Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
Please help with this question asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
no solution
Step-by-step explanation:
We can think of an absolute value as the magnitude of the number. We can also define it as how far the number is from 0 on the number line. Thus, absolute value must always be positive (or 0).
Solve
Start by adding 1 to both sides:
[tex]\frac{|m|}{2}=-2[/tex]
Multiply both sides by 2:
[tex]|m|=-4[/tex]
The absolute value of a number is always positive (with the exception of 0), therefore there is no solution.
Additional CommentsNotice we can only add/multiply (or subtract/divide) an equation because of the Addition/Subtraction/Multiplication/Division Property of Equality which state that if you add/subtract/multiply/divide one side of the equation by a certain value, you must do the same to the other side of the equation.
Solve the system of equations below by graphing. Write the solution as an ordered pair. y = −5x y = x − 6
Answer:
x=1 and y=−5
Step-by-step explanation:
Problem:
Solve y=−5x;y=x−6
Steps:
I will solve your system by substitution.
y=−5x;y=x−6
Step: Solve y=−5x for y:
Step: Substitute −5x for y in y=x−6:
y=x−6
−5x=x−6
−5x+−x=x−6+−x (Add -x to both sides)
−6x=−6
−6x/−6=−6/−6 (Divide both sides by -6)
x = 1
Step: Substitute 1 for x in y=−5x:
y=−5x
y=(−5)(1)
y=−5(Simplify both sides of the equation)
Answer:
x=1 and y=−5
Thank you,
Eddie
A data value is considered _______ if its z-score is less than 2 or greater than 2.
A data value is considered significantly low or significantly high if its z-score is less than -2 or greater than 2.
What does it mean if z-score is 2?
A positive z-score indicates the raw score is higher than the mean average.For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.A negative z-score reveals the raw score is below the mean average.For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.What does a standard deviation of 2 mean?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean.In any distribution, about 95% of values will be within 2 standarddeviations of the mean.
Learn more about standard deviation
brainly.com/question/4252436
#SPJ4
The correct question is -
A data value is considered _______ if its z-score is less than minus−2 or greater than 2.
How many integers between $1$ and $200$ are multiples of both $3$ and $5$ but not of either $4$ or $7$
There are only 13 multiples of both 3 and 5, since
[tex]200 = 3\cdot5\cdot13 + 5[/tex]
From these integers, we eliminate any that are also divisible by 4 or 7.
[tex]3\cdot5\cdot4 = 60 \implies \{60,120,180\}[/tex]
[tex]3\cdot5\cdot7 = 105 \implies \{105\}[/tex]
so there are 13 - 4 = 9 such integers.
What is the number between 8.1 and 8.24?
Answer:
8.17Step-by-step explanation:
What is the number between 8.1 and 8.24?
Add the numbers and divide by 2 and you will find the average
(8.1 + 8.24) : 2 =
8.17
8.17 is exactly half way between them.
A single card is drawn from a standard 52-card deck. find the conditional probability that the card is a club, given that it is a ten______
The probability of getting a Club given that the card is a Ten is 0.25.
According to the statement
we have given that the there is a deck of the 52 cards and we have to find the conditional probability that the card is a club and the given card is a 10 number card.
So, For this purpose we know that the
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
And according to this,
The probability P is
P(Club) = 13/52 = 1/4
P(Ten) = 4/52 = 1/13
P(Club and Ten) = (1/4)(1/13) = 1/52
And we know that the
P(Club|Ten) = P(Club and Ten)/P(Ten)
And then substitute the values and it become
= (1/52)/(1/13) = (1/52)(13/1)
= 13/52 = 1/4
= 0.25
So, The probability of getting a Club given that the card is a Ten is 0.25.
