Each point is of the form (x,y). We replace x with some number to get a paired y value.
For instance, if x = 1, then,
\(y = \sqrt{5-x}\\\\y = \sqrt{5-1}\\\\y = \sqrt{4}\\\\y = 2\)
Meaning x = 1 and y = 2 pair up. The point (x,y) = (1,2) is on the curve.
Then let's try x = 4
\(y = \sqrt{5-x}\\\\y = \sqrt{5-4}\\\\y = \sqrt{1}\\\\y = 1\)
Showing (4,1) is also on the curve.
The point (5,0) is also on the curve too because of the steps below
\(y = \sqrt{5-x}\\\\y = \sqrt{5-5}\\\\y = \sqrt{0}\\\\y = 0\)
We can't go any higher than x = 5 or else the expression 5-x will be negative. Eg: if x = 7, then 5-x = 5-7 = -2. We cannot take the square root of a negative and get some real number output.
So let's go in the opposite direction. Let's try x = -4
\(y = \sqrt{5-x}\\\\y = \sqrt{5-(-4)}\\\\y=\sqrt{5+4}\\\\y = \sqrt{9}\\\\y = 3\)
Showing (-4,3) is also on the curve.
The x values I'm picking are such that the y value is an integer. For the majority of the x values, you'll get some decimal value which is a bit tricky to graph on paper. So effectively you'll have to use trial and error to find the right x values to pick. The goal is to get the stuff under the square root to simplify to some perfect square (0,1,4,9,...etc)
After generating enough points, you draw a curve through them all. The more points, the more accurate the graph.
Homework: Section 11.1 Question 7. Complete the square to find the x-intercepts of the function given by the equation listed. f(x)=x² +34x+104 What are the x-intercepts? **** (Simplify your answer. T
Answer:
x² + 34x + 104 = 0
x² + 34x = -104
x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²
x² + 34x + 17² = -104 + 17²
x² + 34x + 289 = 185
(x + 17)² = 185
x + 17 = +√185
x = -17 + √185
use the method of undetermined coefficients to set up the 5 × 5 vandermonde system that would determine a fourth-order accurate finite difference approximation to u 00(x) based on 5 equally spaced points,
The fourth-order accurate finite difference approximation is:
u00(x) = c−2u(x − 2h) + c−1u(x − h) + c0u(x) + c1u(x + h) + c2u(x + 2h) + O(h4).
Compute the coefficients using the matlab code fdstencil.m and check that they satisfy the system you determined in part (a).
Test this finite difference formula to approximate u
00(1) for u(x) = sin(2x) with values of h from the array hvals = log space(-1, -4, 13). Make a table of the error vs. h for several values of h and compare against the predicted error from the leading term of the expression printed by fdstencils.
You should observe the predicted accuracy for larger values of h. For smaller values, numerical cancellation in computing the linear combination of u values impacts the accuracy observed.
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Work out
(3 × 10^−3)−(6 × 10^−5)
Give your answer in standard form.
Answer:
answer is
\( {2.94 \times 10}^{ - 3} \)
Step-by-step explanation:
3*1/1000-6*1/100000=0.003-0.00006
=
\( {2.94 \times 10}^{ - 3} \)
Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value of p
Answer:
p = 7
Step-by-step explanation:
(x² + px - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor, that is
x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms
= 3x³ +x²(3p - 5) - x(5p + 9) + 15
given the coefficient of the x- term is - 44 , then
-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion
- 5p - 9 = - 44 ( add 9 to both sides )
- 5p = - 35 ( divide both sides by - 5 )
p = 7
Two cars started a journey on the same road from opposite starting points. The speed of the first car is 120 km/h and the speed of the other car is 60 km/h. If it takes the first car 9 hours to cover half the distance, how long will it take the second car to cover the same distance?
It will take the second car 36 hours to cover the same distance.
