estimate the instantaneous velocity at t=7 seconds using the difference quotients with h=0.1,0.01,0.001
Answers
EXPLANATION
Given that the arrow function is as follows:
[tex]f(t)=-16t^2+128t[/tex]The instantaneous velocity is given by the following relationship:
[tex]\frac{f(t+\Delta t)-f(t)}{\Delta t}\text{ at t=7}[/tex]For △t = 0.1:
[tex]Velocity=\frac{\lbrack-16(7+0.1)^2+128\cdot(7+0.1)\rbrack-\lbrack-16\cdot(7)^2+128\cdot7\rbrack}{0.1}[/tex]Computing the powers:
[tex]Velocity=\frac{\lbrack-16\cdot50.41+128\cdot7.1\rbrack-\lbrack-16\cdot49+128\cdot7\rbrack}{0.1}[/tex]Multiplying numbers:
[tex]Velocity_{0.1}=\frac{\lbrack-806.56+908.8\rbrack-\lbrack-784+896\rbrack}{0.1}[/tex]Removing the parentheses and adding numbers:
[tex]Velocity_{0.1}=\frac{-9.76}{0.1}=-97.6\approx98_{\text{ }}ft/s[/tex]For △t=0.01
[tex]Velocity=\frac{\lbrack-16(7+0.01)^2+128\cdot(7+0.01)\rbrack-\lbrack-16\cdot(7)^2+128\cdot7\rbrack}{0.01}[/tex]Computing the powers:
[tex]Velocity=\frac{\lbrack-16\cdot49.1401+128\cdot7.01\rbrack-\lbrack-16\cdot49+128\cdot7\rbrack}{0.01}[/tex]Multiplying numbers:
[tex]Velocity_{0.01}=\frac{\lbrack-786.2416+897.28\rbrack-\lbrack-784+896\rbrack}{0.01}[/tex]Adding numbers:
[tex]Velocity_{0.01}=\frac{-0.9616}{0.01}=-96.16\approx-96ft/s[/tex]For △t = 0.001
Applying the same reasoning than before, give us the following result:
[tex]Velocity_{0.001}=-96.016\text{ ft/s}\approx-96ft/s[/tex]Related Questions
Kimaya decided to by mangos and pineapples for her snack this week.
Mangos, m, cost $1.50 each. Pineapples, p , cost $3.00 each. She wants to spend $18
Here is Kimaya's work to solve 1.5m+3p=18:
1.5m+3p-3p=18-3p
1.5m/1.5=18-3p/1.5
m=12-2p
1. What does the 12 and -2 say about the situation
2. Solve 1.5m+3p=18 for p
Answers
If Kimaya does not buy any Pineapple then the cost of the Mangos will be 12 and for p the equation is p = 6 - 0.5m.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Mangos, m, cost $1.50 each. Pineapples, p, cost $3.00 each. She wants to spend $18
1.5m+3p=18
After solving:
m = [1/1.5](18 - 3p)
m = 12 - 2p
If Kimaya does not buy any Pineapple then the cost of the Mangos will be 12 and -2 represents the slope.
m = 12 - 2p
p = 6 - 0.5m
Thus, if Kimaya does not buy any Pineapple then the cost of the Mangos will be 12 and for p the equation is p = 6 - 0.5m.
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help me with this question!!
Answers
Step-by-step explanation:
only the second option is wrong the rest are correct
obvious the function is geometry
first term of the sequence is 170
Kenny spent $80 of his allowance on food, 2/5 of the remainder on stationery
and saved the rest. He saved 1/3 of his allowance. How much was Kenny's allowance?
Answers
========================================================
Work Shown:
x = total allowance
x/3 = amount saved
2x/3 = amount spent
x-80 = amount left over after spending $80 on food
(2/5)*(x-80) = amount spent on stationary
80+(2/5)(x-80) = total amount spent
80+(2/5)(x-80) = 2x/3
Multiply both sides by the LCD 15 to clear out the fractions
15*( 80+(2/5)(x-80) ) = 15*( 2x/3 )
1200 + 6(x-80) = 10x
1200+6x-480 = 10x
720+6x = 10x
720 = 10x-6x
720 = 4x
4x = 720
x = 720/4
x = 180
Kenny's allowance is $180
-----------------------
Check:
He saves 1/3 of his $180 allowance, so he saves (1/3)*180 = 60 dollars and spends 180-60 = 120. In other words, (2/3)*180 = 120 is spent.
