Answer:
hii baby
how are you
can you be my friend
Which of the following is/are the solution(s) for ‘x’ in the equation:
x^2 = 256
Answer:
16, sqrt 256
Step-by-step explanation:
Answer: it's 16
Step-by-step explanation:
Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5
The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.
To convert the given equation from standard form to vertex form, we need to complete the square.
The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.
Given equation: y = x² - 6x + 14
Move the constant term to the right side:
y - 14 = x² - 6x
Complete the square by adding and subtracting the square of half the coefficient of x:
y - 14 + 9 = x² - 6x + 9 - 9
Group the terms and factor the quadratic:
(y - 5) = (x² - 6x + 9) - 9
Rewrite the quadratic as a perfect square:
(y - 5) = (x - 3)² - 9
Simplify the equation:
y - 5 = (x - 3)² - 9
Move the constant term to the right side:
y = (x - 3)² - 9 + 5
Combine the constants:
y = (x - 3)² - 4
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A $5600 deposit for 45 years at a simple interest rate of 3%
Answer:
13,160
Step-by-step explanation:
\(si \: = \frac{pnr}{100} \)
P = principle amount
n = no.of years
r = rate(%)
\( = \frac{5600 \times 45 \times 3}{100} \)
= 56 × 45× 3
= 7560
The final answer is 5600 + 7560 = 13160
pls like and mark as brainliest if it helped!
(q5) Which of the following is the area of the surface obtained by rotating the curve
, about the x-axis?
The given curve is y = x³ − 2x and it has to be rotated about the x-axis to find the area of the surface. The formula to find the surface area of a curve obtained by rotating about the x-axis is given by:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx
$$Differentiating the curve with respect to x, we get:$$
y = x^3 - 2x
$$$$
\frac{dy}{dx} = 3x^2 - 2$$Now, squaring it, we get:$$
\left(\frac{dy}{dx}\right)^2 = 9x^4 - 12x^2 + 4$$$$
1 + \left(\frac{dy}{dx}\right)^2 = 1 + 9x^4 - 12x^2 + 4$$$$
= 9x^4 - 12x^2 + 5$$Putting the values in the formula, we get:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 12x^2 + 5} dx$$Simplifying it further, we get:$$
A = 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{(3x^2 - 1)^2 + 4} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 6x^2 + 5} dx$$Now, substituting $9x^4 - 6x^2 + 5 = t^2$, we get:$$(18x^3 - 12x)dx = tdt$$$$
(3x^2 - 2)dx = \frac{tdt}{3}$$When $x = -1$, $t = \sqrt{20}$ and when $x = 2$, $t = 5\sqrt{5}$Substituting the values in the formula, we get:$$
A = 2\pi \int_{\sqrt{20}}^{5\sqrt{5}} \frac{t^2}{27} dt$$$$
= \frac{28\pi}{27} \left[ t^3 \right]_{\sqrt{20}}^{5\sqrt{5}}$$$$
= \frac{28\pi}{27} \left[ 125\sqrt{5} - 20\sqrt{20} - 5\sqrt{5} + 2\sqrt{20} \right]$$$$
= \frac{28\pi}{27} \left[ 120\sqrt{5} - 18\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 9\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 18\sqrt{5} \right]$$$$
= \frac{56\pi}{27} \cdot 12\sqrt{5}$$$$
= \boxed{224\sqrt{5}\pi/3}$$Therefore, the area of the surface obtained by rotating the curve $y = x^3 - 2x$ about the x-axis is $\boxed{224\sqrt{5}\pi/3}$.
