A rancher has a pen shown on the grid, where 1 unit represents 1
meter. The rancher needs a larger pen to be a dilation of the
smaller pen by a scale factor of 3.5 with the origin as the center of
dilation.
Answers
The coordinates of the vertices of the rectangle are A'(x, y) = (3.5, 3.5), B'(x, y) = (3.5, 7), C'(x, y) = (10.5, 7) and D'(x, y) = (3.5, 10.5). The graph of the new pen is shown below.
What is the representation of a pen by using a scale factor?
We find a representation of a original pen, whose vertices are shown on Cartesian plane. The new pen is the result of dilating the original one by a scale factor of 3.5 and with center at the origin. The expression that describes the transformation is:
P'(x, y) = k · P(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that A(x, y) = (1, 1), B(x, y) = (1, 2), C(x, y) = (3, 2), D(x, y) = (1, 1) and k = 3.5, then the coordinates of the resulting point are:
A'(x, y) = 3.5 · (1, 1)
A'(x, y) = (3.5, 3.5)
B'(x, y) = 3.5 · (1, 2)
B'(x, y) = (3.5, 7)
C'(x, y) = 3.5 · (3, 2)
C'(x, y) = (10.5, 7)
D'(x, y) = 3.5 · (1, 3)
D'(x, y) = (3.5, 10.5)
The graph of the resulting rectangle is shown below.
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Related Questions
find:when does the motion of the object change direction given:
Answers
The object change direction when the first derivative change its sign,. So we need to find the first derivative and equate this result to zero.
The first derivative is given by
[tex]s(t)=7\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}}[/tex]By equating this result to zero ,we have
[tex]7\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}}=0[/tex]This implies that
[tex]\frac{7}{2}t^{\frac{3}{2}}(5-t^)=0[/tex]so, the first derivative change its sign when
[tex]\begin{gathered} t=0 \\ and \\ t=5 \end{gathered}[/tex]as we can note in the following graph:
because the graphs falls when t= 5seconds.
This means that the motion objects change direction at t=5 seconds.
Find the 12thterm of the following geometric sequence.5, 10, 20, 40,
Answers
5, 10, 20, 40, . . .
SolutionStep1 Find the common ratio(r)[tex]r=\frac{a_2}{a_1}=\frac{10}{5}=2[/tex]Step 2The geometric sequence formula
[tex]a_n=a_1\times r^{n-1}[/tex]Step 3[tex]\begin{gathered} r=2,\text{ } \\ a_1=5 \\ n=12 \end{gathered}[/tex]Step 4[tex]\begin{gathered} a_{12}=5\times2^{12-1} \\ a_{12}=5\times2^{11} \\ a_{12}=10240 \end{gathered}[/tex]The final answer The 12th term of the geometric sequence is 10240Jackson goes to the gym 1, 2, or 3 days in a week, depending on work demands at the office. The probability that he goes 1 day is 0.1, the probability that he goes 2 days is 0.65, and the probability that he goes 3 days is 0.25. What is the expected value of the number of days per week for which Jackson goes to the gym?Do not round your answer.
Answers
We have the following values and their probabilities:
1 day = 0.1
2 days = 0.65
3 days = 0.25
Expected value = 1 (0.1) + 2 (0.65) + 3(0.25) = 0.1 + 1.3+ 0.75 = 2.15
, Assuming that the relationship between the miles driven and the amount of gasneeded is DIRECT VARITION, and that your car uses 1.6 gallons to go to Salt Lake from yourhome in Clinton (32 miles). Find the amount of gallons of gas that your car needs to go to LasVegas from your house, knowing that Salt Lake is 420 away from Vegas.Then, using the right numbers,distanceFirst, find the constant of variation,gasolinesolve the equationMy car needsgallons
Answers
Given:
Car uses 1.6 gallons to go 32 miles
Let's find the amount of gallons of gas the car needs to travel 420 miles.
Here, the relationship between the miles driven and the amount of gas needed is direct variation.
Since it is a direct variation, we have the variation equation when y varies directly with x:
y = kx
Where k is the constant of variation.
Hence, we have:
32 = 1.6k
Let's solve for k.
Divide both sides by 1.6:
[tex]\begin{gathered} \frac{32}{1.6}=\frac{1.6k}{1.6} \\ \\ 20=k \\ \\ k=20 \end{gathered}[/tex]The constant of variation is 20.
The equation that represents this situation is:
y = 20x
Therefore, to find the amount of gallons of gas needed if the car travels 420 miles, substitute 420 for y and solve for x.
