Answer:
Standard form: [tex]\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]
This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]
Step-by-step explanation:
Consider expression [tex]x^2+y^2-9x+10y+15=0.[/tex]
First, form perfect squares:
[tex](x^2-9x)+(y^2+10y)+15=0,\\ \\\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{81}{4}+(y^2+10y+25)-25+15=0,\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=10+\dfrac{81}{4},\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]
This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]
A knife is three times the cost of a spoon. 9 spoons and 12 knifes cost ?82.80 workout the cost of 1 knife.
Let S = spoon
Let K = knife
1 knife is thee times the cost of a spoon, so it would be 3S
Now you have 9S + 12K = 82.80
We can replace the K with 3S:
9S +12(3S) = 82.80
Simplify the left side:
9S + 36S = 82.80
Add:
45S = 82.80
Divide both sides by 45"
S = 82.80 / 45
S = 1.84
One spoon cost $1.84
We know one knife cost 3 times as much, so multiply the cost of a spoon by 3:
Knife = 1.84 x 3 = $5.52
Answer:
1.84 x 3 = $5.52
Justin and Mike are learning how to ski. Justin falls down every 30 feet. Mike falls down every 25 feet. If they both start skiing from the same point, how far is the first point where they will both fall down?
Answer:
150 feet
Step-by-step explanation:
in order to find the solution we have to take the L.C.M of 25 and 30
L.C.M of 25 and 30 is 150
so after 150 feet , they will both fall down
Answer: They will both fall down after 150 feet.
Step-by-step explanation:
Hi, to answer this question we have to find the least common multiple (LCM)
of 30 and 25:
To obtain the multiple of a number we have to multiply that number by another number (not zero) in the multiplication table order (by 1,by 2,by 3,etc)
Multiples of 30:30,60,90,120,150
Multiples of 2525,50,75,100,125,150
The LCM is a number that appears on both lists, and is the smallest.
They will both fall down after 150 feet.
Feel free to ask for more if needed or if you did not understand something.
Terry has 3 gallons of fruit punch to serve at a party right and solve a proportion to determine how many quarts are in 3 gallons
Jordan needs 6 3/10 gallons of milk to make 4 1/2 gallons of ice cream. How much gallons of milk will Jordan need to make one gallon of ice cream.
Answer:
45/63
Step-by-step explanation:
6 3/10=63/10, 4 1/2=45/10,
(45/10)/(63/10)=45/63
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right. What is the equation of the new function g(x) ?
Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right by h units, then
the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then
the new function g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then the new
function g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then the
new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)
vertically compressed by multiplying each of its y-coordinates by k.
* Lets solve the problem
∵ f(x) = sin(x)
∵ f(x) is stretching vertically by a factor of 4
∴ f(x) multiplied by 4
∵ f(x) is shifting 3 units to the right
∴ We will change x to (x - 3)
∵ The new function is g(x)
∴ g(x) = 4 sin(x - 3)
- The attached graph for more understand
f(x) is the red graph
g(x) is the blue graph
Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
The given function is:
f(x) = sin(x)
Stretching by a factor of 4:
A vertical stretch or compression of f(x) can be expressed as:
cf(x), where c is any constant
if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.
Since, given function is being stretched by a factor of 4, the transformed function will become:
4f(x)
Shifting by 3 units right:
A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:
f(x - 3)
Applying both the transformations to f(x), we get g(x) as:
g(x) = 4 f(x - 3)
g(x) = 4 sin(x - 3)
I've been having trouble in my lessons and I need a bit of help. If someone could explain how to do the problem, or work with me to solve it. Either would be amazing!
Given the function h(x) = 3(5)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Answer:
Sorry if this isnt helpful: Im just going off stuff i learned to see if this will help you at all. Im only in 7th so.. Sorry in advance!!
Step-by-step explanation:
To find the rate, you need to create a unit rate table thing, like this:
5/3 = ?/1 To do this, you would need to divide 5 by 3 and 3 by 3 to get y and x. You get: 1.666 continued. Rounded, about 1.7 . so your unit rate for part A is 1.7/1. You would do the same thing. 2/3 = ?/1. I will let you solve that :)))
Finished A! Now B:
To compare, we use the butterfly method! so 1.7/1 o ?1. cross multiply, and whichever number is bigger comes on top. Then you would explain why that number is bigger. BAM
Two trees have a bird on top of each. Distance between birdwatcher and first bird is 37 point 4 feet. Distance between each bird is 17 point 8 feet. Angle of depression between birdwatcher and first bird is unknown. a. 25.5° b. 64.5° c. 28.4° d. 61.6°
Answer:
64.5A
Step-by-step explanation:
Math help on questions #4 and #5
4. -3
5. 3
Step-by-step explanation:4. For x > -2, the value of a is the slope of the line. The line goes down 3 units for each 1 to the right, so the slope is -3/1 = -3. Then a = -3.