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The total area of the regions between the curves is 1.134π square units
Calculating the total area of the regions between the curvesFrom the question, we have the following parameters that can be used in our computation:
x = ∛y
We have the interval to be
0 ≤ y ≤ 1
The area of the regions between the curves is then calculated using
\(A =2\pi \int\limits^a_b {f(x) * \sqrt{1 + (dy/dx)^2} } \, dx\)
From x = ∛y, we have
y = x³
Differentiate
dy/dx = 3x²
So, the area becomes
\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + (3x^2)^2} } \, dx\)
Expand
\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + 9x^4 } \, dx\)
Integrate
\(A =2\pi \frac{(9x^4 + 1)^{\frac{3}{2}}}{54}|\limits^1_0\)
Expand
\(A = 2\pi [\frac{(9(1)^4 + 1)^{\frac{3}{2}}}{54} - \frac{(9(0)^4 + 1)^{\frac{3}{2}}}{54}]\)
This gives
A = 2π * 0.5671
Evaluate the products
A = 1.1342π
Approximate
A = 1.134π
Hence, the total area of the regions between the curves is 1.134π square units
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where h is the altitude above sea level, in meters, and P is the pressure, in kilopascals.
What is the pressure at sea level?
The pressure at sea level is considered to be 101.325 kPa, and as altitude increases, the pressure decreases accordingly.
At sea level, the pressure is referred to as standard atmospheric pressure. The value commonly used for standard atmospheric pressure is 101.325 kilopascals (kPa) or 1 atmosphere (atm).
This value is derived from the average pressure observed at sea level under standard atmospheric conditions.
As altitude increases, the pressure decreases due to the decrease in the density of air molecules in the atmosphere. This decrease in pressure with altitude is primarily caused by the decreasing weight of the air column above.
For every 8.5 kilometers of altitude gain, the pressure approximately halves.
The relationship between altitude and pressure can be described by the barometric formula, which is based on the ideal gas law and takes into account factors such as temperature variations.
However, for simplicity, the common approximation is to consider a linear relationship where the pressure decreases by about 1 kPa for every 10-meter increase in altitude.
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the sum of the percent frequencies for all classes in a frequency distribution will always equalT/F
The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.
The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.
In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.
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Please helppp this is algebra 10 :(
Answer:
x > 10/3 or x > 3 1/3
Step-by-step explanation:
Algebra 10? You sure it's not Algebra 1?
NEED HELP ASAP
The length of a rectangular parking lot at the airport is 2/3 mile.if the area is 1/2 square mile, what is the width of the parking lot?
Answer:
3/4 mile
Step-by-step explanation:
\(A = l *w\\\frac{1}{2} = \frac{2}{3} * w\\w = \frac{3}{2} * \frac{1}{2}\\w = 3/4 mile\)
Find the length of side x in simplest radical form with a rational denominator.
Answer:
x = \(\sqrt{3}\)/6
Step-by-step explanation:
30-60-90 triangles have legs in the ratio of 1 : \(\sqrt{3}\) : 2
create a proportion: (6 ÷\(\sqrt{3}\)) = (1÷x)
cross-multiply: 6x = \(\sqrt{3}\)
divide by 6
Need help on this question as well
The required arc length of sector VW is 8\(\pi\).
Given that, in a circle U, radius UV = 9 and central angle of sector m∠VUW = 160°.
To find the arc length of sector VW, we can use the formula:
Arc length = (central angle / 360) x circumference of the circle.
First, find the circumference of the circle by the formula for the circumference of a circle is given by:
Circumference = 2 x \(\pi\) x radius.
Circumference = 2 x \(\pi\) x 9 = 18π.
Now, let's find the arc length of sector VW using the central angle of 160 degrees:
Arc length = (160/360) x 18π
Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).
Therefore, the arc length of sector VW is 8\(\pi\).
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Suppose A is (-2,4) and M is (3,1) and M is the Midpoint of AB, find the coordinates of AB
Find the quotient and remainder if \( f(x) \) is divided by \( p(x) \). \[ f(x)=3 x^{4}+2 x^{3}-x^{2}-x-6 ; \quad p(x)=x^{2}+1 \] quotient \( \quad 3 x^{4}+2 x^{3}-x^{2}-x-6 \) remainder
To find the quotient and remainder if
�
(
�
)
f(x) is divided by
�
(
�
)
p(x), first, we need to divide the polynomials. Division of polynomials can be done by long division method. So, let's solve the problem and find the quotient and remainder of the polynomial.
In long division, first, we divide the first term of dividend by the first term of divisor.
3x^4/x^2 = 3x^2
Now we multiply this result (3x^2) with divisor and subtract from dividend.
