Please get help with us for I am confused as to have should draw the rotation after a 90° clockwise rotation
Answers
In the given figure we can observe a triangle with vertices located at:
(-3,-2)
(-5,-4)
(1,-5).
We need to draw it after a 90° clockwise rotation.
We can apply the rule for 90° clockwise rotation, which is:
Each point of the given figure has to be changed from (x, y) to (y, -x) and then we need to graph the new coordinates.
By applying the rule to the given coordinates we obtain:
[tex]\begin{gathered} (x,y)\to(y,-x) \\ (-3,-2)\to(-2,3) \\ (-5,-4)\to(-4,5) \\ (1,-5)\to(-5,-1) \end{gathered}[/tex]Now we have to draw the new coordinates:
Related Questions
i need help on number 7. Please use 4 points
Answers
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
Find the measures of the numbered angles in rhombus DEFG. I just need someone to shown me how to find each of the numbered angles
Answers
Step 1
Properties of a Rhombus
Below are some important facts about the rhombus angles:
Rhombus has four interior angles.
The sum of interior angles of a rhombus add up to 360 degrees.
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary.
In a rhombus, diagonals bisect each other at right angles.
The diagonals of a rhombus bisect these angles.
Step 2
From the figure
Angle DGF = Angle DEF = 118
Step 3
Since adjacent angles are supplementary, that is add to 180 degrees
[tex]\begin{gathered} \angle\text{DGF + }\angle GFE\text{ = 180} \\ 118\text{ + }\angle GFE\text{ = 180} \\ \angle GFE\text{ = 180 - 118} \\ \angle GFE\text{ = 62} \end{gathered}[/tex]Step 4
The diagonals of a rhombus bisect these angles
[tex]\begin{gathered} \angle3\text{ = }\angle4\text{ = }\frac{62}{2}\text{ = 31} \\ \angle3\text{ = }\angle4\text{ = 31} \end{gathered}[/tex]Step 5
The opposite angles of a rhombus are equal to each other.
[tex]\angle1\text{ = }\angle\text{ 2 = 31}[/tex]Final answer
[tex]\angle\text{1 = }\angle\text{ 2 = }\angle\text{ 3 = }\angle4\text{ = 31}[/tex]A rectangular room is twice as long as it is wide, and its perimeter is 60 meters. Find the dimensions of the
room.
The length is __
meters and the width is __
meters.
Answers
Answer: 20, 10
Step-by-step explanation:
Let the width be w. Then, the length is 2w. Substituting into the formula for the perimeter of a rectangle,
[tex]2(w+2w)=60\\\\w+2w=30\\\\3w=30\\\\w=10\\\\\implies 2w=2(10)=20[/tex]
i have to find is they similar or not. help im lost
Answers
First we have to find the missing angle on each case.
In the first triangle we have
180°-(28°+80°)=72°
In the second triangle we have
180°-(28°+71°)=81°
Since the values of the angles are not the same for both triangles they are not similar.
An object was dropped off the top of a building. The function f(x) = -16x2 + 36represents the height of the object above the ground, in feet, X seconds after beingdropped. Find and interpret the given function values and determine an appropriatedomain for the function.
Answers
f(x) = -16x^2 + 36
Where:
f(x) = height of the object
x = seconds after being dropped.
f(-1) = -16 (-1)^2 + 36
f(-1) = -16 (1) + 36
f(-1) = 20
-1 seconds after the object was dropped, the object was 20 ft above the ground.
This interpretation does not make sense, because seconds can't be negative.
f(0.5) = -16 (0.5)^2 + 36
f(0.5) = -16 (0.25) +36
f(0.5) = -4 + 36
f(0.5) = 32
0.5 seconds after the object was dropped, the object was 32 ft above the ground.
This interpretation makes sense in the context of the problem.
f(2) = -16 (2)^2 + 36
f(2) = -16 (4) +36
f(2) = -64+36
f(2) = -28
2 seconds after the object was dropped, the object was -28 ft above the ground.
