What is the equation of the line through (-2, -3) with an undefined slope?a.y=-3b. -3x + 2y = 0c. -2x – 3y = 0d.x=-2
Answers
We have an undefined slope. It means that the line is parallel to the y-axis, that is, the slope could be "defined" as an infinite slope (in rough words).
Therefore, the equation of the line through the point (-2, -3) with an undefined slope is:
x = -2 (option d).
This line is represented as a parallel line to the y-axis (x = -2), and it passes through the point (-2, -3).
Related Questions
1. Find the slope 2.what is wrong with the following slopes ?
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Given two points (x₁, y₁) and (x₂, y₂), the slope (m) is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, to solve this question. Follow the steps.
Step 01: Substitute the points in the equation and solve part 1.
(x₁, y₁) = (-3, -1)
(x₂, y₂) = (-2, 6)
[tex]\begin{gathered} m=\frac{6-(-1)}{-2-(-3)} \\ m=\frac{6+1}{-2+3} \\ m=\frac{7}{1} \\ m=7 \end{gathered}[/tex]The slope is 7.
Step 02: Find what is wrong.
The points are:
(x₁, y₁) = (3, 5)
(x₂, y₂) = (-2, 6)
So, substituting in the equation:
[tex]m=\frac{6-5}{-2-3}=\frac{1}{-5}=-\frac{1}{5}[/tex]What is wrong is that the numerator was substituted by (y₁ - y₂), while the denominator was substituted by (x₂ -x₁).
Answer the following questions.(a) 12 is 15% of what?.(b) 45% of 60 is what number?.
Answers
ANSWER:
(a) 80
(b) 27
STEP-BY-STEP EXPLANATION:
(a)
We must calculate what number 15% is equal to 12, therefore, we do the following operation:
[tex]100\cdot\frac{12}{15}=80[/tex](b)
In this case we must calculate 45% of 60, therefore:
[tex]60\cdot\frac{45}{100}=27[/tex]Which method do you prefer over the others describe the method in your own words and give an example of a quadratic equation that can be solved with the method Please help thanks thanks
Answers
The Solution:
We are required to give an example of a quadratic equation.
Describe a chosen method for solving the quadratic equation.
Solve it using the method you described.
A quadratic equation is an equation in the form:
[tex]ax^2+bx+c=0[/tex]So, an example of a quadratic equation is:
[tex]x^2+x-6=0[/tex]My chosen method of solving the quadratic equation is the Formula Method.
The quadratic formula (also known as Formula Method) is given as
Where
[tex]\begin{gathered} a=\text{ coefficient of x}^2 \\ b=\text{ coefficient of x} \\ c=\text{ constant term} \\ \end{gathered}[/tex]Solving the above quadratic equation using the formula method.
[tex]\begin{gathered} x^2+x-6=0 \\ In\text{ this case} \\ a=1 \\ b=1 \\ c=-6 \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]\begin{gathered} x=\frac{-1\pm\sqrt{1^2-4(1)(-6)}}{2(1)} \\ \\ x=\frac{-1\pm\sqrt{1+24}}{2} \\ \\ x=\frac{-1\pm\sqrt{25}}{2} \\ \\ x=\frac{-1\pm5}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-1+5}{2}\text{ or }x=\frac{-1-5}{2} \\ \\ x=\frac{4}{2}\text{ or }x=\frac{-6}{2} \\ \\ x=2\text{ or }x=-3 \end{gathered}[/tex]Therefore, the correct answer is x = 2 or -3
solve for 2 cos x+sqrt2 =0 for o
pi/4
3pi/4
5pi/4
7pi/4
it's 3pi/ 4 and 5pi/4
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Answer:
[tex]\frac{3\pi }{4} \ and \ \frac{5\pi }{4} .[/tex]
Step-by-step explanation:
[tex]1. \ cosx=-\frac{\sqrt{2} }{2};\\x=^+_-\frac{3 \pi}{4}+2 \pi n, \ where \ n=Z.[/tex]
2. finally, the answer is
[tex]\frac{3\pi }{4} \&\frac{5\pi }{4} .[/tex]
The sum of six consecutive integers is -9. What are the integers?