Let's call the distance between the starting points of the two cars "D". Since the cars are moving toward each other, their combined speed is the sum of their individual speeds. Therefore, the combined speed of the two cars is:
120 km/h + 60 km/h = 180 km/h
If it takes the first car 9 hours to cover half the distance (D/2), then we can use the formula for speed, distance, and time:
distance = speed x time
D/2 = 120 km/h x 9 h
D/2 = 1080 km
Multiplying both sides by 2, we get:
D = 2160 km
Now we know that the distance between the starting points is 2160 km. To find out how long it will take the second car to cover the same distance at 60 km/h, we can use the same formula:
distance = speed x time
2160 km = 60 km/h x time
time = 2160 km / 60 km/h
time = 36 hours
Therefore, it will take the second car 36 hours to cover the same distance.
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HELP, WILL GIVE BRAINLEST..
Factor the GCF: -6x³y + 9x²y2 - 12xy³ (5 points)
O 3xy(-2x² + 3xy - 4y²)
O-3xy(2x² + 3xy - 4y²)
O-3xy(2x2-3xy + 4y²)
O-3(2x³y - 3x²y² + 4xy³)
Answer:
\(\sf -3xy\left(2x^2-3xy+4y^2\right)\)
Step-by-step explanation:
\(\sf -6x^3y+9x^2y^2-12xy^3\)
To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-
\(\boxed{\sf a^{b+c}=a^ba^c}\)
\(\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}\)
\(\sf -6xx^2y+9xxyy-12xyy^2\)
Rewrite,
-6 as 2 * 39 as 3 * 3-12 as 4 * 3\(\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2\)
Now, factor out the common term \(\sf -3xy\):-
\(\sf -3xy\left(2x^2-3xy+4y^2\right)\)__________________________
Find the measurement of PQ. Assume the drawings are not drawn to scale
Answer:
25.7 cm
Step-by-step explanation:
Determine the area of the rectangle at the bottom of the rectangular prism(height 15 cm,length 5 cm ,width 2 cm
the answer is 10 cm
Step-by-step explanation:
area= L×H
5×2
Ms. Lane teaches two sections of math class. Below are the results of a pop quiz she gave each section. Which section’s data shows the most variability?
A. Section B; the maximum number of students scored 9.
B. Section A; the maximum number of students scored 6
C. Section B; students in this section scored between 1 and 9
D. Section A; students in this section scored between 1 and 10
Answer:
D. Section A; students in this section scored between 1 and 10
Step-by-step explanation:
This answer is correct because the graph shows everything that was explained in the answer. Hope that helps!!
6.12*10+8.325*10 i literally can't do this can someone please help
One side of a square is 3x + 2. Which expression represents the perimeter?
_____________________________
(A) 2(3x+2)
(B) (3x+2)²
(C) 4(3x+2)
Answer:
C. 4(3x+2)
Step-by-step explanation:
Each side of a square is equal to each other, so the perimeter would be 4*(3x+2).
Perimeter is 25 cm, find x 10 8.2 cm
How can i learned maths hardly?
Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.
Some tips that may help you learn maths quickly and efficientlyStart with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.
Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.
Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.
Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.
Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.
Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.
Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.
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The following is an empirical expression used sometimes to represent the temperaturedependent heat capacity of substances: c
p
=a+bT+
T
2
c
in JK
−1
Calculate the ΔH for aluminum when it is heated from 0.0
∘
C to 100.0
∘
C, if the coefficients are a=20.68JK
−1
mol
−1
,b=12.38×10
−3
JK
−2
mol
−1
, and c=0
The ΔH (enthalpy change) for aluminum when it is heated from 0.0°C to 100.0°C is 2074.19 J.
The expression given for the temperature-dependent heat capacity of a substance is:
c_p = a + bT + cT^2
where c_p is the heat capacity in J/K, T is the temperature in °C, and a, b, and c are coefficients.
To calculate the ΔH (enthalpy change) for aluminum when it is heated from 0.0°C to 100.0°C, we need to integrate the heat capacity expression with respect to temperature over the given temperature range.
ΔH = ∫(c_p dT)
First, let's substitute the given coefficients into the expression:
c_p = 20.68 + (12.38×10^-3)T + 0
Next, we integrate the expression over the temperature range of 0.0°C to 100.0°C:
ΔH = ∫[20.68 + (12.38×10^-3)T] dT
Integrating with respect to T gives:
ΔH = 20.68T + (12.38×10^-3)(T^2/2)
To evaluate the integral, we substitute the upper and lower temperature limits:
ΔH = 20.68(100.0) + (12.38×10^-3)((100.0)^2/2) - [20.68(0.0) + (12.38×10^-3)((0.0)^2/2)]
Simplifying the equation gives:
ΔH = 2068 + 6.19
ΔH = 2074.19 J
Therefore, the enthalpy change (ΔH) for aluminum when it is heated from 0.0°C to 100.0°C is 2074.19 J.
