Answers
[tex]y=4-x^2\\x-y=2 \\ \\ y = 4 - {x}^{2} \\ x = 2 + y \\ \\ y = 4 - {(2 + y)}^{2} \\ {y}^{2} + 5y = 0 \\ y(y + 5) = 0 \\ y = 0 \\ y = - 5[/tex]
[tex]x = 2 + 0 = 2[/tex]
[tex]x = 2 + ( - 5) = -3[/tex]
Related Questions
If the probability that it will rain tomorrow is 15, what is the probability that it will not rain tomorrow?
A .45
B .35
C .25
D .210
Answers
find two numbers that multiply to 17 and add to 18
Answers
Answer:
The numbers are 1 and 17
Step-by-step explanation:
The only factors of 17 are 1 and 17 since 17 is a prime number
1*17 =17
1+17 =18
The two numbers that multiply to 17 and add to 18 are 1 and 17.
To find two numbers that satisfy the conditions of multiplying to 17 and adding to 18, we can set up a system of equations based on these criteria.
Let the two numbers be x and y .
1. Set up the equations:
- [tex]\( xy = 17 \)[/tex] (product of the numbers)
- [tex]\( x + y = 18 \)[/tex] (sum of the numbers)
2. Solve the system of equations:
From x + y = 18, express y in terms of x :
[tex]\[ y = 18 - x \][/tex]
Substitute y = 18 - x into [tex]\( xy = 17 \)[/tex]:
[tex]\[ x(18 - x) = 17 \][/tex]
[tex]\[ 18x - x^2 = 17 \][/tex]
[tex]\[ x^2 - 18x + 17 = 0 \][/tex]
3. Find the roots of the quadratic equation:
Use the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where a = 1 , b = -18, and c = 17:
[tex]\[ x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4 \cdot 1 \cdot 17}}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{324 - 68}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{256}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm 16}{2} \][/tex]
So, [tex]\( x = \frac{34}{2} = 17 \)[/tex] or [tex]\( x = \frac{2}{2} = 1 \)[/tex].
4. Determine the corresponding y values:
- If x = 17, then [tex]\( y = 18 - 17 = 1 \)[/tex].
- If x = 1 , then [tex]\( y = 18 - 1 = 17 \)[/tex].
Therefore, the two numbers that multiply to 17 and add to 18 are 1 and 17.
The numbers 1 and 17 satisfy the conditions of multiplying to 17 and adding to 18, providing a clear solution based on the given criteria of the problem.
Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are:299.4 297.7 301.0 298.9 300.2 297.0Is this convincing evidence that the mean contents of cola bottles is less than the advertised300 ml? Test at the 5% significance level.
Answers
Answer:
No because there is sufficient statistical evidence to suggest that the mean contents of cola bottles is equal to 300 ml as advertised
Step-by-step explanation:
Here we have the measured contents as
299.4
297.7
301.0
298.9
300.2
297.0
Total = 1794.2
∴ Mean = 299.03
Standard deviation = 1.5
We have
[tex]z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]
Where:
[tex]\bar x[/tex] = Mean of sample = 299.03 ml
μ = Mean of population = 300 ml
σ = Standard deviation of population = 3 ml
n = Sample size = 6
α = 5% = 0.05
We set our null hypothesis as H₀ = 300 ml
Our alternative hypothesis is then Hₐ < 300 ml
Therefore, z = -0.792
The probability from z table is P = 0.2142
Since the P value, 0.2142 is > than the 5% significance level, 0.05 we accept the null hypothesis that the mean contents of cola bottles is 300 ml.
Identifying Characteristics of the Exponential Function y = bx (b > 1)
The domain of an exponential function is . The range of an exponential function is .
On a coordinate plane, the graph of y = 2 Superscript x is shown. The curve approaches the x-axis in quadrant 2 and then increases quickly into quadrant 1.
Answers
Answer:
domain (-∞, ∞)range (0, ∞)Step-by-step explanation:
The domain is the horizontal extent: all real numbers. -∞ < x < ∞.
The range is the vertical extent: all numbers greater than zero. 0 < y < ∞. (The graph never actually touches y=0, but comes arbitrarily close.)
For a research project on rodents, 60 groundhogs were tagged and released. Later, researchers
counted 700 groundhogs, 12 of which had tags. To the nearest whole number, what is the best
estimate for the groundhog population?
