Write an equation in slope - intercept form for the line that passes through the given paint andis perpendicular to the given equation.7.(-5, 2), y =1/2x-3
Answers
You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)
Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:
Let the given line be:
[tex]y_1=mx+b[/tex]And the perpendicular line
[tex]y_2=nx+c[/tex]The slope of the perpendicular line will be:
[tex]n=-\frac{1}{m}[/tex]So for the line
[tex]y=\frac{1}{2}x-3[/tex]The slope is
[tex]m=\frac{1}{2}[/tex]For the perpedicular line it will be:
[tex]\begin{gathered} n=-\frac{1}{\frac{1}{2}}=-1\cdot\frac{2}{1} \\ n=-2 \end{gathered}[/tex]Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:
[tex]y-y_1=m(x-x_1)[/tex]Replace the with m=-2 and (-5,2)
[tex]\begin{gathered} y-2=-2(x-(-5)) \\ y-2=-2(x+5) \\ y-2=-2x-10 \\ y=-2x-10+2 \\ y=-2x-8 \end{gathered}[/tex]The equation perpendicular to
[tex]y=\frac{1}{2}x-3[/tex]is
[tex]y=-2x-8[/tex]Now you can draw both lines:
Related Questions
HELP ASAP WILL GET THE BRAINLEST FOR THIS ANSWER PLEASE ANSWER CORRECTLY
Answers
Answer:
(x,y)->(x+4,y-5)
Step-by-step explanation:
Find a set of common points first, for example, A and A', or B and B'
Then, find the coordinates of the two points. I'm choosing B and B'.
B: (1,8) x = 1, y = 8
B':(5,3) x = 5, y = 3
from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct
How many 2-liter bottles of soda will you need to fill ten 500 milliliter containers?1. 4 2. 2 3. 3 4. 1 How many milliliters are 1/5 liter?1. 5002. 2003. 1004. 50
Answers
Hello there. To solve this question, we have to remember some properties about conversion of values.
1. How many 2-liter bottles of soda will you need to fill ten 500 mililiter containers?
First, multiply the number of containers by its capacity, that is
[tex]10\cdot500=5000\text{ mililiters}[/tex]Notice that 1000 mililiters is equivalent to 1 liter, hence
[tex]5000\text{ mililiters }=5\text{ liters}[/tex]To fill these containers with 2-liter bottles of soda, you'll need at least 3 bottles.
The answer to the first question is 3.
2. How many mililiter are 1/5 liter?
Considering 1 liter = 1000 mililiters, we have that
[tex]\dfrac{1}{5}\text{ liter }=\dfrac{1}{5}\cdot1000\text{ mililiters }=200\text{ mililiter}[/tex]Hence the answer to this question is 2. 200
The owners of the Movie Palace use the Illuminator 100 light bulb in their projectors, but are now considering switching to the Illuminator 100 Plus, a more powerful light bulb that projects movies onto larger screens farther away. The Illuminator 100 Plus projects movies onto screens 108 feet wide and 180 feet from the projector, while the Illuminator 100 projects movies onto screens only 81 feet wide, as shown in the figure below. How much farther from the projector, in feet, is the screen for the Illuminator 100 Plus than the screen for the Illuminator 100 ?
Answers
Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;
Illuminator 100 plus bulb
It movies onto screens ;
108 ft wide
180 ft away from the projector
Illuminator 100 bulb
81 ft wide
? : from the projector
Here apply the idea of similarity ratios where;
The ratio
HURRY!!
Describe the end behavior of f(x) = −3x4 + 7x2 − x + 13.
Answers
The end behavior of the given function will be given by Down on the left down on the right.
A function may be defined as the expression in which for one value of input variable there is only one value of output variable. The input variable or the independent variable is x, and the output variable or the dependent variable is y. In the given function f(x) = -3x⁴ + 7x² - x + 13 we will use the Power and Polynomial Functions features. For final behavior of power functions of the form f(x) = axⁿ where n is represented as a non-negative integer depends on the power and the constant. Here, the leading coefficient is -3x⁴. So, when x → ∞ the value of f(x) → -∞ and when x → -∞ then the value of f(x) → -∞. So, the final answer for the behavior will be given by "Down on the left, down on the right".
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what is 1 trillion to the thenth power? .. .. ..