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Therefore the six consecutive integers are -4,-3,-2,-1,0,1 .
What is consecutive integer ?
Integers that follow one another are referred to as consecutive integers. They proceed in a certain order or sequence. For instance, a sequence of natural numbers are all integers. In mathematics, the term "consecutive" refers to an uninterrupted chain of events or a continuous progression, such as when integers follow one another in a sequence where each succeeding number is one more than the one before it. The mean and median are both identical in a collection of successive integers (or in numbers). x + 1 and x + 2 are two consecutive integers if x is an integer.
Here sum of six consecutive integer is -9.
Let us take the 6 consecutive numbers are,
=> x,x+1, x+2, x+3,x+4, x+5
Now sum is -9. Then ,
=> x+x+1+x+2+x+3+x+4+x+5 =-9
=> 6x + 15 = -9
=> 6x = -9-15
=> 6x = -24
=> x = -24/6
=> x= -4
Then 6 integers are ,
=> -4,-3,-2,-1,0,1
Therefore the six consecutive integers are -4,-3,-2,-1,0,1 .
To learn more about consecutive integer
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write the ratio as a fraction in lowest terms. compare in hours.22 hours to 5 days
Answers
We know 1 day = 24 hours
Let's convert 5 days to hours:
[tex]5\text{days}\times\frac{24\text{hour}}{1\text{day}}=5\times24=120hours[/tex]Now, we have the ratio:
22 hours to 120 hours
We can write it as a fraction:
[tex]\frac{22}{120}[/tex]This is not in its lowest terms. We can divide numerator and denominator by "2", to get:
[tex]\frac{22}{120}=\frac{11}{60}[/tex]Thus, final answer is:
11/60
or
[tex]\frac{11}{60}[/tex]What are the coordinates (x,y) of the solution to the system of equations?
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The system of equations given are
[tex]\begin{gathered} y=-8x+10 \\ y=x-8 \end{gathered}[/tex]ExplanationSolve the given system of equations using elimination method
[tex]\begin{gathered} y=-8x+10..........1 \\ y=x-8......2 \end{gathered}[/tex]Subtract equation 1 by equation 2.
[tex]\begin{gathered} (y+8x-10)-(y-x+8)=0 \\ 8x-10+x-8=0 \\ 9x=18 \\ x=2 \end{gathered}[/tex]Now find the value of y by substitute the value of x in equation 1.
[tex]\begin{gathered} y=-8\times2+10 \\ y=-16+10 \\ y=-6 \end{gathered}[/tex]AnswerHence the coordinates of x and y to the system of equations is
[tex](2,-6)[/tex]Find the square root. Assume that the variable is unrestricted, and use absolute value symbols when necessary. (Simplify your answer completely)
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We are given the following expression:
[tex]\sqrt[]{81x^2}[/tex]To simplify this expression we will use the following property of radicals:
[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]Applying the property we get:
[tex]\sqrt[]{81x^2}=\sqrt[]{81}\sqrt[]{x^2}[/tex]Now, the first radical is equal to 9 since 9 x 9 = 81, therefore, we get:
[tex]\sqrt[]{81x^2}=\sqrt[]{81}\sqrt[]{x^2}=9\sqrt[]{x^2}[/tex]For the second radical we will use the following property of absolute values:
[tex]\lvert x\rvert=\sqrt[]{x^2}[/tex]Replacing we get:
[tex]\sqrt[]{81x^2}=\sqrt[]{81}\sqrt[]{x^2}=9\sqrt[]{x^2}=9\lvert x\rvert[/tex]Therefore, the expression reduces to the product of 9 and the absolute value of "x".
generate ordered pairs for tha function y=x² - 9 using x = -4, -2,0,2 and 4
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Generating ordered pairs is to solve for "y" using the function above with the given "x" values -4, -2, 0, 2, and 4.