This interpretation does not make sense in the context of the problem, because the height can't be negative.
Based on the observation, the domain of the function is real numbers in a <- x <-b , possible values of x where f(x) is true.
before the object is released x=0
next, calculate x when f(x)=0 ( after the object hits the ground)
0= -16x^2+36
16x^2 = 36
x^2 = 36/16
x^2 = 2.25
x = √2.25
x = 1.5
0 ≤ x ≤ 1.5
I need help understanding slope
Answers
we know that
the formula to calculate teh slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]where
(x1,y1) is one point
and
(x2,y2) is the other point
substitute the values in the formula and solve for m
Example
you have the points
(1,4) and (3,2)
so
(x1,y1)=(1,4)
(x2,y2)=(3,2)
substitute in te formula
m=(2-4)/(3-1)
m=-2/2
m=-1
the slope is -1
Factor completely. (3.2² - 12x)(x2 – 2x + 1) =
Answers
We will have the following:
Which equation is the best approximation of the trend line
Answers
approximatesThe equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Taking two points from the line of best fit
Point A(14,200) and Point B (18,400)
[tex]\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \frac{400-200}{18-14}=\frac{y-200}{x-14} \\ \frac{200}{4}=\frac{y-200}{x-14} \\ \frac{50}{1}=\frac{y-200}{x-14} \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}[/tex]Hence, the equation that best approximate the trend line is y=50x-500
Check each answer to see whether the students evaluated the expression correctly. If the answer is incorrect cross out the answer and write the correct answer. 8(x+2)when x= 68(6+2) = 48 +2 = 50
Answers
The answer is not correct. There is a mistake applying the distributive property.
The distributive property says:
[tex]a(b+c)=ab+ac[/tex]But in this case, the 8 only multiplies the 6, and not the 2. The correct procedure is:
[tex]8(6+2)=8\cdot6+8\cdot2=48+16=64[/tex]The correct answer is 64
Identify the x intercept(s) from the graphType your answer using set notation {x,x} listing x values in order from least to greatest
Answers
The x-intercept is where the graph passes the x-axis.
The graph extends from {-5 ≤ x ≤ 3}
The x-intercept is {x = -1}.
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
Answers
The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
Given,
Belinda wants to invest $1,000.
The Table is:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Now, According to the question:
When the x-values are sequential (1, 2, 3, ...), the y-values will have a common difference for a linear function, and a common ratio for an exponential function.
For the two investment options, we notice Belinda earns 1300 -1000 = 300 the first year for either option. The difference is the same the next year for Option 2 (1600 -1300 = 300), but is not the same for Option 1. For that option, the ratio is the same for the second year as it was for the first year:
1690/1300 = 1.3 = 1300/1000
Part A :
(Option 1) can be represented by exponential function.
(Option 2) can be represented by a linear function.
Part B:
For Option 1:
To find the value of the investment f(n), in dollars, after n years.
The generic form of an exponential function is ...
f(n) = a·b^n
Now, Amount after 1 year = 1100
Principle (P) is = 1000
Using the formula :
A = P[tex](1+r)^n[/tex]
1100 = 1000[tex]([/tex][tex]1 + r)^1[/tex]
1.10 = 1 + r
r = 0.10
Amount after t years can be given by :
A = 1000(1.10)^t
For Option 2,
The generic form of an exponential function is ...
f(n) = a·n + b
Rate of change (m) = (1100 - 1000) / 1 = 100
Amount after t years can be given by
A = 1000 + 100 x t .
Part C:
Investment in (1) : 1000 [tex](1.10)^2^0[/tex]= $6727
Investment in (2): $3000
Hence, The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
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A certain marine engine has cylinders that are 5.25 cm in diameter and 5.64 cm deep.Find the total volume of 4 cylinders (to the nearest hundredth). Use 3.14 as the approximate value of
Answers
Given:
A cylinder is given with 5.64 cm deep and 5.25 cm diameter.
Required:
Total volume of 4 cylinders.