420 = 20x
Divide both sides by 20:
[tex]\begin{gathered} \frac{420}{20}=\frac{20x}{20} \\ \\ 21=x \\ \\ x=21 \end{gathered}[/tex]Therefore, the car needs 21 gallons of gas
what is the 6th value in the sequence with the explicit formula a n equals -2 and -14?
Answers
Since the explicit formula of the sequence is
[tex]a_n=-2n-14[/tex]Where n is the position of any term
We need to find the sixth term, which means
n = 6
Substitute n by 6 in the formula above
[tex]\begin{gathered} a_6=-2(6)-14 \\ a_6=-12-14 \\ a_6=-26 \end{gathered}[/tex]The sixth term is -26
The answer is B (2nd answer)
You are starting your first job as a salesperson at a clothing store. You receive a base salary of $10.00 per hour with time-and-a half for hours in excess of 40 hours per week. If you are paid biweekly (every two weeks), what will one gross base paycheck be? Assume 40 hours a week, no overtime. a760 b840 c400 d800
Answers
1) Given that you are paid every two weeks, consider that the base salary is $10 per hour. And 1.5 times for hours in excess.
2) But notice that the pay will not include overtime.
3) Thus, we can write out the following:
[tex]\begin{gathered} 40\:hours\:\times2=80\:hours \\ \\ 80\:\times10=800 \end{gathered}[/tex]Note that this is the gross paycheck (no taxes).
A paper airplane is thrown off a 64-foot bridge into the water below. It’s height, in feet, is represented by f(x)= -16(x^2 - 3x - 4), where x is the number of seconds since the airplane was thrown. The height of the airplane is 0 feet when it hits the water. C. What do the zeros mean in terms of the situation?D. Do both zeros have a real world meaning? E. How long does it take the airplane to hit the water?
Answers
According to the problem, the function f(x) represents the height of the airplane, and x is the time in seconds since the airplane was thrown.
C.The graph shows the zeros x = -1 and x = 4, however, the positive zero is the only one that makes sense to the problem because time can't be negative. So, the zero x = 4 means that the paper airplane will reach the water level after 4 seconds.
D.As we said, just the positive zero has meaning to this situation because, in real life, time is not negative.
Therefore, just one zero (x=4) has real-world meaning.
E.According to the zero x = 4, the paper airplane will hit the water after 4 seconds.
What is the answer please
Answers
The measure of angle m∠CGE is 83°
Given,
∠AGF = 62°
∠DGB = 35°
Since, ∠DGB is vertically opposite angle of ∠CGA
Then, ∠CGA = 35°
And also,
∠AGF is vertically opposite angle of ∠EGB
Then, ∠EGB = 62°
Now, we know that CD is straight line
Using angle - sum property,
Then,
∠CGE + ∠EGB + ∠CGA = 180°
Putting the values we get
∠CGE + 62° + 35° = 180°
∠CGE + 97° = 180°
∠CGE = 180° - 97°
∠CGE = 83°
Hence, ∠CGE = 83°
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Directions - Graph the following slope intercept equation:y=2/3x-2
Answers
Answer
Explanation
The best way to plot graphs, especially straight line graphs, is to use the intercepts. The intercepts are the point(s) that the graph of the function crosses or touches the x and y axis.
The equation is
y = (2/3)x - 2
when x = 0,
y = (2/3)x - 2
y = (2/3)(0) - 2
y = 0 - 2
y = -2
The first point on the graph is (0, -2)
when y = 0,
y = (2/3)x - 2
0 = (2/3)x - 2
(2x/3) = 2
Cross multiply
2x = (2) (3)
2x = 6
Divide both sides by 2
(2x/2) = (6/2)
x = 3
The second point on this graph is (3, 0)
So, the two points are (0, -2) and (3, 0)
We can then easily plot this graph by marking out those two points on the graph and connect the two points for the equation of that line.
Find three consecutive odd integers such that the sum of the first and second is 27 less than three times the third
Answers
The consecutive integers that are odd numbers are 17, 19 and 21.
How to determine the value of three consecutive integers
In this problem we need to find the values of three consecutive integers that odd integers such that the following equation is satisfied:
x₁ + x₂ = 3 · x₃ - 27
Please notice that two odd numbers are consecutive when their difference is 2.
x₁ + (x₁ + 2) = 3 · (x₁ + 4) - 27
2 · x₁ + 2 = 3 · x₁ + 12 - 27
2 · x₁ + 2 = 3 · x₁ - 15
17 = x₁
x₁ = 17
Thus, the three odd integers that are consecutive are 17, 19 and 21, respectively.