If x = -4, then y = 7.
y = (-4)² - 9
y = 16 - 9
y = 7
If x = -2, then y = -5.
y = (-2)² - 9
y = 4 - 9
y = -5
If x = 0, then y = -9
y = 0² - 9
y = 0 - 9
y = -9
If x = 2, then y = -5
y = 2² - 9
y = 4 - 9
y = -5
If x = 4, then y = 7
y = (4)² - 9
y = 16 - 9
y = 7
To summarize, the ordered pairs for the function y = x² - 9 using the given x - values are:
1. (-4, 7)
2. (-2, -5)
3. (0, -9)
4. (2, -5)
5. (4, 7)
Below is the graph of the equation. Due to the nature of the equation, the graph is a parabola.
Solve the equation: 3(2y-5)=9 for y
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Applying the distributive property in this case:
[tex]6y-15=9[/tex]Adding 15 at both sides of the equation:
[tex]6y-15+15=9+15\rightarrow6y+0=24[/tex]Then
[tex]6y=24[/tex]Dividing both sides by 6, we finally have:
[tex]\frac{6}{6}y=\frac{24}{6}\rightarrow y=4[/tex]Therefore, the value for y = 4.
GRE verbal reasoning scores has an unknowndistribution with a mean of 150.1 and astandard deviation of 9.4. Using the empirical rule,what do we know about thepercentage of GRE verbal reasoning scoresbetween 131.3 and 168.9?
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Empirically we can see the σ ranges of a Gaussian distribution in the following figure
From exercise we know that:
[tex]\begin{gathered} \bar{x}\bar{}=150.1 \\ \sigma=9.4 \end{gathered}[/tex]We will calculate how many sigmas the given range is to know what the percentage of scores :
[tex]\begin{gathered} x=\bar{x}-A\sigma \\ x=131.3 \\ 131.3=150.1-A(9.4) \\ 150.1-131.3=9.4A \\ A=\frac{18.8}{9.4} \\ A=2 \\ \end{gathered}[/tex]The score 131.3 is 2 sigmas from the mean
[tex]\begin{gathered} x=\bar{x}+A\sigma \\ x=168.9 \\ 168.9=150.1-A(9.4) \\ 168.9-150.1=9.4A \\ A=\frac{18.8}{9.4} \\ A=2 \end{gathered}[/tex]The score 168.9 is 2 sigmas from the mean
The range of reasoning scores between 131.3 and 168.9 is ±2σ which corresponds to 95.5% (see initial graph)Which of the following methods of timekeeping is the least precise?A. Using a stopwatchB. Using a wrist watchC. Counting your heartbeatsO D. Using a calendar
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It’s c counting your heartbeats
My reasoning is that a wrist watch, a calendar and a stop watch all function on metered, constant intervals of time. A heart beat doesn't. It changes from person to person, from moment to moment. It isn't regular enough to be a precise unit of measure.
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 37 minutes of calls is$13.21 and the monthly cost for 70 minutes is $17.50. What is the monthly cost for 45 minutes of calls?
Answers
Given:
The monthly cost is 37 min is $13.21
70 min cost is $17.50
Find-:
The monthly cost for 45 minutes of calls
Explanation-:
The linear equation is:
[tex]\begin{gathered} y=mx+c \\ \end{gathered}[/tex]Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ c=Y-\text{ Intercept} \end{gathered}[/tex]The formula of the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point is:
[tex]\begin{gathered} (x_1,y_1)=(37,13.21) \\ \\ (x_2,y_2)=(70,17.50) \end{gathered}[/tex]So, the slope is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{17.50-13.21}{70-37} \\ \\ m=\frac{4.29}{33} \\ \\ m=0.13 \end{gathered}[/tex]Slope is:
The general equation of a line:
[tex]\begin{gathered} y=mx+c \\ \\ y=0.13x+c \end{gathered}[/tex]The value of "c" is:
[tex]\begin{gathered} y=0.13x+c \\ \\ (x,y)=(37,13.21) \\ \\ 13.21=0.13(37)+c \\ \\ c=13.21-4.81 \\ \\ c=8.4 \end{gathered}[/tex]The equation is:
[tex]\begin{gathered} y=mx+c \\ \\ y=0.13x+8.4 \end{gathered}[/tex]Cost at 45 min. is:
[tex]\begin{gathered} x=45 \\ \\ y=0.13x+8.4 \\ \\ y=0.13(45)+8.4 \\ \\ y=5.85+8.4 \\ \\ y=14.25 \end{gathered}[/tex]The 45 min cost is $14.25
A city has a population of 300,000 people. Suppose that each year the population grows by 4.5%. What will the population be after 14 years?Use the calculator provided and round your answer to the nearest whole number.