$80 of the 120 is spent on food, which means the remaining 120-80 = 40 dollars spent on stationary.
If he starts off at $180 and spends $80 on food, then that's a difference of 180-80 = 100 dollars. Two-fifths of which is (2/5)*100 = 40 dollars to match the amount spent on stationary. This helps confirm we have the correct answer of $180.
The graduated cylinder contains 65 ml of water. The water level raises to 125 ml after the rock was added. What is the volume of the rock?
Answers
Solution: 60 ml
$ | The volume of the rock is calculated by subtracting the final volume from the initial volume. In this case, 125ml - 65ml = 60ml.
ex lorn 3. An expression is given 2x2 + 4x - 6 Determine the values of h and k that make the expression (x - h)2 + k equivalent to the given expression. Identify the vertex and the zeros or roots! 6 . 3 I
Answers
(x+1)²- 8
1) Considering the equation 2x²+4x-6, and that in the expression (x-h)²+k
we have:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=\frac{-\Delta}{4a} \end{gathered}[/tex]2) Then, let's find out h and k the values of the vertex of that quadratic function:
[tex]\begin{gathered} h=\frac{-4}{2(2)}=\frac{-4}{4}=-1 \\ k=\frac{-\Delta}{4(2)}=\frac{-(4^2-4(2)(-6))}{8}=\frac{-64}{8}=-8 \end{gathered}[/tex]So the vertex is (-1, -8). Plugging into that 2nd expression, we'll have an equivalent one:
[tex](x-(-1)^2+(-8)\text{ }\Rightarrow(x+1)^2-8[/tex]3) So the equivalent expression to that quadratic equation is (x+1)²-8
Write the inequality shown by the shaded region in the graph with the boundary line y = 5x − 4.
Answers
As we can see, the line is continuous, and the area is below the line, therefore, we can conclude that the inequality is given by:
[tex]y\le5x-4[/tex]Help me please please
Answers
The angles in the circle are as follows:
a = 90°b = 23°c = 46°How to find the angles in the circle?The angles in the circle can be found using the circle theorem.
Angle subtended at circumference by a semi circle is 90 degrees. This means the opposite angle to the diameter is 90 degrees.
Therefore,
a = 90 degrees
The angle measure of the central angle is congruent to the measure of the intercepted arc.
Therefore,
360 - 134 - 180 = c
c = 360 - 314
c = 46 degrees.
The inscribed angle is half the arc. In other words, the measure of an inscribed angle in a circle equals half the measure of its intercepted arc.
Therefore,
b = 1 / 2c
b = 1 / 2 × 46
b = 23 degrees.
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Brian gets $15.00 to mow the lawn. He saves 0.1 of his earnings. How much money does Brian save?
Answers
The amount of money that Brian saves is $1.50.
What is money?Money simply means anything that's used a medium of exchange and for transactions.
In this case, Brian gets $15.00 to mow the lawn and he saves 0.1 of his earnings.
The amount saved will be:
= Percentage saved × Amount
= 10% × $15
= 0.1 × 15
= $1.5
This illustrates the concept of multiplication.
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What is 267.94 to the nearest hundredth
Answers
Answer:
267.94
Step-by-step explanation:
To round 267.94 to the nearest hundredth consider the thousandths' value of 267.94, which is 0 and less than 5. Therefore, the hundredths' value of 267.94 remains 4.
Trust me im Middle school and just learning this top of my class anyways hope it help
When the digit to the right is less than 5 we round toward 0.
267.94 was rounded toward zero to 267.94
The weight W (in pounds) of a backpack a hiker carries on a multi-day hike can be modeled by W = 2. 5d + 35 were d represents the length of the trip (in days). Identify the slope and the y-intercept. Describe what the slope and the y-intercept represent in this situation
Answers
The slope is 2.5 and y-intercept is 35.
As per the general equation of straight line, which is y = mx + c. Here y is y-axis, x is x-axis, m is slope and c is y-intercept.
Now, the slope is 2.5 and indicates that the weight increased by 2.5 pounds each day. y-intercept indicates there are atleast 35 total days of th trip. The slop represents subsequent increase in weight per day.
Further, y axis value will the total based on the number of days and increase in weight. x axis will be labelled distance and will represent the same.
