The tree statements of the circle are
1) The radius of the circle is 3 units.
2) The center of the circle lies on x-axis.
3) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is center of a circle?
A circle's center is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.
Given equation of circle is
x² + y² - 2x - 8 =0
x² - 2x + 1 - 1 + y² - 8 =0
(x - 1)² - 1 + y² - 8 =0
(x - 1)² + y² - 9 =0
(x - 1)² + y² = 3²
Compare the equation above equation with (x - h)² + (y - k)² = r²:
h = 1, k=0, r=0
The radius of the circle is 3 units. The center of the circle is (1,0) which lies on the x-axis.
Rewrite the equation of circle x² + y² = 9:
x² + y² = 3²
The radius of the circle is 3 units:
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he national flufferball association decides to implement a drug screening procedure to test its athletes for illegal performance enhancing drugs. 3% of the professional flufferball players actually use performance enhancing drugs. a test for the drugs has a false positive rate of 2% and a false negative rate of 4%. in other words, a person who does not take the drugs will test positive with probability 0.02. a person who does take the drugs will test negative with probability 0.04. a randomly selected player is tested and tests positive. what is the probability that she really does take performance enhancing drugs?
The probability is it that she actually uses performance-enhancing drugs is 0.5975.
Given that,
The national flufferball association makes the decision to put in place a drug testing programme to check its athletes for the use of illicit performance-enhancing substances. In reality, 3% of professional flufferball players abuse performance-enhancing substances. A drug test has a 2% false positive rate and a 4% false negative rate. Alternatively, a person who abstains from drug use has a 0.02 percent chance of testing positive. With a 0.04 probability, a person who uses the medications will test negative. A player is tested at random, and the results are positive.
We have to find how probable is it that she actually uses performance-enhancing drugs.
We know that,
The provided data is
P(D)=0.03
P(D')=1-0.03=0.97
P(T|D')= 0.02
P(T'|D)=0.04
P(T|D)=1-P(T'|D)=1-0.04=0.96
The probability that she really takes the drugs is,
P(D|T)=P(D)P(T|D)/P(D)P(T|D)+P(D')P(T|D')
P(D|T)=(0.03×0.96)/(0.03×0.96)+(0.02×0.97)
P(D|T)=0.5975
Therefore, The probability is it that she actually uses performance-enhancing drugs is 0.5975.
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(-4,-2) and (4,0) in linear equations
Answer:
y = 1/4 x - 1
Step-by-step explanation:
y = mx + b
m = slope = (-2 - 0)/(-4 - 4) = -2/(-8) = 1/4
y = 1/4 x + b
0 = 1/4 × 4 + b
0 = 1 + b
b = -1
y = 1/4 x - 1
Evaluate.
12÷(2+23)2
Responses
649
6 and 4 over 9
412
4 and 1 half
323
3 and 2 over 3
1 11/6
The evaluation of the given fraction expression is 1 11/16. The correct option is the last option
Evaluating a fraction expressionFrom the question, we are to evaluate the given expression.
The given expression is
[tex]12 \div (2+\frac{2}{3})^{2}[/tex]
Evaluating the expression
[tex]12 \div (2+\frac{2}{3})^{2}[/tex]
[tex]12 \div (\frac{8}{3})^{2}[/tex]
[tex]12 \div (\frac{8^{2}}{3^{2}})[/tex]
[tex]12 \div \frac{64}{9}[/tex]
= [tex]12 \times \frac{9}{64}[/tex]
= [tex]\frac{108}{64}[/tex]
= [tex]\frac{27 \times 4}{16 \times 4}[/tex]
= [tex]\frac{27}{16}[/tex]
= [tex]1\frac{11}{16}[/tex]
Hence, the fraction is 1 11/16
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The lowest temperature in January was less than−6°. Which could be the lowest temperature in January?
The lowest temperature in January is -10°C if the lowest temperature in January is less than -6°C.
What is meant by temperature?A scaled way of measuring how hot or how chilly something is a living body's normal level of heat production; see thermometer. a condition of extreme body heat with an average oral temperature of 98.6°F. The ideas of hotness and coolness are expressed numerically as a physical value called temperature.
