The coordinates of the vertices of the translated triangle are A'(x, y) = (1, 8), B'(x, y) = (2, 6) and C'(x, y) = (- 1, 6).
How to translate a triangle by transformation rules
Graphically speaking, triangles can be generated by knowing its three vertices. In this question we must apply a kind of rigid transformation known as translation, whose formula is:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorIf we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (1, 2) and T(x, y) = (-2, 4), then the new coordinates are:
A'(x, y) = (3, 4) + (- 2, 4)
A'(x, y) = (1, 8)
B'(x, y) = (4, 2) + (- 2, 4)
B'(x, y) = (2, 6)
C'(x, y) = (1, 2) + (- 2, 4)
C'(x, y) = (- 1, 6)
Remark
The statement presents typing mistakes, correct form is:
Translate the triangle with the vector <- 2, 4>, then enter the new coordinates:
Original coordinates - A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (1, 2).
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Imagine that the figure shown is moved 4 units to the left and 3 units down.
Which point is not a vertex of the transferred image?
(-2, -3)
(-4, -3)
(-3, -1)
(-2, 1)
Answer:
(-4,-3)
Step-by-step explanation:
Just check each vertex point and move them by instruction, write them down and do elimination and you'll find the answer
Help mee plsssssss hurry
Answer:
8
Step-by-step explanation:
Midpoint means half point of a certain shape. This means that if all the points of OPQ are midopoints of the bigger triangle, then OPQ has to be half the size of the big triangle. There are two ways to figure this out. The first way is to add all the numbers up to find the perimeter of the big triangle (6+6+4) which is 16. Then, you can do 16/2 to get the perimeter of the smaller triangle which is 8. The other method is to take each value of the bigger triangle and divide them by 2 (6/2, 6/2, 4/2). When you do that, you get (3, 3, 2). Now, you just add those values (3+3+2) which gets you 8 gor the smaller triangle. I hope this helps!
Consider the paragraph proof. given: d is the midpoint of ab, and e is the midpoint of ac. prove:de = one-halfbc on a coordinate plane, triangle a b c is cut by line segment d e. point d is the midpoint of side a b and point e is the midpoint of side a c. point a is at (2 b, 2 c), point e is at (a b, c), point c is at (2 a, 0), point b is at (0, 0), and point d is at (b, c). it is given that d is the midpoint of ab and e is the midpoint of ac. to prove that de is half the length of bc, the distance formula, d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, can be used to determine the lengths of the two segments. the length of bc can be determined with the equation bc = startroot (2 a minus 0) squared (0 minus 0) squared endroot, which simplifies to 2a. the length of de can be determined with the equation de = startroot (a b minus b) squared (c minus c) squared endroot, which simplifies to ________. therefore, bc is twice de, and de is half bc. which is the missing information in the proof? a 4a a2 4a2
The missing information in the proof is a which is option A.
Given d is the mid point of ab and e is the mid point of ac. Coordinates are point a (2b,2c), point e (ab, c), point c (2a, 0),point b (0,0), point d (b, c).
We have to find the missing proof in the solution.
To find the missing figure we have to just find the distance between point d and point e.
Distance formula for determining the distance between two points on a coordinate plane is given as :
d=[tex]\sqrt{(y_{2} -y_{1} )^{2} +(x_{2} -x_{1} )^{2} }[/tex]
where ([tex]x_{1} ,y_{1} ) (x_{2} ,y_{2} )[/tex] are the coordinates at the end of line.
DE=[tex]\sqrt{(a+b-b)^{2} +(c-c)^{2} }[/tex]
Simplifying this we get:
DE=[tex]\sqrt{(a^{2} +0^{2} }[/tex]
=[tex]\sqrt{a^{2} }[/tex]
=a
Hence the missing proof is a which is the distance or length of DE..
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HELP HELP HELP
Quick algebra 1 question
What is the slope of this graph?
Hello and Good Morning/Afternoon:
To find the slope of something:
⇒ let's consider what the formula of the slope needs
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
⇒ needs any two points on the line (x₁,y₁) and (x₂,y₂)
Let's get the required information:
(x₁,y₁) ==> (0,0)(x₂,y₂) ==> (5,2)Let's solve:
[tex]Slope = \frac{2-0}{5-0} =\frac{2}{5}[/tex]
Answer: 2/5
Hope that helps!
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PLEASE HELP!!! FINDING PROBABILITY MATH!!! expert help would be nice
i need the answer to question 2, 3, and 4. question 1's answer is 9/28 & 32.1%.
The probability that a person wins the game is 32.1%
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴ = 1/1296
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Find the UY segment measurement if
bold increment bold italic X bold italic Y bold italic Z bold approximately equal to bold increment bold italic U bold italic Y bold italic W
.
26
20
24
10
Triangle XYZ = UYW
We know that the 2 triangles are similar using angles Theorem
Let us find XZ to determine UY (for confirmation):
To determine XZ, use the Pythagorean Theorem:
[tex]a^{2} + b^{2} = c^{2} \\ OR\\leg^{2} +leg^{2} = Hypotenuse^{2} \\24^{2} + b^{2} = 26^{2} \\576+b^{2} =676\\b^{2} =100\\b=10[/tex]
You can see that XZ = WU
Now find UY= 26
Corresponding angles
Hope it helps!
31. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
31. f(-1) = 4 and f(5) = 1
Answer:
The required linear equation satisfying the given conditions f(-1)=4 and f(5)=1 is [tex]$y=\frac{-1}{2} x+\frac{7}{2}$[/tex]
Step-by-step explanation:
It is given that f(-1)=4 and f(5)=1.
It is required to find out a linear equation satisfying the conditions f(-1)=4
and f(5)=1. linear equation of the line in the form
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]
Step 1 of 4
Observe, f(-1)=4 gives the point (-1,4)
And f(5)=1 gives the point (5,1).
This means that the function f(x) satisfies the points (-1,4) and (5,1).
Step 2 of 4
Now find out the slope of a line passing through the points (-1,4) and (5,1),
[tex]$$\begin{aligned}&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&m=\frac{1-4}{5-(-1)} \\&m=\frac{-3}{5+1} \\&m=\frac{-3}{6} \\&m=\frac{-1}{2}\end{aligned}$$[/tex]
Step 3 of 4
Now use the slope [tex]$m=\frac{-1}{2}$[/tex] and use one of the two given points and write the equation in point-slope form:
[tex]$(y-1)=\frac{-1}{2}(x-5)$[/tex]
Distribute [tex]$\frac{-1}{2}$[/tex],
[tex]$y-1=\frac{-1}{2} x+\frac{5}{2}$[/tex]
Step 4 of 4
This linear function can be written in the slope-intercept form by adding 1 on both sides,
[tex]$$\begin{aligned}&y-1+1=\frac{-1}{2} x+\frac{5}{2}+1 \\&y=\frac{-1}{2} x+\frac{5}{2}+\frac{2}{2} \\&y=\frac{-1}{2} x+\frac{7}{2}\end{aligned}$$[/tex]
So, this is the required linear equation.
the interest paid on a $8,000 loan is $600, a rate of 4%
how many years did it take to pay back the loan? round to 1 decimal.
It took 1.9 years to pay back the loan.
What is Interest ?Interest is the amount of money given or received when a certain sum of amount is received as a loan or given or deposited for investment.
It is given that
Principal amount of loan = $ 8000
Interest paid = $ 600
Rate = 4%
Time Period = ?
Assuming Simple Interest has been applied
I = ( P* R* T) /100
600 = ( 8000 * 4 * T ) / 100
60000 = 8000 * 4 * T
T = 1.875 years
T = 1.9 years rounded to 1 decimal
T = 22.5 months
Therefore it took 1.9 years to pay back the loan.
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the inverse of the relation y=2x+3 can be obtained graphically by:
A. a reflection in the yaxis
B. a reflection in the line y= 1/2x
C. a reflection in the line y=√x
D. a reflection in the line y= x
Answer:
a reflection in the line y=x
Step-by-step explanation:
The inverse relation of an equation is when the x and y are swapped. For this reason it's going to be reflected over the y=x line. You can also use an online graphing tool to show this as well:
A motorcycle consumes 5 gallons of gas for 300 miles and 7 gallons for 420 miles. Calculate the rate of change per gallon of gas.
Thus, the rate of change per gallon of gas is 60 miles per gallon.
A motorcycle consumes 5 gallons of gas for 300 miles and 7 gallons for 420 miles.
Rate of change is defined as the change in value with rest to the time is called rate of change.
Now,
Rate of change = Difference B/w volume (i.e. in gallons) /difference in miles
= 420-300/7-2
= 60 gallons/mile
Thus, The required rate of change per gallon of gas is 60 miles per gallon.
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there were three parts to Rita's race. she ran the first part, which was 4/9 of the total distance, in 20 minutes. She ran the second part, which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meters per minute.
a) How long was the third part of the race?
20+12+15= 32+15 = 47 minutes in total
300 meters per minute
300 * 47 = 14100 meters in total
with this we can see the first race was 4/9 that distance meaning the first race was 6266.6 meters long
14100 - 6266.6 = 7833.3
2/5 of 7833.3 is 3133.32
therefore 7833.3 - 3133.32 will give the distance of the third part of the race
meaning of course the answer is 4699.98 or rounding up 4700 meters for the third race
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
329. (9c + 5)(9c − 5)
Answer:
The product is the difference of squares is [tex]$$\left(9c+5\right)\left(9c-5\right)=81{{c}^2}-25$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (9 c+5)(9 c-5).We have to multiply the given expression.Square the first term 9c. Square the last term 5 .[tex]$$\begin{aligned}&(9 c+5)(9 c-5)=(9 c)^{2}-(5)^{2} \\&(9 c+5)(9 c-5)=81 c^{2}-25\end{aligned}$$[/tex]
select the true statement about triangle abc
Answer:
Step-by-step explanation:
Please post a picture of the triangle and the choices.
Plis help! Will give brainliest!
Answer: 7) Step 1 8) Step
Step-by-step explanation:
The answer to 7 is 11. The error starts in step 1, as you can see youre supposed to do 8 divided by 2 plus 3 times 3 minus 2, instead it seems like 3+3 were added instead of becoming 9 thus the answer becomes 7.
The answer to 8 is also 11. 18-14/2 is 11.
f(x)=3x-2
h(x)=3x
g(x)=x squared
find the value of x when f(x)=19
The value of f(19) in the given equation is 55.
What is the function of a linear equation?The function of a linear equation illustrates a straight line graph and for a given set of input into the function, there is usually a specific output.
Given that:
f(x) = 3x - 2We are to find the f(x) = 19.
So;
f(19) = 3(19) - 2
f(19) = 57 - 2
f(19) = 55
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(1) Triangle ABC is an isosceles triangle.
Find the altitude h.
B
45°
Step-by-step explanation:
45+45
90
I guess is the answer
Evan has a storage unit that he keeps all his garden tools in. It measures 4 feet by 312 feet by 2 feet.A prism has a length of 4 feet, height of 2 feet, and width of 3 and one-half feet.What is the maximum amount of supplies that the storage unit can hold
The maximum amount of supplies that the storage unit can hold is 28 ft³
How to calculate the volume of a rectangular prism?
For us to calculate the volume or amount of space in Evan's prism, we will first of all calculate the volume of rectangular prisms. Formula is;
V = Length × width × height.
We are given;
length = 4 feet
width = 3.5 feet
height of the prism = 2 feet.
Thus;
V = 4 * 3.5 * 2
V = 28 ft³
Thus, the maximum amount of supplies that the storage unit can hold is 28 ft³
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April works as an emergency medical technician (EMT) and is a photographer. As an EMT she earns $19 per hour. Last week she worked t hours as an EMT and her friend paid her $100 for a photoshoot. Write an expression to represent the total amount April earned last week.
The expression that represents the total amount earned last week $100 + $19t.
What is the expression?
The expression is a function of the amount her friend paid for the photoshoot, the hours worked and the wages per hour.
Total pay = (amount earned per hour x total hours worked) + amount paid for photoshoot
($19 x t) + $100
$19t + $100
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solve this trigonometry question, please by an easy method.
And
sin39=6/yy=6/sin39y=9.5Answer:
x = 7.41 (nearest hundredth)
y = 9.53 (nearest hundredth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)From inspection of the triangle:
[tex]\theta[/tex] = 39°O = 6A = xH = yTo find x, use the tan trigonometric ratio:
[tex]\implies \tan 39^{\circ}=\dfrac{6}{x}[/tex]
[tex]\implies x=\dfrac{6}{\tan 39^{\circ}}[/tex]
[tex]\implies x=7.409382939...[/tex]
Therefore, x = 7.41 (nearest hundredth)
To find y, use the sin trigonometric ratio:
[tex]\implies \sin 39^{\circ}=\dfrac{6}{y}[/tex]
[tex]\implies y=\dfrac{6}{\sin39^{\circ}}[/tex]
[tex]\implies y=9.534094374...[/tex]
Therefore, y = 9.53 (nearest hundredth)
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Pls help to find the coordinate on the line. Will mark brainliest. Thank you!!!
The coordinate of point R is 11/40, so the correct option is C.
How to find the coordinate of point R?
On the number line we can see that:
M = -1/4
T = 5/8
There are 5 segments between T and M, and the difference between T and M is:
5/8 - (-1/4) = 5/8 + 2/8 = 7/8
The measure of each segment will be equal to:
m = (7/8)/5 = 7/(8*5) = 7/40
Now, coordinate R is 2 segments to the left of T, so the coordinate of point R is given by:
R = 5/8 - 2*(7/40)
R = 25/40 - 14/40 = 11/40
The correct option is C.
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Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm! :)
The equation regarding the algebraic information that represents the total earnings is y = 22x + 125.
How to calculate the value?From the information that's given, it can be seen that the expression is:
y = 22x + 125
She earned $555 after working for 15 hours. Therefore, the equation to represent the total earnings will be:
y = 22x + 125.
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Try It #2
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues.
a. Predict the population in 2014
Answer:
The population in year 2014 is 41100.
Step-by-step explanation:
In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .
It is required to predict the population in 2014 .
To do so, use the population given in two years as two points on a line and find the equation of population and year. Then, find the population in year 2014 .
Step 1 of 2
The population in 2008 was 28200 and in 2012 it was, 36800 .
The equation relating population and year is,
[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]
Step 2 of 2
The population in year 2014 can be determined by substituting 2014 for x,
[tex]$$\begin{aligned}&y-28200=2150(2014-2008) \\&y-28200=2150(6) \\&y-28200=12900 \\&y=41100\end{aligned}$$[/tex]
What is the sum of a° + b°?
180°
We need more information to solve this problem.
The answer depends on the values of the individual angles.
360°
Answer:
a=70°
b=120°
we know,
a+b
=70+120
=190
What is the length of the hypotenuse ?
Answer:
3√2
Step-by-step explanation:
In a 45-45-90 triangle, the two legs are the same length while the hypotenuse is √2 times larger.
3*√2 = 3√2
[tex]\frac{x^{2}-5x+6}{2x^{2}-7x+6 }[/tex]
whats the simplest form and the exclusions aka holes
Answer:
[tex]\frac{x-3}{2x-3}[/tex]. hole or removable discontinuity at x=2
Step-by-step explanation:
Well generally if you want the simplest form, you factor each the denominator and numerator and then see if you can cancel any of the factors out (because they're in the denominator and numerator)
So let's start by factoring the first equation:
[tex]x^2-5x+6[/tex]
Now let's find what ac is (it's just c since a=1...)
[tex]AC= 6[/tex]
List factors of -6
[tex]\pm1, \pm2, \pm3, \pm6[/tex].
Now we have to look for two numbers that add up to -5. It's a bit obvious here since there isn't many factors, but it's -2 and -3, and they're both negative since 6 is positive, and -5 is negative...
So using these two factors we get
[tex](x-2)(x-3)[/tex]
Ok now let's factor the second equation:
[tex]2x^2-7x+6[/tex]
Multiply a and c
[tex]AC = 12[/tex]
List factors of 12:
[tex]\pm1, \pm2, \pm3, \pm4, \pm6, \pm12[/tex].
Factors that add up to -7 and multiply to 12:
[tex]-3\ and\ -4[/tex]
Rewrite equation:
[tex]2x^2-4x-3x+6[/tex]
Group terms:
[tex](2x^2-4x)+(-3x+6)[/tex]
Factor out GCF:
[tex]2x(x-2)-3(x-2)[/tex]
Rewrite:
[tex](2x-3)(x-2)[/tex]
Now let's write out the equation using these factors:
[tex]\frac{(x-2)(x-3)}{(2x-3)(x-2)}[/tex].
Here we can factor out the x-2 and the simplified form is:
[tex]\frac{x-3}{2x-3}[/tex]
So we can "technically" define f(2) using the most simplified form, but it's removable discontinuity, so it has a hole as x=2. since it makes (x-2) equal to 0 (2-2) = 0.
In a continuous series, mean(x) = 80, assumed mean(A) = 60 and
EF=40 then find the value of EFd.
Using the given information, the value of Σfd is 800
Calculating mean using Assumed meanFrom the question, we are to determine the value of Σfd
The formula for mean, using the assumed mean method is given by
[tex]\bar x = A + \frac{\sum fd}{\sum f}[/tex]
Where [tex]\bar x[/tex] is the mean
A is the assumed mean
From the given information,
[tex]\bar x = 80[/tex]
[tex]A = 60[/tex]
[tex]\sum f = 40[/tex]
Putting the parameters into the equation, we get
[tex]80 = 60 + \frac{\sum fd}{40}[/tex]
[tex]80-60 = \frac{\sum fd}{40}[/tex]
[tex]20 = \frac{\sum fd}{40}[/tex]
[tex]\sum fd = 20 \times 40[/tex]
[tex]\sum fd = 800[/tex]
Hence, the value of Σfd is 800
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HELP HELP HELP
Just 5 quick algebra 1 questions for 100 points!
1. x = a
2. y = b
3. The slope of a vertical line is undefined..
4. Change in y/change in x (m) or rise/run
5. Rewrite the equation in slope-intercept form to find the value of the y-intercept. The value of x will always be 0.
What is the Equation of a Line?The equation, y = mx + b, in slope-intercept form, defines a line, where m is the slope and the y-intercept = b.
1. Slopes of vertical lines are always undefined, therefore, for a vertical line that contains (a, b), the equation would be: x = a.
2. Horizontal lines have a slope of 0, therefore, the equation of a horizontal line that contains the point, (a, b), will be: y = b.
3. The slope of a vertical line is undefined.
4. Two ways of finding the slope if we are given two points on a line are:
Change in y/change in x (m) = y2 - y1 / x2 - x1
or
rise/run
5. If we have an equation in point-slope form, for example, y - 2 = 2(x - 4), rewrite the equation in slope-intercept form and find the value of the y-intercept:
y - 2 = 2x - 8
y = 2x - 8 + 2
y = 2x - 6
The y-intercept = -6, therefore, the coordinates of the y-intercept would be: (0, -6).
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HELP ASAP
What is the solution to the inequality below?
12+x23(x-6)
OA. x≤ 12
OB. x≤ 5
OC. x≤ 15
OD. x≤9
The solution to the inequality is x ≤ 15
How to solve the inequality?The inequality is given as:
12 + x ≥ 3(x-6)
Open the bracket
12 + x ≥ 3x - 18
Evaluate the like terms
-2x ≥ -30
Divide by -2
x ≤ 15
Hence, the solution to the inequality is x ≤ 15
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Can someone help please
Triangle not drawn to scale
Given: mA = 40°, m▲ B = 88°, and b = 23. Then a = to the nearest hundredth.
Answer: 14.79
Step-by-step explanation:
[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]
AC is a tangent to the circle below at point B.
Calculate the sizes of angle x, angle y and angle z.
Justify each of your answers.
[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)
[tex]x=78^{\circ}[/tex] (alternate segment theorem)
[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)