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A catapult hurls a cantaloupe from a heightof 12 feet at an initial velocity of 47 feetper second n(t)=16t^2+47t+12I need this pleaseeee
Answers
To find the maximun height we need the vertex of the quadratic equation,
To calculate it, we use
[tex]x=\frac{-b}{2a}[/tex]Where x is x value in the maximun value, b is the coefficient of the linear expression and a is the coefficient of the square expression
[tex]x=\frac{-47}{2(-16)}=1.46[/tex]And the y axis is,
[tex]h(1.46)=16(1.46)^2+47(1.46)+12=114.72[/tex]So, to find the maximun height we need the vertex of the quadratic equation. In this case the maximun height is 114.72 feet.
First question)
To write the vertical motion equation we use,
[tex]h(t)=-\frac{1}{2}gt^2+v_0t+h_0[/tex]Where g is the gravity, v0 is the initial velocity and h0 is the initial height.
Then, we need to replace the values
[tex]\begin{gathered} h(t)=-\frac{1}{2}(32)t^2+47t+12 \\ h(t)=-16t^2+47t+12 \end{gathered}[/tex]Alice wondered how many books in the school library are about her favorite subjects. She searched the library'sonline catalog and graphed the results.file3601300240Number of books18012060TATUS0DinosaurInsectPirate SuperheroType of bookHow many more pirate books does the library have than insect books?more pirate books
Answers
From the bar graph given, the following can be deduced from inspection.
[tex]\begin{gathered} D\text{ inosaur = 120books} \\ In\sec t=240\text{books} \\ P\text{ irate = 300 books} \\ \text{Superhero = 240books} \end{gathered}[/tex]From the above, pirate books are more than insect books by;
[tex]\begin{gathered} P\text{ irate=300} \\ In\sec t=240 \\ \text{Difference}=\text{ 300 - 240} \\ =60 \end{gathered}[/tex]Therefore, pirate books in the library are more than insect books by 60 books.
The manufacturing engineers of a renowned pizza brand reduced the manufacturing cost of a pizza delivery box by optimising the shape of the box.To achieve this cost optimisation, the engineers reduced the volume of the box by 25% by flattening the curved side of the box (illustrated by the dashed line) to shape it like a proper prism, as shown in the below diagram.24 cm2836 cm(a) Find the value of 20.(b) (i) Find the area of the sector of the top surface of the old box design:(ii) Find the area of the top surface of the newly designed box.If the volume of the old box design was 3277 cm³, find the volume, V, of the newly designed box. rounding your answer correct to the nearest cubic centimetre:(ii) Hence, find the value of h.
Answers
Given: A pizza box's volume has been reduced by 25% by flattening the curved side of the box. The dimensions of the box are given.
Required: To determine the angle, the area of the sector of the top surface of the old box design, the area of the top surface of the newly designed box, and the volume, V, of the newly designed box. Also, determine the height of the box, h.
Explanation: The given box is-
If we draw a perpendicular as shown in the figure, the angle is bisected, and the side 24 cm is also bisected as the triangle on the top is an isosceles triangle. This can be easily proved by showing that the smaller triangles on the top face are congruent.
Next, we can use the trigonometric ratio sine to determine the angle as follows-
[tex]\begin{gathered} sin\theta=\frac{12}{36} \\ \theta=sin^{-1}(\frac{1}{3}) \\ \theta=19.47\degree \end{gathered}[/tex]Thus,
[tex]2\theta=38.94\degree[/tex]Next, the top of the new box is now a triangle with a base of 24 cm and a height-
[tex]\begin{gathered} \text{ Height of triangle}=36cos\theta \\ =36cos(19.47\degree) \\ =33.94\text{ cm} \end{gathered}[/tex]Hence, the area is-
[tex]\begin{gathered} A=\frac{1}{2}\times24\times33.94 \\ =407.30\text{ cm}^2 \end{gathered}[/tex]Now, the old box is a sector with a central angle of 38.94 degrees and a radius of 36 cm. Hence the area of the old box is-
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}[/tex]Substituting the values as-
[tex]\begin{gathered} A=\frac{38.94}{360}\times3.14\times36\times36 \\ =440.18\text{ cm}^2 \end{gathered}[/tex]Lastly, the volume of the new box is 25% less than the old box. Hence the volume of the new box is-
[tex]\begin{gathered} V=\frac{25}{100}\times3277 \\ =819.25\text{ cm}^3 \end{gathered}[/tex]We can determine the height as follows-
[tex]\begin{gathered} Vol=Area\times h \\ \Rightarrow h=\frac{Vol}{Area} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} h=\frac{819.25}{407.30} \\ =2.011\text{ cm} \end{gathered}[/tex]Final Answer: A)
[tex]2\theta=38.94\degree[/tex]B) i) The area of the top of the old box=440.18 sq centimeters.
ii) The area of the top of the new box=407.30 sq centimeters.