___
5. The ordered pair (h, k) is typically used to name the point to which a function is translated. The vertex of the function f(x) = |x| is (0, 0). When it is translated to (h, k), the function becomes ...
... q(x) = |x -h| +k
If the new vertex is (3, 0), then h = 3 and k = 0. This is consistent with the equation shown. (k = 0 means q(x) = |x -h|.)
Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M. On Tuesday What is the total number of hours she worked
Answer:
[tex]12\frac{1}{2}[/tex] hours.
Step-by-step explanation:
We have been given that Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M.
Let us find the number of hours between 8:00 am to 1:00 pm.
There are 4 hours between 8:00 am to 12 noon and 1 hour from noon to 1:00 pm. So the total number of hours between 8:00 am to 1:00 pm is 5 hours.
Now let us find total number of hours worked by Phyllis Doran by adding 7 1/2 and 5.
[tex]\text{The total number of hours Doran worked}=7\frac{1}{2}+5[/tex]
[tex]\text{The total number of hours Doran worked}=12\frac{1}{2}[/tex]
Therefore, the total number of hours worked by Phyllis Doran is [tex]12\frac{1}{2}[/tex] hours.
Please answer this question! 15 points and brainliest!
Answer:
-1< x< 3 x is an integer
Step-by-step explanation:
There are the dots on the number line. Three points are represented
x= 0,1,2
We want an inequality
-1< x< 3 x is an integer
Help me please Algebra Two!!
Answer:
a. -2, even mult. and 1, odd mult.
b.[tex](x+2)^2(x-1)[/tex]
c. Odd degree of 3 or higher, likely higher due to the turns in the graph.
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -2,1
We can write them in intercept or factored form as (x-1) and (x+2).
Because the graph never crosses the x-axis at x=-2 the zero has an even multiplicity of at least 2. The opposite is true for x=1 because it crosses. Therefore it has an odd multiplicity of at least 1.
The graph is a sideways s shape and ends up so is positive.
This means the function has a degree of 3 or higher with the degree being odd.
If triangle ABC is similar to triangle DEF, which statement is true about the two triangles?
A.)Segment AB is congruent to segment DE, and angles C and F are congruent.
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.
C.)Segment AB is congruent to segment DE, and angles C and F are proportional.
D.)Segment BC is proportional to segment EF, and angles A and D are proportional.
Answer:
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.Step-by-step explanation:
If ΔABC and ΔDEF are similar, then
AB is proportional to DE
BC is proportional to EF
CA is proportional to FD
and
angles A and D are congruent
angles B and E are congruent
angles C and F are congruent
Answer:
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.
Step-by-step explanation:
On Saturday, a local hamburger shop sold a combined total of 520 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer: 173
Step-by-step explanation: 173 x 3 = 519. 520-173 = 347
Which inequality corresponds with the graph?
A) x > -2
B) x < -2
C) x ≤ -2
D) x ≥ -2
Answer:
D
Step-by-step explanation:
An inequality is an expression which means more than one number is a solution. We graph the solutions on a number line to show all possible values. We graph using circles and arrows.
Equal to and less/greater than are graphed with filled in circles on the value.Only less/greater than (not equal to) are graphed with open (not filled in) circles on the value.We draw an arrow the direction the solutions satisfy the inequality. Generally this is the direction the inequality itself points.This is a filled in circle on -2 so this is [tex]\leq or \geq[/tex]. This means only answers C and D are options.
Answer D points to the right.
Answer:
The answer is D
Step-by-step explanation:
MrsStrong was correct!!!! Thank you
Which graph represents the polynomial function f(x)=x^3+3x^2-10x-24
[tex]f(x)=x^3+3x^2-10x-24\\\\y-intercept\ for\ x=0:\\\\f(0)=0^3+3(0)^2-10(0)-24=-24[/tex]
Answer:
The attached image shows he graph for given function.
Step-by-step explanation:
We are given the following expression in the question:
[tex]f(x) = x^3 + 3x^2-10x-24[/tex]
The zeroes of the given function can be calculated as:
[tex]x^3 + 3x^2-10x-24 = 0\\x = -4, x = -2, x=3[/tex]
Thus,the graph for the given function passes through the x-axis on the points (-4,0), (-2,0) and (3,0).
The function crosses the y-axis at the point (0,24)
The attached image shows the graph for given function.
Thus, the second option is the correct graph for given function.
Shemar tips at the rate of 75:5 waiters. How many waiters will he be tipping, if he can afford a $90 tip?