[tex]\sf{}[/tex]
Answers
1 trillion to the tenth power is (10¹⁴)¹⁰ or (10¹³)¹⁰.
What is a trillion?1,000,000,000,000One trillion is equal to one million million, or 1,000,000,000,000, and on the short scale, we write this as 1012. (ten to the twelfth power). This number is now commonly referred to as one trillion because it is a thousand times bigger than the short-scale billion.We need to determine how many crores one trillion represents. Therefore, by dividing one trillion by one crore, we can find the solution to the puzzle. As a result, we discover that 100000 = 1000000000000/10000000. As a result, we learn that $1 trillion is equivalent to 100,000 Indian Rupees.So, 1 trillion to the tenth power:
1 trillion to the tenth power = (10¹⁴)¹⁰ or (10¹³)¹⁰Therefore, 1 trillion to the tenth power is (10¹⁴)¹⁰ or (10¹³)¹⁰.
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State the domain and range for the graph and tell if it is a function.
Answers
The arrows indicate that the graph of the function continues beyond what can be seen in the image.
Notice that the graph does not appear to have asymptotes; then, the domain of the function is:
[tex]\text{domain}=(-\infty,\infty)[/tex]And the range is:
[tex]\text{range}=(-\infty,\infty)[/tex]Since the graph seems to continue towards the +y-direction and the -y-direction
Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; the graph is a function.
the mean absolute
for the following set of Determine
deviation
data: 1, 1, 3, 5, 5, 6, 8, 11
Answers
The mean absolute deviation is 2.5.
What is Mean Absolute Deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.
How to calculate the mean deviation from the mean:
Calculate the mean of the provided observations.Determine how much each observation differs from the estimated mean.Analyze the mean of the differences discovered in step two.Given data:1, 1, 3, 5, 5, 6, 8, 11
So, mean of the data is
= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8
= 40 /8=
5
Now, Mean absolute deviation is
= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8
= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8
= 20/8
=2.5
Hence, the mean absolute deviation is is 2.5.
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1. Line Q goes through (-6,7) and (4,-2). Write the equation of line Q.
Answers
First, find the slope of the line using the slope formula:
Provided two points (a,A) and (b,B) on a line, its slope is given by:
[tex]m=\frac{A-B}{a-b}[/tex]For the points (-6,7) and (4,-2), we have:
[tex]\begin{gathered} m=\frac{7--2}{-6-4} \\ =\frac{7+2}{-10} \\ =\frac{9}{-10} \\ \therefore m=-\frac{9}{10} \end{gathered}[/tex]The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):
[tex]\begin{gathered} 7=-\frac{9}{10}(-6)+b \\ \Rightarrow7=\frac{54}{10}+b \\ \Rightarrow b=7-\frac{54}{10} \\ \therefore b=\frac{8}{5} \end{gathered}[/tex]Substitute b=8/5 and m=-9/10 to find the equation of line Q:
[tex]y=-\frac{9}{10}x+\frac{8}{5}[/tex]I'm In K12" Help me Pleeasee *I Will Give "Brainlyest to The First Person"
Answers
The correct inequality sign for the first number expression is > and for the second number, the expression is <.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The mixed fractions are:
-19 5/6 = -119/6 = -19.83
-20 1/6 = -121/6 = -20.166
-19 5/6 > -20 1/6
|-19 5/6| = |-119/6| = 19.83
|-20 1/6| = |-121/6| = 20.166
|-19 5/6| < |-20 1/6|
Thus, the correct inequality sign for the first number expression is > and for the second number, the expression is <.
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Write a mathematical expression for the following statement
Four times x is more than 13
Answers
Answer:
4x>13
Step-by-step explanation:
4 × X=4x
>=more than symbol
A fair die is rolled 4 times. What is the probability of having no 1 and no 3 among the rolls? Round your answer to three decimal places.
Answers
Answer:
Step-by-step explanation:
You have to assume each roll is independent. The probability of rolling a fair die is 1/6. When you roll the die, you only care about 2,4,5, and 6 since you do not want to get 1 or 3. So the probability is of getting a 2,4,5 and 6 is 4/6.
