Triangle D E F is reflected across D F to form triangle E G F. The lengths of sides E F and F G are congruent. To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed? ∠DEF ≅ ∠ DGF ∠DFE ≅ ∠ DFG DE ≅ DG DG ≅ GF
Answers
Answer:
[tex]\angle DFE = \angle DFG[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
What makes DEF and DGF congruent
We have:
[tex]EF = GF[/tex] --- this is indicated by the single line on both sides
Also:
[tex]DF = DF[/tex] --- both triangle share same side
For SAS to be true;
2 sides and 1 angle must be equal in either triangles
So far, we have:
[tex]EF = GF[/tex] ---- S
[tex]DF = DF[/tex] ---- S
The additional to complete the proof is:
[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides
Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.
Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.
The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.
So that,
GF ≅ FE (given)
DF is the common side to triangles DEF and DFG.
DFG is the included side.
Thus;
∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)
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Related Questions
help asap ---- ---- ---- ---- ----v ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
Answers
Given:
The graph of h(x) is the greed dashed line segment.
To find:
The endpoints of the function [tex]h^{-1}(x)[/tex].
Solution:
If (a,b) is the point on the graph of the function f(x), then (b,a) must be the point on the inverse function [tex]f^{-1}(x)[/tex]
From the given graph, it is clear that the endpoint of the line segment h(x) are (-8,1) and (3,-4).
So, the endpoints of the inverse function [tex]h^{-1}(x)[/tex] are (1,-8) and (-4,3).
Therefore, the endpoints of [tex]y=h^{-1}(x)[/tex] are (1,-8) and (-4,3), and the graph is shown below.
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
(negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)
(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)
{–12, 2}
{–2, 12}
Answers
Answer:
(-12,2)
Step-by-step explanation:
x^2 + 10x = 24
x^2 + 10x + (10/2)^2 = 24 + (10/2)^2
10/2 = 5
5^2 = 25
x^2 + 10x + 25 = 24 + 25
x^2 + 10x + 25 = 49
(x + 5)^2 = 49 Take the square root of both sides
(x + 5) = sqrt(49)
x + 5 = +/- 7
x = +/- 7 - 5
x = +7 - 5 = 2
x = -7 - 5 = -12
Answer:
{ -12 , 2}
Step-by-step explanation:
x² + 10x = 24
In order to complete the square, the equation must first be in the form x² + bx =c.
x² + 10x = 24Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x² + 10x + 5² = 24 + 5²expand exponents.
x² + 10x + 25 = 24 + 25Add 24 and 25
x² + 10x + 25 = 49Factor x² + 10x + 25. In general, when x² + bx + c is a perfect square, it can always be factored as ( x + b/2)².
( x + 5 )² =49Take the square root of both sides of the equation.
[tex] \small \sf \sqrt{(x + 5) {}^{2} } = \sqrt{49} [/tex]
simplify
x + 5 = 7x + 5 = +/- 7Subtract 5 from both sides.
x + 5 - 5 = 7 - 5
x = 2x + 5 - 5 = +/- 7 -5
x = -7 - 5 = -12Annie invests $400 in a bank that offers 5.5% simple annual interest after 6 years her investment will increase by blank dollars
Answers
Answer:
Her investment will increase by 551.54 dollars
Step-by-step explanation:
So we know that the exponential function formula is f(x)=a(1+r)^x
So knowing that we can input values
So now we have f(x)=400(1+0.055)^6
Since it is annual we will only have the interest yearly so that changes are equation to look like this f(x)=400(1+0.055/1)^6
So next we have to add 1 and 0.055 which is 1.055
So we input that into the equation so now we have f(x)=400(1.055/1)^6
Now we have to do (1.055/1) to the power of six, so we get 1.37884280676
Now we have to 1.37884280676 times 400, which would be 551.537122705.
Assuming they want to the nearest 100th it would be 551.54
So the answer is 551.54 dollars
Hopefully, that helped. If I made any mistake or I am incorrect feel free to correct me. :)
If the vertex of a parabola is (-4, 6) and another point on the curve is (-3, 14), what is the coefficient of the squared expression in the parabola's equation?
Answers
Answer:
[tex]y=a(x-h)^{2} +k[/tex]
[tex](x,y)=(-3,14)[/tex]
[tex](h,k)=(-4,6)[/tex]
[tex]14=a(-3-(-4))^{2})+6[/tex]
[tex]14=a(-3+4)^{2} +6[/tex]
[tex]14=a(1)^{2} +6,-6[/tex]
[tex]8=a[/tex]
[tex]ANSWER:8[/tex]
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Instructions: Find AB. given that line AD is the perpendicular bisector of BC.
Answers
Answer:
19
Step-by-step explanation:
because line a d divided the triangle ABC into two equal halves therefore line a b is equal to line AC which is equal to 19
The sales tax rate for the state of Washington was 7.6%.
What is the state sales tax on a $5,300 car in WashingtoN
What is the final cost of the car, including tax?
Answers
Answer:
Sales tax: 402.80 Final cost: 5,702.80
Step-by-step explanation:
Sales price x sales tax rate = sales tax
5300 x .076 (7.6%) = 402.80
Sales price + tax = final cost
5300 + 402.80 = 5702.80
What is the length of AC?
A
8
B
C
O
Answers
Answer:
hi, it's 16 because:
[tex]ab = bc \\ ab = 8 \\ ac = 2 \times 8 = 16 \\ ac = 16[/tex]
Answer:
16
Step-by-step explanation:
Theorem: In a circle, if a radius is perpendicular to a chord, then the radius is the perpendicular bisector of the chord.
In this case, the radius containing points O and B is perpendicular to chord AC, so the radius bisects chord AC making AB = BC.
Also,
AB + BC = AC
By substitution, we have
AB + AB = AC
AC = 2AB
AC = 2(8)
AC = 16
use the graph to find the value of y=sin q for the value of q 330
Answers
Answer: A) -0.5
Explanation:
Each tickmark is an increment of 30. Start at 270 and move 1 tickmark over to get to 270+30 = 300. Then another tickmark to the right gets us to 330.
Then from here, head straight down until you get to the curve. You should arrive at the point (330, -0.5)
So q = 330 pairs up with y = -0.5
Will give brainliest!!!
2.6(5.5p – 12.4) = 127.92
p=
Answers
Answer:
[tex]p=11.2[/tex]
Step-by-step explanation:
Given [tex]2.6(5.5p-12.4)=127.92[/tex], distribute to remove the parentheses:
[tex]2.6\cdot 5.5p-2.6\cdot 12.4=127.92[/tex]
Simplify:
[tex]14.3p-32.24=127.92[/tex]
Add 32.24 to both sides:
[tex]14.3p=160.16[/tex]
Divide both sides by 14.3:
[tex]p=\frac{160.16}{14.3}=\boxed{11.2}[/tex]
What is the slope of the line? What is the y-intercept of the line? y = 1
Answers
Answer:
m = 0
y intercept = 1
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 1[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 0 [/tex]
[tex]\implies y - intercept= 1[/tex]
Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1
y intercept of the line is y = 1.
Answered by GAUTHMATH
The simple interest on certain principal is 1/5 of the amount in 5 years, find the rate of interest.
a. 5%
b. 80%
c 6 2/3
d 10%
Answers
The rate is 4% per year.
It is required to find the rate of interest.
What is simple interest ?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Given that:
Let, principal is P,
so, interest is P/5 in 5 yrs.
As from the formula of simple interest,
So, P/5 = P× R ×5/ 100 (R = rate)Or, R = 4%
So, rate is 4% per year.
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The missing option is e. 4%
A boat is heading towards a lighthouse, where Riley is watching from a vertical distance of 120 feet above the water. Riley measures an angle of depression to the boat at point A to be 18 degrees . At some later time , Riley takes another measurement and finds the angle of depression to the boat (now at point B) to be 65 degrees . Find the distance from point A to point B. Round your answer to the nearest foot if necessary .
Answers
Answer:
313 ft
Step-by-step explanation:
It's hard to explain because its geometry, but there will be a right triangle with angle of 72 and another with angle of 25. do tan72 * 120 - tan25 * 120
The distance from point A to point B is given by the trigonometric relations and d = 313 feet
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the first triangle be represented as ΔAOD
Let the second triangle be represented as ΔBOD
where the distance from point A to point B = d
And , Riley is watching from a vertical distance of 120 feet above the water
Riley measures an angle of depression to the boat at point A to be 18 degrees
Riley takes another measurement and finds the angle of depression to the boat (now at point B) to be 65 degrees
So , ∠BOD = 25° and ∠AOD = 72°
From the trigonometric relations ,
tan θ = opposite / adjacent
tan AOD = AD / OD = tan 72°
tan 72° = 3.087
tan BOD = tan 25° = 0.47
Now , the measure of AD = 120 x 3.087 = 369.6 feet
And , the measure of BD = 120 x 0.74 = 56.4 feet
Therefore , the distance from A to B = 369.6 feet - 56.4 feet
d = 313 feet
Hence , the distance is 313 feet
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large pies cost £3.25 each
small pies cost £1.80 each
five children together buy 2 large pies and 1 small pie. they share the cost equally - how much does each child pay
Answers
Answer:
1.66 £
Step-by-step explanation:
(2 * 3.25 + 1.80) : 5 =
8.3 : 5
1.66 £
Cosella is conducting an experiment where she assesses how quickly teenagers can run a 100-meter race after consuming specific amounts of caffeine. She divides her sample up into three groups. Group 1 receives a glass of water with no caffeine added. Group 2 receives a glass of water with an amount of caffeine equivalent to that in one cup of coffee. Group 3 receives a glass of water with an amount of caffeine equivalent to that in two cups of coffee. Each participant is then timed as they run the course. In this study, the dependent variable is
Answers
Answer:
The dependent variable is the time taken to run 100 metres
Step-by-step explanation:
A dependent variable is simply one that is being measured or sometimes tested in an experiment.
Now, in this case, what is being determined is the time each group of participants will take to run a 100-meter race.
Thus, the dependent variable is the time each group of participants will take to run a 100-meter race.
convert 9.56 cm = ________________ M
Answers
Answer:
[see below]
Step-by-step explanation:
There are 100 cm in a meter.
9.56/100 = 0.0956
Hope this helps you.
(PS: You can mark the other user as Branliest)
Far behind does anyone know this?
Answers
Answer:
the answer is A
Step-by-step explanation:
comment if you want explanation
Answer:
A is the answer to your question
Please help me asap!
Answers
Answer:
Its 48
Step-by-step explanation:
subtract 69 and 56 from 173, what you have left is your answer
48
Step-by-step explanation:
total 176 subtract 69 and 58 since they are given.
176 - 69 -56 = 48
Please help me with this problem
Answers
Answer:
Step-by-step explanation:
a*b *c = abc
15c = 15 . c
2a * 10b = 2* 10 * a * b = 20ab
The above mentioned expressions are true
That are false
12ab = 12a * 12b ----> false because 12ab = 12 * a* b
7a *7b = 14ab is false because 7a * 7b = 7 * 7* a *b = 49ab
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answers
Answer:
i dont know
Step-by-step explanation:
figure it out yourself
For each journey between work and home, Arjun uses 1.3 gallons of petrol. Arjun has 52 litres of petrol in his car. How many complete journeys between work and home can he do?
1 gallon = 4.5 litres.
Answers
Answer: 9 full journeys
Step-by-step explanation:
4.5 litres * 1.3 gallons = 5.8 litres of petrol
52 litres ÷ 5.8 litres of petrol = 8.9 journeys ≈ 9 full journeys
A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.
Answers
Hello,
Let's assume x the length of the north's wall
and y the length of west side .
Area:x*y=600 ==> y=600/x
Cost: 2*y*4+5*x=8y+5x= 4800/x+5x
Minimize cost: (4800/x+5x)'=0
-4800/x²+5=0
x²=4800/5
x²=960
[tex]x=8\sqrt{15} \\\\y=5\sqrt{15} \\[/tex]
What is the order of rotational symmetry of a regular pentagon?
Answers
Answer:
yeet
Step-by-step explanation:
urmom
PLEASE HELP.
if v1….
Answers
What is the measure of x in the figure below?
Answers
Answer:
115 degree
Step-by-step explanation:
x + 65 = 180 (Sum of angles in a straight line = 180 [Also known as Linear pair])
x = 180 - 65
x = 115 degree
Express each of the following negative angles as its equivalent positive angle between 0°and360°
+120°
Answers
Answer:
Dilated pupils
Long periods of wakefulness
Loss of appetite
Overconfidence
Over-excitement
Paranoia
Runny nose or frequent sniffles
White powder around nostrils
Legal issues
Missing or being late to work
Financial problems
Mood swings
Irritability
Depression
I need the answer ASAP anyone could help me please
Answers
Answer:
Is it the answer is C?
2+4+3+5+1=15
Answer: (C) 15
What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at the origin?
Answers
The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:
(x', y') = (kx, ky)
where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.
Substituting the values given in the problem, we get:
(x', y') = (4*(-6), 4*(-2))
Simplifying,
(x', y') = (-24, -8)
Therefore,
The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).
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Sven determined that the x-coordinate is approximately 3.6 because the point is closer to 4 than 3 and seems to be a little more than halfway between them. What is the approximate value for the y-coordinate? y Almost-equals –1.1 y Almost-equals –1.4 y Almost-equals –1.8 y Almost-equals –1.9
Answers
Answer:
The answer is "[tex]y\approx 1.4[/tex]".
Step-by-step explanation:
In the given question the y-coordinates range between -1 to -2. Its distance between -1 and -2 is near, and less than halfway.
Answer:
b
Step-by-step explanation:
A department store holds a year-end clearance sale that includes a 5.5% discount on cosmetics. Find the sale price of a bottle of perfume if its original price was $48.41.
Answers
Answer:
Sale price = $45.75
Step-by-step explanation:
Original price = $48.41
Percentage Discount = 5.5%
Amount of discount = Percentage Discount × Original price
= 5.5% × $48.41
= 5.5/100 × $48.41
= 0.055 × $48.41
= $2.66255
Sale price = Original price - Amount of discount
= $48.41 - $2.66255
= $45.74745
Approximately,
Sale price = $45.75
Instructions: Find the measure of
Answers
Answer:
93
Step-by-step explanation:
Add the two angles 48 and 39 =87. 180-87=93