Learn more about probability here
https://brainly.com/question/24756209
#SPJ4
Find where the sequence converges
Answer: [tex]\\ \lim\limits_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]
Step-by-step explanation:
[tex]\displaystyle\\ \lim_{k \to \infty} (1+\frac{4}{k})^k \\x=\frac{x}{4} *4\\So,\ \lim_{k \to \infty} (1+\frac{4}{k})^\frac{k}{4}*4 \\ \lim_{k \to \infty} ((1+\frac{4}{k})^\frac{k}{4} )^4.\\Use\ the\ second\ wonderful\ limit:\\\boxed { \lim_{x \to \infty} (1+\frac{1}{x})^x=e },\\\\So,\\ \lim_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]
We can also apply l'Hôpital's rule by first rewriting the limit as
[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp\left(\ln \left(1 + \frac4k\right)^k\right) = \exp\left(\lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k}\right)[/tex]
Applying the rule gives
[tex]\displaystyle \lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k} = \lim_{k\to\infty} \frac{\left(-\frac4{k^2}\right)/\left(1+\frac4k\right)}{-\frac1{k^2}} = 4 \lim_{k\to\infty} \frac1{1 + 4k} = 4[/tex]
so that the overall limit is
[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp(4) = \boxed{e^4}[/tex]
The floor of a rectangular room measures 5m by 4m and the ceiling is 3m from the floor. An ant is at the top of a corner of the room and crawls to the opposite bottom corner of the room. Find the shortest distance it can travel. (Cannot do its diagonal distance)
Answer:
12 m
Step-by-step explanation:
Well, imagine you got this nice room. How can it reach the other corner? It has to go along the 3 dimensions. So the shortest path would be: 5 + 4 + 3 12m
Answer:
3 + √(41) = 9.4 m (nearest tenth)
Step-by-step explanation:
The room can be modeled as a rectangular prism with:
width = 4 mlength = 5 mheight = 3 mIf the ant is at the top of a corner of a room and crawls to the opposite bottom corner of the room, the shortest distance will be to travel down one vertical edge of the room then to travel the diagonal of the floor of the room (or to travel the diagonal of the ceiling and then one vertical edge).
Vertical edge = height of room = 3m
The diagonal of the floor (or ceiling) is the hypotenuse of a right triangle with legs of the width and length. Therefore, to find the diagonal, use Pythagoras Theorem.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleGiven:
a = width = 4 mb = length = 5 mc = diagonalSubstitute the given values into the formula and solve for c:
[tex]\implies 4^2+5^2=c^2[/tex]
[tex]\implies c^2=41[/tex]
[tex]\implies c=\sqrt{41}[/tex]
Therefore, the shortest distance the ant can travel is:
⇒ 3 + √(41) = 9.4 m (nearest tenth)
Learn more about Pythagoras Theorem here:
https://brainly.com/question/27707750
https://brainly.com/question/27988757
Suppose that w varies directly as the product of x and the square of y and inersely as z. when x = 2, y = 3, and z = 36, the value of w is 1/2. find the value of w when x = 5, y = 5, and z = 10.
The value of w is 12.5 when x = 5 , y= 5 and z = 10.
What is Equation of variation?
A variation is a relation between a set of values of one variable and a set of values of other variables. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.Equation of variation w = [tex]\frac{kxy^{2} }{z}[/tex]
Constant of variation k = [tex]\frac{wz}{xy^{2} }[/tex]
Find k when w = 1/2, x = 2 and z = 36
k = [tex]\frac{wz}{xy^{2} }[/tex]
[tex]k = \frac{\frac{1}{2} * 36 }{2 * 3^{2} }[/tex]
[tex]k = \frac{18}{2 * 9}[/tex]
[tex]k = \frac{18}{18}[/tex]
k= 1
find the value of w when x = 5 , y = 5 and z = 10
[tex]w = \frac{kxy^{2} }{z} \\w= \frac{1 * 5 * 5^{2} }{10}[/tex]
[tex]w = \frac{5^{3} }{10}[/tex]
w = 125 /10
w = 25 /2
w = 12 . 5
Therefore, the value of w is 12.5 when x = 5 , y= 5 and z = 10
Learn more about Equation of variation
brainly.com/question/6669994
#SPJ4
25. A chocolate bar which weighs of a pound is 9/16 cut into seven equal parts. How much do three parts weigh? (A) pound 21/112 (B) pound/27/112 (C) pound 16/63 (D) pound 47/63
The three parts weigh 27/112 pound ( letter B).