You could of also see it as the probability of NOT getting a 1 or 3 is:
[tex]1-\frac{2}{6} =\frac{4}{6}=\frac{2}{3}[/tex]
Now you roll the die 4 times with each success being 2/3
[tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} =(\frac{2}{3})^4=.197530864[/tex]
2(3x - 1) + 2(4x + 5) = 8
Answers
Answer:
0
Step-by-step explanation:
2(3x -1) + 2(4x + 5) = 8 Distribute the 2's
2(3x) + 2(-1) + 2(4x) + 2(5) = 8
6x - 2 + 8x +10 = 8 Combine like terms
14x + 8 = 8 Subtract 8 from both sides of the equaion
14x = 0 Divide both sides by 14
x = 0
When given a line of 3x + 6y = 8, how do you find slope intercept?
Answers
The line is given by 3x + 6y = 8
To find the slope and the y-intercept, we must rewrite the equation in the form y = ax + b, where a is the slope and b is the y-intercept.
The first step is subtract 3x from both sides of the equation:
3x + 6y - 3x = -3x + 8
6y = -3x + 8
Then, we divide both sides by 6:
6y/6 = (-3x + 8)/6
y = -x/2 + 4/3
Therefore, the slope is -1/2 and the y-intercept is 4/3
Jen draws a polygon with Vertices E (-2, 3.5), F (3,3.5) G (3,-1.5) And H (-2, "-1.5)." Is EFGH a square? Justify your answer
Answers
The polygon EFGH is a polygon.
What is polygon?
A polygon is a form of planar figure in geometry and is defined as a closed polygonal chain made up of a finite number of straight line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both is referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.
To check the polygon EFGH is a square or not, first to find the length of each side of polygon.
If the length of each side is equal then the polygon EFGH is a square.
(Since length of each side of square is equal).
We know,
[tex]d \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex]
where,
d = distance
[tex](x_1, x_2)[/tex] = Coordinates of the first point.
[tex](x_2, y_2)[/tex] = Coordinates of the second point.
So,
[tex]EF = \sqrt{(3-(-2))^2 + (3.5-3.5)^2} = \sqrt{25 + 0} = 5[/tex]
[tex]FG = \sqrt{(3-3)^2 + (-1.5-3.5)^2 } = \sqrt{0 + 25} = 5[/tex]
[tex]GH = \sqrt{(-2-3)^2 + (-1.5-(-1.5))^2} = \sqrt{25 + 0} = 5[/tex]
[tex]EH = \sqrt{(-2-(-2))^2 + (-1.5-3.5)^2} = \sqrt{0 + 25} = 5[/tex]
From above the length of each side is equal.
Therefore, given polygon EFGH is a square.
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At the Kerry Hotel Pudong in Shanghai, China, theonce swimming pool is now the world's largest ballpit. The ball pit is 82 feet long and 41 feet wide,with an average depth of 4.25 feet. Each ball in the ball pit is the same size. They each have a diameterof 4 inches. 1. What is the volume of this pool? 2. How many ball pit balls will we need to fill the pool up to the top?
Answers
Answer: We have to find the volume of the pool and the number of pit balls that can fill it.
(1) We can find the volume of the pool with the following formula:
[tex]V=L\times W\times D\rightarrow(1)[/tex]Using the equation (1) the volume of the pool is determined as follows:
[tex]\begin{gathered} L=82ft \\ \\ W=41ft \\ \\ D=4.25ft \\ \\ \therefore\rightarrow \\ \\ \begin{equation*} V=L\times W\times D \end{equation*} \\ \\ V=(82ft)\times(41ft)\times(4.25ft)=14,288.5ft^3 \\ \\ V=14,288.5ft^3 \end{gathered}[/tex](2) The number of ball pits that can fill the pool is as follows:
[tex]\begin{gathered} V_b=\frac{4}{3}\pi r^3 \\ \\ \\ 4in=\frac{1}{3} \\ \\ \therefore\rightarrow \\ \\ V_b=\frac{4}{3}\pi(\frac{1}{3})^3=\frac{4}{81}\pi ft^3 \\ \\ V_b=\frac{4}{81}\pi ft^3=0.16ft^3 \end{gathered}[/tex]Therefore the answer is:
[tex]\begin{gathered} N=\frac{V}{V_b}=\frac{14,288.5ft^3}{0.16ft^3}=89,303.125 \\ \\ N=89,303.125 \end{gathered}[/tex](4x + 7) + 35 = 90 solve for x
Answers
Answer:
x=12
Step-by-step explanation:
(4x + 7) + 35 = 90
(4x+7)=90-35
4x+7=55
4x=55-7
4x=48
x=12
Answer:
x=12
Step-by-step explanation:
it just is.,...........