Explanation:
Diameter of cylinder d = 5.25 cm
Height of cylinder or deepness of cylinder h = 5.64 cm
Radius r of cylinder is
[tex]r=\frac{d}{2}=\frac{5.25}{2}=2.625\text{ cm}[/tex]volume of cylinder is
[tex]v=\pi r^2h=3.14*2.625^2*5.64=122.03\text{ cm}^3[/tex]here we need volume of 4 cylinder
for this we just multiply v with 4
[tex]V=4v=4*122.03=488.121\text{ cm}^3[/tex]Final Answer:
The volume of 4 cylinder is 488.121 cube cm
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answerbox. Also, specify any restrictions on the variable.a²-3a-4/a² + 5a + 4Rational expression in lowest terms:Variable restrictions for the original expression: a
Answers
Factorize both quadratic polynomials, as shown below
[tex]\begin{gathered} a^2-3a-4=0 \\ \Rightarrow a=\frac{3\pm\sqrt{9+16}}{2}=\frac{3\pm\sqrt{25}}{2}=\frac{3\pm5}{2}\Rightarrow a=-1,4 \\ \Rightarrow a^2-3a-4=(a+1)(a-4) \\ \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} a^2+5a+4=0 \\ \Rightarrow a=\frac{-5\pm\sqrt{25-16}}{2}=\frac{-5\pm3}{2}\Rightarrow a=-1,-4 \\ \Rightarrow a^2+5a+4=(a+1)(a+4) \end{gathered}[/tex]Thus,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{(a+1)(a-4)}{(a+1)(a+4)}[/tex]Therefore, since the denominator cannot be equal to zero.
The variable restrictions for the original expression are a≠-1,-4Then, provided that a is different than -1,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{x-4}{x+4}[/tex]The rational expression in the lowest terms is (x-4)/(x+4)For the equation, complete the given table.
Answers
Answer:
Step-by-step explanation:
first row: 4
second: 2
third: 6
fourth: 9
plug in x for x in the equation/plug in y for y in the equation for whichever is given.
Pls help ASAP!!! Ill give you 5.0
Answers
The equivalent equation of 6x + 9 = 12 is 2x + 3 = 4.
Another equivalent equation of 6x + 9 = 12 is 3x + 4.5 = 6
What are equivalent equations?Equivalent equations are algebraic equations that have identical solutions or roots. In other words, equivalent equations are equations that have the same answer or solution.
Therefore, the equivalent equation of 6x + 9 = 12 can be calculated as follows:
6x + 9 = 12
Divide through by 3
6x / 3 + 9 / 3 = 12 / 3
2x + 3 = 4
Therefore, the equivalent equation of 6x + 9 = 12 is 2x + 3 = 4
Another equation that is equivalent to 6x + 9 = 12 is 3x + 4.5 = 6
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(Solve the problem & round to four decimal places as needed.)
Answers
SOLUTION
Given:
[tex]ln0.0664=-2.7121[/tex]Final answer:
-2.7121
The formula to calculate the gravitational force between two objects is F_g=\frac{GM_1M_2}{r^2},F
g
=
r
2
GM
1
M
2
, where M_1M
1
and M_2M
2
are the masses of the objects, GG is the gravitational constant and rr is the distance between the objects. Solve for M_2M
2
in terms of F_g,F
g
, G,G, M_1M
1
and r.r.
Answers
The expression for M in terms of other variables is M = Fr^2/Gm
Subject of formulaThe variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own.
In order to make one of the the variables the subject of the formula, we place rewrite the expression in a different form.
Given the formula to calculate the gravitational force between two objects as;
Fg = GMm/r^2
We are to make M the subject of the formula in terms of other variables.
F = GMm/r^2
Cross multiply
Fr^2 = GMm
Divide both sides by Gm
Fr^2/Gm = GMm/Gm
Fr^2/Gm = M
Swap
M = Fr^2/Gm
This gives the expression for the variable M.