C) i) The volume of the new box is 819 cubic centimeters.
ii) h=2.01 cm
I need help please this is so confusing.Which points is not on line AB?
Answers
Solution;
From the given transversal lines;
Points A and B are on line AB, while points C, D and E are not.
Hence, the answer is
[tex]\begin{gathered} Point\text{ D} \\ Point\text{ C} \\ Point\text{ E} \end{gathered}[/tex]Convert the given from of the function into the other two forms
Answers
Step 1: Standard form to vertex form of rows 1 and 2:
[tex]\begin{gathered} S\tan dard\text{ form} \\ y=ax^2\text{ + bx + c} \\ \text{Vertex form } \\ y\text{ = }a(x-h)^2\text{ + k} \end{gathered}[/tex]Standard form of row 1 to vertex form
[tex]\begin{gathered} y=x^2\text{ - 2x - 3} \\ y=x^2-2x+1^2-3-1^2 \\ \text{y = (x -1 )}^2\text{ - 3 - 1} \\ y=(x-1)^2\text{ - }4 \end{gathered}[/tex]Intercept form of row 3 to vertex form.
[tex]\begin{gathered} y\text{ = (}x\text{ + 2)(x - 3)} \\ y=x^2\text{ - 3x + 2x - 6} \\ y=x^2\text{ - x - 6} \\ y=x^2\text{ - x + (}\frac{1}{2})^2\text{ - 6 - (}\frac{1}{2})^2 \\ y\text{ = (x - }\frac{1}{2})^2\text{ - 6 - }\frac{1}{4} \\ y\text{ = (x - }\frac{1}{2})^2\text{ - }\frac{25}{4} \end{gathered}[/tex]Standard form to intercept form row 1
[tex]\begin{gathered} y=x^2\text{ - 2x - 3} \\ \text{method: factorize} \\ y=x^2\text{ - 3x + x - 3} \\ y\text{ = x(x - 3) +1( x - 3)} \\ y\text{ = (x + 1)(x - 3)} \end{gathered}[/tex]Intercept form to standard form row 3
[tex]\begin{gathered} y\text{ = (x + 2)(x - 3)} \\ y\text{ = x(x - 3) + 2(x - 3) by distribution} \\ y=x^2\text{ - 3x + 2x - 6} \\ y=x^2\text{ - x - 6} \end{gathered}[/tex]Vertice form to intercept fomr
For problem 2 - 25, what is the slope of line ?
Answers
Please help! ASAP. Which graph? A, B, C, D
Answers
Based on the equation given, the graph that matches the equation is Graph D.
How to find the graph?To find the graph that matches the equation, solve for the values of y based on values of x and the equation.
Assuming x is -1, y is:
= 1/5 (-1) + 2
= 1.8
x = 0
= 1/5(0) + 2
= 2
x = 1
= 1/5(1) + 2
= 2.2
The graph that has the points:
(-1, 1.8) (0, 2) and (1, 2.2) is the last graph so this is the correct graph.
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Instructions: Determine the shape and direction of the parabola formed by the given function.
Answers
We have the parabola with equation y = 4x².
We have to determine the shape and direction of it.
If we compare it to the standard equation y = ax² + bx + c, we can see that a = 4, b = 0 and c = 0.
As the value of a is positive, the parabola will open upward.
The parameter has an absolute value greater than 1. This means that y increases "faster" relative to x that a parabola with a = 1.
This means that the parabola will be narrow about its line of symmetry which we call vertical strecth.
Answer:
Because a is positive the parabola opens upward.
Because a has an absolute value larger than 1 the parabola is narrow about its line of symmetry which we call vertical stretch.
Evaluate the algebraic expression for the given value of the variable.x²-16; x = -3
Answers
We have to evaluate the expression x² - 16 when x = -3.
To do that we replace x with its value, -3, and calculate:
[tex]\begin{gathered} x^2-16 \\ (-3)^2-16 \\ 9-16 \\ -7 \end{gathered}[/tex]Answer: -7
The perimeter of a rectangle is 36 units. The width, w, of the rectangle is 8 units.