Rules for Multiplication and Division of FractionsFor Multiplication - First, you should multiply both numerators after that you should multiply both denominators. Finally, you can simplify if it is necessary.For Division- First, you should repeat the numerator and after that you should multiply the numerator by the reciprocal of denominators. Finally, you can simplify if it is necessary.The question gives:
A chocolate bar that weighs = 9/16A chocolate bar cut into seven equal parts.Therefore, each part will be [tex]\frac{\frac{9}{16} }{7} =\frac{9}{16} *\frac{1}{7} =\frac{9}{112}[/tex].
For knowing the three parts weigh, you should mulitiply the previous value for 3. Thus,
[tex]\frac{9}{112}*3=\frac{27}{112}[/tex].
Read more about fraction division here:
https://brainly.com/question/15804439
#SPJ1
The weight of three parts is 27/112 pounds
How to determine the weight of three parts?The weight of the chocolate bar is given as:
Weight = 9/16
When it is cut into 7 equal parts, the weight of each part is
Each = Weight/7
This gives
Each = 9/16 * 1/7
Evaluate the product
Each = 9/112
The weight of three parts is then calculated as:
Three parts = Each * 3
This gives
Three parts = 9/112 * 3
Evaluate the product
Three parts = 27/112
Hence, the weight of three parts is 27/112 pounds
Read more about fractions at:
https://brainly.com/question/11562149
#SPJ1
please answer this I give u thanks and f0ll0w u and mark brainiest
Use of identity for sum of cubes:
x³ + y³ = (x + y)(x² - xy + y²)Change it as:
x³ + y³ = (x + y)(x² + 2xy + y² - 3xy) = (x + y)[(x + y)² - 3xy)]It is easy to notice that:
64a³ = (4a)³ and125b³ = (5b)³.So the sum of cubes for the given expression will be:
64a³ + 125b³ = (4a + 5b)[(4a + 5b)² - 3(4a*5b)] =(4a + 5b)[(4a + 5b)² - 60ab]Now substitute the values and calculate each of these:
(a) 4a + 5b = 5, ab = -1.
(4a + 5b)[(4a + 5b)² - 60ab] = 5[5² - 60(-1)] = 5(25 + 60) = 5(85) = 425(b) 4a + 5b = -2, ab = 1/15.
(4a + 5b)[(4a + 5b)² - 60ab] = -2[(-2)² - 60(1/15)] =-2(4 - 4) = -2(0) = 0(c) 4a + 5b = 1/3, ab = -1/9.
(4a + 5b)[(4a + 5b)² - 60ab] = (1/3)[(1/3)² - 60(-1/9)] =(1/3)(1/9 + 60/9) = (1/3)(61/9) = 61/27 = 2 7/27(d) 4a + 5b = -1, ab = 1.
(4a + 5b)[(4a + 5b)² - 60ab] = -1[(-1)² - 60(1)] = -1(1 - 60) = -1(-59) = 59How many 3-yard straight pieces does Vince need altogether to build the three slides?
Based on the dimensions of the support for the slides, the missing length and slide length is 15 yards.
The number of 3-yard straight pieces needed is 15 straight pieces.
What number of straight pieces are needed?The length of a single slide is the hypotenuse of the triangle which can be found using the Pythagoras theorem as:
Hypotenuse² = 9² + 12²
Hypotenuse = √(81 + 144)
= 15 yards
If a single slide is 15 yards, then 3 slides would be:
= 15 x 3
= 45 yards
The number of 3-yard straight pieces needed are:
= 45 / 3
= 15 pieces
Find out more on the Pythagoras theorem at https://brainly.com/question/343682
#SPJ1
Answer: 39
Explain:
The length of each slanted area for each slide is 15 yards. The length of each straight piece is 3 yards. So, the number of straight pieces needed for 15 yards is 15 - 3, or 5. There are two slanted areas on each slide.
The number of straight pieces required for the flat area at the bottom of each slide is 3.
Adding them up, the total number of straight pieces required for one slide is 5 + 5 + 3, or 13. Because there are three slides, the total number of straight pieces needed is 13 • 3, or 39
Vince needs 39 straight pieces to build the three slides.