The calibration of thermometers involves employing a variety of temperature scales with clearly defined reference points and thermometric materials. The Celsius scale (°C), formerly known as centigrade, with the unit symbol °C, is the most commonly used scale, followed by the Fahrenheit scale (°F) and the Kelvin scale (K), which is mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).
Given,
Less than 6° was the lowest temperature recorded in January.
The lowest temperature in January will be=?
It is -10°C.
Therefore, the lowest temperature in January is -10°C.
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What is 2/3 of 1 5/16
Answer:
7/8
Step-by-step explanation:
2/3 * 1 5/16 =
2/3 * (1 + 5/16)=
2/3 * (16/16 + 5/16)= -> common denominator numbers are easy to simplify
2/3 * (16+5)/16 =
2/3 * 21/16=
(2*21)/(3*16)=
42/48=
21/24=7/8
In a hurry, will give 40 points.
Answer:
A: 74.9
B: 51.4
C: 53.7
Sorry I don't have enough time for the rest
Step-by-step explanation:
all angles should add up to 180
Write the equation of the line in slope-intercept form (y=mx+b) for each of the following.
ill brainlist
The equation of the line in slope intercept form of y is -2x + 19
How to calculate the equation slope intercept ?When you know the slope of the line to be examined and the given point is also the y intercept, you can use the slope intercept formula, y = mx + b. The y value of the y intercept point is denoted by the symbol b in the formula.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
To find this, we can use the point and the slope in point-slope form. The we solve for y.
y - y1 = m(x - x1)
y - 7 = -2(x - 6)
y - 7 = -2x + 12
y = -2x + 19
The equation would be y = -2x + 19
The complete question is : Write an equation in slope- intercept form y=mx=b of the line through point p(6,7) with slope -2
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Find the value of the variable BC, if B is between A and C. AB=19, BC = 4y, AC = 8y-1
The value of the variable BC will be equal to 20.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that B is between A and C. AB=19, BC = 4y, AC = 8y-1.
Here If B is between the segment AC the value of BC will be calculated as,
BC = AC - AB
Substitute the values in the above equation and solve for the value of y,
4y = 8y - 1 - 19
4y = 8y - 20
8y - 4y = 20
4y = 20
y = 5
The value of segment BC will be.
BC = 4y
BC = 4 x 5
BC = 20
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a person leaves home and walks 4 miles west, then 5 miles southwest. how far from home is she? miles in what direction must she walk to head directly home? degrees north of east
The person is 8.325 miles far from her home and she should walk in the direction of 64.86° North Of East to head directly home .
In the question ,
from the figure ,
we see that point O is home of the person ,
it is given that person leaves the home and walks 4 miles west to point A , then 5 miles in south west direction to the point B .
So ,distance OA = 4 miles
AB = 5 miles .
In triangle OAB ,
angle OAB = 45+90 = 135°
Using Cosine Rule ,
OB² = OA² + AB² - 2*OA*AB*Cos(135)°
= 16 + 25 + 28.2843 = 69.2843
So ,OB = √69.2843 = 8.325 miles .
Now using Sine Rule ,
Sinθ/OA = Sin(135°)/OB
Sinθ = 4*Sin(135°)/8.324
Sinθ = 0.339792
So , θ = 19.86°
hence the direction from North of East is
= 45° + θ
= 45° + 19.86°
= 64.86° North Of East .
Therefore , the distance is 8.325 miles and the direction is 64.86° North Of East .
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n a conference, 75% of the attendees have been to germany, and 15% of the attendees have been to both england and germany. what is the probability that a randomly selected attendee has been to england, if it is known that they have been to germany? assume event e: the attendee has been to england; event g: the attendee has been to germany.
Simple probability is the calculation of an outcome or the chance of an event ever happening.
What is a probability in math?In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.18.65% probability that the person is from Washington
Two events, A and B.
[tex]P(B/A)=\frac{P(B)*P(A/B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Arrived by train.
Event B: From Washington.
15% are from Washington
This means that [tex]P(B)=0.15[/tex]
12% of the attendees from Washington came to the conference by train.
