Which of these triangle pairs can be mapped to each other using a single reflection?
Answers
Answer:
The correct answer should be figure 1 which is also attached in the solution.
Step-by-step explanation:
Reflection of any object is the mirror image of the object about any line or plane. Reflection always shows a congruent figure but inverted.
In first figure, triangle EFG makes a mirror image as triangle FGL. Here, EG is equal to GL, EF is equal to FL and angle E is congruent to angle L.
So, the figure obtained is congruent and inverted. Thus, triangles can be mapped to each other in single reflection in this image.
Figure 2 shows two congruent triangles but the reflection is not a mirror image as it should be inverted.
Figure 3 shows two congruent triangles but here they are aligned in a similar manner and not inverted. So, it is incorrect.
Figure 4 has inverted and congruent triangles but the axis about which the image is taken doesn't match with them. While reflection, they will not overlap each other and hence, it is incorrect.
Therefore, the correct answer should be figure 1 which is also attached in the solution.
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Related Questions
Write an expression of the verbal phrase: the quotient of twelve and the product of three times x
Answers
The expression of the verbal phrase 'the quotient of twelve and the product of three times x' is 12 / (3x).
Explanation:The verbal phrase 'the quotient of twelve and the product of three times x' can be expressed as:
12 / (3x)
In this expression, '12' represents the dividend or numerator, '3' represents the factor or multiplier, and 'x' represents the variable or unknown. The quotient symbol '/' represents division, and the multiplication symbol 'x' represents the product of three times x.
what is an equation of the line in slope intercept form m=3 and the y-intercept is (0 4)
Answers
y = 3x + 4
hope this helps, God bless!
A car travel at an average speed of 48 miles per hour. how many miles does it travel in 4 hours and 15 minutes
Answers
or
48 miles in 60 minutes
4 Hours and 15 minutes are 255 minutes
48/60=.08 miles per minute
255 * .08 = 204 miles
Find the value of x that makes m ∥ n, m ∥ n.
Answers
[tex]3x = 120[/tex]
[tex]x=40[/tex]
The value of x that will make m parallel to n is: 40.
Recall:According to the Converse of Corresponding Angles Theorem, the two lines cut across by a transversal line are parallel to each other if the two corresponding angles formed are congruent.
Therefore, let's find the value of x that will make m parallel to n.
Thus,[tex]3x^{\circ} = 120^{\circ}[/tex] (corresponding angles)
Solve for x. Divide both sides by 3[tex]x = 40[/tex]
Therefore, the value of x that will make lines m and n to be parallel to each other is 40.
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Need help on answer I’m not so sure what to do
Answers
OK. This problem isn't that hard if you just take it in pieces.
First, calculate how much oil Mr Leonard needs to buy. That will be the capacity of his oil tank minus how much oil is already in it. So
1200 litres - 450 litres = 750 litres
Now figure out how much that 750 litres of oil will cost at full price.
750 litres * 81.5 p/litre = 61125 p
Now, calculate how much is 7.5% of 61125 p
7.5% * 61125 p = 0.075 * 61125 p = 4584.375 p
Finally, since there's 100 pence in a pound, divide the number of pence saved by 100. So
4584.375 p / 100 = 45.84 pounds
a bag contains 42 cups of dog food. your dog eats 2 1 3 cups of dog food each day how many days does the bag of dog food last
Answers
divide 42 by 2 1/3
2 1/3 = 7/3
42 / 7/3 =
42 * 3/7 =
126/7 = 18
it will last 18 days
The number of days it will take the dog to consume the 42 cup of food will be 18 days.
Total cups of dog food = 42 cups Amount of cups consumed per day = [tex] 2 \frac{1}{3} \: cups [/tex]To obtain the number of days it will take to consume the entire food :
Divide the total amount of food by the amount consumed per dayHence,
(42 ÷ (7/3))
Take the reciprocal of 7/3 and change the operation sign to multiplication
42 × 3/7 = (42 × 3) / 7 = 126 / 7 = 18 days
Therefore, it will take the dog 18 days to finish up the 42 cups of food.
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Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) – 6 = 0?
(u + 2)2 + 5(u + 2) – 6 = 0 where u = (x – 2) u2 + 4 + 5u – 6 = 0 where u = (x – 2) u2 + 5u – 6 = 0 where u = (x + 2) u2 + u – 6 = 0 where u = (x + 2)
Answers
we have
[tex](x+2)^{2} +5(x+2)-6=0[/tex]
Let
[tex]u=(x+2)[/tex]
Substitute in the expression
[tex](u)^{2} +5(u)-6=0[/tex]
therefore
the answer is
[tex](u)^{2} +5(u)-6=0[/tex] is equivalent to [tex](x+2)^{2} +5(x+2)-6=0[/tex]
Answer: C
Step-by-step explanation:
Took the test
Which of the following is a fundamental quantity?
A) Volume
B) Density
C) Area
D) Mass
E) Acceleration
Answers
What is the slope of the line passing through the points (2,7) and (-1,3)?
Answers
Slope of line passing through 2 points, The slope of line passing through points (2,7) and (-1,3) is 4/3.
What is formula for slope of line passing through 2 points?Slope=(y2-y1)/(x2-x1)
The line is passing through two points (2,7) and (-1,3).
The formula for slope is (y2-y1)/(x2-x1).
x1=2,x2=-1,y1=7,y2=3
Slope=3-7/-1-2
=-4/-3
=4/3
Therefore slope of line is 4/3 if line passing through the points (2,7) and (-1,3).
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If angle A and angle B are complementary then the measure of angle A is 45, find a counterexample
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The measure of a angle B is 45°.
Given that, angle A and angle B are complementary and ∠A=45°.
What are complementary angles?In geometry, complementary angles are defined as two angles whose sum is 90 degrees.
Now, ∠A + ∠B = 90°
⇒ 45° + ∠B = 90°
⇒ ∠B = 45°
Counter example: If angle A is 90°, then the angle A and angle B are not complementary angles.
Therefore, the measure of a angle B is 45°.
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Find the derivative of y = sin2 (4x) cos (3x) with respect to x.
A. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)
B. 8 sin (4x) cos (3x) - 3 sin2 (4x) sin (3x)
C. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x) cos (3x)
D. 8 cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)
Answers
y = sin(4x)*sin(4x)*cos(3x)
need to use the product rule and chain rule
look at individual derivatives, use chain rule
d/dx sin(4x) = 4cos(4x)
d/dx cos(3x) = -3sin(3x)
put it together using product rule
dy/dx = 4cos(4x)*sin(4x)*cos(3x) + 4cos(4x)*sin(4x)*cos(3x) - 3sin(3x)*sin(4x)*sin(4x)
simplify
dy/dx = 8cos(4x)*sin(4x)*cos(3x) - 3sin(3x)*sin2(4x)
answer is A.
what is 0.0018 in scientific notation
Answers
=
1.8 x 10^-3
Scientific notation makes it easier to work with very small numbers, like 0.0018.
To express the number 0.0018 in scientific notation, we need to rewrite it as a product of a number between 1 and 10, and a power of 10. Here are the steps:
Identify the Initial Decimal Point Position: The number 0.0018 initially has the decimal point immediately after the zero whole part, before any significant figures.
Move the Decimal Point to the Right: Move the decimal point to the right until there is exactly one non-zero digit to the left of the decimal point. For 0.0018, moving the decimal point three places to the right converts it to 1.8.
Count the Moves: In this case, we moved the decimal three places to the right. Each move to the right represents a negative exponent in scientific notation.
Write in Scientific Notation: The scientific notation form of 0.0018 is written as:
[tex]1.8 \times 10^{-3}[/tex]
The [tex]10^{-3}[/tex] indicates that the decimal point was moved three places to the right.
Which is greater 300 kelvins or 34 degrees Celsius ? Show your work
Answers
To answer this item, we are to convert one of the unit to the other. The approach to answering is to convert the 34 degrees Celsius to kelvin by the equation,
T = C + 273.15
Substituting the known value,
T = (34) + 273.15 = 307.15 K
Since 307.15K is greater than 300K then, the greater value is 34 degrees C.
ANSWER: 34 degrees C
When fractions share the same number on the bottom what is it called?
Answers
Step-by-step explanation: When fractions have the same bottom number, they're called like fractions. When adding and subtracting fractions, our goal is to get like fractions or fractions that have the same denominator.
Also, it's easy to compare like fractions because you just have to look at the numerators of each of the fractions you are givemn.
Best answer ????...........
Answers
-6 - -2 = -4
-5 - - 1 = -4
so y would = x -4
-6 = -2-4
-5 = -1-4
Answer is C
An item costs $410 before tax, and the sales tax is $20.50 . find the sales tax rate. write your answer as a percentage.
Answers
The percentage of sales tax is 5%.
Given that, an item costs $410 before tax, and the sales tax is $20.50.
What is the sales tax?Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.
Let x% be the sales tax.
Now, x% of 410 = 20.50
0.01x ×410 = 20.50
⇒ 4.1x=20.50
⇒ x=20.50/4.1
⇒ x=5
Therefore, the percentage of sales tax is 5%.
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Jose drives a truck for a soft drink company. His truck is filled with
15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the truck is carrying, and let b be the number of 70-ounce bottles.Suppose the truck can carry at most 6000 pounds (96,000 ounces).
Using the values and variables given, write an inequality describing this.
PLEASE HELP! I'm struggling so much
Answers
wt = 14 x + (820-x) 70
Answer : 15c+70b<96,000
Step-by-step explanation:
Given the quadratic function 3x^(2) =8x-5 what are the values of x?
Answers
3x^2 - 8x + 5 = 0 move all terms to one side
3x^2 - 3x - 5x + 5 = 0 split them into two terms
3x(x - 1) - 5(x - 1) = 0 factor out common terms in the first two terms, then the last two terms.
(x - 1)(3x - 5) = 0
x = 1, 5/3
hope this helped, God bless!
Answer:
The values of x are [tex]\frac{5}{3}[/tex] and 1.
Step-by-step explanation:
Given quadratic function[tex]3x^2=8x-5[/tex]
We have to solve for x.
Consider the given quadratic function [tex]3x^2=8x-5[/tex]
This can be written as [tex]3x^2-8x+5=0[/tex]
We can solve the above quadratic equation using middle term split method,
-8x can be written as -3x - 5x
Thus, the equation becomes,
[tex]3x^2-8x+5=0[/tex]
[tex]\Rightarrow 3x^2-3x-5x+5=0[/tex]
Taking 3x common from first two term and -5 common from last two terms, we get,
[tex]\Rightarrow 3x(x-1)-5(x-1)=0[/tex]
[tex]\Rightarrow (3x-5)(x-1)=0[/tex]
Now using zero product property [tex]a.b=0 \Rightarrow a=0\ or\ b=0[/tex] , we have,
[tex]\Rightarrow (3x-5)=0[/tex] or [tex]\Rightarrow (x-1)=0[/tex]
[tex]\Rightarrow x=\frac{5}{3}[/tex] or [tex]\Rightarrow x=1[/tex]
Thus, The values of x are [tex]\frac{5}{3}[/tex] and 1.
Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD
Answers
Answer: The answer is (d) BC + CD = BD.
Step-by-step explanation: We are given the number line and four points A, B, C and D on the line with co-ordinate -6, -1, 2 and 8 respectively.
We are to select the correct statement out of the given four.
(a) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = AD = 14 ≠ 8.
So, this option is incorrect.
(b) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = CD = 6 ≠ 8.
So, this option is incorrect.
(c) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = AD = 14 ≠ 9.
So, this option is incorrect.
(d) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = BD = 9.
So, this option is correct.
Thus, the correct option is (d).
Solve for x: −2x − 4 > 8 (1 point)
x < −6
x > −6
x < −2
x > −2
Answers
-2x > 12
x < -6
answer
x < −6
Option A : x < -6 is the correct choice.
We have a inequality -
−2x − 4 > 8
We have solve and find the solutions to this inequality.
What is an Inequality in mathematics ?An inequality compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
−2x − 4 > 8
Add 4 on both sides -
-2x - 4 + 4 > 8 + 4
-2x > 12
Multiply both sides by -1, we get -
2x < - 12
Divide by 2 on both sides -
x < -6
Hence, x < -6 represents the solution of the inequality.
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The picture below shows a pole and its shadow: What is the height of the pole? A.196 B.244 C.388 D.364
Answers
Answer: 364
Step-by-step explanation: a^2+b^2=c^2
27^2+b^2=365^2
729+b=133,225
-
729 cancel that out then
133,225
-
729
————
132,496 squared~ 364
in the diagram below eg=100, ef=4x-20, and fg=2x+30
Answers
The lengths of segments x=15, EF=40, FG=60.
To solve for x, we can use the fact that the total length of segment EG is equal to the sum of the lengths of segments EF and FG.
EG = EF + FG
Substituting the given values, we get:
100 = 4x - 20 + 2x + 30
Combining like terms, we get:
100 = 6x + 10
Subtracting 10 from both sides, we get:
90 = 6x
Dividing both sides by 6, we get:
15 = x
Therefore, the value of x is 15.
We can now solve for the lengths of segments EF and FG.
EF = 4x - 20
Substituting the value of x, we get:
EF = 4(15) - 20
EF = 60 - 20
EF = 40
FG = 2x + 30
Substituting the value of x, we get:
FG = 2(15) + 30
FG = 30 + 30
FG = 60
Therefore, the lengths of segments EF and FG are 40 and 60, respectively.
Answer:
x = 15
EF = 40
FG = 60
Ms. Rao buys a computer, a printer, and a scanner for $2,543. The computer costs $1,502 more than the printer. The printer costs $123 more than the scanner. How much does Ms. Rao pay for the computer?
How did you get the answer? I got the answer of $1808. Please explain...
Answers
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is:
A)5
B)3
C) 2.5
D) 0.2
The slope represents:
A)The total cost of the taxi ride
B)The total number of miles driven
C)The cost per mile traveled
D) the initial cost of the ride
Answers
the slope is 2.5
i know this because:
(0,2) (6,18)
18-2 = 16/6 = 2.5
6 - 0 =16/6 = 2.5
The function g(x) is a continuous quadratic function defined for all real numbers, with some of its values given by the table below.The quadratic function ƒ(x) is represented by the parabola below. x g(x) -3 0 -2 5 0 9 2 5 3 0 Select all the statements that are true. The function ƒ(x) has a maximum value at x = 4.5. The function g(x) has a minimum value of 0. The maximum value of g(x) is twice the maximum value of ƒ(x). Neither function has a minimum value.
Answers
To solve other problems, look at f(x): if it has the top, where y is the biggest, then it is the maximum value (so if y = 4.5 is the biggest y, first statement is correct); if it has the bottom, where y is the smallest, then it is minimum value (factually, statement 3 will be correct if statement 1 is correct because 9/4.5 = 2). Finally, if f(x) has the top, then statement 4 is correct because f(x) and g(x) would be both constantly decreasing functions.
Hope this helps.
The function g(x) has a minimum value of 0, but we cannot determine the maximum value of g(x) or compare it to the maximum value of f(x). The statements about the maximum value of ƒ(x) and the lack of minimum value for both functions are not supported by the given information.
Explanation:The function g(x) is a continuous quadratic function that can be represented by a parabola. From the given table, we can observe that the minimum value of g(x) is 0 and it occurs when x = -3 or x = 3. Therefore, the statement 'The function g(x) has a minimum value of 0' is true.
To determine the maximum value of g(x), we need to find the vertex of the parabola representing g(x). Since the function is continuous and quadratic, the vertex occurs at the axis of symmetry. The axis of symmetry is given by x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, the equation representing g(x) is not given, so we cannot determine the exact maximum value of g(x) or compare it to the maximum value of f(x).
Based on the given information, we cannot determine whether the function f(x) has a maximum value at x = 4.5 or if the maximum value of g(x) is twice the maximum value of f(x). Therefore, the statements 'The function ƒ(x) has a maximum value at x = 4.5' and 'The maximum value of g(x) is twice the maximum value of ƒ(x)' are false.
Regarding the statement 'Neither function has a minimum value,' it is not accurate based on the given information. We already established that g(x) has a minimum value of 0.
Bettina’s age is three times Melvina’s age. If 20 is added to Melvina’s age and 20 is subtracted from Bettina’s age, their ages will be equal. How old is each now?
Answers
A water tank is in the shape of a cone.Its diameter is 50 meter and slant edge is also 50 meter.How much water it can store In it ? it releases water to a gated apartment building at the rate of 400 liters per second. In how many minutes tank will be empty?
Answers
Assessing the situation:
Let's get a feel for the shape of the problem here: what step should we be aiming to get to by the end? We want to find out how long it will take, in minutes, for the tank to drain completely, given a drainage rate of 400 L/s. Let's name a few key variables we'll need to keep track of here:
[tex]V[/tex] - the storage volume of our tank (in liters)
[tex]t[/tex] - the amount of time it will take for the tank to drain (in minutes)
We're about ready to set up an expression using those variables, but first, we should address a subtlety: the question provides us with the drainage rate in liters per second. We want the answer expressed in liters per minute, so we'll have to make that conversion beforehand. Since one second is 1/60 of a minute, a drainage rate of 400 L/s becomes 400 · 60 = 24,000 L/min.
From here, we can set up our expression. We want to find out when the tank is completely drained - when the water volume is equal to 0. If we assume that it starts full with a water volume of [tex]V[/tex] L, and we know that 24,000 L is drained - or subtracted - from that volume every minute, we can model our problem with the equation
[tex]V-24000t=0[/tex]
To isolate [tex]t[/tex], we can take the following steps:
[tex]V-24000t=0\\ V=24000t\\ \frac{V}{24000}=t [/tex]
So, all we need to do now to find [tex]t[/tex] is find [tex]V[/tex]. As it turns out, this is a pretty tall order. Let's begin:
Solving for [tex]V[/tex]:
About units: all of our measurements for the cone-shaped tank have been provided for us in meters, which means that our calculations will produce a value for the volume in cubic meters. This is a problem, since our drainage rate is given to us in liters per second. To account for this, we should find the conversion rate between cubic meters and liters so we can use it to convert at the end.
It turns out that 1 cubic meter is equal to 1000 liters, which means that we'll need to multiply our result by 1000 to switch them to the correct units.
Down to business: We begin with the formula for the area of a cone,
[tex]V= \frac{1}{3}\pi r^2h [/tex]
which is to say, 1/3 multiplied by the area of the circular base and the height of the cone. We don't know [tex]h[/tex] yet, but we are given the diameter of the base: 50 m. To find the radius [tex]r[/tex], we divide that diameter in half to obtain r = 50/2 = 25 m. All that's left now is to find the height.
To find that, we'll use another piece of information we've been given: a slant edge of 50 m. Together with the height and the radius of the cone, we have a right triangle, with the slant edge as the hypotenuse and the height and radius as legs. Since we've been given the slant edge (50 m) and the radius (25 m), we can use the Pythagorean Theorem to solve for the height [tex]h[/tex]:
[tex]h^2+25^2=50^2\\ h^2+625=2500\\ h^2=1875\\ h=\sqrt{1875}=\sqrt{625\cdot3}=25\sqrt{3}[/tex]
With [tex]h=25\sqrt{3}[/tex] and [tex]r=25[/tex], we're ready to solve for [tex]V[/tex]:
[tex]V= \frac{1}{3} \pi(25)^2\cdot25\sqrt{3}\\ V= \frac{1}{3} \pi\cdot625\cdot25\sqrt{3}\\ V= \frac{1}{3} \pi\cdot15625\sqrt{3}\\\\ V= \frac{15625\sqrt{3}\pi}{3} [/tex]
This gives us our volume in cubic meters. To convert it to liters, we multiply this monstrosity by 1000 to obtain:
[tex]\frac{15625\sqrt{3}\pi}{3}\cdot1000= \frac{15625000\sqrt{3}\pi}{3}[/tex]
We're almost there.
Bringing it home:
Remember that formula for [tex]t[/tex] we derived at the beginning? Let's revisit that. The number of minutes [tex]t[/tex] that it will take for this tank to drain completely is:
[tex]t= \frac{V}{24000} [/tex]
We have our [tex]V[/tex] now, so let's do this:
[tex]t= \frac{\frac{15625000\sqrt{3}\pi}{3}}{24000} \\ t= \frac{15625000\sqrt{3}\pi}{3}\cdot \frac{1}{24000} \\ t=\frac{15625000\sqrt{3}\pi}{3\cdot24000}\\ t=\frac{15625\sqrt{3}\pi}{3\cdot24}\\ t=\frac{15625\sqrt{3}\pi}{72}\\ t\approx1180.86[/tex]
So, it will take approximately 1180.86 minutes to completely drain the tank, which can hold approximately [tex]V= \frac{15625000\sqrt{3}\pi}{3}\approx 28340615.06[/tex] L of fluid.
What does it mean for event b to be independent of event​ a?
Answers
Fred the clown can create 17 animal balloons every 15 minutes.how many animal balloons he could create in 30 minutes and in 60 minutes.
Answers
Answer:
34 balloons in 30 minutes.
68 balloons in 60 minutes.
Step-by-step explanation:
We have been given that Fred the clown can create 17 animal balloons every 15 minutes. We are asked to find the number of balloons created by Fred in 30 minutes and 60 minutes.
To find number of balloons created by Fred in 30 minutes, we will multiply 17 by 2 as 30 is 2 times 15.
[tex]\text{Balloons created in 30 minutes}=2\times 17[/tex]
[tex]\text{Balloons created in 30 minutes}=34[/tex]
Therefore, Fred can create 34 balloons in 30 minutes.
To find number of balloons created by Fred in 60 minutes, we will multiply 17 by 4 as 60 is 4 times 15. This means Fred will create 4 times more balloons in 60 minutes than 15 minutes.
[tex]\text{Balloons created in 60 minutes}=4\times 17[/tex]
[tex]\text{Balloons created in 60 minutes}=68[/tex]
Therefore, Fred can create 68 balloons in 60 minutes.
And object is traveling at a steady speed of 8 2/3 mph how long will it take to object to travel 5 1/5 miles
Answers
which is just 36 minutes.