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(8x+6)=mL(blank)
8x+6) =
8x=
x=
the L is an angle
Answers
The value of the unknown angle is as follows;
∠ = 62 degreesHow to find the unknown angle?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle 4 can be found as follows:
∠4 = 8x + 6 (alternate angles)
Hence,
8x + 6 + 118 = 180(sum of angles on a straight line)
8x = 180 - 118 - 6
8x = 56
divide both sides by 8
x = 56 / 8
x = 7
Therefore,
∠4 = 8(7) + 6 = 56 + 6 = 62 degrees
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you get a student loan from the educational assistance Foundation to pay for your educational expenses as you earn your associate's degree you will be allowed 10 years to pay the loan back find the simple interest on the loan if you borrow $3,600 at 8 percent
Answers
Simple interest = PRT/100
where p = $3600
R=8
T=10
Substituting into the formula;
S.I = $3600 x 8 x 10 /100
=$36 x 8 x 10
=$2880
you pull with 45nm on a torque wrench of 1m what's the tourqe at the end
Answers
The torque at the end is equal to 45 Nm.
What is torque?Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.
Mathematically, torque can be calculated by using this formula:
τ = Fd
Where:
τ represents the torque.F represents the force.d represents the perpendicular distance.In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.
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Rewrite the following equation in slope-intercept form.
10x − 10y = –1 ?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y = x + 1/10
Step-by-step explanation:
Rewrite the following equation in slope-intercept form: 10x − 10y = –1 ?
slope intercept form: y = mx + b so you are solving for y:
10x − 10y = –1
subtract 10x from both sides:
10x − 10y – 10x = –1 – 10x
-10y = –1 – 10x
divide all terms by -10:
-10y/(-10) = –1/(-10) – 10x/(-10)
y = 1/10 + x
rearrange for slope intercept form: y = mx + b
y = x + 1/10
Answer:
[tex]y=x+\dfrac{1}{10}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]10x-10y=-1[/tex]
To write the given equation in slope-intercept form, perform algebraic operations to isolate y.
Add 10y to both sides of the equation:
[tex]\implies 10x-10y+10y=10y-1[/tex]
[tex]\implies 10x=10y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies 10x+1=10y-1+1[/tex]
[tex]\implies 10x+1=10y[/tex]
[tex]\implies 10y=10x+1[/tex]
Divide both sides of the equation by 10:
[tex]\implies \dfrac{10y}{10}=\dfrac{10x+1}{10}[/tex]
[tex]\implies \dfrac{10y}{10}=\dfrac{10x}{10}+\dfrac{1}{10}[/tex]
[tex]\implies y=x+\dfrac{1}{10}[/tex]
Therefore, the given equation in slope-intercept form is:
[tex]\boxed{y=x+\dfrac{1}{10}}[/tex]
Can you help me figure this out
Answers
By using the fact that the interior angles of a triangle must add up to 180, we will see that the value of x is 15.
How to get the value of x?Here we have 3 expressions for the measures of the interior angles of a triangle.
Now, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write:
(8x - 7)° + (x + 7)° + (2x + 15)° = 180°
Ignoring the degrees and solving this for x, we get:
8x - 7 + x + 7 + 2x + 15 = 180
11x + 15 = 180
11x = 180 - 15 = 165
x = 165/11 =15
The value of x is 15.
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The semi annual compound interest of a sum of money in 1 year and 2years are Rs400 and Rs441 respectively.Find the annual compound interest for 2years
Answers
Answer:
Step-by-step explanation
Correct option is A)
C.I. for the third year = Rs. 1,452.
C.I. for the second year = Rs. 1,320
∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.
Rate of interest =
1,320
132×100
=10%.
Let the original money be Rs. P.
Amount after 2 year − amount after one year =C.I. for second year.
P(1+
100
10
)
2
−P(1+
100
10
)=1,320
P[(
100
110
)
2
−
100
110
]=1,320
⇒P[(
10
11
)
2
−
10
11
]=1,320⇒P(
100
121
−
10
11
)= Rs. 1,320
⇒P×
100
11
=Rs.1,320⇒P=
11
1,320×100
= Rs. 12,000
∴ Rate of interest =10%
and Original sum of money = Rs. 12,000
When you convert 0.0045 to scientific notation, the exponent will be
positive.