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PLEASE HELP! ITS DUE SOON AND I LOST MY CALULATER I HAVE 7 QUESTIONS I NEED HELP WITH!!!!! WILL ONLY LET ME UPLOAD 5! BUT ILL ADD THAT IN AN OTHER QUESTIO I HAVE 35 MINTUTES LEFT TO GET THIS DONE! PLEASE HELP!! WILL GET 100 POINTS! MANY THANKS!!!!
Answers
Answer:
Step-by-step explanation:
d
c
a
b i think
a
work for question #4:
Side a = 30.27382
Side b = 30
Side c = 27.83241
Angle ∠A = 63° = 1.09956 rad = 7/20π
Angle ∠B = 62° = 1.0821 rad
Angle ∠C = 55° = 0.95993 rad
can you please help me
Answers
In this problem we can see that the intercept with the y axis is positive one, so we know that the answer is A) or D), now we can see that the slope is positie so the term with the x has to be positive so the correct function is:
[tex]y=x+1[/tex]I need help with this question:
Find the value of y that satisfies the given conditions.
The line is containing (−4, 9) and (4, 3) which is parallel to the line containing (−8, 1) and (4, y).
y= ?
Answers
The value of "y" that satisfies the given conditions is -8.
The first straight line passes through two points. The coordinates of the two points are (−4, 9) and (4, 3). The second straight line passes through two points. The coordinates of the two points are (−8, 1) and (4, y).
We know that the first line is parallel to the second line. Hence, the slope of both the lines must be equal.
The slope of the first line is :
m1 = (3-9)/[4-(-4)]
m1 = -6/8
m1 = -3/4
The slope of the second line is :
m2 = (y-1)/[4-(-8)]
m2 = (y-1)/12
We know that m1 = m2.
-3/4 = (y-1)/12
y = -8
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The equation of a line is given below.Find the x-intercept and the y-intercept.Then use them to graph the line.SHOW POINTS WHEN GRAPHING
Answers
Given
2x + 6y = -18
Find
x intercept and y intercept. Then use them to graph the line.
Explanation
to find the y intercept , put x = 0
2(0) + 6y = -18
6y = -18
y = -3
now , put y = 0 to find the x intercept
2x + 6(0) = -18
2x = -18
x = -9
we have two points ; (0 , -3) and (-9 , 0)
plot these points on graph to make a line
Final Answer
Hence , the x intercept is -9 and y intercept is -3. The required graph is shown above.
Imagine that you are a scientist studying the effects of a new medication on the treatment of patients who get headaches. You separate all the patients into three groups. Group A is given 1 pill with a dose of 20 milligrams of medication once per day. Group B is given 1 pill with a dose of 40 milligrams of the medication once per day. Group C is given 1 pill that looks like the others but is really a sugar pill that contains no medication. The results: 20 percent of the people in Group A claimed that they got fewer headaches, while 80 percent of the people in Group B daimed that they had fewer headaches. Only 1 percent of people in Group C noticed a decrease in their headaches. What might you be able to conclude from this experiment? Explain by identifying the control, the dependent variable, and the independent variable in the experiment.
Answers
The control group is the group C, since they take sugar pills.
The dependent variable is the percentage of people that got fewer headaches.
The independent variables is the type of pills they gave to each of the groups.
Write a multiplication expression with a product of x^20
Answers
Answer:
x¹¹ • x⁹
Step-by-step explanation:
so hope it help
have a nice day
Can you help me find the cube root of .216
Answers
Given
0.216
Find
Cube root of the given number
Explanation
Cube root is the value which when multiplying by itself thrice or three times produces the original number
0.216 can be written as the product of
[tex]\begin{gathered} 0.216=\frac{216}{1000} \\ \end{gathered}[/tex]prime factorization of 216 and 1000
prime factorization of 216 =
[tex]\begin{gathered} 2\times2\times2\times3\times3\times3 \\ \end{gathered}[/tex]1000 -
[tex]\begin{gathered} 10\times10\times10 \\ 10 \end{gathered}[/tex]we have to find the cube root so , we make pair of three
so
[tex]\begin{gathered} (2\times2\times2)\times(3\times3\times3) \\ 2\times3 \\ 6 \end{gathered}[/tex]hence
[tex]\begin{gathered} \frac{6}{10} \\ 0.6 \end{gathered}[/tex]so , the cube root of 0.216 is 0.6
Final Answer
Therefore , The cube root of 0.216 is 0.6
If the dividend is 415 and the quotient is 83 what is the divisor
Answers
the divisor = 5
Explanation:
let the divisor be = x
dividend = number to be divided = 415
quotient = result of the division = 83
dividend/divisor = quotient
415/x = 83
cross multiply:
415 = 83x
Divide both sides by 83:
83x/83 = 415/83
x = 5
Hence, the divisor = 5
Ada drank 5/8 of a glass of water. What percentage of a glassof water did Ada drink?%Pls help
Answers
Answer:
[tex]\begin{gathered} \frac{5}{8}=\frac{x}{100} \\ \therefore\rightarrow \\ x=\frac{100\cdot5}{8}=\frac{500}{8}=62.5\text{ percent} \end{gathered}[/tex]Therefore he drank 62.5% of the glass. a little bit above half.
