On a coordinate plane, triangle A B C is shifted 4 units up and 3 units to the left to form triangle A prime B prime C prime.
Use the figure to identify the correct rule for the translation.
(x, y) Right-arrow (x – 3, y + 4)
(x, y) Right-arrow (x + 3, y – 4)
(x, y) Right-arrow (x – 4, y + 3)
(x, y) Right-arrow (x + 4, y – 3)
Answers
In accordance with the definitions of rigid transformation and translation, the correct rule for the translation is defined by (x, y) → (x - 3, y + 4). (Right choice: A)
How to derive the mathematic expression behind a transformation rule
Mathematically speaking, transformations are rigid transformations that are modelled according to the following formula:
P'(x, y) = P(x, y) + (h, k) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointh - Horizontal rightward translationk - Vertical upward translationHence, a leftward translation indicates that h < 0. The correct rule for the translation is defined by (x, y) → (x - 3, y + 4).
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Answer:
a
Step-by-step explanation:
the picture
Related Questions
Use the law of cosines to find the value of cos0. Round your answer to two decimal places.
A.0.22
B.0.84
C.0.35
D.-1.04
Answers
Using the law of cosines on the given triangle, we see that; cosθ = 0.22
How to use the law of cosines?The law of cosines is expressed as;
c² = a² + b² - 2ab cos C
Now, in this case the angle is θ and employing this law of cosines gives us;
10.2² = 5.7² + 9.8² - 2(5.7 * 9.8)*cosθ
104.04 = 32.49 + 96.04 - 111.72 * cosθ
104.04 = 128.53 - 111.72 * cosθ
(128.53 - 104.04)/111.72 = cosθ
cosθ = 0.22
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A supplier delivers an order for 20 electric toothbrushes to a store. By accident, three of the electric toothbrushes are defective. What is the probability that the first two electric toothbrushes sold are defective
Answers
The probability that the first two electric toothbrushes sold are defective is 0.016.
The probability of an event, say E occurring is:
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable outcomes
N = total number of outcomes
Let X = the number of defective electric toothbrushes sold.
The number of electric toothbrushes that were delivered to a store is n = 20.
The number of defective electric toothbrushes is x = 3.
The number of ways to select two toothbrushes to sell from the 20 toothbrushes is:
[tex](\left {{20} \atop {2}} \right. )[/tex][tex]=\frac{20!}{2!(20-2)!} =\frac{20!}{2!18!} =\frac{20*19*18!}{2!*18!} = 190[/tex]
The number of ways to select two defective toothbrushes to sell from the 3 defective toothbrushes is:
[tex](\left {{3} \atop {2}} \right. )[/tex][tex]=\frac{3!}{2!(3-2)!} =\frac{3!}{2!1!} =\frac{3*2!}{1!2!} =3[/tex]
Compute the probability that the first two electric toothbrushes sold are defective as follows:
P (Selling 2 defective toothbrushes) = Favorable outcomes ÷ Total no. of outcomes
[tex]\frac{3}{190}\\ =0.01579\\=0.016[/tex]
Thus, the probability that the first two electric toothbrushes sold are defective is 0.016.
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How do you Calculate the mean,median and mode in grouped data.
Answers
Answer:
The mean:
data: 3,6,9,10
You first add all of the numbers together.
3+6+9+10= 28
There 4 numbers in the data set, so you divide 4 by the sum of all of the numbers.
28/4= 7
So the mean is 7.
The median:
data: 3,6,9,10
first put all of the numbers in numerical order.
3,6,9,10
Then you find the middle number in the data set.
3,6,(the middle number here),9,10
to find the middle number, do the mean of 6 and 9
The mean of 6 and 9 is 7.5
So, 7.5 is the median
another example: 3,4,7,9,13
The middle number is 7
so 7 is the median
The mode:
data: 3,6,9,10
The mode is the number that is repeated the most
in this data, there is no mode.
but in this data: 4,4,6,9,11
4 is the mode because it was repeated the most
Triangle ABC has side lengths:
AB = 3.5 cm, BC = 2.4 cm, and AC = 4.2 cm
ΔABC ≅ ΔHJK
What is the length of side HJ?
Answers
The length of HJ is 3.5 cm
What is Congruency?Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
Given:
AB = 3.5 cm, BC = 2.4 cm, and AC = 4.2 cm
As, ΔABC ≅ ΔHJK
So,
AB = HJ
BC = JK
AC = HK
Thus, HJ= AB = 3.5 cm
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Solve the Percent Discount Application.
The local grocery store has just marked down a patio set by 20%. If the patio set costs $79.90, what is the discounted price?
$63.92
$94.80
$15.80
$70.00
Answers
Answer
63.92
What are two angles next to each other called?
Answers
Two angles which are next to each other is referred to as adjacent angle in this case.
What is an Adjacent angle?These are angles which have a common vertex and side and do not overlap with one another.
This angle lie next to each other when plotted hence the reason why they share a common vertex.
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Which equation represents a line that passes through the two points in the
table?
Answers
y-3 = 2/3(x-3)
5-3 = 2/3(6-3)
2 = 2
Translation: (x,y)→(x+7,y+5) Coordinates: Y(−5,−4), X(−5,−1), W(−2,0), V(−2,−5)
Answers
Answer:
Y - (2,1)
X - (2,4)
W - 5,5)
V - (5,0)
Step-by-step explanation:
Translation: (x,y) → (x+7,y+5)
Coordinates:
Y(−5,−4) => (-5 + 7, -4 + 5) => (2,1)
X(−5,−1) => (-5 + 7, -1 + 5) = > (2,4)
W(−2,0) => (-2 + 7, 0 + 5) => (5,5)
V(−2,−5) => (-2 + 7, -5 + 5) => (5,0)
30 mi / h = ____ ft / min
a.
2640
c.
880
b.
264
d.
2112
Answers
Answer:
its a 2640 trust me
Step-by-step explanation:
Step-by-step explanation:
Observe this as a fraction 30 min/ 1 hr
First Convert miles to ft
1 mile = 5280 ft
so 30 miles * (5280ft/1 mile) = 30 * 5280 ft (Note miles unit cancels) = 158,400 ft
Then convert hours to minutes
1 hr = 60 min
158400 ft/1 hr * (1 hr/60 min) = 158400ft / 60 min (hr unit cancels) = 2640 ft/ min
Show that √5×√20 is an integer?
Answers
Answer:
See below.
Step-by-step explanation:
1) Simplify √20 to 2√5.
√5 × 2√5
2) Simplify.
2√5×5
3) Simplify 5 × 5 to 25.
2√25
4) Since 5 × 5 = 25, the square root of 25 is 5.
2 × 5
5) Simplify.
10
When evaluated, this expression equals a positive whole number, therefore showing it is a integer.
Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two thirds the distance from point P to point R.
4.9
4.7
2.5
2.3
Answers
Answer:
4.7
Explanation:
A point is positioned at minus two, seven. At one, zero, you'll find point R. Determine the value of Y. Regarding point Q. That is 2/3 of the distance between points P. So, negative two becomes positive seven. So, we have minus twenty-seven and 1 common zero. So, if we place a line between these, we must calculate the distance. First, you should be aware that you may achieve this using the distance formula. I prefer to conceive of it as the Pythagorean Theorem. So, the distance is 3^2 and 7^2, which is D^2. So, 9+49=58. And, we'll take the square root of it. As a result, the square root of 58=D. And, you want to be 2/3 the distance between points P and B. So, divide this by 2/3. So, this is close to 5.1. But, you want to get the Y value; found the distance, 2/3 of the way. When the distance is 5.1 instead of round 7.6, we've arrived at point P. We want to be 5. 1 yard away on this line. This is point P and we want to be at point Q. Since it'll have the same slope. As a result, the slope will be 7/3. So, it'll be proportionate 7. Since the square root of fifty-eight is too large. Route 58/3 is the destination. The square root of 258 is canceled. Such that 7=3y/2. 7x2=14/3=4.7. It's by locating comparable figures.
Write the following using index notation:
a) 4×4
b) 5x5x5x5
c) 3 × 7 × 7 × 7 × 7
d) 2× 9 × 9 × 9×2×9
Answers
b. 5^4
c. 3 x 7^4
d. 2^2 x 9^4
Step-by-step explanation:
4^2
5^4
3^1×7^4
2^2 ×9^4
can so.eone explain to me by what bisecting intervals are?
Answers
When you bisect something, you cut it into two equally sized pieces. (from Latin: "bi" = two, "sect" = cut)
Bisecting an interval creates two smaller intervals each with half the length of the original interval. Some examples:
• bisecting [0, 2] gives the intervals [0, 1] and [1, 2]
• bisecting [-1, 1] gives the intervals [-1, 0] and [0, 1]
• bisecting an arbitrary interval [tex][a,b][/tex] gives the intervals [tex]\left[a,\frac{a+b}2\right][/tex] and [tex]\left[\frac{a+b}2,b\right][/tex]
What is the solution set for
O s-4 and x-16
O s--4 and s-4
Os--8 and s-8
Ox--16 and x-16
||-8₂
Answers
Answer:
4th option
Step-by-step explanation:
the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is
[tex]\frac{x}{2}[/tex] = 8 or - [tex]\frac{x}{2}[/tex] = 8
solving each equation
[tex]\frac{x}{2}[/tex] = 8 ( multiply both sides by 2 to clear the fraction )
x = 2 × 8 = 16
or
- [tex]\frac{x}{2}[/tex] = 8 ( multiply both sides by 2 )
- x = 16 ( multiply both sides by - 1 )
x = - 16
then x = - 16 , x = 16
Write a proof
given: angle 1 and angle 3 are supplementary
prove: m is parallel to n
Answers
Answer:
angle 2 is equal to angle 1 ... vertically opposite angles equal
therefore angle 2 and angle 3 are supplementary...co-interior angles supplementary
therefore m is parallel to n
What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5
x minus 3.x – 3?
Answers
The slope of the line represented by the given equation is 0.8
Slope of a lineFrom the question, we are to determine the slope of the line represented by the given equation
The given equation is
[tex]y = \frac{4}{5} x-3[/tex]
The slope-intercept form of the equation of a line is given as
y = mx + c
Where m is the slope or gradient
and c is the y-intercept
By comparing with the given equation,
m = 4/5
m = 0.8
Hence, the slope of the line represented by the given equation is 0.8
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A quantity with an initial value of 130 decays exponentially at a rate such that the
quantity cuts in half every 9 weeks. What is the value of the quantity after 21 days
Answers
A quantity with an initial value of 130 decays exponentially at a rate such that the quantity cuts in half every 9 weeks. 103.18 is the value of the quantity after 21 days.
What is exponential decay?A process known as exponential decay is when a quantity diminishes over time at a pace that reduces proportionately as the amount shrinks.
The term "exponential decay" refers to a population's or group's rate of decline when it is proportionate to the size of the population. The overall value falls in exponential decay, yet the percentage that departs stays constant over time.
Let, y = 130. aˣ
here, x = number of days
Given that,
A quantity with an initial value of 130 decays exponentially.
the quantity cuts in half every 9 weeks
the value of the quantity after 21 days = ?
So, 130 × [tex]a^{(7\times9) }[/tex] = 130 × (1/2)
or, a⁶³ = 1/2
or, a [tex](1/2)^{(1/63)}[/tex]
Thus, y = 130 × [tex](1/2)^{(x/63)}[/tex]
when x = 21
thus, y = 130 ×[tex](1/2)^{(21/63)}[/tex]
y = 130 × [tex](1/2)^{(1/3)}[/tex]
y ≈ 103.18
Hence, 103.18 is the value of the quantity after 21 days.
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What is the value of cos(Tan^-1 1)?
a. 2
b.square root 2
c. 2 square root 2
d. square root 2 over 2
Answers
Answer:
D
Step-by-step explanation:
So you have the equation: [tex]cos(tan^-1(1))[/tex]. So let's work in order and focus on the [tex]tan^-1(1)[/tex] part first. The inverse of tan is essentially taking in the value of [tex]tan(\theta)[/tex] and returning [tex]\theta[/tex]. And the value of [tex]tan(\theta)[/tex] can be defined as [tex]\frac{sin(\theta)}{cos(\theta)}[/tex]. So if you look at the unit circle, you'll need to look for two values that are exactly the same. You'll notice when the angle is 45 degrees, the value of sine, and cosine are the exact same. They're both [tex]\frac{\sqrt2}{2}[/tex]. So the inverse of tan(1 degree) = 45 degrees. Now we can literally refer to the same point, because when finding the cosine of 45 degrees, we can just use the x-value. This gives a solution of [tex]\frac{\sqrt2}{2}[/tex]
The formula for the perimeter of a rectangle is P = 2 (1+w).
Answers
The equation of L is L = 0.5P - W
How to solve for L?The formula is given as:
P = 2(L + W)
Divide through by 2
0.5P = L + W
Subtract W from both sides
L = 0.5P - W
Hence, the equation of L is L = 0.5P - W
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Complete question
The formula for the perimeter of a rectangle is P=2(l+w). Solve for l.
Prove that
cos^4∆ - sin^4∆ = 2cos^2∆ - 1
Answers
[tex]\cos^{4} x-\sin^{4} x\\\\=(\cos^{2} x+\sin^{2} x)(\cos^{2} x-\sin^{2} x)\\\\=\cos^{2} x-\sin^{2} x\\\\=\cos^{2} x-(1-\cos^{2} x)\\\\=2\cos^{2} x-1[/tex]
quadratic formula 2x^2-9x-35=0
Answers
Hello,
2x² - 9x - 35 = 0
a = 2 ; b = -9 ; c = -35
∆ = b² - 4ac = (-9)² - 4 × 2 × (-35) = 361 > 0
x1 = (-b - √∆)/2a = (9 - 19)/4 = -10/4 = -5/2
x2 = (-b + √∆)/2a = (9 + 19)/4 = 28/4 = 7
S = {-5/2 ; 7}
Answer:
So x = -5/2, 7.
Step-by-step explanation:
2x^2 - 9x - 35 = 0
Let's see if we can factor this.
We need 2 numbers whose product is 2* -35 ( that is -70) and whose sum is -9.
They are -14 and 5, so we write:
2x^2 - 14x + 5x - 35 = 0
Now we factor by grouping:
2x(x - 7) + 5(x - 7) = 0
(2x + 5)(x - 7) = 0
So x = -5/2, 7.
I am not able to solve this question
Answers
Answer:
C
Step-by-step explanation:
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Answer:
Choice C
Step-by-step explanation:
2654^0 and 5^0
Which is greater?
There's a law of exponents for solving this type of question.
The law states that,
x^0 = 1Same case here.
2654^01And,
5^0 1Hence, they are same.
2654⁰ = 5⁰
You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answers
Answer:
4 legs from the bed and 4 from the chair im guessing since not all have 4
Step-by-step explanation:
.
Answer:
36 legs
Step-by-step explanation:
Write a compound inequality that represents the given graph:
OA.x < -2 and x ≥ 4
OB.x < -2 or x ≥4
OC.-2
OD.-2≥x>4
Answers
Answer: the correct answer is choice A
Step-by-step explanation:
This is because the inequality symbols are pointed the correct way. The symbols are also showing the correct answers with the greater than or equal to sign is on the correct point value. You find the place for the equal to or greater/less than symbol by the open or closed circle point. An open circle means the number is not included in the answer while a closed circle is included in the answer.
look at the image.......
Answers
Answer: 70.9 miles per hour
Step-by-step explanation:
The total distance traveled is 1188 miles (66313- 65125).
Since this was over 16.75, you'll want to divide 1188 by 16.75.
1188/16.75 = 70.9253731
And then round that off to 70.9
Help pls asap
If sine < 0 and tans > 0 then:
OA. 180° << 270°
OB. 0° <9< 90°
C. 270° << 360°
OD. 90° << 180°
Answers
Answer:
The answer is C. 270° < ∅ < 360°
Step-by-step explanation:
Given information:
sine < 0 and tans > 0.
Quadrant where sine < 0 is either III or IV.
Quadrant where tans > 0 is either I or III.
It is Quadrant III that has both sines < 0 and tans > 0.
x^3 - y^3 = 218 where x and y are positive integers. Find x+y
Answers
The value of x + y is 12
How to solve for x + y?The equation is given as:
x^3 - y^3 = 218
Make x^3 the subject
x^3 = 218 + y^3
The next cubic expression greater than 218 is 343.
So, we assume
x^3 = 343
This gives
x = 7
Substitute x^3 = 343 in x^3 = 218 + y^3
343 = 218 + y^3
Evaluate the like terms
y^3 = 125
This gives
y = 5
So, we have:
x + y = 7 + 5
Evaluate
x + y = 12
Hence, the value of x + y is 12
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Can you help me with these two because I don't understand
Answers
Answer: 1: 34 units 2: 24.5
Step-by-step explanation:
For figure 1, just split the area into squares and triangles and find the area of each. If you split figure 1 into 1 square and 3 triangles you get...
4x4= 16
(4x3)/2= 6
(4x4)/2= 8
(4x2)/2= 3
16+6+8+3 = 34
You do the same for figure 2, but use 4 triangles and 1 tiny square
1x1= 1
(4x3)/2= 6
(3x3)/2= 4.5
(4x4)/2= 8
(5x5)/2= 5
1+6+4.5+8+5= 24.5
You shouldn't need to worry about negative numbers because you are looking at the area
Can you divide 2 by 9? Explain your response.
Answers
Answer:
0.22222222222
Step-by-step explanation:
To divide two by nine, you need to use your long division skills. Unfortunately, this interface doesn't lend itself well to showing you the actual long division problem, so try to follow the steps with me.
draw a division symbol (should look like half a rectangle). Put the 9 in front of the rectangle and a 2 inside it. Make the top of the rectangle long.
Note that the result of the division 2÷9 is not an exact value and is equivalent to recurring decimal 0.22... (which has 2 as the period).
what is the slope of y=5/4x-7/4?
Answers
Answer:
5/4 or 1.25
Step-by-step explanation:
y=mx+b is the form of all linear equations
m is the slope
here m = 5/4 so the slope is 5/4 or 1.25