Answers
The estimated size of the lemur population can be calculated using the mark and recapture technique.
Explanation:The estimated size of the lemur population can be calculated using the mark and recapture technique. The formula to estimate population size is:
N = (M * C) / R
where N is the estimated population size, M is the number of marked individuals in the second capture, C is the total number of individuals in the second capture, and R is the number of marked individuals recaptured in the second capture.
In this case, the number of marked individuals in the second capture is 11, the total number of individuals in the second capture is 49, and the number of marked individuals recaptured is 11. Plugging these values into the formula:
N = (11 * 49) / 11 = 49
Rounding to the nearest whole number, the estimated size of the lemur population is 49.
Learn more about estimating population size using mark and recapture here:
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The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate of 12 cms/sec, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
Answers
Answer:
The volume of cone is increasing at a rate 1808.64 cubic cm per second.
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}[/tex]
Volume of cone =
[tex]V = \dfrac{1}{3}\pi r^2 h[/tex]
where r is the radius and h is the height of the cone.
Instant height = 9 cm
Instant radius = 6 cm
Rate of change of volume =
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})[/tex]
Putting values, we get,
[tex]\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}[/tex]
Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.
Final answer:
The volume of a cone can be found using the formula V = πr²h³. To find the rate at which the volume is increasing, we differentiate the volume formula with respect to time and substitute the given values into the derivative formula. The volume is increasing at a rate of 15552π cubic centimeters per second.
Explanation:
To find the rate at which the volume is increasing, we need to differentiate the volume formula with respect to time.
Let's differentiate the volume formula V = πr²h³ with respect to time t:
dV/dt = π(2rh³(dr/dt) + r²h²(dh/dt))
Given that dr/dt = dh/dt = 12 cm/sec, r = 6 cm, and h = 9 cm, we substitute these values into the derivative formula:
dV/dt = π(2(6)(9³)(12) + (6²)(9²)(12))
dV/dt = π(11664 + 3888)
dV/dt = 15552π
Therefore, the volume is increasing at a rate of 15552π cubic centimeters per second.
Is it A)50 degrees, B) 60 degrees C) 74 degrees or D) 78 degrees
Answers
What is the answer to this? I need help :(.
Answers
Answer:
Not proportional
Step-by-step explanation:
Hope it helps you in your learning process.
[tex] \frac{6}{6}=1\\\\
\frac{8}{24}= \frac{1}{3}\\\\
\frac{10}{50}= \frac{1}{5}\\\\
\frac{12}{84}= \frac{1}{7}\\\\
\therefore \frac{6}{6}\neq \frac{8}{24}\neq \frac{10}{50}\neq \frac{12}{84}[/tex]
Hence, given ratios are not proportional.
Which animal shelter has the dog that weighs the least?
A)- shelter A
B)- shelter B
C)- Both shelters have a dog with the lowest weight of 8 pounds.
D)- Both shelters have a dog with the lowest weight of 10 pounds.
WILL GIVE BRAINLIEST ANSWER IF YOU ANSWER RIGHT!!!
Answers
Answer:
A_A_A_A_A_A_A_A_A_A_A_A_A_A_Step-by-step explanation:
on the box chart it shows that shelter A has the lightest dog
hope i helped :D
Answer:
shelter A. shelter B. Both shelters have a dog with the lowest weight of 8 pounds.
Step-by-step explanation:
Hope this helps :)
Which one is bigger 4.5 kg or 4.050
Answers
Answer:
4.5 kg
Step-by-step explanation: if you have 4.050 take off the zero and it is only 4.05 which is less then 4.5 or 4.50
Final answer:
When comparing 4.5 kg to 4.050 kg, 4.5 kg is the larger weight since both are in kilograms and 4.5 is greater than 4.050.
Explanation:
The question asks which number is larger, 4.5 kg or 4.050 kg. In the metric system, weights are compared directly as they are expressed in the same units. Here, we compare 4.5 to 4.050. Since 4.5 can also be thought of as 4.500 when considering the decimal places, it becomes clear that 4.5 kg is the larger value because both represent kilograms, and 4.5 is greater than 4.050.
For five days, several hikers walk the distance and direction described by the vector
⟨5, –2⟩ each day. The next day, they walk the distance and direction described by the vector ⟨–1, 8⟩. At the end of the six-day trip, what is their bearing from their starting location?
Answers
Answer:
94.76°
Step-by-step explanation:
Assuming the coordinates are <E, N>, the total distance from the start is ...
5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>
These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...
arctan(24/2) = 85.24°
The bearing is 180° -85.24° = 94.76°.
what does x equal in this equation x−9.37+5.77=1.3x
Answers
Answer:
-12
Step-by-step explanation:
x-9.37+5.77=1.3x
(3x+5) is a factor of the polynomial (a-1)x^3 + (a+1)x^2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorize the given expression completely.
Answers
Answer:
(3x + 5)(x + √3)(x - √3)
Answer:
a = 4
Step-by-step explanation:
(3x+5) is a factor of the polynomial (a-1)x³ + (a+1)x² - (2a + 1)x - 15
Means x = -5/3 is a root
(a-1)(-5/3)³ + (a+1)(-5/3)² - (2a + 1)(-5/3) - 15 = 0
-125a/27 + 125/27 + 25a/9 + 25/9 + 10a/3 + 5/3 - 15 = 0
a(-125/27 + 25/9 + 10/3) = 15 - 5/3 - 25/9 - 125/27
a(40/27) = 160/27
a = 4
find an angle in the normal range (0 degrees to 360 degrees, or 0 to 2pi radians) whose terminal side points in the same direction as the terminal side of an angle measuring -11pi/3.
Answers
Answer:
a) pi/3
Step-by-step explanation:
-11pi/3 + 4pi
(-11+12)pi/3
pi/3
Answer:
A
Step-by-step explanation:
We see that the angle is -11[tex]\pi[/tex]/3, which means that when drawing this angle on the graph, we need to move clockwise from 0 (see the drawing).
We see that this angle is actually the exact same as an angle in the first quadrant. This angle is [tex]\pi[/tex]/3.
Thus, the answer is A.
Hope this helps!
A box of cereal has a volume of 336 cubic inches. If the width of the box is 4 inches and the length is 7 inches, what is the height of the box
I'm confused
Answers
Answer:
12 inches
Step-by-step explanation:
Volume = length × width × height
336 = 4 × 7 × height
height = 12
Answer:
12 cubic inches.
Step-by-step explanation:
Since volume is length x width x height, you just do 7 x 4 (28) and then the total, 336 and divide that by 28. So, 12 cubic inches!
Which lists the steps in the correct order to find the median of this data set?
24, 16, 23, 30, 18, 29
Answers
Answer:
23.5
Step-by-step explanation:
you put it in order and find the middle in this case is 23 and 24 then you add them and divide by two and get 23.5
The number of pupils in school A is equal to half the number of pupils in school B. The ratio of the boys in school A and the boys in school B is 1:3 and the ratio of the girls in school A and the girls in school B is 3:5. The number of boys in school B is 200 higher than the number of boys in school A. Find the number of boys and girls in each school.
Answers
Answer:
There are 100 boys and 300 girls in School A and there are 300 boys and 500 girls in School B .
Step-by-step explanation:
The ratio of the boys in school A and the boys in school B is 1:3
Let the ratio be x
No. of boys in School A = x
No. of boys in School B = 3x
We are given that The number of boys in school B is 200 higher than the number of boys in school A.
So,[tex]x+200=3x[/tex]
[tex]200=3x-x[/tex]
[tex]200=2x[/tex]
[tex]\frac{200}{2}=x[/tex]
100=x
So, No. of boys in School A = x = 100
No. of boys in School B = 3x =3(100)=300
We are given that the ratio of the girls in school A and the girls in school B is 3:5.
Let the ratio be y
So, No. of girls in School A = 3y
No. of girls in School B = 5y
So, Total No. of students in School A= No. of boys in school A + No. of girls in school A=100+3y
Total No. of students in School B= No. of boys in school B + No. of girls in school B=300+5y
We are given that The number of pupils in school A is equal to half the number of pupils in school B.
So, [tex]100+3y=\frac{1}{2}(300+5y)[/tex]
[tex]200+6y=300+5y[/tex]
[tex]y=100[/tex]
No. of girls in School A = 3y=3(100)=300
No. of girls in School B = 5y=5(100)=500
Hence there are 100 boys and 300 girls in School A and there are 300 boys and 500 girls in School B .