From ED
Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:
A)
ƒ(n) = 9 + 2(n – 1)
B)
ƒ(n) = 5 + 3(n – 1)
C)
ƒ(n) = –3 + 2(n – 1)
D)
ƒ(n) = 3 + 2(n – 1)
Answer: D
Step-by-step explanation:
The first term is 3 and the common difference is 2.
Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.
Ariel completed the work below to show that a triangle with side lengths of 9, 15, and 12 does not form a right triangle. 9 squared 15 squared = 12 squared. 81 225 = 144. 306 not-equals 144.
Answer:
Work is incorrect
Step-by-step explanation:
I'm assuming this question is asking whether the work is correct or not? In which case the work is not correct.
The Pythagorean Theorem states: [tex]a^2+b^2=c^2[/tex] where c=hypotenuse, and "a" and "b" are the other two sides. The main thing to note here, is that the hypotenuse is the largest side of all three sides.
So the equation Arial set up: [tex]9^2+15^2=12^2[/tex] is incorrect, since the 15 would need to be on the right side. This forms the correct equation: [tex]9^2+12^2=15^2[/tex] which then simplifies to: [tex]81 + 144 =225 \implies 225=225[/tex].
Thus a right triangle can be formed using these side lengths. You can of course set up a similar equation to Ariels, where the "c" or hypotenuse is not isolated, but you would have to rearrange the equation so that: [tex]a^2+b^2=c^2\implies b^2=c^2-a^2[/tex] but see how "a squared" is being subtracted from "c squared"? So it's a similar equation to Ariels, but not quite the same, and if she set it up like this, then she would reach the same conclussion
Which equation represents the function? f(x)=−1/2x+4 f begin argument x end argument equals negative fraction 1 over 2 end fraction x plus 4 f(x)=2x+12 f begin argument x end argument equals 2 x plus 1 half f(x)=4x−2 f begin argument x end argument equals 4 x minus 2 f(x)=−2x+4
The equation that represents the function is y = -x - 1
How to determine the equation of the function?The complete question is added as an attachment
From the table of values, we have the following points
(x, y) = (-1,0) and (0,-1)
Calculate the slope (m) using
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-1 -0)/(0 + 1)
Evaluate the exponent
m = -1
The equation is then calculated as:
y = mx + c
This gives
y = -x + c
Using the point (0,-1), we have:
0 = 1 + c
Solve for c
c = -1
So, we have
y = -x - 1
Hence, the equation that represents the function is y = -x - 1
Read more about linear functions at:
https://brainly.com/question/1884491
#SPJ1
Determine the number of terms, n, given the geometric series 1 3 9 27 ... and sn=3280.
The number of terms, 'n' is 8
How to determine the number of termsLet's determine the common ratio;
common ratio, r = 3/1 = 3
The formula for sum of geometric series with 'r' greater than 1 is given as; Sn = a( r^n - 1) / (r - 1)
n is unknown
Sn = 3280
Substitute the value
3280 = 1 ( 3^n - 1) / 3- 1
3280 = 3^n -1 /2
Cross multiply
3280 × 2 = 3^n - 1
6560 + 1 = 3^n
6561 = 3^n
This could be represented as;
3^8 = 3^n
like coefficient cancels out
n = 8
Thus, the number of terms, 'n' is 8
Learn more about geometric series here:
https://brainly.com/question/24643676
#SPJ1
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=3y2−3x2; 2x y=9
There is a minimum value of -81 located at (x, y) = (6, -3).
The function given to us is f(x, y) = 3y² - 3x².
The constraint given to us is 2x + y = 9.
Rearranging the constraint, we get:
2x + y = 9,
or, y = 9 - 2x.
Substituting this in the function, we get:
f(x, y) = 3y² - 3x²,
or, f(x) = 3(9 - 2x)² - 3x² = 3(81 - 36x + 4x²) - 3x² = 243 - 108x + 12x² - 3x² = 243 - 108x + 9x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = - 108 + 18x ... (i)
Equating to 0, we get:
- 108 + 18x = 0,
or, 18x = 108,
or, x = 6.
Differentiating (i), with respect to x again, we get:
f''(x) = 18, which is greater than 0, showing f(x) is minimum at x = 6.
The value of y, when x = 6 is,
y = 9 - 2x,
or, y = 9 - 2*6 = 9 - 12 = -3.