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2 is what percent of 50?
Write your answer using a percent sign (%).
Pls help
Answer:
4%
Step-by-step explanation:
Divide 2 by 50
2 / 50 = 0.04
0.04 x 100 = 4%
Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. Note the equations of the two cylinders could be the following x2+y2=r2,y2+z2=r2 which their axes are at right angles to each other. To solve the volume we will be using the triple integrals formula in rectangular coordinates which is V=∫∫∫dzdydx
The total volume of the two circular cylinders intersecting perpendicularly is\(V=πr2+πr3=πr2(1+r)\).
The volume of the two circular cylinders intersecting perpendicularly can be calculated using the triple integral formula in rectangular coordinates. The triple integral formula is V=∫∫∫dzdydx.
We can separate the integral into three components. The x-component is ∫dx from \(-√r2-y2 to √r2-y2\). The y-component is ∫dy from -r to r. The z-component is ∫dz from 0 to r.
Substituting the components into the equation for the triple integral, we get \(V=∫-rrdr∫-√r2-y2√r2-y2dx∫0rdz\).
We can solve the integral by splitting the y-component into two pieces:
\(V=∫-rrdr∫-r0dx∫0rdz+∫-rrdr∫0√r2-y2dx∫0rdz\)
The first integral can be solved easily and yields V=πr2. The second integral can be solved using the substitution u=r2-y2 and yields V=πr3.
Hence, the total volume of the two circular cylinders intersecting perpendicularly is V=πr2+πr3=πr2(1+r).
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What is the distance between the following points?
Answer:
\(\sqrt{85}\) or 9.21954
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
\(d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }\)
d = distance
\((x_{1}, y_{1})\) = coordinates of the first point
\((x_{2}, y_{2})\) = coordinates of the second point
hellppp meeeeee......
Angle 4 and 7= Interior angles
Angle 12 and 16= Corresponding angles
Angle 1 and 14= Alternate exterior angles
Angle 5 and 10=Alternate angles
angle 6 and 7 are alternate angles I think.
Who can access your credit report? a. Friends b. Employers c. Neighbors d. Teachers.
Employers can use your credit report for the purpose of getting information. Then the correct option is B.
What is decision-making?The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.
Employers can access your credit score or report. However, depending on the state you live in, it may be able to pull a credit score, or at least a modified version. The pulled score by your employer likely will not include your number or date of birth, but it does not pose a security risk for you.
a. Friends - They can not use your credit report.
b. Employers - They can use your credit report.
c. Neighbors - They can not use your credit report.
d. Teachers - They can not use your credit report.
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In a survey of 1094 adults, 83% responded "yes" to the survey question.
How many adults answered "yes"? (round to the nearest whole person as needed)
Answer:
Pretty sure its 909. 83 percent of 1093 is 908.02. If you round it to the nearest person, it is 909
Step-by-step explanation:
In survey of 3005 randomly selected adults aged 57 through 85 years old, it was found that 2455 used at least one prescribed medication. a) Find the sample proportion p-hat as a percentage to 1 decimal place. b) Find the 90% confidence interval that estimates the percentage of adults aged 57 through 85 who use at least one prescribed medication. Answer as percentages to 1 decimal place. to
a) To find the sample proportion, we divide the number of adults who use at least one prescribed medication (2455) by the total number of adults surveyed (3005):
Sample proportion (p-hat) = 2455/3005 ≈ 0.816 (rounded to three decimal places)
To express it as a percentage, we multiply by 100:
Sample proportion (p-hat) = 0.816 * 100 ≈ 81.6% (rounded to one decimal place)
Therefore, the sample proportion is approximately 81.6%.
b) To find the 90% confidence interval, we can use the formula for the confidence interval of a proportion. The formula is:
CI = p-hat ± z * sqrt((p-hat * (1 - p-hat)) / n)
Where:
p-hat is the sample proportion,
z is the z-score corresponding to the desired confidence level (90% in this case),
sqrt represents the square root,
and n is the sample size.