This means that [tex]P(A/B)=0.12[/tex]
Probability of arriving by train:
6% of 60%(from California), 17% of 25%(from Oregon) or 12% of 15%(from Washington). So
[tex]P(A)=0.06*0.6+0.17*0.25+0.12*0.15=0.0965[/tex]
If an attendee is selected at random and found to have arrived by train,
[tex]P(B/A)=\frac{0.15+0.12}{0.0965} =0.1865[/tex]
=0.1865
18.65% probability that the person is from Washington
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Y=2x^2 + 3x+1
a.Find the x - and y-intercept
b. Where is the line of symmetry of this parábola? Write its equation
c. Find the coordinates of the vertex
For the parabola y = 2x² + 3x + 1,
a. i. The x-intercepts are x = -1/2 and x = -1
a. ii. The y-intercept is y = 1
b. i. The line of symmetry is at x = -3/4
b. ii. The equation of the line of symmetry is x = -3/4
c. The vertex is at (-3/4, -1/8)
What is a parabola?A parabola is part of a conic section which is a curve.
a. i. Find the x - interceptGiven the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.
So, y = 2x² + 3x + 1
2x² + 3x + 1 = 0
2x² + 2x + x + 1 = 0
Factorizing, we have
2x(x + 1) + (x + 1) = 0
(2x + 1)(x + 1) = 0
2x + 1 = 0 or x + 1 = 0
2x = -1 or x = -1
x = -1/2 or x = -1
So, the x-intercepts are x = -1/2 and x = -1
ii Find the y intercept?Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.
So, y = 2x² + 3x + 1
So, y = 2(0)² + 3(0) + 1
y = 0 + 0 + 1
y = 1
So, the y-intercept is y = 1
b. i. Where is the line of symmetry of this parábola?The line of symmetry passes through the vertex of the parabola where dy/dx = 0.
So, y = 2x² + 3x + 1
dy/dx = d(2x² + 3x + 1)/dx
= d(2x²)/dx + d3x/dx + d1/dx
= 4x + 3 + 0
= 4x + 3
So, when dy/dx = 0,we have
4x + 3 = 0
4x = -3
x = -3/4
So, the line of symmetry is at x = -3/4
ii. Write its equationThe equation of the line of symmetry is x = -3/4
c. Find the coordinates of the vertex?Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have
y = 2x² + 3x + 1
y = 2(-3/4)² + 3(-3/4) + 1
y = 2(9/16) - 9/4 + 1
y = 9/8 - 9/4 + 1
y = (9 - 18 + 8)/8
y = (17 - 18)/8
y = -1/8
So, the vertex is at (-3/4, -1/8)
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jenny buys 222222 sports drinks for her soccer team. they are on sale for \$0.35$0.35dollar sign, 0, point, 35 off per drink. jenny paid \$18.70$18.70dollar sign, 18, point, 70 for the 222222 sports drinks. what question does the equation 22(x-0.35)
The original cost of each sports drink that Jenny bought for her soccer team was $1.20.
Number of sports drink that Jenny bought for her soccer team
= 22
The amount of discount that Jenny got on each drink as they were on sale
= $0.35
Amount that Jenny paid for 22 sports drinks
= $18.70
Let the original cost of each sports drink be $x
Amount that Jenny paid for each drink
= $(x-0.35)
Therefore, amount that Jenny paid for 22 sports drink
= 22× (x-35) = 18.70
(x-0.35) = 18.70/22
x = 0.85 + 0.35
x = $1.20
The question is incomplete, the complete question is:
Jenny buys 22 sports drinks for her soccer team, they are on sale for $0.35 off per drink. Jenny paid $18.70 for 22 sports drink. How much does each drink cost originally?
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How do you find the derivative of 1/logx?
The derivative of 1/logx is With the chain rule.
1log(x)=log(x)−1 is ,= -1xlog(x)2 .
The by-product of logₐ x (log x with base a) is 1/(x ln a). Here, the thrilling issue is that we have "ln" withinside the by-product of "log x". Note that "ln" is referred to as the logarithm (or) it's miles a logarithm with base "e".
The by-product of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of log.
[tex]With the chain rule. \\
1log(x)=log(x)−1 \\
So you follow the chain rule to the electricity after which to the log: \\
ddxlog(x)−1=−1⋅log(x) \\ \\−2⋅ddxlog(x)
\\ =−1log(x)21x
\\ =−1xlog(x)2 .[/tex]
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(6.8 times 10 to the power 2) times(1.3 times 10 to the power -3)
The answer of the given scientific multiplication is, 8.84 x 10^-1.
What is scientific multiplication?
Multiply the decimal numbers to multiply the numbers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.
Given:
(6.8 x 10^2) x (1.3 x 10^-3)
We have to solve this using scientific multiplication.
First to multiply the decimals,
6.8 x 1.3 = 8.84
Now to solve
10^2 x 10^-3 = 10^(2-3) = 10^-1
⇒ (6.8 x 10^2) x (1.3 x 10^-3) = 8.84 x 10^-1
Hence, the answer of the given scientific multiplication is, 8.84 x 10^-1.
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Which of the following is not a quadratic equation, a. 2(x - 1)² = 4x² - 2x + 1, b. 2x - x² = x² + 5, c. (√2x + √3)² + x² = 3x² - 5x, d. (x² + 2x)² = x⁴ + 3 + 4x³
The equation (C) (√2x + √3)² + x² = 3x² - 5x is not a quadratic equation.
What is a quadratic equation?A quadratic equation, or second-order polynomial equation with a single variable, is x ax2 + bx + c = 0.
Since it is a second-order polynomial equation, which is ensured by the algebraic 's theorem, it must have at least one answer.
The solution might be simple or difficult.
(A) 2(x - 1)² = 4x² - 2x + 1
Algebraic identity:
(a - b)² = a² - 2ab + b²
2(x² + 1 - 2x) = 4x² - 2x + 1
2x² + 2 - 4x = 4x² - 2x + 1
4x² - 2x² - 2x + 4x + 1 - 2 = 0
2x² + 2x - 1 = 0
The equation has a degree of two.
As a result, the equation 2(x - 1)² = 4x² - 2x + 1 is quadratic.
(B) 2x - x² = x² + 5
x² + x² + 5 - 2x = 0
2x² - 2x + 5 = 0
The equation has a degree of two.
As a result, the equation 2x - x² = x² + 5 is quadratic.
(C) (√2x + √3)² + x² = 3x² - 5x
Algebraic identity is used:
(a + b)² = a² + 2ab + b²
2x² + 3 + 2√6x + x² = 3x² - 5x
3x² - 3x² + 2√6x + 5x + 3 = 0
5x + 2√6x + 3 = 0
The equation has a degree of 1.
As a result, the equation (√2x + √3)² + x² = 3x² - 5x is not quadratic.
(We got our answer so we don't need to solve further)
Therefore, the equation (C) (√2x + √3)² + x² = 3x² - 5x is not a quadratic equation.
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Find the absolute value.
|-3 + 2i| = []
(Simplify your answer. Type an exact answer, using radicals as needed.)
√13 is the absolute value of |-3 + 2i| .
What is Complex Number?Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number.
For a complex number z = x + iy,
The absolute value |z| as being the distance from z to 0 in the complex plane C
Complex numbers are the numbers that are expressed in the form of a+ib
The complex number here is minus three plus two i.
|-3 + 2i|
Absolute value=√(-3)²+(2)²
=√9+4
=√13
Hence, √13 is the absolute value of |-3 + 2i| .
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Kareem cannot decide which of two washing machines to buy. The selling price of each is $385. The first is
marked down by 30%. The second is marked down by 20% with an additional 10% off. Find the sale price of each
washing machine. Use pencil and paper. Explain why Kareem should buy the first washing machine rather than the
second if the machines are the same except for the selling price.
Answer:
$385 discounted by 30% the final price would be $269.50
$385 discounted by 20% the final price would be $308.00
$385 discounted by 10% the final price would be $346.50
Step-by-step explanation:
Answer:
The first option is cheaper and hence Kareem should buy it.--------------------------------------
The selling price is $385.
Option 130% off ⇒ $385×(1 - 0.3) = $385×0.7 = $269.5Option 220% off ⇒ $385×(1 - 0.2) = $385×0.8 = $30810% off ⇒ $308×(1 - 0.1) = $308×0.9 = $277.2As we see the first option is cheaper:
$269.5 < $277.2activity a1 takes 5 weeks, a2 takes 7 weeks, and a3 takes 3 weeks with a 50% probability and 9 weeks with a 50% probability. what is the expected project completion time?
The probability to determine the time needed to complete the project, we simply added the time required for activities 1 and 2.
1 (1): the chance that a given event will occur
(2): the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes a branch of mathematics concerned with the study of probabilities
2 : something (such as an event or circumstance) that is probable
3: the quality or state of being probable
4: a logical relation between statements such that evidence confirming one confirms the other to some degree
The best-case scenario's calculation of the project's completion time is displayed below;
= Week spent on Activities A1 + Week spent on Activities A2.
= 5 weeks plus 7 weeks.
= 12
To determine the time needed to complete the project, we simply added the time required for activities 1 and 2.
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Find the value of x. Show all work.
Area of the rectangle is 30 sq. Ft
Answer:
The answer is 3 ft
Step-by-step explanation:
Given;Area of rectangle (A) = 30 sq ft.Length (l) = xWidth (w) = 3x + 1To Find;Value of xNow, we know that
A = l × w
30 = (x) × (3x + 1)
30 = 3x² + x
3x² + x = 30
3x² + x - 30 = 0
3x² - 9x + 10x - 30 = 0
3x(x - 3) + 10(x - 3) = 0
(x - 3) (3x + 10) = 0
x = 3 ft
Thus, The value of x is 3
For Verification Only ;
30 = (x) × (3x + 1)
30 = (3) × (3*3 + 1)
30 = 3 × 10
30 = 30
Hence, L.H.S = R.H.S
please help me
100 points
Answer:
100 is the answer
Step-by-step explanation:
Determine a series of transformations that would map polygon ABCD onto polygon A'B'C'D'?
Therefore , Due to a sequence of transformations, polygon ABCD will therefore overlap polygon A'B'C'D'.
What is polygon?A polygon is a closed, two-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. The edges of a polygon are another name for its sides. A polygon's vertices (or corners) are the places where two sides converge.
Here,
a 4 unit translation to the left after reflecting polygon ABCD across the x-axis.
The coordinates for point A in the polygon ABCD are (1, -5).
ABCD's polygon should be mapped onto A'B'C'D',
Reflect the ABCD polygon across the x-axis in accordance with the rule,
A(x, y) → A'(x, -y) (x, -y)
Following this criterion, A's coordinates will be,
A(1, -5) → A'(1, 5) (1, 5)
ABCD is also moved four units to the left.
The rule for the translation is,
A'(x, y)=> A"(x - 4, y) (x - 4, y)
A'(1, 5) => A"(1 - 4, 5) (1 - 4, 5)
=> A"(-3, 5) (-3, 5)
Due to a sequence of transformations, polygon ABCD will therefore overlap polygon A'B'C'D'.
a 4 unit translation to the left after reflecting polygon ABCD across the x-axis.
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a rectangular poster is to contain 200 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?
dimensions of the poster with margin are L = 12 in and h = 24 in
What is the area of a rectangular poster?The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.
We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.
Rectangle area equals length times width.
SolutionLet call length of printed area of the poster be " x " and height of printed area of the poster be " y ".
Area of the poster = length and height
200 = x*y
y = 200/x
We also know that dimensions of the poster with margin is:
L = x + 2 in and H = y + 4 in
Therefore area of the poster is:
A(p) = ( x + 2 ) * ( y + 4 )
And area as function of x is:
A(x) = ( x + 2 ) * ( 200/x + 4 )
A(x) = 200 + 4*x + 400 /x + 8
Taking derivatives on both sides of the equation we have:
A´(x) = 4 - 400/x²
By taking A´(x) = 0
4 - 400/x² = 0 ⇒ 4*x² - 400 = 0
x² = 400 / 4
x² = 100
x = 10 in
and y = 200/x ⇒ y = 20
The second derivative A´´(x) = 400/x4 which is > 0
there is a minimum for the function at the point x = 10
As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are
L = x + 2 = 10 + 2 = 12 in and
h = y + 4 = 20 + 4 = 24 in
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a company surveyed college students to determine their need and want for a new portable computer accessory. once the data was gathered, the company began designing the accessory to specifications determined by the data. this is an example of .
On solving the provided question, from the information we can say that this is a example of Research and development (R&D).
What means research and development?Research and development (R&D) refers to the knowledge a business accumulates to create new items or discover innovative ways to enhance current goods and services. Before using their products or processes for commercial purposes, large corporations may have their own R&D teams that test and improve them.