Answer: 100 boys, 300 girls in School A. 300 boys,500 girls in School B
Step-by-step explanation:
Use properties of rational number to simplify the expression.
A.)129/7
B.)262/15
C.)122/7
D.)507/28
Answers
Answer:
A.)129/7
Step-by-step explanation:
25/4 + 24/7 + 35/4
I will add the two with common denominator together first
25/4 + 35/4 +24/7
60/4 +24/7
15 + 24/7
We need to get a common denominator of 7
15 *7/7 + 24/7
105/7 + 24/7
129/7
hellplppppppp800x40÷80=
Answers
Answer:
400
Step-by-step explanation:
Answer:
800*400/80=400
Step-by-step explanation:
To work this out you would first start with 40/80. This is because when using BODMAS / BIDMAS you would start with whatever operation that comes first out of all the operations in the question. This gives you 0.5. Then you would multiply 0.5 by 800, this gives you 400.
1) Find what operation you should do first.
B- Brackets
O -Orders
D-Division
M-Multiplication
A-Addition
S-Subtraction
2) Divide 40 by 80.
[tex]40/80=0.5[/tex]
3) Multiply 0.5 by 800.
[tex]0.5*800=400[/tex]
We have 2 stacks or styrofoam cups one has 6cups and it's height is 15cm.The other stack has 12cups and Height is 23cm. How many cups are needed for a stack with the height of 50cm?
Answers
Answer:
Given
Number of stacks = 2
Stack 1 = 6 cups; h1 = 15cm
Stack 2 = 12 cups; h2 = 23cm
Let's first find the average:
[tex] \frac{H_1 - H_2}{ n_1 - n_2}[/tex]
[tex]= \frac{15-23}{6-12} [/tex]
[tex] = \frac{-8}{-6} = \frac{4}{3} [/tex]
With an average of 4/3, to obtain the number of cups needed to obtain a height of 50m, we have:
50 / (4/3)
= 50 * 3/4
= 150/4
= 37.5
From the answer, we can see that the number of cups is not really proportional to the height of the stack, because the average of stack one and stack 2 are different.
Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 240 students and recorded how long it took each of them to find a parking spot. Identify the population of interest to the university administration.
Answers
Answer:
In this particular case,the target population of interest to the university administration constitutes the university students.Step-by-step explanation:
The university administration is interested to conduct a statistical study to identify the average or mean time taken by the students to find a vacant parking spot.Therefore,the research topic here is the average time taken by the university students to find parking spot. The administrator collects an inconspicuous sample of 240 samples from the target population of the study,which is the overall student population of the university.The sample collected by the university administration is used to observe the average or mean parking time by the university students.To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52). The order in which the selections is made does not matter. How many different 6-number selections are possible?
Answers
Answer:
The answer is 20,358,520
Step-by-step explanation:
Selecting 6 numbers from a collection of 52 numbers regardless of order involves a combination.
Note: if regards was taken into order of selection, this would be a permutation.
Hence, the different 6 number selections out of 52 is
52C6 = 52! / [6!*(52-6)!]
= 52!/(6!*46!)
= 20,358,520
At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean.Which of the following conditions for inference have not been met?1. The data are collected using a random sampling method.2. The sample size is large enough to assume normality of the distribution of sample means.3. The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III
Answers
Population distribution is probability distribution that measures the frequency of sample provided. For the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.
Given-Total students 500.
Total students surveyed by the counselor is 20.
Population distribution
Population distribution is probability distribution that measures the frequency of sample provided.
I)The data are collected using a random sampling method- All the students surveyed by the counselor is 20 is collected using a random sampling method. Hence the condition I is met for the inference.II) The sample size is large enough to assume normality of the distribution of sample means- The sample size for the given problem is 20. For a large population the sample size must equal to or greater than the 30.Hence the condition II is not met for the inference.III)The sample size is less than 10 percent of the population size- We have total student 500. The 10 percent of the population size is,[tex]P=\dfrac{10\times500}{100}[/tex]
[tex]P=50[/tex]
Here the 10 percent of the population size is 50. Our sample size is 20. Thus the sample size is less than 10 percent of the population size.Hence the condition III is met for the inference.