The value of f(x, y) when (x, y) = (6, -3) is,
f(x, y) = 3y² - 3x²,
or, f(x, y) = 3*(-3)² - 3*6² = 3*9 - 3*36 = 27 - 108 = -81.
Thus, there is a minimum value of -81 located at (x, y) = (6, -3).
Learn more about maximum and minimum at
brainly.com/question/2437551
#SPJ4
Bank a charges a $35 monthly fee for a checking account debit card with the limited train fashion bank b charges a $15 monthly fee for a checking account and debit card plus $0.70 for each transaction 25 transaction is giving a month
Total charges from bank A exists $15.
Total charges on Bank B spending exists $45.
How to estimate the Total charges on bank B?Given: Bank A charges a $15 monthly fee for a checking account and debit card, with unlimited transactions.
Shade 25 transactions.
Total charges from bank A = $15 monthly
Bank B charged a $35 monthly fee for a checking account and debit card, plus $ 0.70 for each transaction.
She made 25 transactions.
Total charges on bank B = $35 + (0.40)25
Total charges on bank B = $35+10
Total charges on bank B = $45
To learn more about Total charges on the bank refer to:
https://brainly.com/question/17226704
#SPJ4
John has a 3/4 of a quart of orange juice and needs to fill it equally in cups that hold 1/10 of a quart. how many cups can he fill?
Answer: 7 1/2 cups
Step-by-step explanation:
We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.
Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.
HELP ASAP!!
ABC is similar to QRS. If AB=3 when QR=1,
what is the measure of BC if RS=1.5?
A: 1.5
B: 3
C: 4.5
D: 5
Answer:
C
Step-by-step explanation:
Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1 and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5
Answer:
C
Step-by-step explanation:
___ AA
*~/■ ■ ⊂ P
| ■ ■.(_)
U U ̄ ̄U U
Helpppppppppp show your steps to the answer
Answer:
9
Step-by-step explanation:
you have to plug in the numbers and solve it, so it would go as follows:
-(-3^2)- 2(-5)(2) - /2/
-9 + 20 - 2 =
9
i hope this helps
Could somebody help me with this? I'm terrible at these problems
Answer:
1. to add 9 to both sides
2. to multiply by 2 to both sides (horrible English)
3. x = -8
Step-by-step explanation:
why do you feel you are terrible at this ?
this is like a riddle or puzzle to solve. like a magic cube or changing a match in a pattern of matches to create another pattern.
let's try and explain this to you.
an equation is like a balance, where both cups are in perfect balance.
whatever value is on the left side, is exactly also on the right side. although it is not plainly visible and explainable, why they are equal.
so, to find out we need to transform the equation. and to keep the balance while transforming you have to do the same changes on both sides of the balance. until you find out what makes the cups equal.
if we destroy the balance at any point, we have no more chance to find out what made both sides equal in the first place, because there is no more original balance.
we can do all mathematical operations in the transformation.
we can add things, subtract things, multiply by a factor, divide by something, ... - anything.
x/2 - 9 = -13
to get clarity in our search for the reason of the equality we try to combine the same type of terms on one side of the equation, and the other type (or types) on the other side.
what types of terms do we have here ?
there is one with a variable (x/2), and there are constant terms (-9, -13).
so, what do I need to do to get rid of the constant term (-9) on the side of the variable term (so that this becomes the side with only variable terms) ?
I need to add 9, so the constant term on that side turns 0 and therefore disappears in the sum. but remember, the action has to be done on both sides.
so,
x/2 - 9 = -13 | + 9 on both sides
x/2 - 9 + 9 = -13 + 9
x/2 = -4
what else is now blocking our view on what x is ?
there is this 1/2 factor of x.
how do we get rid of this 1/2 ? by multiplying by 2. because 2× 1/2 = 1, and a factor of 1 disappears in a multiplication.
x/2 = -4 | ×2 on both sides
x/2 × 2 = -4 × 2
x = -8
and now we see what it is that kept both cups or sides in balance : x = -8
What is the equation for the line of best fit on the scatter plot below?
We've got a negative slope, but it doesn't look steep enough to go through 6 on the y-axis.