Since we want a 90% confidence interval, the z-score corresponding to a 90% confidence level is approximately 1.645.
Plugging in the values:
CI = 0.816 ± 1.645 * sqrt((0.816 * (1 - 0.816)) / 3005)
Calculating the expression inside the square root:
sqrt((0.816 * (1 - 0.816)) / 3005) ≈ 0.007
Plugging it back into the confidence interval formula:
CI = 0.816 ± 1.645 * 0.007
Calculating the product:
1.645 * 0.007 ≈ 0.011
Finally, the confidence interval is:
CI = 0.816 ± 0.011
Expressing it as percentages:
Lower bound = (0.816 - 0.011) * 100 ≈ 80.5%
Upper bound = (0.816 + 0.011) * 100 ≈ 82.7%
Therefore, the 90% confidence interval that estimates the percentage of adults aged 57 through 85 who use at least one prescribed medication is approximately 80.5% to 82.7%.
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Will give brainliest to correct answer
Answer:
30 lamps
Step-by-step explanation:
30*2= 60
PLEASE ANYONE HEEELLLLPP.......I NEED HELP I DONT UNDERSTAND!!!
Answer:
\(\large \boxed{\mathrm{Option \ 4}}\)
Step-by-step explanation:
The area has to be found for the floor.
The whole rectangle = length × width = x × (x-4), has an area of x(x-4).
The area x(x-4) has to be subtracted from the area of the stage and closet.
Area of stage = area of triangle : base × height × 1/2
(x-4) × 8 × 1/2
(0.5) × (8) × (x-4)
Area of closet = area of rectangle : length × width
(3) × (7)
The area of the floor = x(x-4) - 0.5(8)(x-4) - 3(7)
Answer:
i don’t understand it either
Step-by-step explanation:
20 POINTS!!!!!!!
pic shown below :)
Answer:
16,849,464 ft³
Step-by-step explanation:
subtract the two volumes of the pyramids.
A nurse has an annual income of $52, 175. The income tax that she must pay is 9%. How much does she have to pay in taxes in dollars and cents?
ответ на картинке !!!!
due now pls help!!!!!!!!!!!
Answer:
A and D
Step-by-step explanation:
so sorry im in school
x+y=4
-y. -y
x=4-y
4-y-y=2
4-2y=2
-4 -4
-2y= -2
/-2. /-2
y=1
x+1=4
-1 -1
x=3
so A and D is correct
what is the value of x
Answer:
Step-by-step explanation:
Figure it out yourself
I dont under stand how i am supposed to answer
Let f(x)=x^4 and g(x)=x+2 . Find (fg)(x) and (f/g)(x) .
The value for the functions (fg)(x) and (f/g)(x) are \(x^5 + 2x^4\) and \(\frac{x^4}{(x+2)}\) respectively.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To find (fg)(x), we simply need to multiply the two functions f(x) and g(x) -
(fg)(x) = f(x) × g(x)
\(= x^4 \times (x+2)\)
\(= x^5 + 2x^4\)
Therefore, (fg)(x) = \(x^5 + 2x^4\).
To find (f/g)(x), we divide the function f(x) by the function g(x) -
(f/g)(x) = f(x) / g(x)
= \(\frac{x^4}{(x+2)}\)
We cannot simplify this expression any further, so this is our final answer for (f/g)(x).
Therefore, (f/g)(x) = \(\frac{x^4}{(x+2)}\).
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NEED HELP ASAP *picture included* what percent of the area underneath this normal curve is shaded?
Answer:
68.26
Step-by-step explanation:
The symbol σ represents standard deviation. 1 standard deviation (in both directions) under a normal distribution= 68.26
Answer:
68%.
Step-by-step explanation:
The 68-95-99.7 rule (also know as the Empirical Rule) states that 68% of the data lies within 1 standard deviation of the mean. 95% of the data lies within 2 standard deviations of the mean. 99.7% of the data lies within 3 standard deviations of the mean.
According to the diagram, the area shaded shows data within 1 standard deviation of the mean (one standard deviation to the left, and one to the right). That means that 68% of the data is within the shaded area.
Hope this helps!