Answers
Given:
Population =300000
Growth rate = 4.5 %.
time = 14 years.
consider the exponential growth equation.
[tex]y=a(1+r)^t[/tex]where a is the initial value and r=growth rate.
Let y be the number of population after t years.
Substitute a=300000, r=4.5/100. t-14 in exponential growth equation, we get
[tex]y=300000(1+\frac{4.5}{100})^{14}[/tex][tex]y=300000(\frac{100}{100}+\frac{4.5}{100})^{14}[/tex][tex]y=300000(\frac{104.5}{100})^{14}[/tex][tex]y=300000(1.045)^{14}[/tex][tex]y=555583.476485[/tex]Hence the population after 14 years is 555584 people.
i forgot how i solved this and i need help understanding the second step done by lorne, thank u!
Answers
Given:
[tex](-3x^3+5x^2+4x-7)+(-6x^3+2x-3)[/tex]The second step is writing the terms individually and the addition sign between them, so, we will use the property of the opposite addition
For example, instead of writing: (1 - a), we can write it as 1 + (-a)
So, the expression will be:
[tex](-3x^3)+5x^2+4x+(-7)+(-6x^3)+2x+(-3)[/tex]the next model of a sports car will cost 14.4% more than the current model the current model cost $41,000 how much would a price increase in dollars what would the price of the next model?
Answers
Given that the current model of the car cost;
[tex]\text{ \$41,000}[/tex]We are informed that the next model of a sports car will cost 14.4% more than the current model.
The price increase in dollars will then be given as;
[tex]\begin{gathered} \frac{14.4}{100}\times41000 \\ =\text{ \$}5904 \end{gathered}[/tex]Answer 1: Price increase in dollars is $5904
The cost of the next model will then be the sum of the current model and the price increase in dollars.
This would give;
[tex]\text{ \$41000+\$5904=\$46904}[/tex]Answer 2: The cost of the next price model is $46904
If the lateral areas of two similar prisms are in a ratio of 8 to 18, what is the ratio of the volumes? Enter answers in the same format and order as the original ratio. Round any decimals to the nearest 10th.
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The ration of the lateral areas of the smaller prism to the larger prism is 8 to 18
The first step is t find the scale factor. Recall,
area = square of scale factor
Thus, scale factor = square root of area
Thus,
[tex]\begin{gathered} \text{scale factor = }\sqrt[]{\frac{8}{18}} \\ \text{Dividing the numerator and denominator by 2, we have} \\ \text{scale factor = }\sqrt[]{\frac{4}{9}} \\ scale\text{ factor = 2/3} \end{gathered}[/tex]Volume = cube of scale factor. Thus,
[tex]\begin{gathered} \text{volume = (}\frac{2}{3})^3 \\ \text{Volume = }\frac{8}{27} \\ \end{gathered}[/tex]I need help with this please. I have tried multiple times but still could not get the correct answers
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Recall that the diagonals of a rhombus are perpendicular bisectors of each other, therefore all the right triangles formed by the diagonals as shown in the given diagram are congruent, therefore:
[tex]\begin{gathered} \measuredangle1=\measuredangle4=\measuredangle2, \\ \measuredangle3=39^{\circ}, \\ \measuredangle1+39^{\circ}=90^{\circ}. \end{gathered}[/tex]Solving the last equation for angle 1 we get:
[tex]\begin{gathered} \measuredangle1=90^{\circ}-39^{\circ}, \\ \measuredangle1=51^{\circ}. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} m\angle1=51^{\circ}, \\ m\angle2=51^{\circ}, \\ m\angle3=39^{\circ}, \\ m\angle4=51^{\circ}. \end{gathered}[/tex]let f(x)=2x+1. write a function g(x) whose grass is a rotation of f (x) about (0,1) by a factor of 3 , followed buy a vertical translation 6 units down
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1) Considering f(x)= 2x+1, And g(x) be f(x) rotated about y=1, with a factor of 3 this
A vertical translation 6 units down= g(x) = 2x -5
A factor of 3: g(x)= 3(2x)-5
State with the equation has one solution, new solution, or infinitely many solutions.