3x^4 + 2x^3 - x^2 - x - 6 - (3x^2(x^2 + 1))= -3x^3 - x - 6
Next, we bring down the next term of the dividend. And repeat the process until we cannot divide further.
-3x^3/x^2 = -3x
Now, we multiply this result (-3x) with divisor and subtract from the last dividend.
-3x^3 - x - 6 - (-3x(x^2 + 1))= 3x^2 - x - 6
Now, we again bring down the next term of the dividend.
3x^2/x^2 = 3
Next, we multiply this result (3) with divisor and subtract from the last dividend.
3x^2 - x - 6 - (3(x^2 + 1))= -x - 9
-x/x^2 = -
Now, we multiply this result (-1) with divisor and subtract from the last dividend.
-x - 9 - (-1(x^2 + 1))= -x - 10
So, the quotient and remainder if
�
(
�
)
f(x) is divided by
�
(
�
)
p(x) are:
quotient = 3x^2 - 3
remainder = -x - 10
QUAD is not relevant to this question.
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answer to one out of every seven mathematicians is a philosopher, and one out of every nine philosophers is a mathematician. are there more philosophers or mathematicians?
Based on the information that has been provided, it is not possible to conclude whether there are a greater number of philosophers or mathematicians.
The statement only provides information regarding the proportion of mathematicians to philosophers and vice versa; it does not provide information regarding the total number of people working in either subject. It is possible that there are a greater number of philosophers, a greater number of mathematicians, or an equal number of both. We would need further information, such as the overall number of people in the fields, in order to accurately establish the number of persons who are present in each field specifically.
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i need this done please
Answer:
27.15
Step-by-step explanation:
Let us name the vertices as shown below
A(- 1, 6)
B(5, 1)
C(- 4, - 3)
We would calculate the distance between each vertex by applying the formula for calculating distance between 2 points. It is expressed as
The perimeter of the triangle is the sum of the length of each side. Thus,
Perimeter = 7.81 + 9.85 + 9.49
Perimeter = The perimeter of the triangle is the sum of the length of each side. Thus,
Perimeter = 27.15
Which is a better deal per ounce? 24 ounces for $2. 99 or 36 ounces for $4. 99?
Answer:
24 for 2.99
Step-by-step explanation:
2.99/24 = $0.1245 per ounce
4.99/36 = $0.1386 per ounce
So the 36 cost more per ounce.
Solve by factoring Show all your steps
-x²-2x=0
xả +5x +1= 5x+2
x²-4x-8--6x
3x² +12=-21x-24
Solve by completing the square. Show all your steps.
x² - 4x = 32
x²-11 = -4x
Solve by using the Quadratic Formula. Show all your steps.
16x² +8x-8= 4
-x²-3x-13 = -2x²
Answer: To solve -x²-2x=0 by factoring, we can factor out x from the left-hand side:
x(-x-2) = 0
This equation is true if either x = 0 or -x-2 = 0. Solving for x in the second equation:
-x-2 = 0
-x = 2
x = -2
Therefore, the solutions to the equation -x²-2x=0 are x = 0 and x = -2.
To solve x²-4x-8--6x by factoring, we can simplify it first by combining like terms:
x²-10x-8 = 0
To factor this quadratic, we need to find two numbers that multiply to -8 and add to -10. These numbers are -2 and -8, so we can write:
x²-2x-8x-8 = 0
(x²-2x) - (8x+8) = 0
x(x-2) - 8(x+1) = 0
(x-8)(x-2) = 0
Therefore, the solutions to the equation x²-4x-8--6x are x = 8 and x = 2.
To solve 3x² +12=-21x-24 by completing the square, we first need to move all the terms to one side:
3x² + 21x + 36 = 0
Next, we divide both sides by 3 to simplify the coefficient of x²:
x² + 7x + 12 = 0
To complete the square, we need to add and subtract (7/2)² = 49/4 inside the parentheses:
x² + 7x + 49/4 - 49/4 + 12 = 0
(x + 7/2)² = 1/4
Taking the square root of both sides and solving for x, we get:
x + 7/2 = ±1/2
x = -7/2 ± 1/2
Therefore, the solutions to the equation 3x² +12=-21x-24 by completing the square are x = -4 and x = -3.