. Joan has a prescription for 100 Theophylline capsules. Joan informs the pharmacist that she only has enough money to purchase ¼ of the prescription today. How many capsules will Joan pay for today
100 * 4=
100*1/1*4=
100 / 4=
25
How do I check my answers to make sure it correct?
Answer:
25
Step-by-step explanation:
There are 100 capsules and she can only buy 1/4
Multiply 100 * 1/4
100 * 1/4 =
100/4
25
We can check by calculating how many she leaves at the store
100 * 3/4 =
300 /4 = 75
The ones she bought , plus the ones she left behind should be 100 capsules
25+ 75 = 100
100 = 100
Check
please help me with this question
Answer: 5, 3, [tex]\dfrac{1}{6}[/tex], D
Step-by-step explanation:
-5 < 0 so f(-5) = | -5 | = 5
-3 < 0 so f(-3) = | -3 | = 3
6 > 0 so f(6) = [tex]\dfrac{1}{6}[/tex]
graph D (since x can equal zero)
A plane flies at an average speed of 300 miles per hour the expreesion 300t gives the distance traveled by the plane in t hours find the distance traveled by the plane in 8 hours
What value in the replacement set is a solution to this equation? 3(n+7)=48 Replacement set: {8, 9, 10} Drag the solution into the box.
Answer:
n = 9 is the value in the replacement set is a solution to the equation [tex]3(n+7)=48[/tex]
Step-by-step explanation:
Given an equation: [tex]3(n+7)=48[/tex] .....[1]
Replacement set: {8, 9, 10}
For n = 8
Substitute in equation [1], we get;
[tex]3(8+7)=48[/tex]
[tex]3(15)=48[/tex]
[tex]45=48[/tex] False.
Similarly, For n = 9
Substitute in equation [1], we get;
[tex]3(9+7)=48[/tex]
[tex]3(16)=48[/tex]
[tex]48=48[/tex] True.
for n = 10
Substitute in equation [1], we get;
[tex]3(10+7)=48[/tex]
[tex]3(17)=48[/tex]
[tex]51=48[/tex] False.
Therefore, the value in the replacement set is a solution to this equation [tex]3(n+7)=48[/tex] is, 9
Answer:
9
Step-by-step explanation:
Help please answer this
Answer:i cant see it good
Step-by-step explanation:
Marvin has piece of chain that is 3_5 12 feet long. He uses 2 1_3 feet of the chain for his art project. How much chain does marvin have left? A 1__1 12 feet , B 1__2 12 feet , C 2__1 12 feet , D 2__2 12 feet
Answer:
The answer is A. 1 1/2
Step-by-step explanation:
You have 3 5/12 - 2 1/3
1/3 of 12 is 4.
So change 2 1/3 to 2 4/12
3 5/12 - 2 4/12 = 1 1/2
I hope this helps!
Cheers, July.
Find f(4) for f(x)=-1/2x+5
Answer:
HELLO :
f(4) = -1/2(4)+5 = -2+5=3
QUESTION 34
What is the variance of the following data? If necessary, round your answer to two decimal places.
82, 44, 67, 52, 120
QUESTION 35
What is the variance of the following data? If necessary, round your answer to two decimal places.
10, 12, 15, 18, 11, 13, 14, 16, 19, 20
QUESTION 36
What is the standard deviation of the following data? If necessary, round your answer to two decimal places.
100, 140, 130, 180, 80, 160
QUESTION 34
We want to find the variance of [tex]82,44,67,52,120[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]
[tex]\bar X =\frac{365}{5}[/tex]
[tex]\Rightarrow \bar X =73[/tex]
This means that,
[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]
This gives us,
[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]
[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]
[tex]\sigma^2=\frac{3608}{5}[/tex]
[tex]\sigma^2=721.6[/tex]
QUESTION 35
We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]
[tex]\bar X =\frac{148}{10}[/tex]
[tex]\fRightarrow \bar X =14.8[/tex]
This means that,
[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]
This gives us,
[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]
[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]
[tex]\sigma^2=\frac{105.6}{10}[/tex]
[tex]\sigma^2=10.56[/tex]
QUESTION 36
We want to find the variance of [tex]100,140,130,180,80,160[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]
[tex]\bar X =\frac{790}{6}[/tex]
[tex]\Rightarrow \bar X =131.67[/tex]
This means that,
[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]
This gives us,
[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]
[tex]\sigma^2=\frac{10325}{9}[/tex]
[tex]\sigma^2=1147.22[/tex]
To find the variance of a set of data, find the mean, subtract the mean from each data point, square the differences, and find the average of the squared differences. The standard deviation is the square root of the variance.
Explanation:To find the variance of a set of data, follow these steps:
Find the mean of the data.Subtract the mean from each data point and square the result.Find the average of the squared differences.For the data set 82, 44, 67, 52, 120 (Question 34), the mean is 73, the squared differences are 81, 841, 36, 441, and 1849, and the average of the squared differences is 631.20, rounding to two decimal places.
