The image is the result of an isometric transformation of its pre-image because _____.
a reflection has occurred
a rotation has occurred
the two triangles are congruent
a dilation has occurred
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Related Questions
A cylinder is a type of prism.
true
false
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What is the correct way to write 6.3 × 10^8 in standard notation? (25 Points)
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hope this helps:)
(7 zeros behind the decimal.)
Hope this helps!!!
The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.What is the value of x?
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To answer this question you need to know how to count formula of a rectangle. Area of a rectangle is count by length x width formula. Then if you put the number into the formula it would be:
area = length x width
0.8 square unit= 3.2 unit * x
3.2 x unit = 0.8 square unit
x= 0.8 square unit / 3.2 unit= 0.25 unit
The triangle JKL shown on the coordinate grid below is reflected once to map onto triangle J'K'L': Triangle JKL is drawn on a 4 quadrant coordinate grid with vertices J is at 8, 1. K is at 5, 7. L is at 3, 4. If vertex L' is at (−3, 4), what are the coordinates of vertex J'?
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(1, −8)
(−8, 1)
(−1, 8)
(8, −1)
Answer:
The vertex J' is at (-8,1).
Step-by-step explanation:
If is given that the triangle JKL reflected once to map onto triangle J'K'L'.
The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).
[tex]L(3,4)\rightarrow L'(-3,4)[/tex]
It is in the form of
[tex](x,y)\rightarrow (-x,y)[/tex]
Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.
The vertices of image are,
[tex]K(5,7)\rightarrow K'(-5,7)[/tex]
[tex]J(8,1)\rightarrow J'(-8,1)[/tex]
Therefore the vertex J' is at (-8,1).
You're studying different function tools and begin working with this function:
y=-200-12(x)
Use the equation to answer the question:
What is the y-value when x equals -16?
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y = -200 - 12*-16 = -200 + 192 = -8
Answer:
-8
Step-by-step explanation:
Given : [tex]y=-200-12(x)[/tex]
To Find:What is the y-value when x equals -16?
Solution:
We are given that You're studying different function tools and begin working with this function:
[tex]y=-200-12(x)[/tex]
Now we are supposed to find the value of y when x is -16
So, substitute x = -16 in the equation
[tex]y=-200-12(-16)[/tex]
[tex]y=-200+192[/tex]
[tex]y=-8[/tex]
So, Value of y is -8
Hence the y-value when x equals -16 is -8
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
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When a point in quadrant 2 is rotated 180 degrees counterclockwise, it will land in quadrant 4.
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
Begin in quadrant 2 (Q2).Rotating 180 degrees counterclockwise leads to the point's final position in quadrant 4 (Q4).The circle shown below has ab and bc as its tangents: ab and bc are two tangents to a circle which intersect outside the circle at a point
b. if the measure of arc ac is 160°, what is the measure of angle abc? 80° 40° 60° 20°
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One of the theorems of circle is that the measure of the intercepted arc is twice as that of its opposite angle. In this case, since the intercepted arc measures 160°, then the measure of angle abc is 160/2 = 80°.
Therefore, the answer is 80°.
Answer:
Answer: 20°
Step-by-step explanation:
The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
What is the ratio between neighboring y-values?
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notice, the first value is 1, but any subsequent values are just the product of 4 and the current value. Thus the "common ratio" is 4.
In given table of exponential function,
The interval between neighboring x-values is of 1 unit.
The ratio is 4 between neighboring y-values
Observing given table.
To find interval between neighboring x-values . We have to take difference between consecutive x - values.
[tex]1-0=2-1=3-2=4-3=5-4=1[/tex]
Since, in every consecutive x- values , difference of 1 is present.
So, The interval between neighboring x-values is of 1 unit.
To find ratio between neighboring y-values , we have to take ratio of consecutive y - values.
[tex]\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=\frac{256}{64}=4[/tex]
Thus, The ratio is 4 between neighboring y-values
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how to solve for -5x^2-2x-6=-2 ?
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-5x^2-2x-6+2=-2+2
2. Simplify
-5x^2-2x-4=0
3.
x=-1/5 - i (square root of 19/5)
a rectangle has sides 2x + 3 and x - 4. what is the perimeter of the rectangle
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A movie theater sold 422 tickets on Friday. On Saturday, they sold 518 tickets. What was the approximate percentage that ticket sales increased on Saturday?
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Hope that helps!
NEED HELP ASAP PLEASE!!!
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Women athletes at the university of colorado, boulder, have a long-term graduation rate of 67% (source: the chronicle of higher education). over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university of colorado, boulder, is not less than 67%? use a 5% level of significance. find the p-value of the test statistic (round to the nearest ten thousandths).
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The solution would be like this for this specific problem:
H0: p = p0, or
H0: p ≥ p0, or
H0: p ≤ p0
find the test statistic z = (pHat - p0) / sqrt(p0 * (1-p0) / n)
where pHat = X / n
The p-value of the test is
the area under the normal curve that is in agreement with the alternate
hypothesis.
H1: p ≠ p0; p-value is the area in the tails greater than |z|
H1: p < p0; p-value is the area to the left of z
H1: p > p0; p-value is the area to the right of z
Hypothesis equation:
H0: p ≥ 0.67 vs. H1: p < 0.67
The test statistic is:
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 )
z = -1.538681
The p-value = P( Z < z
)
= P( Z < -1.538681 )
= 0.0619
Ben measures the height of two bottles. one is 12 centimeters, and the other is 15 centimeters. in millimeters, what is the difference of the two heights?
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One bottle has a height of 12 centimeters or 12 cm. Let us call this h1, so h1 = 12 cm
While the other bottle has a height of 15 centimeters or 15 cm. Let us call this h2, so h2 = 15 cm
The difference in height can be calculated by subtracting the smaller number from the bigger number, therefore:
difference in height = h2 – h1
difference in height = 15 cm – 12 cm
difference in height = 3 cm
We know that in 1 meter there is:
1 meter = 100 centimeters = 1000 millimeters
Therefore,
difference in height = 3 cm (1000 millimeters / 100 centimeters)
difference in height = 30 mm
Answer:
difference in height = 30 mm
if f(x) = (x+1)^-1 and g(x) = x-2, what is the domain of f(x) divided by g(x)
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f(x)=1/(x+1) so
f(x)/g(x) is
1/[(x+1)(x-2)]
Since division by zero approaches infinity, it is not a real value, and is said to be undefined. Division by zero is "not allowed", which just really means that it does not have a real value. So in this case x cannot equal -1 or 2 so the domain is:
All real numbers except -1 or 2...which can be expressed as:
(-oo,-1),(-1,2),(2,+oo)
Verify the Pythagorean Identity.
1 + cot^2 0 = csc^2 6
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To prove this Pythagorean Identity, we have to know that:
cot = 1 / tan
and we also know that:
tan = sin / cos
Therefore,
cot = 1 / tan = cos / sin
So we can write the given equation in the form of:
1 + (cos^2 θ / sin^2 θ) = csc^2 θ
Expanding the left hand side of the equation:
(sin^2 θ / sin^2 θ) + (cos^2 θ / sin^2 θ) = csc^2 θ
(sin^2 θ + cos^2 θ) / sin^2 θ = csc^2 θ
We know that given a unit circle, sin^2 θ + cos^2 θ = 1. So:
1 / sin^2 θ = csc^2 θ
The equation above is already true basing on the trigonometric identities. Therefore:
csc^2 θ = csc^2 θ
which angles are corresponding angles? check all that aply
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<1 and <3
Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.
n an
1 | 3
2 | −6
3 | 12
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The explicit formula for this geometric sequence is: a_n = 3 (-2)^{n-1}. he common ratio is negative, so the domain is all odd positive integers.
Explicit formula:
The explicit formula for a geometric sequence is of the form: a_n = a_1 r^{n-1}
In this case, the first term is 3 and the common ratio is −2. Therefore, the explicit formula for this geometric sequence is:
a_n = 3 (-2)^{n-1}
Restrictions to the domain:
The domain of a geometric sequence is all positive integers, unless the common ratio is negative. In this case, the common ratio is negative, so the domain is all odd positive integers.
Example:
Using the explicit formula, we can find the fourth term of the sequence as follows:
a_4 = 3 (-2)^{4-1} = 3 (-2)^3 = -24
We can also verify that the domain of the sequence is all odd positive integers by checking the first few terms:
n | a_n
1 | 3
2 | -6
3 | 12
4 | -24
5 | 48
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Express 8.5454545454... as a rational number, in the form p/q where p and q are positive integers with no common factors.
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The value of a dirt bike decreases by 15% each year. If you purchased this dirt bike today for $500, to the nearest dollar how much would the bike be worth five years later? $84 $119 $164 $222
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500*.15=75. 500-75=425
425*.15=63.75. 425-63.75=361.25
361.25*.15=54.19. 361.25-54.19=307.06
307.06*.15=46.06. 307.06-46.06=261
261*.15=39.15. 261-39.15=221.85
Round up to $222
The answer is 222
All you do is multiply 500 by 0.15, which gives you 75. Then subtract that from 500 to give you 425. Now multiply this 425 by 0.15 then subtract the product form 425. Continue this process until it is done 5 times. Your answer on the fifth time will be your answer.
Find the 6th term of a geometric sequence with t1=5 and r = -1/2
-5/8
-5/16
-5/32
-5/64
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An = (A₀)(r)ⁿ ⁻ ¹
where An is the nth term, A₀ is the first term (in this item is referred to as t₀), r is the common ratio, and n is the number of terms.
Substitute the known values to the equation,
An = (5)(-1/2)⁶ ⁻ ¹
An = -5/32
Hence, the answer to this item is the third choice, -5/32.
A phone banking password consists of 2 letters followed by 4 digits. The letters B, I, S, and O are not used, and the last digit cannot be 0. How many different passwords are possible?
5,148,000
4,840,000
4,356,000
3,175,524
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There are 4,356,000 different passwords are possible.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A phone banking password consists of 2 letters followed by 4 digits.
And, The letters B, I, S, and O are not used, and the last digit cannot be 0.
Hence, We can formulate;
Number of different passwords are possible are,
⇒ 22 × 22 × 10× 10 × 10 × 9.
⇒ 4,356,000
Thus, There are 4,356,000 different passwords are possible.
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A paper popcorn cone measures 4 inches in diameter and is 9 inches high. What is the volume of popcorn that can be contained within this cone? Use 3.14 for pi. Round your answer to the nearest hundredth. 37.68 cubic inches 39.45 cubic inches 40.23 cubic inches 41.90 cubic inches
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V=(3.14)(r^2)(h/3)
With this formula in mind, you would simply substitute in.
V=(3.14)(2^2)(9/3)
You could work that out for yourself on your own, but to save you the time, it is 37.68 in. cubed.
So, we know that the formula to find the volume of a cone is [tex]V=\frac{3.14* r^2h}{3}[/tex]
The radius is half the diameter, so in this case our radius would be 2. Let's plug in the values.
[tex]V=\frac{3.14* 2^2\cdot \:9}{3}[/tex]
Simplify.
[tex]V=12*3.14 [/tex]
The thing we are left with is just a multiplication problem. Let's simplify it. Let's remember to also input the units since we are talking about the volume of a figure.
V≈37.68 in³
Instead of using the equal sign (=), we had to use the approximation sign (≈) since we are using a rounded version of pi ([tex] \pi [/tex])
Thanks!
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Factor the polynomial below.
30x^2 + 15x^2 +10x
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hope this helps
hope this helps!
Find the sum of the first 15 terms of the series 4+16+64+256+...
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Can a geometry expert help me ASAP Please!!!!!!! and can you show me how you got the answer please
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All 3 angles of a triangle sum to 180.
Therefore angle W = 180 -63 -63
angle W = 54
We are not told that line WY is perpendicular to line XZ.
If it is perpendicular, then angle YWZ is one half of angle W and it equals 27 degrees.
A delivery truck uses $375 in gasoline during a 3 week period. if the truck is driven 5 days per week, how much is spent on gas each day?
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Final answer:
Approximately $17.86 is spent on gas each day.
Explanation:
To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.
First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.
Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86
Therefore, approximately $17.86 is spent on gas each day.
Relations and functions need help please.
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So, [tex]f(x) = -x^2 + 1[/tex] becomes [tex]f(-3) = -(-3)^2 + 1[/tex]
[tex]f(-3) = 3^2 + 1 \\ \\ f(-3) = 9 + 1 \\ \\ f(-3) = 10[/tex]
So, f(-3) is equal to 10.
What are the solutions of the equation z2-12z+36=0
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(z - 6)(z - 6) = 0
z - 6 = 0
z = 6
solution is : 6,6
Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
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The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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