To solve -x²-3x-13 = -2x² by using the quadratic formula, we first need to move all the terms to one side:
-x² + x - 13 = 0
Next, we identify the coefficients a, b, and c:
a = -1, b = 1, c = -13
Substituting these values into the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
x = (-1 ± sqrt(1² - 4(-1)(-13))) / 2(-1)
x = (-1 ± sqrt(1 + 52)) / (-2)
x = (-1 ± sqrt(53)) / (-2)
Therefore, the solutions to the equation -x²-3x-13 = -2x² by using the quadratic formula are approximately x = -3.25 and x = 4.25.
Step-by-step explanation:
HURRY PLEASE I ONLY HAVE A MINUTE LEFT IM BEING TIMED!!!
A restaurant earned a profit of $175,000 in its first year of operation. After taxes were paid, $122,499 was left. How much money did the restaurant pay in taxes?
a.
$297,499
c.
$52,501
b.
$52,511
d.
$122,499
Answer:
$52,501
Step-by-step explanation:
You need to subtract $122,499.
Choose the expression that describes the Field of Values (outputs) and the Amplitude of the graph of f(x)=−2sin(x).
The expression that describes the field of values (outputs) of the graph of f(x) = -2sin(x) is [-2, 2], and the amplitude of the graph is 2.
In the given function f(x) = -2sin(x), the coefficient of sin(x) is -2. The coefficient, also known as the amplitude, determines the vertical stretching or compressing of the graph. The absolute value of the amplitude represents the maximum displacement from the midline of the graph.
Since the amplitude is -2, we take its absolute value to obtain 2. This means that the graph of f(x) = -2sin(x) has a maximum displacement of 2 units above and below the midline.
Therefore, the field of values (outputs) of the graph is [-2, 2], representing the range of y-values that the graph of f(x) = -2sin(x) can attain.
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What is the area of the pentagon, rounded to the nearest tenth?
Answer:
not sure until i know the lengths
Step-by-step explanation:
"If f(x) = 6x3 + 5x, g(x) = 3x2 + 5, and h(x) = 9x2 – 8, what is the degree of f(g(h(x)))?"
2
3
7
12
Answer:
the degree of f(g(h(x))) is 12
Step-by-step explanation: I know you want simple and easy answers and thats what im here for, . :D
Answer:
D. 12
Step-by-step explanation:
Edge 2020
A bathtub, in the shape of a rectangular prism, measures 8 feet long by 3 feet wide by 2 feet deep. If the tub fills at a rate of 5 cubic feet per minute, then how many minutes will it take to fill the bathtub?
Answer:
Step-by-step explanation:
The volume of the tub is 5 ft * 3 ft * 1.5 ft = 22.5 ft^3
Three-fourths full makes the amount (3/4)(22.5 ft^3) = 16.875 ft^3
Draining at 1 ft^3 / min, it takes almost 17 minutes (16 7/8
is 103 perfect square? show your work
Answer:
yes
Step-by-step explanation:
Could not simplify further
Answer:
No, it's not a perfect square.
Step-by-step explanation:
First of all a perfact square should never end with 2, 3, 7 or 8, if it does than its not a perfect square.
103 ends with "3", so therefore, it's not a perfect square.
Hailey is the oldest of four siblings whose ages are consecutive integers. If the sum of their ages is 66, find Hailey's age.
Considering the definition of an equation and the way to solve it, Hailey's age is 18 years.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Hailey's ageBeing "x" the age of the youngest child, then you have:
"x" the age of the youngest child."x + 1" the age of one middle child."x + 2" the age of the other middle child."x + 3" the age of the oldest child, in this case Hailey's age.On the other hand, you know that the sum of their ages is 66. Then, the equation is:
x + x + 1 + x + 2 + x + 3 = 66
Solving:
4x + 6 = 66
4x = 66 - 6
4x = 60
x= 60 ÷ 4
x= 15
Remembering that "x + 3" is Hailey's age, then her age is calculated as: x+3= 15 +3= 18
Finally, Hailey's age is 18 years.