While sailing a boat offshore, Bobby sees a lighthouse and calculates thatthe angle of elevation to the top of the lighthouse is 3°. When she sails her boat700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.How tall, to the nearest tenth of a meter, is the lighthouse?
Answers
Given
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
To find:
How tall, to the nearest tenth of a meter, is the lighthouse?
Explanation:
It is given that,
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
That implies,
[tex]\tan3\degree=\frac{y}{x+700}[/tex]Also,
[tex]\begin{gathered} \tan5\degree=\frac{y}{x} \\ y=x\tan5\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \tan3\degree=\frac{x\tan5\degree}{x+700} \\ (x+700)\tan3\degree=x\tan5\degree \\ x\tan3\degree+700\tan3\degree=x\tan5\degree \\ (\tan5\degree-\tan3\degree)x=700\tan3\degree \\ 0.0351x=36.6854 \\ x=1045.7m \end{gathered}[/tex]Then,
[tex]\begin{gathered} \tan5\degree=\frac{y}{1045.7} \\ y=1045.7\tan5\degree \\ y=91.5m \end{gathered}[/tex]Hence, the height of the light house is, 91.5m.
without graphing, describe the transformation of each parabola or absolute value function y = 2 |x|+ 1
Answers
Remember the following transformations of a function:
[tex]c\cdot f(x)[/tex]This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0
If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1
[tex]f(x)+c[/tex]This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.
Therefore, starting with the absolute value function:
[tex]\lvert x\rvert[/tex]Multiply the function by 2:
[tex]2\cdot\lvert x\rvert[/tex]Since 2>1, then this is a vertical stretching by a factor of 2.
Next, add 1:
[tex]2\cdot\lvert x\rvert+1[/tex]This will translate the stretched absolute value function one unit upwards.
Therefore, the complete description of the transfromation would be:
[tex]y=2\cdot\lvert x\rvert+1[/tex]Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.
Calculate the perimeter for each of the following
Answers
a) Perimeter = 17.4 cm
b) Perimeter =210.6 cm
How are the perimeters calculated?
a) The perimeter of an irregular polygon = Sum of all the sides of the polygon.
Converting value of all sides to centimetres.
Perimeter = 3.4 +3.2 +4.3 +3.7+2.8
= 17.4 cm
b) The perimeter of an irregular polygon = Sum of all the sides of the polygon.
Converting value of all sides to centimetres.
Perimeter = 29.1+25.3+30+28.6+32.6+36.5+28.5
=210.6 cm
What is the perimeter of a polygon?
The total length of a polygon's boundary is what is referred to as its perimeter. To put it another way, a polygon's perimeter is equal to the sum of its sides. Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane.If the lengths of the sides of a polygon are known, it is possible to determine its area and perimeter.To learn more about perimeter of a polygon, refer:
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please help me solve,the question is A cylinder with a diameter of 8 feet is cut out of a cube that measures 8 feet on each side.What is the volume of the resulting shape? ( use Pi and round to the nearest tenth.) ______ ft3
Answers
Side of cube = 8 ft
Volume of cube = Side x Side x Side
Volume of cube = 8 x 8 x 8
Volume of cube = 512 feet^3
A cylinder with diameter 8feet is cute form the cube
Height of cylinder = Side of cube
Height of cylinder = 8 feet
Diameter of cylinder = 8 feet
Radius of cylinder = 4feet
[tex]\begin{gathered} \text{Volume of cylinder =}\Pi\times radius^2\times Height \\ \text{Volume of cylinder =}\Pi\times4\times4\times8 \\ \text{Volume of cylinder =}401.92ft^3 \end{gathered}[/tex]The volume of resulting shape = Volume of cube - Volume of cylinder
Volume of resulting shape = 512 - 401.92
Volume of resulting shape = 110.08 ft^3
Answer: 110.08 ft^3
I need help with this practice problem solving• I believe the subject is complex numbers and vectors I will send an additional picture that goes along with this, it is a graph, use the graph to answer this
Answers
Solution
a + b = (-2, -1)
Using Parallelogram method
HELP PLEASE MARKING BRAINLIEST Han cell phone plan cost $200 to start then there's $50 charged each month(a)what is the total cost to use the cell phone plan for one month(b)what is the total cost for x months (c)which graph shows the cost of the cell phone plan over a period of two years using months as the units of time(d) is there a proportional relationship between time and the cost of the cell phone plan explain how you know
Answers
Answer:
• $250
,• y=200+50x
,• Graph A
,• Yes
Explanation:
(a)Han cellphone's plan costs a fixed fee of $200 and an extra $50 per month.
