The solution is ΔFHE ≅ ΔGEH. [SAS], i.e. triangle FHE is similar to triangle GEH, by SAS rule.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Given: An Isosceles trapezoid EFGH in which EF =GH
To prove: ΔFHE ≅ ΔGEH
Proof: In Isosceles trapezoid EFGH, Considering two triangles ΔFHE and ΔGEH
1. FE ≅ G H → [ Given]
2. ∠H = ∠E
→ Draw GM⊥HE and FN ⊥EH, and In Δ GMH and ΔFNE,
GH=FE [Given]
∠M+∠N=180°
so, GM║FN and GF║EH, So GFMN is a rectangle.]
∴ GM =FN [opposite sides of rectangle]
∠GMH = ∠FNE [ Each being 90°]
Δ GMH ≅ ΔFNE [ Right hand side congruency]
→∠H =∠E [CPCT]
→ Side EH is common i.e EH ≅ EH .
→ΔFHE ≅ ΔGEH. [SAS]
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Study the following figure, where two concentric circles share center C.
Segment AB is a diameter of the larger circle.
Segment AB intersects a chord of the smaller circle, PQ, at a right angle at point Z.
Segment AB intersects a chord of the larger circle, MN, at a right angle at point 0.
If MO=7x-4, and NO=6x, what is the length of MN
Answer:
Length of MN = 48 units
Step-by-step explanation:
AB is the diameter of the larger circle which is perpendicular to both the chords PQ (chord of the smaller circle) and MN(chord of the larger circle).
Theorem says,
"Radius or a diameter of a circle which is perpendicular to the chord divides the chord in two equal parts."
Therefore, MO ≅ ON
m(MO) = m(ON)
7x - 4 = 6x
7x - 6x = 4
x = 4
m(MN) = m(MO) + m(ON)
= (7x - 4) + (6x)
= 13x - 4
= (13 × 4) - 4
= 52 - 4
= 48
Length of chord MN will be 48 units.
HELP ASAP Linear Relations Question
Answer:
8.8
Step-by-step explanation:
set up a system
let x be sour keys and y be chocolate bars
2.65=15x+2y
3.35=10x+3y
then solve
X turns out to be 0.05
y turns out to be 0.95
multiply : 24*0.05=1.2
multiply : 0.95*8=7.6
add : 1.2+7.6 = 8.8
find the value of x in the isoscleles triangle sqrt45 and altitude 3
Answer:
[tex]c.\hspace{3}x=12[/tex]
Step-by-step explanation:
Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.
You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached. As you can see:
[tex]x=2a[/tex]
And we can find a easily using pythagorean theorem:
[tex](\sqrt{45} )^{2} =3^{2} +a^{2}[/tex]
Solving for a:
[tex]a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\[/tex]
[tex]a^{2} =36\\\\a=\sqrt{36} \\\\a=6[/tex]
Therefore:
[tex]x=2a\\\\x=2(6)\\\\x=12[/tex]
Which of the following are solutions to the quadratic equation? Check all that
apply.
2x2 + 7x- 14 = x2 + 4
Answer:
[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]
Step-by-step explanation:
hello,
[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]
hope this helps
Which of the following statements could be used in the proof?
Answer:
Option (3)
Step-by-step explanation:
To prove ΔULV ≅ ΔKLY,
Statements Reasons
1). VL ≅ LY 1). Radii of a circle are equal
2). UL ≅ KL 2). Radii of a circle are equal
3). ∠ULV ≅ ∠KLY 3). Vertical angles are equal
4). ΔULV ≅ ΔKLY 4). SAS property of congruence
Therefore, property (3) given in the options will be used to prove the triangles congruent.
A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel?
Answer: 240 seconds OR 4 minutes
Step-by-step explanation:
Length of the train = 1 km
Length of the tunnel = 1 km
Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km
= 2000 m
Speed of the train = 30 km/hr = 8.333 metres per second
Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.
= 240 seconds = 4 minutes
A bag contains 16 cards numbered 1 through 16. A card is randomly chosen from the bag. What is the probability that the card has a multiple of 3 on it?
Answer:
Step-by-step explanation:
Probability is expressed as
Number of favorable outcomes/total number of possible outcomes
From the information given,
Total number of outcomes = 16
Starting from 1, the multiples of 3 between 1 and 16 are 3, 6, 9, 12 and 15
This means that the number of favorable outcomes is 5
Therefore, the probability that the card has a multiple of 3 on it is
5/16 = 0.3125
Help !!!! Match the written mathematical operation to the equivalent symbolic form
Answer:
The matched pairs are:
(A, 4), (B, 1), (C, 2) and (D, 3)
Step-by-step explanation:
The complete question is:
Match each description of an algebraic expression with the symbolic form of that expression :
A. 2 terms; variables = x and y
B. 3 terms; variables = x and y; constant = 3
C. 2 terms; variable = x; constant = 4.5
D. 3 terms; variables = x and y; constant = 2
1. x - 2y + 3
2. 4.5 - 2x
3. 4.5x + 2 - 3y
4. 4.5y - 2x
Solution:
A. 2 terms; variables = x and y ⇒ 4. 4.5y - 2x
B. 3 terms; variables = x and y; constant = 3 ⇒ 1. x - 2y + 3
C. 2 terms; variable = x; constant = 4.5 ⇒ 2. 4.5 - 2x
D. 3 terms; variables = x and y; constant = 2 ⇒ 3. 4.5x + 2 - 3y
Which statements are true regarding the diagram? Check all that apply.
The side opposite the 60° angle has a length of
The side opposite the 60° angle has a length of .
sin(60°) =
sin(60°) =
The other acute angle of the triangle is 30°.
Answer:
A. The side opposite the 60° angle has a length of √3/2
C.Sin(60°)=√3/2
E.The other acute angle of the triangle is 30°
Step-by-step explanation:
The diagram has been attached to the answer
A. The side opposite the 60° angle has a length of
B. The side opposite the 60° angle has a length of .
C. sin(60°) =
D. sin(60°) =
E. The other acute angle of the triangle is 30°.
Answer
The side opposite the 60° angle has a length of the square root of 3/2
Opposite side of the 60° angle has a length of √3/2
sin(60°) = the square root of 3/2
Sin(60°)=√3/2
The other acute angle of the triangle is 30°
Proof:
Total angle in a triangle=180°
180°-60°-90°
=30°
Answer:
A, D, E
Step-by-step explanation:
I do is big smart
Which answers are equivalent to the fraction below? Check all that apply
12/16
A.1/2 B.6/8 C2/3 D.2/6 E.3/4 F.6/4
Answer: e
Step-by-step explanation: 12/16 6/8 3/4
Answer:
B and E.
Step-by-step Explanation:
B: 6/8
6*2=12
8*2=16
12/16
E: 3/4
3*4=12
4*4=16
12/16
Hope this helps!!!!!
Gwendolyn shot a coin with a sling shot up into the air from the top of a building. The graph below represents the height of the coin after
x seconds.
Answer: A
Step-by-step explanation:
g(x)=5-2x what is the domain of g
Answer:
all real values of x
Step-by-step explanation:
The domain of g is the values that x can take
There are no restrictions on the values that x can take
Answer:
[tex]\boxed{\mathrm{E}}[/tex]
Step-by-step explanation:
[tex]g(x)=5-2x[/tex]
The domain of a function is the set of all possible inputs for the function.
The value of [tex]x[/tex] can be all real numbers,
There are no restrictions on the value of [tex]x[/tex].
Lincoln is measuring the angles of quadrilateral WXYZ to determine whether it is congruent to the quadrilateral below.
Quadrilateral R S T Q. Angle R is 140 degrees, angle S is 94 degrees, angle T is 79 degrees, and angle Q is 47 degrees.
Which pair of measurements are possible if they are congruent figures?
Measure of angle W = 47 degrees and Measure of angle X = 94 degrees
Measure of angle X = 94 degrees and Measure of angle Z = 79 degrees
Measure of angle W = 47 degrees and Measure of angle Y = 140 degrees
Measure of angle X = 140 degrees and Measure of angle = 94 degrees
Answer:
None of these
Step-by-step explanation:
The congruent occurs when the two diagrams are matched with each other in terms of the same sides and same angles
In other terms, we can say that if both quadrilaterals contain the same sides and same angles so we called as congruent
As we can see in the figure that there is only angles are given but not the sides that are totally different
Hence, none of these is the right answer
Answer:
D.) Measure of angle X = 140 degrees and Measure of angle = 94 degrees
Step-by-step explanation:
Find the area of this triangle..
Answer:
39.936 ( not rounded )
Step-by-step explanation:
Use Pythagorean theorem
a^2 + 6.4^2 = 9^2
height = 6.24 (rounded to nearest hundredth)
1/2 * base * height = area
1/2 * 12.8 * 6.24
= 39.936 ( not rounded )
Which statement is true about the ranges for the box plots? A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix.
*The box plots are shown in the attachment
Answer/Step-by-step explanation:
Range is the difference between the largest value of a data set and the lowest value in that data set.
In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.
For Crackers, the range = 100-70 = 30
For Cookies, the range = 115-70 = 45
Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).
Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
A rectangular plot measures 20 ft. By 30ft. A 3ft wide side walk surrounds it. Find the area of the side walk
Answer:
336 feet²
Step-by-step explanation:
If we have a rectangle that is 30 by 20 feet, that means the area of that rectangle would be 20 × 30 feet squared, which is 600 ft².
If there is a 3 feet sidewalk surrounding it, that means that the end of the sidewalk will extend 3 feet extra around each side of plot. Since there are two ends to one side, that means an extra six feet is added on to each dimension. Therefore, 36 × 26 are the dimensions of the sidewalk+plot. 36 × 26 = 936 ft².
To find the area of the sidewalk itself, we subtract 600 ft² from 936 ft². This gets us with 336 ft².
Hope this helped!
How do I solve this?
Answer:
See below.
Step-by-step explanation:
[tex](5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}[/tex]
First, note that everything to the zeroth power is 1. Thus:
[tex]=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}[/tex]
Distribute using Power of a Power property:
[tex]=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}[/tex]
Make the exponents positive by putting them to the numerator:
[tex]=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}[/tex]
[tex]=\frac{4x^{-6}y^{10}}{1}[/tex]
Make the exponent positive by this time putting it to the denominator:
[tex]=\frac{4y^{10}}{x^6}[/tex]
Find the interquartile range (IQR) of the data in the dot plot below. chocolate chips 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10. Number of chocolate chips. Chocolate chips in different cookies in a package
*The dot plot is shown in the attachment below
Answer:
2
Step-by-step explanation:
Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).
First, let's write out each value given in the data. Each dot represents a data point.
We have:
2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
=>Find the median:
Our median is the middle value. The middle value is the 6th value = 4
==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.
2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7
Our upper median = 5
==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.
2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7
Lower median = 3
==>Interquartile range = Q3 - Q1 = 5-3 = 2
Answer:
2
Step-by-step explanation:
What is the speed of a plane that goes 15000 miles per hour in per seconds?
Answer:
There are 60 * 60 = 3600 seconds in one hour so the plane goes 15000 / 3600 = 4 and 1/6 miles per second.
Answer:
[tex]4 \frac{1}{6} \: miles \: per \: seconds[/tex]Step-by-step explanation:
[tex]1500 \: miles \: \: per \: hour[/tex]
[tex] = \frac{15000}{60 \times 60} [/tex]
[tex] = \frac{15000}{3600} [/tex]
[tex] = \frac{25}{6} [/tex]
[tex] = 4 \frac{1}{6} \: miles \: per \: second[/tex]
Hope this helps...
Good luck on your assignment...
Polynomial function in standard form with zeros 5,-4,1
Answer:
[tex]\boxed{\sf \ \ \ x^3-2x^2-19x+20 \ \ \ }[/tex]
Step-by-step explanation:
hello,
by definition we can write
[tex](x-5)(x+4)(x-1)[/tex]
as 5,-4,1 are the zeroes
now we have to write it in the standard form, let's do it
[tex](x-5)(x+4)(x-1)=(x^2+4x-5x-20)(x-1)\\=(x^2-x-20)(x-1)=x^3-x^2-20x-x^2+x+20\\=x^3-2x^2-19x+20[/tex]
hope this helps
If A and B are two random events with probabilities of P(A) = 1/4 P(B) = 3/8 P(A ∩ B) = 1/5 calculate P(A|B).
Answer:
P(A|B) = 8/15
Step-by-step explanation:
Mathematically;
P(A|B) = P(A ∩ B)/P(B)
Thus we have
P(A|B) = 1/5 divided by 3/8
= 1/5 * 8/3 = 8/15
Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes.
The function with the lowest output values as x approaches infinity is _. The function with the greatest output values as x approaches infinity is _.
The function with the lowest output values as x approaches infinity is A.
The function with the greatest output values as x approaches infinity is B
The graphs below have the same shape.What is the equation of the red graph ?
Answer:
B. f(x) = 1 - x²
Step-by-step explanation:
Since we are dealing with only vertical movement, all we change is the constant. Since the red graph is up one from the reflected parent graph, we know our graph is f(x) = -x² + 1 or f(x) = 1 - x².
Answer:
B. F(x) = 1 - x^2
Step-by-step explanation:
The red graph is the blue graph translated 3 units down. It has a vertical translation of -3 units.
F(x) = G(x) - 3
F(x) = 4 - x^2 - 3
F(x) = 1 - x^2
If f(x) = x2 + 3x - 4, find f(4).
Answer:
f(4) = 24
Step-by-step explanation:
Plug in 4 for x in the equation:
f(x) = x² + 3x - 4
f(4) = (4)² + 3(4) - 4
Remember to follow PEMDAS. PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
and is the order of operation.
First, solve the power:
(4)² = 4 * 4 = 16
Next, multiply 3 with 4:
3 * 4 = 12
Next, combine the terms:
f(4) = 16 + 12 - 4
f(4) = (16 + 12) - 4
f(4) = 28 - 4
f(4) = 24
f(4) = 24 is your answer.
~
Answer:
24
Step-by-step explanation:
Plug x as 4.
(4)² + 3(4) - 4
16 + 12 - 4
= 24
Two different families pay for entry into a water park.
Family 1 has 2 adults and 3 children and costs a total of £20 to enter the park.
Family 2 has 1 adult and 4 children and costs a total of £15 to enter the park.
Work out the cost of the adult ticket, and the child ticket.
Answer:
Adult ticket: $7
Child ticket: $2
Step-by-step explanation:
Set up a system of equations where a represents the cost of one adult ticket and c is the cost of one child ticket:
2a + 3c = 20
a + 4c = 15
Solve by elimination by multiplying the bottom equation by -2:
2a + 3c = 20
-2a -8c = -30
Add them together:
-5c = -10
c = 2
Now, we can plug in 2 as c to find the value of a:
2a + 3c = 20
2a + 3(2) = 20
2a + 6 = 20
2a = 14
a = 7
The solution is
The cost of one adult ticket = $ 7
The cost of one child ticket = $ 2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of one adult ticket be = x
Let the cost of one child ticket be = y
Now , for Family 1 :
2 adults and 3 children and costs a total of £20 to enter the park
Substituting the values in the equation , we get
2x + 3y = 20 be equation (1)
Now , for Family 2 :
1 adult and 4 children and costs a total of £15 to enter the park
Substituting the values in the equation , we get
x + 4y = 15 be equation (2)
On simplifying the equations , we get
Multiply equation (2) by 2 , we get
2x + 8y = 30 be equation (3)
Subtracting equation (1) from equation (3) , we get
5y = 30 - 20
5y = 10
Divide by 5 on both sides of the equation , we get
y = 2
So , the cost of one child ticket is $ 2
Now , substituting the value of y in equation (2) , we get
x + 4y = 15
x + 4 ( 2 ) = 15
x + 8 = 15
Subtracting 8 on both sides of the equation , we get
x = 15 - 8
x = 7
So , the cost of one adult ticket is $ 7
Hence , the value of x is $ 7 and value of y is $ 2
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On a nearby pond, black and white ducks are swimming in groups of 3. James wants to find the experimental probability of two white ducks and one black duck swimming together. Design a simulation using a coin flip and explain why it is the best choice for James.U Will get BRAINLIEST
Answer:
The answer is below
Step-by-step explanation:
Given that, there are only two available choices, which are a black or white duck, this can be represented using a coin: H→White duck, T→Black Duck
Hence, to represent a set of possible outcomes, the coin has to be tossed three times.
Thus, we assume that, at the minimum we have total number of Ducks = 3 Black + 3 White = 6 Ducks
Total Favorable Outcome = 2 White + 1 Black
Total Possible Outcome = Selecting 3 Ducks (2 White +1 Black) from 6 Ducks
Formula to Calculate Probability
= Total favourable outcome ÷ Total possible outcome
Use ,C(n,r)= n! / (n - r)! r!
Therefore, the Probability of two white ducks one black duck swimming together
= ³C² * ³C¹ ÷ 6C3 = 9/20
To use Simulation Coin Flip, we have the following:
H→White duck, T→Black Duck
HHH→Three White Ducks Swimming together
TTT→Three black ducks Swimming together
HHT→Two white duck and a Black Duck swimming together
HTH→Two white duck and a Black Duck swimming together
THH→Two white duck and a Black Duck swimming together
TTH→Two Black duck and a White Duck swimming together
THT→Two Black duck and a White Duck swimming together
HTT→Two Black duck and a White Duck swimming together
Finally, to find the probability, divide the observed desired outcomes by the total number of trials.
Answer:
There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trials.
Step-by-step explanation:
edg2020
Can someone help me with this question please.
Answer: The total number of vehicles in the bar graph does not add up to 30.
The spacing between the bars should be equal.
It would be helpful to put the number of each type at the top of its bar.
It may be useful to give the location and time/date of the observation in the title of the graph.
Step-by-step explanation: The total 12 + 8 + 6 = 26.
My other observations would depend on the purpose of the graph. Many people use color to make the graph more visually appealing.
An intelligent trader travels from 1 place to another carrying 3 sacks having
30 coconuts each. No sack can hold more than 30 coconuts. On the way
he passes through 30 checkpoints and on each checkpoint he has to give 1
coconut for each sack he is carrying. How many coconuts are left in the
end? *
Answer:
none
Step-by-step explanation:
the man is carrying 3 sacks
each has 30 coconuts
so at total he has 90 coconuts: 30*3= 90
he passe through 30 checkpoints
ha has to give 1 coconut for each sack
so he gives 3 coconuts each time: 3*1=3
there are 30 ckeckpoints so : 3*30= 90
he has spent all the coconuts unless he has a trick
He starts with 3 sacks with 30 in each sack.
He has to give 1 coconut per sack away. So at first he gives 3 coconuts away.
The first 10 checkpoints he gives away 30 coconuts, so he is left with 2 sacks.
Now he has to give 2 coconuts away. 30/2 = 15, so the next 15 checkpoints he ends up giving away another full sack, so he is left with 1 full sack of 30 coconuts and he has 5 checkpoints left.
Giving away 1 coconut at those checkpoints, he would have 25 left
find the height of a tree whose shadow is 42m long when the shadow of a man 1.8m tall is 2.4m long
Answer:
The ratio 1.8 : 2.4 can be rewritten as 3 : 4. We have to solve:
3 : 4 = x : 42
3 * 42 = 4x
x = 3 * 42 / 4 = 31.5
The Egyptians used a ramp
that could hold 1,000 pounds.
If 6 people got on the ramp
and they weighed 780 pounds
total. What percentage of the
ramp's weight capacity is still
available?
Answer:
22%
Step-by-step explanation:
Well if the ramp can hold 1000lbs and 6 people all weight 780 in total (they must be really fat lol, but anyway) we can make the following fraction.
780/1000
So now we simplify the fraction to 39/50.
And do 39 / 50 = .78
To make that a percent we move the decimal point 2 times to the right so 78% of the ramp‘s capacity is being used meaning there is stil 22% capacity left.