:
Sea Turtles: 65 - 45 = 20
Sharks: 55 - 10 = 45
Sharks have a larger range, validating OPTION D
find a slope of the line that passes through (6,8) and (95,86)
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find a slope of the line that passes through (6,8) and (95,86)
Applying the formula to calculate the slope
we ahve
m=(86-8)/(95-6)
m=78/89
therefore
the slope is 78/89What is the answer to 720x+(-20x)
Answers
720x + (-20x)
Remember
(+)(+) = (+)
(+)(-) = (-)
So + (-20x) will equal - 20x, so
720x + (-20x) = 720x - 20x
Subtract 20 from 720
720 - 20 = 700, so
720x + (-20x) = 720x - 20x = 700x
8. Bobbie is self-employed and made a profit of $22, 150 last year. She mustpay $2572 in income tax. She also must pay social security tax of 13.3% ofher profit. What is Bobbie's total tax liability? Round to the nearestdollar,a $5912b. $4998c. $5518
Answers
income tax = $2572
social security tax = 13.3% of the profit
= 13.3% of $22,150
= 13.3/100 * 22,150 = $2,945.95
So, the total tax =
2572 + 2,945.95 = $5,517.95
Rounding to the nearest dollar
the total tax = $5,518
The answer is option C. $5,518
Determine the Coordinate represented in the Table of Values. ch on at 2 7 9 6 3 5 una) f(9) = 5b) f(5) = 9c) f(5, 9) = 14d) f(9, 5) = 14
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Given the table:
x f(x)
2 6
7 3
9 5
To determine the coordinate given in the table, we have the following:
f(2) = 6
f(7) = 3
f(9) = 5
From the answer choices, the only coordinate given is:
f(5) = 9
ANSWER:
f(9) = 5
Which best describes what happens when the number of trials increases significantly
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Solution:
Given:
[tex]\begin{gathered} Head,H=4 \\ Total=12 \\ P(H)=\frac{4}{12} \\ P(H)=\frac{1}{3} \end{gathered}[/tex]From the probability, it can be deduced that as the number of trials increases, the observed frequency will get closer to the expected frequency.
Therefore, if the number of trials increases significantly, then the observed frequency of landing heads up gets closer to the expected frequency based on the probability of the coin landing heads up.
Determine The Domain for the relation below
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Answer:
The domain would be all real numbers.
Step-by-step explanation:
For Interval notation, it would be written as (-∝, ∝)
(I don't know what signs those are, but they are supposed to be infinity signs)
Domain is what x can or can't be. In the function that is in the image, the function is y=a constant. So, no matter what x is, y will always be the constant. So, x can be all real numbers.
Hope this helps!
Part DWhat if the second six-sided die is replaced by an eight-sided die. How can you change the table to show the sample space for rolling a six-sideddie and then an eight-sided die? Explain.
Answers
For a sample space for rolling a six-sided die and then an eight-sided die is constructed as
We just change the probable events of the second die up to 8 and then combine it with the possible combinations with a normal six die, which is shown in the table above.
which costes more , a hamburger or a Chicken salad ? use. The vives princesa to write a n inequality that show your answer Hamburger $ 4.30, hot Dog $ 2.35, Chicken salad $ 4.49 pizza 2.49
Answers
Chicken salad costs more
Explanation:Cost of Hamburger = $ 4.30
Cost of hot Dog = $ 2.35
Cost of Chicken salad = $ 4.49
Cost of pizza = $2.49
$4.49 is greater than $4.30
Cost of of Chicken salad is greater than Cost of Hamburger
Hence, Chicken salad costs more
An inequality that shows the answer:
4.49 > 4.30
According to the United States Treasury Department, the U.S national debt was 1.815 x 10 to the 13th power dollars on September 30, 2015 . On September 29, 2005 , the national debt was 4.974 x 10 to the power of 12 dollars . Find the amount of Increase in the national debt from September of 2005 to september of 2015? Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
Answers
The U.S national debt on 2015 was 1.815 * 10^13
The U.S national debt on 2005 was 4.974 * 10^12
So, the amount of increase =
1.815 * 10^13 - 4.974 * 10^12 =
18.15 * 10^12 - 4.974 * 10^12 =
(18.15 - 4.974) * 10^12 = 13.176 * 10^12
= 1.3176 * 10 * 10^12 = 1.3176 * 10^13
factor the equation 3x^2y^2-15xy^2
Answers
3xy²(x - 5)
Explanation:The equation: 3x²y²-15xy²
x is common to both expression, we factorise it:
x(3xy² - 15y²)
y² is common to both expression, we factorise it:
xy²(3x - 15)
3 is common to both expression, we factorise it:
3xy²(x - 5)
I need help with the hidden message. Help me please. Thank You I really appreciate it if you have helped me.
Answers
We have symbols that represent a letter and a number.
With the equations or relations in the left we have to find the numeric value for each picture, and then use the letter to complete the hidden message.
First equation is:
[tex]\begin{gathered} \text{spyder web + spyder web =16} \\ 2\cdot\text{spyder web = 16} \\ \text{spyder web = }\frac{16}{2}=8 \end{gathered}[/tex]So, the value of a spyder web is 8 and the letter for that is i.
The second equation is:
[tex]\begin{gathered} \text{candy - spyder web = 9} \\ \text{candy - 8 =9} \\ candy\text{ = 9+8=17} \end{gathered}[/tex]The value of candy is 17 and the letter is T.
The Third equation is:
[tex]\begin{gathered} \text{spyder web }\cdot\text{ cat - candy = 7} \\ 8\cdot\text{cat - 17 =7} \\ 8\cdot\text{cat=7+17=24} \\ \text{cat}=\frac{24}{8}=3 \end{gathered}[/tex]The value of cat is 3 and the letter is S.
The fourth equation is:
[tex]\begin{gathered} ballons\text{ / cat =11} \\ \text{ballons /3 =11} \\ \text{ballons}=11\cdot3=33 \end{gathered}[/tex]The value of ballons is 33 and the letter is E.
The fifth equation is:
[tex]\begin{gathered} \text{bat + (ballons - candy) = 23} \\ \text{bat + (33-17) = 23} \\ bat+16=23 \\ \text{bat = 23 - 16 = 7} \end{gathered}[/tex]The value of bat is 7, but there is some mistake, it must be 6 and the letter C.
The sixth equation is:
[tex]\begin{gathered} \text{bat}+\text{cat}\cdot pumpkin\text{ = 27} \\ 6+3\cdot\text{pumpkin}=27 \\ 3\cdot\text{ pumpkin = 27-6=21} \\ \text{pumpkin =}\frac{21}{3}=7 \end{gathered}[/tex]The value of pumpkin is 7 and the letter is O.
The seventh equation is:
[tex]\begin{gathered} \text{spyder / spyder web }\cdot\text{ pumpkin = 21} \\ \frac{spyder}{8}\text{ }\cdot7=21 \\ \text{spyder = 21}\cdot\frac{8}{7}=3\cdot8=24 \end{gathered}[/tex]The value of spyder is 24 and the letter is B.
The last equation is:
[tex]\begin{gathered} tree\text{ +ghost}=0 \\ tree\text{ + 0=0} \\ \text{tre}e\text{ = 0} \end{gathered}[/tex]The only value for ghost is zero and the letter L and the value of tree is zero too and the letter is O.
The hidden message is:
BOIL IS IOOOCEOT