Therefore:
[tex]\begin{gathered} \text{The total cost for one month=}200+50 \\ =\$250 \end{gathered}[/tex](b)If Han uses the phone for x months
Extra Cost = 50x
Therefore:
[tex]\text{The total cost for x months, y=}200+50x[/tex](c)Since the number of months = x; and
Total cost for x months = y
When x=24
[tex]\begin{gathered} y=200+50(24) \\ =1400 \end{gathered}[/tex]The graph that shows the cost of the cell phone plan over a period of two years using months as the units of time is Graph A.
(d)We see that the equation y=50x+200 has a proportional constant (50).
Another approach is to say that it is a linear equation.
Therefore, there is a proportional relationship between time and the cost of the cell phone plan.
A map state where your friend lives have a scale 1/2 inch: 10 miles.
Your friend measured the distance between her town and the state capital on the map. Her measurements were 4 1/2 inches. Based on your friend's measurement, what is the actual distance in miles between her town and the state capital?
Answers
The actual distance is 90 miles between the town and the state capital based on the scale of the map
1/2 inch on the map = 10 miles
So, 1 inch = 20 miles
Distance between the town and state capital = 4 1/2 inches
The mathematical relationship between a small unit of measurement on a map, such as an inch or centimetre, and the corresponding real-world unit of distance, such as a kilometre or a mile, is known as a map scale.
The actual distance in miles between the town and the state capital is given by:
Distance between town and state capital* Scale of the map
= 4.5*20
= 90 miles
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Write a function and use a table and graph to predict when the population will reach 20,000
Answers
The formula for exponential growth is expressed as
y = a(1 + r)^t
where
y is the population after t years
ais the initial population
r is the growth rate
t is the number of years
From the information given,
a = 350
r = 14% = 14/100 = 0.14
By substituting these values into the equation, the function to model th growth rate is
y = 350(1 + 0.14)^t
y = 350(1.14)^t
We would substitute values of t into the equation to determine corresponding values of y. We have
For t = 2, y = 350(1.14)^2 = 454.86
For t = 6, y = 350(1.14)^6 = 768.24
For t = 10, y = 350(1.14)^10 = 1297.52
We would plot these values of y on the y axis and the corresponding values of t on the x axis. The graph is shown below
The time when the population will reach 20000 would be the value of x at the point where y = 20000 on the graph. It is around y = 30.87
Thus, the population will reach 20000 in approximately 31 years
We can confirm this by solving the equation. We have
20000 = 350(1.14)^t
20000/350 = 1.14^t
57.14 = 1.14^t
Taking natural log of both sides, we have
ln 57.14 = ln1.14^t = tln1.14
t = ln 57.14/ln1.14
t = 30.87505
The costs of repairing iPads in UAE are normally distributed with a standard deviation 73 Dhs. If 8% of the costs exceed 279 Dhs, find the mean of the costs. Round your answer to the nearest diham.
Answers
The costs of repairing iPads in UAE are normally distributed with a standard deviation of 73 Dhs. If 8% of the costs exceed 279 Dhs, then the mean of the costs is 1.405072
The mean of the Costs stands for the typical sum of money spent on a product's production. Depending on how many units are made, this amount may change.
Let X be the price of fixing iPads in the UAE (in Dhs)
X ~ N (μ, σ = 73)
if 8% of the costs are greater than 297 Dhs.
P (X > 297) = 8%
P(X > 297) = 0.08
We must determine the mean value (μ)
P (X > 297) = 0.08
P [(X - μ) / σ > (297 - μ) / 73] = 0.08
P [Z < (297 - μ) / 73] = 0.08
P [Z < (297 - μ) / 73] = 1 - 0.08
P [Z < (297 - μ) / 73] = 0.92
(297 - μ) / 73 = Z⁻¹(0.92)
(297 - μ) / 73 = 1.405072 (Using R software)
297 - μ = 73 * 1.405072
μ = 297 - (73 * 1.405072)
μ = 297 - 102.5702
μ = 194.4298
μ ≅ 194
Therefore, the mean of the cost (μ) = 194 dhs.