Answers
SOLUTION:
The equation is;
[tex]\begin{gathered} -2g+10=8g \\ 10=10g \\ g=1 \\ \end{gathered}[/tex]The equation has one solution
in triangle XYZ, point M is the centroid. If XM=8, find the length of MA
Answers
Centroid theorem: the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.
For the given triangle:
[tex]XM=\frac{2}{3}XA[/tex]XA is the sum of XM and MA:
[tex]XA=XM+MA[/tex]Use the two equations above to find MA:
[tex]\begin{gathered} XM=8 \\ \\ 8=\frac{2}{3}XA \\ \\ XA=\frac{3}{2}(8) \\ \\ XA=12 \\ \\ \\ 12=8+MA \\ MA=12-8 \\ \\ MA=4 \end{gathered}[/tex]Then, MA is equal to 4A probability experiment consist of rolling a 15-sided die. Find the probability of the event below. rolling a number divisible by 6
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SOLUTION
A 15-sided die has 15 faces numbered 1 to 15.
So the total possible outcome is 15.
Of all the numbers from 1 to 15, only 6 and 12 are divisible by 6. Therefore the numbers divisible by 6 is 2.
So the required outcome = 2
Probability =
[tex]\text{Probability = }\frac{required\text{ outcome}}{\text{total possible outcome}}[/tex]So,
[tex]\begin{gathered} \text{Probability = }\frac{required\text{ outcome}}{\text{total possible outcome}} \\ \\ \text{Probability = }\frac{2}{\text{1}5} \end{gathered}[/tex](50k³ + 10k² − 35k – 7) ÷ (5k − 4)How do I simplify this problem
Answers
ANSWER :
[tex]10k^{2}+10k+1-\frac{3}{5k-4}[/tex]
EXPLANATION :
From the problem, we have an expression :
[tex](50k^3+10k^2-35k-7)\div(5k-4)[/tex]The divisor is (5k - 4)
Step 1 :
Divide the 1st term by the first term of the divisor.
[tex]\frac{50k^3}{5k}=10k^2[/tex]The result is 10k^2
Step 2 :
Multiply the result to the divisor :
[tex]10k^2(5k-4)=50k^3-40k^2[/tex]Step 3 :
Subtract the result from the polynomial :
[tex](50k^3+10k^2-35k-7)-(50k^3-40k^2)=50k^2-35k-7[/tex]Now we have the polynomial :
[tex]50k^2-35k-7[/tex]Repeat Step 1 :
[tex]\frac{50k^2}{5k}=10k[/tex]The result is 10k
Repeat Step 2 :
[tex]10k(5k-4)=50k^2-40k[/tex]Repeat Step 3 :
[tex](50k^2-35k-7)-(50k^2-40k)=5k-7[/tex]Now we have the polynomial :
[tex]5k-7[/tex]Repeat Step 1 :
[tex]\frac{5k}{5k}=1[/tex]The result is 1
Repeat Step 2 :
[tex]1(5k-4)=5k-4[/tex]Repeat Step 3 :
[tex](5k-7)-(5k-4)=-3[/tex]Since -3 is a number, this will be the remainder.
Collect the bold results we had from above :
(10k^2 + 10k + 1) remainder -3
Note that the remainder can be expressed as remainder over divisor.
That will be :
[tex]\begin{gathered} 10k^2+10k+1+\frac{-3}{5k-4} \\ or \\ 10k^2+10k+1-\frac{3}{5k-4} \end{gathered}[/tex]Find the measure of angle R, given that the largest triangle is a right triangle.A)27B)18C)72D)45
Answers
we know that
The central angle is 90 degrees
so
18+R=45 degrees
R=45-18
R=27 degreesThe number of accidents that occureach day at a certain intersection alongwith the corresponding probabilities areshown.Accidents01234Probability.935.03.02.01.005Find the expected number of accidentseach day.