So, it's the last option:
y = - 1.25x + 5.75
Hope this helps!
Please help!! 100 points
A system of inequalities is shown.
Which system is represented in the graph
Answer:
The second option.
y > x^2 + 4x -2
y < 3x +4
Step-by-step explanation:
First off, we can eliminate the last option because the graph shows that both inequalities are greater than or less than, but not equal to. We come to this conclusion because both lines on the graph are dashed meaning not equal to. Look at the attached image below (1).
Next, we can input the point (0,0) and test to see if the inequality works. If we input the point (0,0) into the second equation in the second option, we end up with 0 < 4. This is factual meaning that this is your answer.
Hope this helps! If I wasn’t clear enough or you need more information, please let me know in the comments. Have an amazing day!
At the end of the soccer season, the player who scored the most goals had 8 more goals than the player who had the second most goals. The player who had the second most goals had 15 more goals than the third player. The total number of goals scored by all three of the players was 98. Determine the number of goals scored by the player with the most goals. Show your working out.
Step-by-step explanation:
x = the number of goals of the top scorer.
y = the number of goals of the second top scorer.
z = the number of goals of the third top scorer.
x + y + z = 98
x = y + 8
y = z + 15
using the third in the second equation we get
x = z + 15 + 8 = z + 23
and now using this and the third equation in the first equation gives us
z + 23 + z + 15 + z = 98
3z + 38 = 98
3z = 60
z = 20
y = z + 15 = 20 + 15 = 35
x = y + 8 = 35 + 8 = 43
the player with the most goals scored 43 goals.
Based on our Starbucks analysis report, 4 out of every 20 drinks are returned because of a customer complaint and 16/20 are not returned. Starbucks makes $4 on a typical drink not returned (probability of 16/20 ), but loses -$6 (probability of 4/20) when a drink is returned because the employee has to re-make it. What is the Expected Value of this problem and are they going to make a profit ?
Answer:
Step-by-step explanation:
the expected profit should be 2 dollars a drink
Find the center of a circle with the equation: x2 y2−32x−60y 1122=0 x 2 y 2 − 32 x − 60 y 1122 = 0
The equation of a circle exists:
[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.
The center of the circle exists at (16, 30).
What is the equation of a circle?
Let, the equation of a circle exists:
[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.
We rewrite the equation and set them equal :
[tex]$(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2- 32x - 60y +1122=0[/tex]
[tex]$x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0[/tex]
We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.
-2hx = -32x
h = -32/-2
⇒ h = 16.
-2ky = -60y
k = -60/-2
⇒ k = 30.
The center of the circle exists at (16, 30).
To learn more about center of the circle refer to:
https://brainly.com/question/10633821
#SPJ4
At a football game
number of men : number of women : number of children = 13:5:7
There are 4152 more men then women.
Work out the number of children at the game
Answer:
Step-by-step explanation:
let the ratio of men women and children be 13x 5x and 7x
now
13x + 5x + 7x = 4152
25x = 4152
x = 4152/25
x = 166.08
what is the missing number?
Answer:
17
Step-by-step explanation:
the pattern
x is the blank
1+5 = 6
5+6 = 11
6+11 = x
11 + x = 28
so x = 17
One week, taylor earned $203.40 at her job when she worked for 9 hours. if she is paid the same hourly wage, how many hours would she have to work the next week to earn $881.40?
Answer:
39 hours
Step-by-step explanation:
First solve for how much Taylor would earn per hour which is to divide 203.40 by 9
= 203.40÷9 = 22.6
Let x represent the unknown hours
If 22.6 = 1 hr
Then 881.40 = x solving this simultaneously becomes
881.40 ÷ 22.6 = 39
x = 39, hence it'll take Taylor 39 hours to earn $881.40
She have to work 39 hours the next week to earn $881.40.
In simple terms, the unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.
In 9 hours she earned $203.40
∴ In 1 hour she earned $203.40/9 = $22.6
Let number of hours she worked to earn $881.40 be x.
∴ x = $881.40/ $22.6
x = 39 hours
Thus she have to work 39 hours the next week to earn $881.40.
Learn more about Unitary Method here :
https://brainly.com/question/23423168
#SPJ1