Using R Software, we can compute;
Z⁻¹ (0.92) is,
=qnorm(0.92) ` → (Command)
'1.405072 → (Output)
⇒ Z⁻¹ (0.92) = 1.405072
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I only need help with part "b." I have provided the answer for "a" to help.
Answers
Part b.
If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:
Factor of 3
[tex]3\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {3} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Multiply:
[tex]\begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix}[/tex]Answer:
[tex]\begin{equation*} \begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix} \end{equation*}[/tex]Given f(x) = x3 - 5, find f-'(x).
Answers
the inverse function = f^-1(x) is option C
First let's state what we are given:
f(x) = x^3 - 5
We are to find the inverse of f(x).
To do this, first let's represent f(x) with y
y = = x^3 - 5
Then, we would interchange x and y
[tex]\begin{gathered} x=y^3\text{ - 5 (make y the subject of formula)} \\ x+5=y^3 \\ find\text{ cube root both sides} \\ \sqrt[3]{y^3\text{ }}=\sqrt[3]{(x+5)} \\ y\text{ = }\sqrt[3]{(x+5)} \end{gathered}[/tex]From the answer we got, the inverse function = f^-1(x) is option C
Write in point slope form the equation for the line that goes through the points (0,0) and (-4,7)
Answers
PROBLEM:
To find the point-slope form of the equation of the line passing through points (0, 0) and (-4, 7)
METHOD:
The point-slope form of the equation of a line is given to be:
[tex]\begin{gathered} (y-y_0)=m(x-x_0) \\ \text{where} \\ m=\text{ slope} \\ (x_0,y_0)=\text{ Point on the line} \end{gathered}[/tex]Step 1: Find the slope of the line.
The formula to calculate the slope of a line is given to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can use the two points provided to find the slope of the line such that:
[tex]\begin{gathered} (x_1,y_1)=(0,0)_{} \\ (x_2,y_2)=(-4,7) \end{gathered}[/tex]Therefore, the slope is given to be:
[tex]\begin{gathered} m=\frac{7-0}{-4-0} \\ m=-\frac{7}{4} \end{gathered}[/tex]Step 2: Pick a point on the line to use for the equation.
[tex](x_0,y_0)=(-4,7)[/tex]Step 3: Use the values gotten from Steps 1 and 2 to write out the equation of the line in the point-slope form:
[tex]\begin{gathered} \Rightarrow y-7=-\frac{7}{4}(x-\lbrack-4\rbrack) \\ \therefore \\ y-7=-\frac{7}{4}(x+4) \end{gathered}[/tex]ANSWER:
The slope-intercept form of the line is given to be:
[tex]y-7=-\frac{7}{4}(x+4)[/tex]Sam biked 2/3 km in 4 minutes. How far did he bike in 1 minute?
Answers
we can make a relation
[tex]\begin{gathered} \frac{2}{3}\longrightarrow4 \\ \\ x\longrightarrow1 \end{gathered}[/tex]where x is the missing value
if she bikes 2/3km in 4 minutes how much kilometers she bike on 1 minute?
we solv using cross multiplication
we multiply 1 and 2/3 and the divide by 4
[tex]\begin{gathered} x=\frac{1\times\frac{2}{3}}{4} \\ \\ x=\frac{\frac{2}{3}}{4} \\ \\ x=\frac{1}{6} \end{gathered}[/tex]she will bike 1/6km in one minute
please help me out thanks
Answers
A non-zero matrix A with A² = 0 is A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex].
We need to find a 2 x 2 non- zero matrix with A² = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
A² = A x A
If A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex], then A x A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}a^2+bc&ab+bd\\ac+dc&bc+d^2\end{array}\right][/tex]
This is called matrix multiplication.
Now consider the matrixes of the form A = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]
Then A² = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
Also Consider a matrix A = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]
Then A² = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
So any matrix of the form [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] with x any number, will give A² = 0
In particular, A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex] is a non-zero matrix with A² = 0.
Learn more about matrix multiplication at https://brainly.com/question/12073691
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