What is the role of research and development?Research and development (R&D) refers to the processes businesses use to innovate and launch new goods and services. It is frequently the initial stage of the development process. Typically, the objective is to expand the company's revenue while introducing a new good or service to the market.
This is an example of Research and development (R&D)
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The elevation of City A is 60 feet above sea level. The elevation of City C is 12 feet above sea level. The elevation of City D is 1 over 2 of the elevation of City C.
Part A: Write an expression to represent the elevation, in feet, of City D. (5 points)
Part B: Solve the expression, and explain why the answer is negative or positive. (5 points)
A) D = 1/2[C] = 1/2[-16]
B) Elevation of city D is -8 feet.
Answer is negative due to -8 feet below sea level.
What is elevation?
The elevation is the height above sea level. Typically, elevations are expressed in feet or meters. Maps can depict them using contour lines, which link points of the same elevation, color bands, or numbers that indicate the precise elevations of specific points on the surface of the Earth.
The elevation of city A is 60 feet below sea level
⇒ A = -60
The elevation of city C is 16 feet below sea level
⇒ C = -16
The elevation of city D is 1 over 2 of the elevation of city C.
⇒ D = 1/2[C]
Part A: Write an expression to represent the elevation, in feet, of city D.
⇒ D = 1/2[C] = 1/2[-16]
Part B: Solve the expression and explain why the answer is negative or positive.
⇒ D = 1/2[-16]
D = -8
As a result Elevation of city D is -8 feet.
Here founded answer is negative due to -8 feet below sea level.
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Which of the following is a zero of 3x² + 5x - 2?
The zeros of the expression 3x² + 5x - 2 are 1/3 and -2
What is a quadratic equation?A quadratic equation can simply be defined as an algebraic equation having the second degree of x.
From the information given, we have that;
3x² + 5x - 2
Equate the expression to zero
3x² + 5x - 2 = 0
Find the pair factors of -6 that sum up to + 5, we get;
+ 6 and -1
Substitute the values into the equation;
3x² + 6x - x - 2 = 0
Enclose in brackets
(3x² + 6x) - ( x - 2) = 0
Factor the common terms
3x( x + 2) - 1( x + 2)
Then,
3x - 1 = 0
x = 1/3
x +2 = 0
x = -2
Hence, the values are 1/3 and -2
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The equation y = 20x + 500 models the relationship between the number of video games, x, a company manufactures and the cost in dollars, y, to manufacture that number.
Rewrite 18x4y3 − 36x3y4 using a common factor.
2x4y4(9 − 18x)
2x3y3(9y − 18x)
9x3y3(2x − 4y)
9x4y3(2 − 4y)
The expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y), so option C is correct.
What is a common factor?Common factors are those that apply to two or more different integers. To put it another way, a common factor is a number that will divide a group of two numbers exactly.
Given:
18 x⁴y³− 36x³y⁴
Factorize the above expression,
9 × 2 x⁴y³ - 9 × 4x³y⁴
Take common 9 x³y³
9 x³y³(2x - 4y)
Therefore, the expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y).
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find the percentage of the first quantity with
reference to the second quantity: 480 units, 560 units.
Answer:
85.7142857%
Step-by-step explanation:
To find the percentage, take the first quantity and divide by the second quantity
480/560 =.857142857
Then multiply by 100 %
857142857 * 100% = 85.7142857%
skye is laying a brick barrier around a circular flower bed with a radius of 4 yards. Which of the following expression can be used to find the circumference around the flower bed in yards? Circle ALL that apply.
A 2xn B 4xn C 2x4xn D 8xn
The circumference around the flower bed in yards is D) 8×π.
What is the circumference of the circle?
The circumference of a circle is defined as the linear distance around it.
The formula for the circumference of a circle is [tex]2\pi r[/tex]. Where r is the radius of the circle.
It is given that the radius of the flower bed is 4 yards.
The flower bed is in the shape of a circle.
The circumference of the flower bed is 2×π×r.
Substitute the value of r in the equation.
Therefore the circumference around the flower bed is 8×π.
The correct option is D) 8×π.
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Stan made changes to
his driving habits and
went from 18 mpg to
22 mpg. What was
Stan' s percent
increase in his gas
mileage?