Answers
Answer:
The length of the rectangle is 10 units.
Step-by-step explanation:
These formulas can find the perimeter of a rectangle:
l + w + l + w = P or (l × 2) + (w × 2) = P
We know that the perimeter is 36 units, and the width is 8 units.
We can add 8 + 8 to get 16 because there are two sides. Then to find the length we can subtract 36 by 16 to get 20. We then divide 20 by 2 to get 10. That means that the length of the rectangle is 10 units. To check we can use the formula from before and do:
10 + 8 + 10 + 8 which does equal 36.
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Answer:
Length = 10 Width = 8
Step-by-step explanation:
After traveling for 4 hours and 1800 miles, an airplane begins a steady descent. When it beginsdescending, its altitude (height) is 33,000 feet. After 8 minutes, it is at 17,000 feet.
Answers
2. When it begins descending, the airplane's altitude (height) is 33,000 feet. Then, the starting value for its altitude would be 33,000
3. y = mx + b
where m is the slope,b the y-intercept, x represents time (in minutes), and y represents altitude (in feet).
In the context of this problem, the starting value for the airplane's altitude is the y-intercept.
The slope is found finding the ratio between altitude lost and time. Given that after 8 minutes, the airplane lost 33,000 - 17,000 = 16,000 feet, the slope is:
16,000/8 = 2,000 ft/min. Then the equation is:
y = 2000x + 33000
4. The information "After traveling for 4 hours and 1800 miles, an airplane begins a steady descent" is not relevant
MODELING REAL LIFE The function D(t) = 75 -0.3r represents the number of gigabytes left after downloading a video game for t
minutes.
a. How many gigabytes are left to download after 90 minutes?
gigabytes
b. How long will it take to download the entire video game?
min or
hr
min
Answers
Answer:
a) 48 gigabytes
b) 250 minutes, or 4 hours 10 minutes
Step-by-step explanation:
For D(t) = 75 -0.3t modeling the number of remaining gigabytes to download after t minutes, you want to find D(90) and t such that D(t) = 0.
a) RemainingD(90) = 75 -0.3·90 = 48
After 90 minutes, 48 gigabytes are left to download.
b) Total timeThe time required to complete the entire download is given by ...
0 = 75 - 0.3t
0 = 250 -t . . . . . divide by 0.3
t = 250 . . . . . . add t
It will take 250 minutes, or 4 hours 10 minutes to download the entire game.
__
Additional comment
The attached calculator screen shows conversion to hours and minutes. Hours, minutes, seconds are computed "base-60" the same way that Degrees, minutes, seconds are computed "base-60". 250 minutes is converted to hours by dividing by 60 min/hour. We can use the →DMS function of the calculator to show decimal or fractional hours in hours : minutes : seconds. In this use of that function, degrees represents hours.
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Which of the following statements are true?a.) All rectangles are squares.b.) All squares are rectangles.c.) All rhombi are squares.d.) All parallelograms are rectangles
Answers
c.) All rhombus are squares.
d.) All parallelograms are rectangles.
EXPLANATION
First, list out the properties of each with regards to side lengths
Rectangle: The opposite are parallel and equal to each other.
Square: All 4 sides of a square are equal.
Opposite sides of a square are both parallel and equal in length.
Rhombus:
All sides of the rhombus are equal.
The opposite sides of a rhombus are parallel.
Parallelogram:
Opposite sides are parallel and equal to each other.
From the above properties, we can now conclude that the true statements are;
c.) All rhombus are squares.
d.) All parallelograms are rectangles.
I need help I’m in the answer to this question
Answers
The order of rotational symmetry is the number of times the figure can be rotated and will still look the same.
From the figure, we have three rectangles, and those three rectangles can share the position of the one rectangle.
Since there are three, the figure can be rotated 3 times.