Answers
Answer:
0.12
Explanation:
The expected value of a probability distribution can be obtained using the formula:
[tex]\sum ^n_{i\mathop=1}x_i\cdot P(x_i)[/tex]Therefore, the expected number of accidents will be:
[tex]\begin{gathered} E(X)=(0\times0.935)+(1\times0.03)+(2\times0.02)+(3\times0.01)+(4\times0.005) \\ =0+0.03+0.04+0.03+0.02 \\ =0.12 \end{gathered}[/tex]The expected number of accidents each day is 0.12.
determine the composition of transformation that would map figure ABCD to figure A"B"C"D". 1. the transformation that would map vertex B to B' isa: a transformation down and rightb: a rotation of 90° about Bc: a rotation of 360° about B
Answers
Answer:
b: a rotation of 90° about B
Explanation:
A transformation down and right of the figure look like this:
Where the figure is just translated, so the orientation of the figure is the same.
In the same way, a rotation of 360° doesn't change the figure, because it is equivalent to make a full turn of the figure.
Finally, a rotation of 90° about B looks like this:
Where each segment of the initial figure forms an angle of 90° with its corresponding segment of the reflected figure. For example, BA is perpendicular to B'A'
Therefore, the answer is b: a rotation of 90° about B.
Can you help me figure out if figure in a polygon. is it a polygon the name of it by the number of the size
Answers
2)
A polygon has an infinite number of sides and they are connected to each other end to end. This means that it is an enclosed figure. Looking at the figure, it has all these characteristics. Thus,
It is a polygon
Next, we would count the number of sides. In this case, it is 10. A 10 sided polygon is called a Decagon. Thus, the given figure is a Decagon
Which equation represents a line which is perpendicular to the line y - 6x = -3? Submit Answer Oy= 6x +3 Oy= 1/6x +4 O y= - 1/6x + 8 O y = -6x + 2
Answers
When we have two perpendicular lines their slopes are opposite and inverse.
In this case, we have the equation of the line:
y-6x= -3
Let's solve for y and arrange this equation to make it look like the general form of a linear equation: y=mx+b, where m is the slope of the line.
y-6x= -3
y-6x+6x= -3+6x
y= 6x-3
As we can see, the number that is multiplying the x variable in our equation is 6, the slope of this line is 6.
As mentioned, a perpendicular line to the line y= 6x-3 would have a slope opposite and inverse, then the slope of the line perpendicular to the first line (m2) would be:
[tex]m2=-\frac{1}{6}[/tex]from the options that we have, we can see that the only line that has a slope of -1/6 is the line y= -1/6+8, so that is the right option.
What are the next 4 terms of the sequence 1, 6, 11...?
Answers
The formula to find the sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]Where a1 is the first term of the sequence, n is the number of terms and d is the common difference. We can find the common difference by the following formula:
[tex]d=a_n-a_{n-1}[/tex]With the given terms of the sequence we can find d:
[tex]\begin{gathered} d=11-6=5 \\ or \\ d=6-1=5 \end{gathered}[/tex]The common difference is d=5.
Now, apply the formual to find the next 4 terms of the sequence:
[tex]\begin{gathered} a_4=1+(4-1)\cdot5=1+3\cdot5=1+15=16 \\ a_5=1+(5-1)\cdot5=1+4\cdot5=1+20=21 \\ a_6=1+(6-1)\cdot5=1+5\cdot5=1+25=26 \\ a_7=1+(7-1)\cdot5=1+6\cdot5=1+30=31 \end{gathered}[/tex]The next 4 terms are: A. 16,21,26,31
the solution set of an equation of a circle is all if the points that lie on the circle true or false
Answers
A circle is the set of all points in a plane at a given distance called the radius of a given point called the center. In this sense the points that lie on the circle represent the solutions for the equation of a given circle. Therefore, the statement is true