Answer:62.5 percentage of water
Step-by-step explanation: divide 5 by 8 the whole, then multiply by 100 to get the percentage
What number should be in the box to make the equation below true
Answers
So,
We want to find the value in the box such that:
[tex]\frac{(\frac{2+x}{6}+1)}{4}=\frac{3}{8}[/tex]I wrote x instead the box.
To solve this equation, the first thing we need to do is to let the "x term" alone.
For this, we could start by multiplying both sides of the equation by 4:
[tex]\frac{2+x}{6}+1=\frac{12}{8}[/tex]Now, we could substract 1 to both sides:
[tex]\begin{gathered} \frac{2+x}{6}=\frac{12}{8}-1 \\ \\ \frac{2+x}{6}=\frac{4}{8} \end{gathered}[/tex]And then multiply by 6:
[tex]2+x=\frac{24}{8}[/tex]Now, substract 2:
[tex]\begin{gathered} x=\frac{24}{8}-2 \\ \\ x=3-2 \\ x=1 \end{gathered}[/tex]Therefore, the value in the box should be 1.
If xy + 7ey = 7e, find the value of y'' at the point where x = 0.
Answers
Answer:
Please read my updated answer.
I am wasn't sure what you were asking so here and 2 answers.
1st answer [tex]y=\frac{1}{e}[/tex]
2nd answer [tex]\frac{dy}{dx}=-\frac{y}{x+7e}[/tex]
Step-by-step explanation:
[tex]xy+7ey=7[/tex]
[tex]when \\ x=0[/tex]
Substitute [tex]0[/tex] for [tex]x[/tex] then simplify.
[tex](0*y)+7ey=7\\ 0+7ey=7\\ 7ey=7[/tex]
Divide each term in [tex]7ey=7[/tex] by [tex]7e[/tex] and simplify.
[tex]\frac{7ey}{7e}=\frac{7}{7e}[/tex]
Cancel the common factor of [tex]7[/tex] on the left side.
Rewrite the expression.
[tex]\frac{ey}{e}=\frac{7}{7e}[/tex]
Cancel the common factor of [tex]e[/tex] on the left side.
[tex]y=\frac{7}{7e}[/tex]
Cancel the common factor of 7 on the right side.
Rewrite the expression.
[tex]y=\frac{1}{e}[/tex]
2nd Answer
Step-by-step explanation:
[tex]xy+7ey=7[/tex]
Differentiate both sides of the equation.
[tex]\frac{d}{dx} (xy+7ey)=\frac{d}{dx}(7e)[/tex]
Differentiate the left side of the equation.
By the Sum Rule, the derivative of [tex]xy+7ey[/tex] with respect to x is [tex]\frac{d}{dx} [xy]+\frac{d}{dx}[7ey][/tex]
Evaluate [tex]\frac{d}{dx} [xy][/tex]
Differentiate using the Product Rule
Rewrite [tex]\frac{d}{dx} [xy][/tex] as [tex]y'[/tex].
[tex]xy'+y+\frac{d}{dx} [7ey][/tex]
Evaluate [tex]\frac{d}{dx} [7ey][/tex]
Since [tex]7e[/tex] is constant with respect to [tex]x[/tex], the derivative of [tex]7e[/tex] with respect to [tex]x[/tex] is [tex]0[/tex].
Reform the equation by setting the left side equal to the right side.
[tex]xy'+7ey'+y=0[/tex]
Solve for [tex]y'[/tex].
Subtract [tex]y[/tex] from both sides of the equation.
[tex]xy'+7ey'=-y[/tex]
Factor [tex]y'[/tex] out of [tex]xy'[/tex].
[tex]y'x+7ey'=-y[/tex]
Factor [tex]y'[/tex] out of [tex]7ey'[/tex].