The answer is C. 3
Then choose whether you would find the percent increase or percent decrease: A town’s population was 36,067 in 2005. Ten years later, the population is 37,902. *
Answers
To answer this question, we can proceed as follows:
1. We have that the change is (in percentage):
Then, we have:
[tex]\frac{37902-36067}{36067}\cdot100=\frac{1835}{36067}\cdot100\approx0.0508\cdot100\approx5.087[/tex]Therefore, the percent increase was about 5.1%.
circleFind the area and the circumference of a circle with radius 5 ft.Use the value 3.14 for T, and do not round your answers. Be sure to include the correct units in your answers.ftft?ftArea:5 ftCircumference:Х$
Answers
Given the figure of a circle
As shown the radius of the circle = r = 5 ft
[tex]\text{Area}=\pi\cdot r^2=3.14\cdot5^2=3.14\cdot25=78.5ft^2[/tex][tex]Circumference=2\cdot\pi\cdot r=2\cdot3.14\cdot5=31.4ft[/tex]so, the answer will be:
Area = 78.5 ft^2
Circumference = 31.4 ft
Do not show work. It is not needed. I just need the answers
Answers
The first table shows the number of each item that was ordered by each family. The second table shows the cost of each item. For instance, the total cost of appetizer for Kelly's family is 2 x 11 = 22
For Dale's family, it is 1 x 11 = 11
We would show this total cost by using matrix multiplication as shown below.
[tex]\begin{gathered} \begin{bmatrix}{2} & {4} & {2} \\ {1} & {3} & {1} \\ {3} & {2} & {2}\end{bmatrix}\begin{bmatrix}{11} & {} & {} \\ {17} & {} & {} \\ {8} & & \end{bmatrix} \\ \end{gathered}[/tex]By applying matrix multiplication,
Total cost of dinner for Kelly's family is
2 x 11 + 4 x 17 + 2 x 8 = 22 + 68 + 16 = 106
Total cost of dinner for Dale's family is
1 x 11 + 3 x 17 + 1 x 8 = 11 + 51 + 8 = 70
Total cost of dinner for Jan's family is
3 x 11 + 2 x 17 + 2 x 8 = 22 + 34 + 16 = 72
The total costs are
Kelly's family = $106
Dale's family = $70
Jan's family = $72
Question 1 of 32
A submarine has a "crush depth" (that is, the depth at which water pressure will crush the submarine) of 250 m. What is the approximate pressure (water plus atmospheric) at this depth? (Recall that the density of seawater is 1025
kg/m3
19 - 9. 81 m/s?, and 1 kg/(m. 2) - 1 Pa - 9,8692
70-% atm
Answers
At this depth, the pressure is approximately 25.8 atm (water plus atmosphere).
Given that,
The crush depth of a submarine, or the depth at which water pressure will crush it, is 250 m.
Total pressure is calculated as follows:
Total pressure is calculated as follows:
P = P atm + ρgh,
where P atm is atmosphere pressure,
ρ is fluid density,
g is gravity's acceleration,
and h is fluid depth.
P = (1 atm) + (1025 kg/m³) (9.81 m/s²) (250 m) (9.8692×10⁻⁶ atm/Pa)
P = 1 atm + 24.8 atm
P = 25.8 atm
Hence, the pressure is approximately 25.8 atm (water plus atmosphere).
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De diagram shows two quadrilaterals graphed on a coordinate plane Which transformation on quadrilateral I can be used to verify that is similar to quadrilateral 22
Answers
Given two similar quadrilaterals
As the quadrilaterals are not of the same size, the transformation used will be dilation
The size of quadrilateral 2 is smaller than the quadrilateral one
So, the factor of dilation will be less than 1
To find the factor of dilation we will use 2 corresponding points
From quadrilateral 1 we will use the point (-6, 0)
From quadrilateral 2 we will use the point (-3, 0)
So, the factor of dilation will be:
[tex]\frac{-3}{-6}=\frac{1}{2}=0.5[/tex]The center of dilation will be the point (0, 0)
So, the answer will be:
The transformation is dilation from the point (0, 0) and the factor is 1/2
which system of linear equations has a solution of (-2,1)?
Answers
Explanation
the easiest way to solve this is by checking the pair orderer on each system of equations and see it the equation becomes true, so
Step 1
check the solution on each system
a)
[tex]\begin{gathered} 2x+3y=-1 \\ x-y=-3 \end{gathered}[/tex]let
[tex]\begin{gathered} (x,y)\Rightarrow(-2,1) \\ x=-2 \\ y=1 \end{gathered}[/tex]replace
[tex]\begin{gathered} 2x+3y=-1 \\ 2(-2)+3(1)=-1 \\ -4+3=-1 \\ -1=-1\Rightarrow true \end{gathered}[/tex]and
[tex]\begin{gathered} x-y=-3 \\ -2-(1)=-3 \\ -3=-3\Rightarrow true \end{gathered}[/tex]so, A is the solution
Step 2
b)
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