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state the measurement of <1
Answer:
57 degrees
Step-by-step explanation:
because it is the same as the other side
Dave owns 1/4 of a business. Delta owns 1/5 and Alice owns 1/2. The banks owns the rest. Who owns the smallest portion on the business? What fraction of the business does the bank own?
Answer: bank owns smallest portion 1/20
Step-by-step explanation: Dave 1/4= 0.25 = 25 %. Delta 1/5 = 0.20 = 20%
And Alice 1/2 = 0.5 =50%. Bank owns 5% = 5/100 = 1/20
Chang is building a circular sandbox with a circumference of 31.4 meters. She uses a string tied to a metal stake to trace out a circle in her backyard.
Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter
What exactly is pi?
The proportion of a circle's circumference to its diameter is denoted by the mathematical constant pi (). It cannot be written as a simple fraction since it is an irrational number. Pi is approximately equal to 3.141592, or 3.15.
We must first determine the circle's radius in order to determine the length of Mr. Chang's string.
C = 2πr, where C is the circle's circumference and r is its radius, is the formula for a circle's circumference.
Given that the circle's circumference is 31.4 meters, we can solve for r using the following method:
C = 2r 31.4
=2x3.14xr
= 31.4/(2x3.14)r
= 3.14/6.28r
r = 5
Thus, the circle's radius is roughly 5 meters.
The diameter of the circle, which is twice as long as its radius, will be equal to Mr. Chang's stake because it is in the center of the circle.
Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter
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A closed half-plane is the solution of a linear inequality that comes close to the boundary line.
O True
O False
Answer:false
Step-by-step explanation:
Solve the equation and enter the value of x below. x(8 + 9) = 34
\( \huge\boxed{\mathfrak{Answer}}\)
\(x(8 + 9) = 34 \\ 8x + 9x = 34 \\ 17x = 34 \\ x = \frac{34}{17} \\ x = 2\)
=> The answer is 2.
morgan is analyzing her data and notices that the value of her mean is quite a bit smaller than the value of her median. she asks for your help in interpreting these results. what would you tell her?
We can interpret from the results that the distribution of data might be negatively skewed.
In the given question it is mentioned that while Morgan was analyzing her data, she notices that the value of her mean is quite a bit smaller than the value of her median.
As we know that, in statistics, when the mean is smaller than the median and mode, it indicates a negatively skewed distribution.
A negatively skewed distribution or left skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution graph while the left side of the graph is longer.
Hence, we can interpret from these information that the distribution of data of Morgan are negatively skewed.
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A hospital tracked the day of the week each baby was born and whether or not the delivery was scheduled in advance. The following two-way table displays data for the sample of babies born in a particular year at that hospital. Day of birth Scheduled Unscheduled TOTAL
Sunday 999 313131 404040
Monday 191919 666666 858585
Tuesday 202020 707070 909090
Wednesday 171717 616161 787878
Thursday 191919 686868 878787
Friday 151515 555555 707070
Saturday 111111 393939 505050
TOTAL 110110110 390390390 500500500
Find the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday
There is a very small chance (less than 1%) that a randomly selected baby from this sample was born on Tuesday OR on Friday.
To find the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday, we need to add the number of babies born on Tuesday to the number of babies born on Friday, and then divide by the total number of babies in the sample.
The number of babies born on Tuesday is 202020, and the number of babies born on Friday is 151515. Therefore, the total number of babies born on Tuesday or on Friday is 202020 + 151515 = 353535.
The total number of babies in the sample is 500500500. Therefore, the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday is:
353535 / 500500500 = 0.0007061
It is interesting to note that the number of babies born on different days of the week varies in this sample. For example, there are more babies born on weekdays (Monday-Friday) than on weekends (Saturday and Sunday), and there are more babies born on Tuesday than on Wednesday or Thursday.
The number of scheduled deliveries is higher than the number of unscheduled deliveries overall, but there are some days (e.g., Friday and Saturday) where there are more unscheduled deliveries than scheduled deliveries. These patterns could be explored further to understand the factors that influence the timing and scheduling of deliveries.
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