[tex]y'(x)+y'(7e)=-y[/tex]
Factor out [tex]y'[/tex] out of [tex]y'(x)+y'(7e)[/tex]
[tex]y'(x+7e)=-y[/tex]
Divide each term in [tex]y'(x+7e)=-y[/tex] by [tex]x+7e[/tex] and simplify.
[tex]\frac{y'(x+7e)}{x+7e} =\frac{-y}{x+7e}[/tex]
Cancel the common factor of [tex]x+7e[/tex].
[tex]y'=-\frac{-y}{x+7e}[/tex]
Replace [tex]y'[/tex] with [tex]\frac{dy}{dx}=-\frac{y}{x+7e}[/tex]
[tex]\frac{dy}{dx}=-\frac{y}{x+7e}[/tex]
The price of a technology stock has risen to $9.74 today. Yesterday's price was 9.65. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Answer:-0.924025
Step-by-step explanation:
[(9.65 - 9.74) / 9.74] × 100%
= -0.0092402464066 × 100%
= -0.92402464066%
What number is 345% of 8.6?
Answers
Answer:
29.7
Step-by-step explanation:
To calculate this we need to convert the percentage to a decimal and then multiply. 345% is 3.45, so our math problem is 8.6 x 3.45. If you put that into a calculator you will get 29.67, but since the least precise number is to one decimal place (8.6), I put my answer to one decimal place as well - I rounded 29.67 to the nearest tenth.
1/8 x 240 please???? Hurry
Answers
Answer:
30
Step-by-step explanation:
Hi, I was absent today in class and I really need help with question 6I will be much appreciated if you show work and the step so I can be more understanding thank you!
Answers
Recall that:
[tex]\log _ba=\frac{\ln a}{\ln b}\text{.}[/tex]Therefore:
[tex]\begin{gathered} x=\log _7513=\frac{\ln (513)}{\ln (7)} \\ x\approx\frac{6.24027584}{1.94591014}, \\ x\approx3.207. \end{gathered}[/tex]Answer:
[tex]x\approx3.207.[/tex]The point Q(3,-4) is translated 1 unit right and 1 unit down. What are the coordinates of the
resulting point, Q?
Answers
Answer:Q(2,-3)
Step-by-step explanation:
65% of the people at the party were females. The rest were males. How many
were males were there at the school party? There are 1,600 people
Answers
Answer:
560
Step-by-step explanation:
If 65% were females, 35% were males.
1600(35%) = 1600(0.35) = 560
90 marbles in a bag represent three colors of the US flag there are three times as many red marbles as white marbles there are twice as many blue marbles as white marbles find the number of marbles for each color you select one marble at random from the bag find the probability you picked a red or blue marble
Answers
For the given question.
US flag has to be made by total 90 marbles.
Let the number of white marbles be 'x'.
Red marbles are three times the white marble = '3x'.
Blue marbles be twice of white marble = '2x'.
Total marbles = white marble + red marble + blue marble
90 = x + 2x + 3x
6x = 90
x = 15
White marble = 15.
Blue marble 2x = 2×15 = 30.
Red marble 3x = 3×15 = 45.
Probability = favourable outcomes /total outcome
The probability for picking red marble = 45/90 = 1/2.
The probability for picking blue marble = 30/90 = 1/3.
Probability (red or blue) = 1/2 × 1/3
Probability (red or blue) = 1/6
Thus, the probability for picking red or blue marble is 1/6.
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The points (−7,−4) and (3,8) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answers
The length of the radius of the circle is √61.
Here there are two endpoints of the circle (-7,-4) and (3,8)
To find the length between the two points we have a formula:
length = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }[/tex]
So here we have
([tex]x_{1} , y_{1}[/tex]) = (-7, -4)
([tex]x_{2} , y_{2}[/tex]) = ( 3,8)
Putting the value we have,
[tex]\sqrt{(3 -(-7)^{2} + ( 8-(-4)^{2} }[/tex]
=[tex]\sqrt{10^{2} + 12^{2} }[/tex]
=[tex]\sqrt{100+ 144}[/tex]
=√244
=2√61
The diameter is 2√61
radius = diameter/2
= 2√61/2
= √61
Therefore the length of the radius of a circle is √61.
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Sketch and label a graph of both an increasing and a decreasing exponential function.
Answers
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
[tex]f(x)=a^x[/tex]With a being a positive real, a > 0, and different from 1, a ≠ 1.
When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.
For example: the function
[tex]f(x)=2^x[/tex]Since a = 2 > 1, the function is increasing. We have the graph below:
And the function
[tex]f(x)=0.5^x[/tex]Since a = 0.5 < 1, the function is decreasing. Then, the graph is:
