According to the Angle-Angle-Angle (AAA) criterion, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."
Proof:
Consider two triangles ABC and DEF, such that ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F
Now, cut DP= AB and DQ= AC and join PQ. Hence, we can say that a triangle ABC is congruent to the triangle DPQ.
(i.e) ∆ ABC ≅ ∆ DPQ, which gives ∠B = ∠P = ∠E, and also, the line PQ is parallel to EF.
Therefore, by using the basic proportionality theorem, we can write
DP/PE = DQ/QF.
(i.e) AB/DE = AC/DF. …(1)
Similarly,
AB/DE = BC/EF …(2)
From (1) and (2), we can write:
AB/DE = BC/EF = AC/DF.
Therefore, the two triangles ABC and DEF are similar.
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If you flip a coin ten times, how many different sequences of heads and tails are possible? a. b. c. d.
The number of possible different sequences of heads and tails is 1024.
A list of numbers (or other components) that follow a specific pattern is called a sequence. An arithmetic progression is one of the common examples of sequence and series.
A sequence can be arranged in either ascending or descending order.
Each flip has two outcomes H or T, so in ten flips you can get a sequence like HTHHTHTTTH
The number of possible different sequences is simply 2*2*2*2*2*2*2*2*2*2 = 2^10 = 1024
Thus, The number of possible different sequences of heads and tails is 1024.
Complete question:
If you flip a coin ten times, how many different sequences of heads and tails are possible?
a. 2° = 512
b. 10 = 100
C. 102 = 1024
d. 210 = 1024
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Write (-6,3) (4,-3) in slope intercept form
Answer:
y=-3/5x-3/5
Step-by-step explanation:
I started off by finding the slope by using the slope formula. then i plugged in one of the ordered pairs into thr slope intercept form to find the value of b.
What is the formula of perimeter Class 6?
The perimeter of a closed shape is the overall length of the boundary. As a result, the perimeter of that shape is determined by adding up all of its sides. Therefore, Perimeter(P) = Sum of All Sides is the perimeter formula.
The formula is:
Perimeter = (the distance all the way around the outside of the figure).
How to calculate the distance all the way around the outside of the figure
is different for every shape.
A few of them are:
The perimeter of a Square, (P) = 4 × Side units.
The perimeter of a Rectangle, (P) = 2(l + b) units.
The perimeter of a Triangle is = Sum of all three sides.
The perimeter of a Circle = 2 π r = π d.
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The difference between two numbers is 10. The smaller number is 8.
Which of the following is the equation of the statement above?
10 - x = 8
x + 8 = 10
x - 8 = 10
8 - x = 10
Answer:
x - 8 = 10
Step-by-step explanation:
The smallest number is 8 so it's subtracting 8. 10 is the difference between the two numbers because it's the answer.
can someone please help me
Answer:
58
Step-by-step explanation:
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Helps Plz! I have no idea how to do this
g(t) = 2t - 1
f(t) = t - 1
Find g(f(t))
Answer:
The Answer is g ( t − 1 ) = 2 t − 3
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
solve for b; 5ba - x = y
Answer and Step-by-step explanation:
First, add x to both sides.
5ba = x + y
Now, divide both sides by 5a.
[tex]b = \frac{x+ y}{5a}[/tex] is the answer.
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If 2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0, find lim x→2 f(x).
The value of [tex]\lim _{x \rightarrow 2}[/tex] f(x) by Sandwich theorem is 2.
As per the given data the function limits are:
2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0
Here we have to determine the value of [tex]\lim _{x \rightarrow 2}[/tex] f(x)
Hence by Sandwich theorem:
The sandwich theorem, also known as the squeeze theorem, asserts that if two functions, g (x) and h (x), are squeezed between one another and their respective limits at a given position are both equal to L, then the limit of f (x) at that point is also equal to L.
We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" [tex]\frac{sin(x)}{x}[/tex] between two nicer functions and using them to find the limit at x = 0.
[tex]& \lim_{x \rightarrow 2}(2 x-2) \leq\lim_{x \rightarrow 2} f(x) \leq \lim_{x \rightarrow 2}\left(x^2-2 x+2\right) \\[/tex]
[tex]& \Rightarrow 2 \leq \lim _{x \rightarrow 2} f(x) \leq 2 \\[/tex]
Hence [tex]\lim _{x \rightarrow 2}[/tex] f(x) = 2
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Between which two positive integers does V33 lie?
Answer:
0-1 Integers are whole numbers
Step-by-step explanation:
which graph represents 7x-2y_<5
Answer:.
Step-by-step explanation:.
Isaac buys 17 anti-pollution masks for £5. 25 each
He pays with five £20 notes.
a) How much change should Isaac get?
Write your answer in £.
The normal price of an e-scooter is £370
1
In a sale, there is off the normal price of the e-sc
4
hlork out the nice of the e-scooter in the sale
a) Issac get £10.75 as change after buying all masks
b) The price of the e-scooter in the sale is £277.50
a)
Isaac buys 17 anti-pollution masks for £5.25 each, so the total cost is
17 * 5.25 = £89.25
He pays with five £20 notes, which is a total of 5 * 20 = £100
So, the change he should get is £100 - £89.25 = £10.75
Therefore, Isaac should get £10.75 as change.
b)
In the sale, there is 1/4 off the cost price of the e-scooter, which means that the scooter is discounted by 1/4 * £370 = £92.50.
To work out the price of the e-scooter in the sale, you need to subtract the discount from the normal price, so
£370 - £92.50 = £277.50
Therefore, the price of the e-scooter in the sale is £277.50
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Which expression can represent 4 less than the quotient of 192 and 3?
A (192 x 3) - 4
B (192 ÷ 3) - 4
C 4 - (192 x 3)
D 4 - (192 ÷ 3)
Answer: B
Step-by-step explanation:
Because if you were finding the quotient, you would divide, then subtract 4.
Shawn keeps his photos in a box like the one shown.
What is the volume of the box?
Answer:
288 in.
Step-by-step explanation:
when it comes to finding the volume of a box you just multiply the width, length and height and you will get the volume
6 in. x 12 in. x 4 in. = 288 in.
In ΔEFG, g = 8.4 inches, mm∠G=79° and mm∠E=25°. Find the length of f, to the nearest 10th of an inch.
The 8.4 inches length of g and the 79° and 25° measures of the angles ∠G and ∠E, using the law of sines, indicates that the length of the side EG = f is about 8,3 inches.
What is the law of sines?The law of sines states that the ratio of the sine of an interior angle of a triangle to the length of the opposite side to the angle is the same for the three sides and angles in a triangle.
Mathematically, the law of sines can be presented as follows;
[tex]\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]
Where;
a, b, and c are the length of each of the sides of the triangle, and ∠A, ∠B, and ∠C are the measure of each of the interior angles of the triangle.
The details of the triangle ΔEFG, specifying the side g as the side opposite the angle ∠G, and the side f as the side opposite the ∠F we get;
The length of EF = g = 8.4 inches
Length of EG = f
The angle sum property of a triangle indicates that we get;
∠E + ∠F + ∠G = 180°
∠F = 180° - (∠E + ∠G)
∠F = 180° - (25° + 79°) = 76°
According to the law of sines, we get;
8.4/(sin(79°) = f/(sin(76°))
f = (sin(76°)) × 8.4/(sin(79°) ≈ 8.3
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How do you know if a triangle is a 45 45 90 triangle?
The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.
A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
properties of 45°-45°-90°:
It's the only possible right triangle that is also an isosceles triangle, and it has the smallest ratio of the hypotenuse to the sum of the legs.It has the greatest ratio of the altitude from the hypotenuse to the sum of the legs.To know more about 45° 45° 90° triangle:
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Name the property that is shown by each equation.
A. 6a + 4 = 4 + 6a
B. 30 + 60 = 15(2 + 4)
C. 3(8x + 4) = 3(4 + 8x)
D. 4(6a) = (4 · 6)a
A. Commutative property of addition
B. Distributive property
C. Commutative property of addition
D. Associative property of multiplication
Please help!!! Very confused on my homework.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is v1=36pir2/1 where r1 is the radius of the tank in feet.
PROBLEM IS ON THE ATTACHMENT!
Step-by-step explanation:
we need to use both equations for the volumes.
the only variables in them are r1 and r2.
when we say both results (volumes) are equal, that means we can create an equation with one formula on one side and the other formula on the other side.
and then we can easily transform the equation into "r1 = ..." or "r2 = ..."
and yes, your teacher made a mistake by hinting to solve for r1 in a. and b. it is r1 in a. and r2 in b.
a.
the goal here is an equation in the form
"r1 = ..."
that means r1 is a function of r2.
36×pi×r1² = 1/2 × 4/3 × pi × r2³ = 4/6 × pi × r2³ =
= 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
r1² = (2/3 / 36) × r2³ = (1/(3×18)) × r2³ = 1/54 × r2³
r1 = sqrt(1/54 × r2³) = 1/3 × sqrt(1/6 × r2³)
b.
the goal here is
"r2 = ..."
again
36×pi×r1² = 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
3×36 × r1² = 2 × r2³
3×18 × r1² = r2³
54 × r1² = r2³
[tex]r2 = \sqrt[3]{54 \times {r1}^{2} } = 3 \times \sqrt[3]{2 \times {r1}^{2} } [/tex]
c.
r2 is doubled.
so, we have to go back to our equation of a.
r1 = sqrt(1/54 × r2³).
when r2 is doubled, we get
r1 = sqrt(1/54 × (2×r2)³) = sqrt(1/54 × 8 × r2³) =
= sqrt(8) × sqrt(1/54 × r2³)
so, when r2 doubles, r1 has to grow by the factor of sqrt(8) to keep the equality intact.
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Answer:
See below.
Step-by-step explanation:
f(x) = x² - 2x - 8 (Graph 3)
g(x) = (x + 3)(x - 1) (Graph 2)
h(x) = 2(x + 6)² + 2 (Graph 1)
Is 8:2 greater than 5:1?
I need someone to help me clarify if this is correct. Thanks.
Answer:
No, 8:2 = 4:1 which is less than 5:1
Step-by-step explanation:
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
[tex]8 : 2 \\ = \frac{8}{2} \\ = 4[/tex]
[tex]5 : 1 \\ = \frac{5}{1} \\ = 5[/tex]
8 : 2 = 4, while 5 : 1 = 5.
4 < 5.
•°• 8 : 2 is not greater than 5 : 1.
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[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Evaluate the expression 2a+3d
Answer:
Step-by-step explanation:
Nothing further can be done with this topic
So, your answer would have to be 2a+3d
Use pattern blocks to represent each multiplication equation. Use the trapezoid to
represent 1 whole.
a. 3 • 1/3 = 1
b. 3 • 2/3 = 2
when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,
Describe area.The size of a region on a flat or curved surface is expressed mathematically as area. The area of a form is defined as the "space encompassed inside the perimeter or the border." The area of various shapes is calculated using mathematical methods.
given
The trapezoid's surface area is 70 units.
first base is worth 20 units, while second base is worth 10 units.
how long CE
[tex]1/2(b1 + b2)*h is the area of a trapezoid.\\70= 1/2 (20 + 10 )*h\\70 = 1/2(30)*h\\4.6 units of h[/tex]
when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,
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What is the area of the base in the figure below? A cylinder with height 12 and diameter 6. 9 square units 9 pi square units 72 square units 72 pi square units
Answer:
Area of circle = 9π square unit
Step-by-step explanation:
Given:
Height of cylinder = 12 units
Base diameter of cylinder = 6 units
Find:
Area of base
Computation:
Base Radius of cylinder = Base diameter of cylinder / 2
Base Radius of cylinder = 6 / 2
Base Radius of cylinder = 3 unit
Area of circle = πr²
Area of circle = (π)(3)²
Area of circle = 9π square unit
Answer:
Option B, 9 pi square units.
Step-by-step explanation:
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hey guys can anyone help me!.
Answer:
m=4
Step-by-step explanation:
Answer:
m = 4
Step-by-step explanation:
The shape on the right is 2/3 times smaller than the shape on the left.
This means multiplying the side lengths of the shape on the left by 2/3 will give you the side lengths of the shape on the right.
Take a look.
[tex]9 * \frac{2}{3} = 18/3 = 6[/tex]
[tex]6 *\frac{2}{3} = 12/3 = 4[/tex]
Therefore, the value of the missing side length, m, is 4.
On a certain hot summer day, 431 people used the public swimming pool. The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled to $788.50. How many children and how many adults swam at the public pool that day?
The number of adults at the public pool that day is 284 and the number of children is 147.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Let x be the number of adults and y be the number of children who used the swimming pool.
Total number of people used the swimming pool = 431
x + y = 431
Daily price for adults = $2.00
Daily price for children = $1.50
Total amount for admission = $788.50
2x + 1.5y = 788.5
We got two linear equations here :
x + y = 431 and 2x + 1.5y = 788.5
x + y = 431 ⇒ x = 431 - y
Substituting this in second equation,
2(431 - y) + 1.5y = 788.5
862 - 2y + 1.5y = 788.5
-0.5y = -73.5
y = 147
x = 431 - 147 = 284
Hence the number of adults is 284 and the number of children is 147.
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Graph the line that passes through the points (9, -1) and (6, 1) and determine the equation of the line.
The equation of the line will be y = -2/3x + 5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line passes through points (9, -1) and (6, 1).
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 1 - (-1) / ( 6 - 9 )
Sloe = - 2 / 3
The y-intercept will be calculated as,
y = mx + c
-1 = (-2/3) x 9 + c
c = 5
The equation of the line,
y = mx + c
y = -2/3x + 5
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What percent students have height between 62 inches and 64 inch
Answer:The following list of data represents highway fuel consumption in miles per gallon. (mpg) for Hint: you will need to calculate the midpoint for each class. Age (yrs) C. What percentage of women are between 62.5 inches and 67.5 inches? 65. 68 ... If the top 15% of the students get A's, what is the cut-off score for an A? 75.
Step-by-step explanation:
sorry if this is wrong
Percent students having height between 62 & 64 inches, is 25%
As per the linear presentation, data is spread evenly between 58 to 66 inches.
The total 100% students are divided evenly in 8 segments, from 58 - 59 inches to 65 - 66 inches. So each segment has 100 / 8 = 12.5%
Hence, percentage students having 62 to 64 inches has 2 unit segments. They are 12.5 x 2 = 25% students.
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The area of a parcel of land can be represented by the expression 9x2 - 6x + 10. The parcel must be divided into 3 equal parts. What is an expression that represents the area of each part?
A) 3x2 - 2x + 3 1 3
B) 9x2 - 6x + 13
C) 9x6 - 6x3 + 10
D) 27x2 - 18x + 30
What is the easiest way to learn linear equations class 8?
The easiest way to solve linear equations is to use the elimination method.
A linear equation is an equation that has two variables and when it is graphed it gives a straight line. Linear equations can be graphed according to their slope and y-intercept. The standard equation for a line is y = mx + b, where b is the y-intercept and m is the slope.
To solve linear equations in the easiest and simplest way use the elimination method. In this method, you either add or subtract the equations to obtain an equation in one variable. When the coefficients of one variable are opposites, you add the equations to eliminate a variable and when the coefficients of one variable are equal, you subtract the equations to eliminate a variable.
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A hybrid car can cover 45 miles per gallon. How much gas does it need to cover 15 miles?
Answer:
45 divided by 15 = 3 gallons of gas
Another way:
Ratio: 45 miles : 15 gallon
Divide by 15 on both sides to make unit rate:
3 miles : 1 gallon
3 miles x 5 = 15 miles
1 gallon x 3 = 3 gallons
15 miles: 3 gallons.