Or
negative.
Answers
Standard form
i need help with my homework PLEASEMCHECK WORK WHEN FINISHED
Answers
Given:
The population of a town increases by 9 % annually.
The current population is 4,500.
Required:
We need to find the equation that gives the population of the town.
Explanation:
The population can be found by the following equation.
[tex]Th\text{e population =4500+9 \% of 4500}[/tex]Let now be the current population of the town =4500.
Let Next be the population of the town.
The population can be found by the following equation.
[tex]Next\text{ =Now+9\% of Now.}[/tex][tex]Next\text{ =Now+}\frac{9}{100}\times\text{Now.}[/tex]Take the common term now out.
[tex]Next\text{ =Now\lparen1+}\frac{9}{100})[/tex][tex]Use\text{ }\frac{9}{100}=0.09.[/tex][tex]Next\text{ =Now\lparen1+0.09})[/tex][tex]Next\text{ =Now\lparen1.09})[/tex][tex]Next\text{ =Now}\times\text{1.09}[/tex]Final answer:
[tex]Next\text{ =Now}\times\text{1.09}[/tex]What is the unknown angle b?
Answers
Answer:
48°
Explanation:
A line always equals 180°. The angle on the right is a 90° angle (we know this because or the little red box shown) and the angle in the middle is 42°. We would add 42° and 90° to get the combination of both which is 132°
42+90=132
Then subtract 132° from 180° to find unknown angle b.
180-132=48
Unknown angle b= 48°
The figure below is an iscoceles trapezoid. If m
Answers
..Given an isosceles trapezoid
The following are the properties of an isosceles trapezoid
The legs are congruent by definition (From the diagram, the legs are JM and KL)
The lower base angles are congruent. The lower base angles are
[tex]m\angle M\cong m\angle L[/tex]The upper base angles are congruent. The upper base angles are
[tex]m\angle J\cong m\angle K[/tex]Any lower base angle is supplementary to any upper base angle. This means that
[tex]\begin{gathered} m\angle J+m\angle M=180^0 \\ m\angle K+m\angle L=180^0 \end{gathered}[/tex][tex]\begin{gathered} \text{If} \\ m\angle K=61^0 \\ \text{Therefore} \\ m\angle J\cong m\angle K=61^0 \\ m\angle J=61^0 \end{gathered}[/tex]Also,
[tex]\begin{gathered} m\angle L+m\angle K=180^0 \\ m\angle L+61^0=180^0 \\ m\angle L=180^0-61^0 \\ m\angle L=119^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle L\cong m\angle M,m\angle L=119^0 \\ Therefore\colon \\ m\angle M=119^0 \end{gathered}[/tex]Hence
m∠J = 61⁰
m∠L = 119⁰
m∠M = 119⁰
y-intercept of y=3/2|x-2|
Answers
Answer:
Combine [tex]\frac{3}{2 }[/tex] and | x - 2 |
[tex]y\frac{3|x-2|}{2}[/tex]
If the LM follows the reference trajectory, what is the reference velocity vref (t) ?
Answers
Answer:
Explanation:
10 pts What is x and y intercept for the following equation? 8x + y = 12 A. x intercept = 0 y intercept = 4 B. x intercept = 12 y intercept = 0 C. x intercept = 4 y intercept = 6 D. x intercept = 3/4 y intercept = 12 OB ОА Oc
Answers
To find the x intercept of the equation make y=0 and solve for x.
[tex]\begin{gathered} 8x+y=12 \\ 8x=12 \\ x=\frac{12}{8} \\ x=\frac{6}{4} \\ x=\frac{3}{2} \end{gathered}[/tex]The x intercept is 3/2
To find the y intercept, make x=0 and solve for y
[tex]\begin{gathered} 8x+y=12 \\ 8(0)+y=12 \\ y\text{=}12 \end{gathered}[/tex]The y intercept is 12.