Hence, for the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.
For more about the population distribution follow the link below-
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Charlie has 7 cards, numbered 2, 3, 4, 5, 6, 7, 8, 9. What is the probability of picking an odd card? Give your answer as a fraction, a decimal, and a percent. Round to the nearest hundredth.
Answers
There are 4 out of the 7 cards that are odd numbers.
As a fraction: 4/7
As a percent: 57.14%
As a decimal: 0.57
Marta and Kim are sisters. Five years ago Kim's age was twice as great as martas age. If Marta is no m years old, what expression represents Kim's age now?
Answers
Answer:
y = 2m-5
Kim's age now is y = 2m-5
Step-by-step explanation:
Let m represent martas age now and y represent Kim's age now
Given;
Five years ago Kim's age was twice as great as martas age.
(y-5) = 2(m-5)
Solving for y;
y-5 = 2m-10
y = 2m-10+5
y = 2m-5
Kim's age now is y = 2m-5
Final answer:
Kim's current age is represented by the expression 2m - 5, where m is Marta's current age. This is determined by considering the age difference and relationship of their ages five years ago.
Explanation:
The question is about determining Kim's current age given that Marta is currently m years old and five years ago Kim's age was twice that of Marta's. To solve this, we can follow these steps:
Let's represent Marta's age five years ago as m - 5.
Since Kim's age was twice Marta's age five years ago, we express Kim's age at that time as 2(m - 5).
To find Kim's current age, we add five years to her age at that time: 2(m - 5) + 5.
Simplifying the expression gives us Kim's current age as 2m - 5.
Therefore, the expression that represents Kim's age now, given that Marta is m years old, is 2m - 5.
Can someone help solve for X
Answers
Answer:
x = 2sqrt(5)
Step-by-step explanation:
We can use the Pythagorean theorem to solve
The legs are x and 8/2 =4
and the hypotenuse is 6
a^2 + b^2 = c^2
x^2 +4^2 = 6^2
x^2 +16 = 36
Subtract 16 from each side
x^2 +16-16=36-16
x^2 = 20
Take the square root of each side
sqrt(x^2) = sqrt(20)
x = sqrt(4*5)
x = sqrt(4) sqrt(5)
x = 2sqrt(5)
Answer:
Step-by-step explanation:
x² +10x+3=0
how do I slove it with the quadratic formula?
Answers
Answer:
Step-by-step explanation:
The equation is already in standard form [ ax² + bx + c = y ] so we can find the values of each variable.
a = 1
b = 10
c = 3
y = 0
Quadratic formula: [tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Solve using the formula:
[tex]x=\frac{-10+-\sqrt{10^2-4(1)(3)} }{2(1)}[/tex]
[tex]x=\frac{-10+-\sqrt{100 - 12} }{2}[/tex]
[tex]x=\frac{-10+-\sqrt{88} }{2}[/tex]
[tex]x=-5+-\sqrt{22}[/tex]
Therefore, the answer is [ x = -5 ± √22 ]
Best of Luck!
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether NL is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can NL be best described as?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answers
Answer:
You right in this one.
Step-by-step explanation:
Answer:
D) secant
Step-by-step explanation:
NL doesn't pass through the centre, so not radius or diameter
Passes through two points on the circle so not a tangent
Extends to a point outside the circle, so not a chord
Really need to know this for math!
Which number represents 10. Helpful if you answer all the rest ASAP
Answers
Answer:
I had to look up the problem B4 because your image doesn't show the rest of the information
B4 = 12
B5 = 1,738
Step-by-step explanation:
if you need help on any other questions on this, i can't see them in the image
Ryan charges his neighbors $17.50 to wash their car. How many cars must he wash next summer if his goal is to earn at least $1,500?
Answers
Answer:
86 cars
Step-by-step explanation:
1,500/17.50=85.71 so you just round it a little
He must wash 86 cars.
What is division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. It is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.
Example: 4 / 2 = 2.
Given, Ryan charges his neighbors $17.50 to wash their car.
So, he earns $17.50 per car.
Let Ryan washes x cars to earn $1500
$17.50(x)=$1500
x = $1500/$17.50
x = 85.71 ≈ 86
Hence, Ryan needs to wash 86 cars to earn at least $1500.
Learn more about division:
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