The lines of the functions f(x) = ²/₃x - 5 and g(x) = -³/₂x + 7 have slopes that are negative reciprocals and are said to be perpendicular lines.
How to interpret the slope of a linear equation?The general formula for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are given the linear equations as; f(x) = ²/₃x - 5 and g(x) = -³/₂x + 7
Now, when two lines are parallel, their slopes will be the same and equal. However, when two lines are perpendicular, their slopes will be a negative reciprocal of each other.
In our given functions, we see that the slope of g(x) is a negative reciprocal of the slope of f(x). Thus, both lines are concluded to be perpendicular to each other.
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The complete question is;
Consider the functions f(x) = ²/₃x - 5 and g(x) = -³/₂x + 7. what do the slopes indicate about the lines?
Also do stepbystep pls
Answer:
-25
Step-by-step explanation:
[tex]-5^2=-25[/tex]
consider the probability distribution of x, where x is the number of times a college graduate changed majors. x 0 1 2 3 4 5 6 7 8 p(x) 0.135 0.271 0.271 0.180 0.090 0.036 0.012 0.003 0.002 what is the probability that a randomly selected college graduate has changed majors more than two times?
When the probability distribution of x, where x is the number of times a college graduate changed majors where P(0) = 0.135, P(1) = 0.271, P(2) = 0.271, P(3) = 0.180, P(4) = 0.090, P(5) = 0.036, P(6) = 0.012, P(7) = 0.003 and P(8) = 0.002, the probability that a randomly selected college graduate has changed majors more than two times is 0.323.
Therefore, the answer is 0.323.
The probability that a randomly selected college graduate has changed majors more than two times is obtained by
P( x > 2) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8)
P(x > 2) = 0.180 + 0.090 + 0.036 + 0.012 + 0.003 + 0.002
P(x > 2) = 0.323
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100 points + brainliest
Answer:
(-1,5), (0,4), and (-6,7)
Step-by-step explanation:
One may enter each point in both equations and solve matematically to find which points satisfy both equations. But with access to a free, and easy, online graphing utility, it is more illuminating to plot both inequalites to identify the region containing mutual points (faster, also). The attached plot illustrates the result. Each inequality adds a shaded area showing the points satisfying the equation. The color is darkest where the solution areas overlap, as seen in the upper left of the graph. All points in this area satify both inequalities. They are:
(-1,5)
(0,4), and
(-6,7)
Of the remaining three, only (2,-3) satifies neither equation.
Answer:
(-1,5), (0,4), and (-6,7)
Step-by-step explanation:
They find pearl on their coat, and diamond and carbuncle on their rock; they do not look after them, but, if they find them by chance, they polih them, and with them they adorn their children, who are delighted with them, and glory in them during their childhood; but when they grow to year, and ee that none but children ue uch bauble, they of their own accord, without being bid by their parent, lay them aide, and would be a much ahamed to ue them afterward a children among u, when they come to year, are of their puppet and other toy. –Utopia,
Thoma More
How do the detail about how the Utopian treat valuable develop the central idea?
the Utopian treat valuable develop the central idea is the Utopians give valuables to children, who treat them as toys.
The central idea of the above passage is that the Utopians give valuables, such as diamonds and carbuncles to children, who treat them as toys. As such, the Utopians are delighted with these valuables, and glory in them during their childhood but lay them aside when they come to years.
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The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44. Find x
The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44 then x= 10
since the triangle is isosceles then the 2 legs are congruent, that is both 2x - 3
the perimeter is the sum of the 3 sides , that is
x + 2x - 3 + 2x - 3 = 44
5x - 6 = 44 ( add 6 to both sides )
5x = 50 ( divide both sides by 5)
x = 10
hence The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44 then x= 10
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please help me slove this q
Answer:
Step-by-step explanation:
I plotted this graph on Desmos**
When I plotted the line I got (3,-2) as the point where they intercept.
1st Equation Y=3x-11:
x: 0, 1, 2
y: -11, -8, -5
2nd Equation Y=-2x+4:
x: 0, 1, 2
y: 4, 2, 0
(Hopefully these points are right I went along with the graph I plotted, if wrong, I'm sorry.)
interpreting slope - item 21021 Question 4 of 7 What is the slope of the line shown?
please answer quickly im on a time limit
The slope of the line shown in this graph is equal to: B. 1/2.
How to calculate the slope of a line?Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph, we have the following points on the line:
Points on x-axis = (-2, 2).Points on y-axis = (-4, -2).Substituting the given points into the formula, we have;
Slope, m = (-2 - (-4))/(2 - (-2))
Slope, m = (-2 + 4)/(2 + 2)
Slope, m = 2/4
Slope, m = 1/2
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. a 11-bit string is selected at random so that each 11-bit string is equally likely. what is the probability that the string is a palindrome
The probability that an 11-bit string is a palindrome is 1 in 2048, or 0.00048828125%.
A group of characters known as a palindrome read the same both forward and backward
For an 11-bit string, there are 2048 possible combinations of 0s and 1s. Of those, only one combination is a palindrome. Therefore, the probability of randomly selecting an 11-bit string that is a palindrome is 1 in 2048, or 0.00048828125%.
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Which option below provides the best description of the relationship between a quadratic parent function and a square root parent function? A. The square root function is the quadratic function reflected across the line y = x, with a limited domain. B. The square root function is the quadratic function reflected across the y-axis. C. The square root function is the quadratic function reflected across the x-axis. D. The quadratic function and square root functions have no inverse.
The option that provides the best description of the relationship between a quadratic parent function and a square root parent function is A. The square root function is the quadratic function reflected across the line y = x, with a limited domain.
How to illustrate the function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
The square root function is the quadratic function reflected across the line y = x, with a limited domain. The graph y=x² and y=√x and y=x. The graph is attached.
In conclusion, the correct option is A.
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a. There are 18 salt shakers and 48
pepper shakers. Write the ratio of
pepper shakers to salt shakers.
Answer:
The ratio is 8:3
Step-by-step explanation:
18 salt shakers and 48 pepper shakers.
Ratio of pepper shakers to salt shakers
48 : 18
Divide each side by 6
48/6 : 18/6
8 : 3
The ratio is 8:3
center (1,-2) radius 2
The equation of a circle with center (1,-2) and radius 2 is ( x - 1 )² + ( y + 2 )² = 4.
What is the equation of the circle?The standard form of the circle is x² + y² = r²
Where r is the radius.
h and k is the horizontal and vertical translation which represent the center of the circle..
Hence, the formula is derived from the distance formula where the distance is between the center and every point on the circle is equal to the length of the radius.
( x - h )² + ( y - k )² = r²
Given that;
Center: (1,-2)
h = 1k = -2Radius r = 2Plug the given values into the equation and simplify.
( x - h )² + ( y - k )² = r²
( x - 1 )² + ( y - (-2) )² = 2²
( x - 1 )² + ( y + 2 )² = 2²
( x - 1 )² + ( y + 2 )² = 4
Therefore, the equation of the circle is ( x - 1 )² + ( y + 2 )² = 4
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What is the prime factorization of 168? 22 x 32 x 5 34 x 7 22 x 17 23 x 3 x 7
The prime factorization of 168 is (d) 2³ × 3 × 7
How to determine the prime factorization of 168?From the question, we have the following expression that can be used in our computation:
Number = 168
Express 168 as the products of numbers
So, we have the following representation
168 = 2 × 2 × 2 × 3 × 7
Express as exponents
168 = 2³ × 3 × 7
Hence, the prime factorization is 2³ × 3 × 7
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PLEASE IM IN NEED OF HELP!!!
Find the value of a.
Answer:a=17
Step-by-step explanation:
3(4a-8)=180
4a-8=60
4(a-2)=60
a-2=15
a=17
Hope this help!!!!
Is there a proportional relationship between the cost of items before tax and the cost of items after tax?
Answer:Yes,
There is a direct proportional relationship
between the cost of items before tax and the
cost of items after tax.
5.0
Step-by-step explanation:
Given - A city has a 5% sales tax.
To find - Is there a proportional relationship
between the cost of items
before tax and the cost of items after
tax?
Proof
Yes, cost of items before tax is directly
proportional to cost of items after tax.
Reason
With the increase in the sales tax, there is
increase in the cost of items after tax, therefore,
there is a direct relation between cost of items
before tax and cost of items after tax.
Step-by-step explanation:
Question 1
(02.01 LC)
What is the solution for the equation 4x 10 = 2x? x =______. (Input whole number
only). (5 points)
Po p
5
7=x
I hope i read the question right, but use this to help you!
Find the nth term of this number sequence 15, 12, 9, 6, ....
Answer: -3n + 18
Step-by-step explanation:
When examining the sequence, you can see that every time, it decreases by 3, therefore the first part of your rule should be:
-3n
(Extra note to wow your maths teacher! This is a linear sequence as it decreases/increases by the same amount each time.)
Next, you will need to find the number before the given sequence. As it decreases by 3 every time, to find the number before you need to increase by 3. Therefore, the next part you need is + 18.
Leave a comment if you don't understand anything :)
Answer:
The nth term is 18 - 3n------------------------------------
Given sequence:
15, 12, 9, 6, .... This is an AP, with the first term a = 15 and common difference of - 3, as it is decreasing by 3.
Use nth term equation for an AP:
t(n) = a + (n - 1)dt(n) = 15 + (n - 1)(-3) = 15 - 3n + 3 = 18 - 3nHow can I solve this?
[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{w}{4}~~ = ~~\cfrac{2}{~~1 \frac{2 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{2}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{\frac{2}{1}}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}=\cfrac{2}{1}\cdot \cfrac{3}{5} \\\\\\ \cfrac{w}{4}=\cfrac{6}{5}\implies 5w=24\implies w=\cfrac{24}{5}\implies {\Large \begin{array}{llll} w=4\frac{4}{5} \end{array}}[/tex]
find the exact length of the curve. y = 1 + 8x3/2, 0 ≤ x ≤ 1
The exact length of the curve is [tex]\frac{1}{216}[145^{\frac{3}{2} } -1][/tex].
The given equation is [tex]$y=1+8 x^{\frac{3}{2}}$[/tex].
The point is [tex]$$0 \leq x \leq 1$.[/tex]
Arc length: To find the arc length of the function y=f(x), use the power rule. After that use the integration.
Let f(x) be a smooth function over the interval [a,b] . Then the arc length of the portion of the graph of f(x) from the point (a, f(a)) to the point (b, f(b)) is given by
The formula of the arc length is: [tex]$=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2}$[/tex]
Differentiate this equation
[tex]$$\begin{aligned}& y^{\prime}=8 \frac{\mathrm{d}\left(x^{\frac{3}{2}}\right)}{\mathrm{d} x} \\& =8 \frac{3}{2} x^{\frac{1}{2}} \\& =12 \sqrt{x}\end{aligned}$$[/tex]
Now, find the arc-length.
[tex]$$\begin{aligned}& \text { Arc-length }=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2} \\& =\int_0^1 \sqrt{1+144 x}\end{aligned}$$[/tex]
Use the substitution method.
[tex]$$\begin{aligned}& u=1+144 x \\& d x=\frac{1}{144} d u \\& =\frac{1}{144} \int_1^{145} \sqrt{u} d u \\& =\frac{1}{144}\left[\frac{u^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^{145} \\& =\frac{1}{216}\left[145^{\frac{3}{2}}-1\right]\end{aligned}$$[/tex]
Hence, the exact length is [tex]\frac{1}{216}\left[145^{\frac{3}{2}}-1\right][/tex].
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A hendecagon is graphed on a coordinate grid and then dilated by a scale factor of 5 with the origin as the center of dilation. Vertex A of
the original hendecagon is located at (-8, 7). Write the ordered pair
that represents the location of vertex A after the dilation.
Answer: The ordered pair that represents the location of vertex A after the dilation is (-40, 35).
Step-by-step explanation:
How do we dilate a figure with the origin as the center of dilation?
To dilate a figure with the origin as the center of dilation, we multiply the coordinates of each point by the scale factor. This has the effect of stretching or shrinking the figure, depending on whether the scale factor is greater than or less than 1.
To dilate a figure by a scale factor of 5 with the origin as the center of dilation, we need to multiply the x- and y-coordinates of each point in the figure by 5.
So, to find the coordinates of vertex A after the dilation, we start with the coordinates of vertex A before the dilation, which are (-8, 7).
Then, we multiply the x-coordinate by 5 to get (-8)5 = -40, and we multiply the y-coordinate by 5 to get (7)5 = 35.
Vertex A is located at (-8, 7). If we multiply these coordinates by 5, we get (-40, 35). Therefore, the coordinates of vertex A after the dilation are (-40, 35).
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After the dilation, the ordered pair that depicts where vertex A is located is (-40, 35).
How can we increase a figure so that the origin serves as the dilation center?
We multiply the coordinates of each point by the scale factor to dilate a figure with the origin as the center of dilation. Depending on whether the scale factor is larger than or less than 1, this has the effect of either expanding or shrinking the figure.
The x- and y-coordinates of each point in the figure must be multiplied by 5 in order to dilate it by a scale factor of 5, with the origin serving as the centre of dilation.
Thus, we begin with the coordinates of vertex A before the dilation, which are, in order to obtain the coordinates of vertex A after the dilation (-8, 7).
The x-coordinate is then multiplied by 5 to get (-8)5 =-40, while the y-coordinate is multiplied by 5 to get (7)5 = 35.
Vertex A can be observed at (-8, 7). These coordinates are multiplied by 5 to get (-40, 35). As a consequence, vertex A's coordinates after dilation are (-40, 35).
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Gabby worked 60 hours in 7 days. determine the rate for a ratio of the two different quantities. a. 60 over 7 hours per day b. 60 over 67 hours per day c. 7 over 60 hours per day d. 7 over 67 hours per day
Answer:
a
Step-by-step explanation:
60 hours in 7 days = 60/7 hours per day
Answer:
A is correct
Step-by-step explanation:
I got it right on my test
Solve 7+x/3=2x-5 need it asap
Answer:
x = [tex]\frac{36}{5}[/tex]
Step-by-step explanation:
7 + [tex]\frac{x}{3}[/tex] = 2x - 5 ( subtract 7 from both sides )
[tex]\frac{x}{3}[/tex] = 2x - 12 ( multiply through by 3 to clear the fraction )
x = 6x - 36 ( subtract 6x from both sides )
- 5x = - 36 ( divide both sides by - 5 )
x = [tex]\frac{-36}{-5}[/tex] = [tex]\frac{36}{5}[/tex] = 7.2 ( in decimal form )
Choose "function" or "not a function" for the problem. {(30,-9), (15,9), (–15, -9), (-30, 9)}
g sio2 is always 0.4 mg too high regardless of the weight of the sample taken for analysis. calculate the relative error in parts per thousand in a sample which contains 10% sio2, if the siz
g sio2 is always 0.4 mg too high regardless of the weight of the sample taken for analysis. The relative error in parts per thousand would be 400.
This is because the relative error is calculated by taking the difference between the actual value and the measured value, and dividing this by the actual value.
In this case, the actual value is 0.4 mg and the measured value is
0.4 mg + (10% x 0.4 mg) = 0.44 mg. Thus the relative error is
(0.44 – 0.4)/0.4 = 0.1/0.4 = 0.25 = 400 parts per thousand.
The relative error in parts per thousand would be 400.
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la pyramide du louvre
D'après ce que je sais. La pyramide du Louvre (Pyramide du Louvre) est une grande structure de verre et de métal conçue par l'architecte sino-américain I. M. Pei. La pyramide se trouve dans la cour principale (Cour Napoléon) du Palais du Louvre à Paris, entourée de trois pyramides plus petites. La grande pyramide sert d'entrée principale au musée du Louvre. Achevé en 1988 dans le cadre du projet plus large du Grand Louvre, il est devenu un point de repère de la ville de Paris.
(-5+ i)(12- i)(-3).
Answer:
177 - 51i
Step-by-step explanation:
[tex](-5+ i)(12- i)(-3).[/tex]
[tex](-5+ i)(12- i)[/tex]
Apply the distributive property[tex]-5X12-5(-i)[/tex]+[tex](-i)X12+(i)[/tex][tex](-i)[/tex]
Simplify[tex]-60+5i+12i-1i^{2}[/tex]
Reduce the imaginary units using the property [tex]i^{2} =-1[/tex][tex]-60+5i+12i-1(-1)[/tex]
Simplify and write in the standard form of [tex]a+bi[/tex][tex]-59+17i\\(-59+17i)(-3)\\177-51i[/tex]
Hope it helps u:)
Answer:
[tex]177 - 51i[/tex]
Step-by-step explanation:
Given expression:
[tex](-5+i)(12-i)(-3)[/tex]
Use the FOIL method to multiply the first two parentheses:
[tex]\implies \left(-5 \cdot 12 -5 \cdot -i +i \cdot 12 + i \cdot -i\right)(-3)[/tex]
[tex]\implies \left(-60 +5i +12i -i^2\right)(-3)[/tex]
[tex]\implies \left(-60 +17i -i^2\right)(-3)[/tex]
Multiply:
[tex]\implies -60 \cdot -3 +17i \cdot -3 -i^2 \cdot -3[/tex]
[tex]\implies 180-51i+3i^2[/tex]
Apply the imaginary number rule: i² = -1
[tex]\implies 180-51i+3(-1)[/tex]
Simplify:
[tex]\implies 180-51i-3[/tex]
[tex]\implies 177-51i[/tex]
Which one is not a function and function?
Answer:
1st and 3rd pictures are not functions. 2nd one is a function.
Step-by-step explanation:
Perform the Vertical Line Test by drawing a line in the functions. If they touch the function twice, they are not a functions. However, if the line touches once, it's a function.
Solve for x: 9x2 + 10x - 3 = 0
(Look at the screenshot)
The value of x we get from the equation is [tex]\frac{- 10 ±\sqrt{208}}{18}\\[/tex]
The given equation is [tex]9x^{2} + 10x -3=0[/tex]
We know, the quadratic formula is [tex]x=\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/tex] where [tex]a\neq 0[/tex]
Using the Quadratic Formula where
a = 9, b = 10, and c = -3
We get,
[tex]x=\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x=\frac{- 10± \sqrt{10^{2}-4(9)(-3) }}{2(9)}\\[/tex]
[tex]x=\frac{- 10± \sqrt{100--108 }}{18}\\[/tex]
[tex]x=\frac{- 10± \sqrt{208}}{18}\\[/tex]
The discriminant [tex]b^{2} -4ac[/tex]>0 so, there are two real roots
From this, we get 2 values of x
[tex]x=0.245678[/tex]
[tex]x= -1.35679[/tex]
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Answer:-10±√208÷18
Step-by-step explanation
1) so, there is a formula that is x= -b±√b²-4ac÷2a, we can use this to solve this equation.
2) put these value in the formula, then we will get
here, a=9
b=10
c=-3
x=-10±√100-4*9*-3÷2*9
x=-10±√208÷18
the yield of good chips during a certain step in silicon processing of integrated circuits averages 89%. this processing step is considered to be in statistical control. the number of chips per wafer is 156. determine the center line, lcl, and ucl for the p chart that would be used for this processing step.
The center line, LCL, and UCL for the p chart that would be used for this processing step are 89%, 88.3%, and 89.7%, respectively.
The center line of a p chart is the average yield of good chips during a processing step, and is calculated as follows:
Centerline = average yield of good chips = 89%
The lower control limit (LCL) and upper control limit (UCL) for a p chart are calculated using the following equations:
LCL = average yield of good chips - 3 × standard deviation
UCL = average yield of good chips + 3 × standard deviation
To calculate the standard deviation, we need to know the number of chips per wafer (156 in this case). The standard deviation is calculated using the equation:
standard deviation = √(p × (1 - p) / n)
where p is the average yield of good chips (89% in this case), (1 - p) is the average yield of defective chips (11% in this case), and n is the number of chips per wafer (156 in this case).
Plugging the values for p, (1 - p), and n into the equation gives us:
standard deviation = √(0.89 × 0.11 / 156) = 0.0256
Substituting the standard deviation into the equations for the LCL and UCL gives us:
LCL = 89% - 3 × 0.0256 = 88.3%
UCL = 89% + 3 × 0.0256 = 89.7%
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someone help me please asap
The value of the discriminant of f is 0.
There is one distinct real number of zeroes.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 3x² + 24x + 48
This is in the form of ax² + bx + c
a = 3
b = 24
c = 48
The discriminant is given by b² - 4ac.
There are two real solutions when it is greater than 0.
There is one real solution when it is equal to 0.
There are two imaginary solutions when it is less than 0.
Now,
= 24² - 4 x 3 x 48
= 576 - 576
= 0
So,
There is one real solution.
Thus,
The value of the discriminant of f is 0.
There is one distinct real number of zeroes since the discriminant is zero.
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if a basketball team won 32 games and won three times as many games as it lost. how many games did they win?
The team won 24 games out of the 32 they played.
A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer equal 0. A proportion is an equation wherein two ratios are set the same for every other. In arithmetic, a ratio suggests how commonly one wide variety contains every other. as instance, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6 (this is, eight:6, that is equivalent to the ratio four: three).
The share system is used to depict if two ratios or fractions are the same. we are able to locate the lacking fee by using dividing the given values. the share components can be given as a: b::c : d = a/b = c/d, where a and d are the extreme phrases and b and c, are the suggested phrases.
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