For the data set 10, 12, 15, 18, 11, 13, 14, 16, 19, 20 (Question 35), the mean is 14.8, the squared differences are 23.04, 4.84, 0.64, 8.84, 12.96, 3.24, 1.44, 2.56, 19.36, and 29.16, and the average of the squared differences is 10.10, rounding to two decimal places.
To find the standard deviation of a set of data, take the square root of the variance. For the data set 100, 140, 130, 180, 80, 160 (Question 36), the variance is 9300, and the standard deviation is 96.49, rounding to two decimal places.
Learn more about Variance and Standard Deviation here:https://brainly.com/question/29758680
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Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4
The x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.
To find the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4, we can use the slope formula:
slope = (change in y) / (change in x)
Given that the slope is -4 and the two points are (x, -9) and (0, 1), we can plug the values into the slope formula:
-4 = (-9 - 1) / (x - 0)
Now, simplify the equation:
-4 = -10 / x
Now, cross-multiply:
-4x = -10
Now, solve for x by dividing both sides by -4:
x = -10 / -4
x = 5/2
So, the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.
To know more about slope click here :
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In Ivy's neighborhood, 40% of the homes have a swimming pool. If there are 80 homes , how many have a pool
Answer:
32 houses will have a pool
Step-by-step explanation:
40% of 80 is 32
Find the perimeter of the regular parallelogram.
Answer:
Approx. 48 cm
Step-by-step explanation:
The two horizontal sides of this parallelogram have length 12 cm each.
The length of one slanting side can be estimated by (eye: the base of the triangle partially outlined with a dashed line is approx. 3 cm. Then, using the Pyth. Thm., we estimate the hypotenuse of this triangle to be
sqrt(3^2 + 10^2), or sqrt(109), which is approx. 10.45.
Thus, the estimated perimeter is
P = 2L + 2W, which, here, is
P = 2(12 cm) + 2(10.45 cm), or 44.9 cm.
The fourth answer, 48 cm, is the one closest to this estimated 44.9 cm.
The earth travels one full rotation around the sun 365.25. Ow many minutes does it take for the earth to travel one full rotation?
Given two events A and B of a sample set where P[A] = .20 P[not B] = .40 P[B|A] = .25 What is P[A or B]?
Answer:
Given two events A and B of a sample set :-
P[A] = 0.20
P[not B]=0.40
[tex]P[B/A]=0.25[/tex]
To find P[A or B]:
[tex]P[A or B] = P[A] + P[B] - P[A \cap B][/tex] ......[1]
Calculate for [tex]P[B][/tex] and [tex]P[A \cap B][/tex]
P[B] = 1- P[not B]
Substitute the value P[not B] we get;
P[B] = 1-0.40 = 0.60
[tex]P[A \cap B] = P[B/A] \cdot P[A][/tex]
Substitute the given values we get;
[tex]P[A \cap B] = 0.25 \cdot 0.20 = 0.05[/tex]
Then;
[tex]P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75[/tex]
Therefore, the value of P[A or B] is, 0.75.
The probability of P(A∪B) is 0.35.
ProbabilityProbability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
P(A) = 0.20
P(B) = 0.40
P(A∩B) = 0.25
To findThe probability of P(A∪B).
How to find the probability of P(A∪B)?We know the formula
P(A∪B) = P(A) + P(B) - (A∩B)
P(A∪B) = 0.20 + 0.40 - 0.25
P(A∪B) = 0.60 - 0.25
P(A∪B) = 0.35
Thus the probability of P(A∪B) is 0.35.
More about the probability link is given below.
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BRAINLIEST AND 60 POINTS!!!!!!!
1.) A coin is flipped. What is the theoretical probability that the coin lands on tails?
2.) A six sided number cube is rolled. What is the theoretical probability that a number greater than 4 is rolled?
3.) 2 six-sided number cubes are rolled. What is the theoretical probability that the sum of the number cubes is 8?
Answer:
1. P ( tails) = 1/2
2.P (number greater than 4) = 1/3
3. P (2 die sum to 8) = 5/36
Step-by-step explanation:
A coin only has 2 possibilities, head or tails, and they are equally likely
So the probability of getting a tails is 1/2
P ( tails) = 1/2
A die has the numbers 1,2,3,4,5,6 . There are 2 numbers greater than 4. They are 5 and 6. So there are 2 of the 6 choices that work.
P (number greater than 4) = 2/6 = 1/3
See the dice chart
There are 36 possibilities when you roll the die.
There are 5 that sum to 8
P (2 die sum to 8) = 5/36
Answer:
Guy above is correct
Step-by-step explanation: