which of the following congruence postulates can be used to prove that the triangles are
congruent.
SSS
SAS
ASA
HL

Answer:

See explanation

Step-by-step explanation:

You are given the equality

[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]

where x, y are two positive integers with x>y.

1. x=2,y=1, then

[tex]c=x^2+y^2=2^2+1^2=5\\ \\a=x^2-y^2=2^2-1^2=3\\ \\b=2xy=2\cdot 2\cdot 1=4[/tex]

First Pythagorean triple is (3,4,5)

2. x=3,y=1, then

[tex]c=x^2+y^2=3^2+1^2=10\\ \\a=x^2-y^2=3^2-1^2=8\\ \\b=2xy=2\cdot 3\cdot 1=6[/tex]

Second Pythagorean triple is (6,8,10)

3. x=3,y=2, then

[tex]c=x^2+y^2=3^2+2^2=13\\ \\a=x^2-y^2=3^2-2^2=5\\ \\b=2xy=2\cdot 3\cdot 2=12[/tex]

Third Pythagorean triple is (5,12,13)

4. x=4,y=1, then

[tex]c=x^2+y^2=4^2+1^2=17\\ \\a=x^2-y^2=4^2-1^2=15\\ \\b=2xy=2\cdot 4\cdot 1=8[/tex]

Fourth Pythagorean triple is (8,15,17)

5. x=4,y=2, then

[tex]c=x^2+y^2=4^2+2^2=20\\ \\a=x^2-y^2=4^2-2^2=12\\ \\b=2xy=2\cdot 4\cdot 2=16[/tex]

Fifth Pythagorean triple is (12,16,20)

6. x=4,y=3, then

[tex]c=x^2+y^2=4^2+3^2=25\\ \\a=x^2-y^2=4^2-3^2=7\\ \\b=2xy=2\cdot 4\cdot 3=24[/tex]

Sixth Pythagorean triple is (7,24,25)

7. x=5,y=1, then

[tex]c=x^2+y^2=5^2+1^2=26\\ \\a=x^2-y^2=5^2-1^2=24\\ \\b=2xy=2\cdot 5\cdot 1=10[/tex]

Seventh Pythagorean triple is (10,24,26)

8. x=5,y=2, then

[tex]c=x^2+y^2=5^2+2^2=29\\ \\a=x^2-y^2=5^2-2^2=21\\ \\b=2xy=2\cdot 5\cdot 2=20[/tex]

8th Pythagorean triple is (20,21,29)

9. x=5,y=3, then

[tex]c=x^2+y^2=5^2+3^2=34\\ \\a=x^2-y^2=5^2-3^2=16\\ \\b=2xy=2\cdot 5\cdot 3=30[/tex]

9th Pythagorean triple is (16,30,34)

10. x=5,y=4, then

[tex]c=x^2+y^2=5^2+4^2=41\\ \\a=x^2-y^2=5^2-4^2=9\\ \\b=2xy=2\cdot 5\cdot 4=40[/tex]

10th Pythagorean triple is (9,40,41)

23.

If we take the triangle on the right and put it on the left we have a rectangle, 15 by 11, so area 165.

Answer: 165

24.

Perimeter: 11 + 14 + 11 + 14 = 50

Area: 9 by 14 = 126

Step-by-step answer:

Between similar figures, if the ratio between the sides is k, then

- ratio between linear measurements, such as diagonals, perimeter, width, heights, etc, are also linear.

Therefore, if the ratio of the corresponding sides is 1:4, the ratio of their perimeters is also 1:4.

Note:

the ratio of area measurements,  or surface areas of similar solids, are proportional to k^2.

Similarly, the ratio of volumes of similar solids are proportional to k^3.

Answer:

  1.5

Step-by-step explanation:

The slope is given by ...

  (change in dependent variable)/(change in independent variable)

  = (65 -80)/(74-84) = -15/-10 = 1.5

The slope of the line of best fit is 1.5.

Answer:

The slope of the line of best fit is 1.5 degrees Fahrenheit per gallon.

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The given two points are (84,80) and (74,65).

The slope of the line of best fit is

[tex]m=\frac{65-80}{74-84}[/tex]

[tex]m=\frac{-15}{-10}[/tex]

[tex]m=1.5[/tex]

Therefore the slope of the line of best fit is 1.5 degrees Fahrenheit per gallon.

Answer: D) 5832

Step-by-step explanation:

The y values are the x values cubed. Since the x values are increasing by 3, the last x would be 18. 18 cubed is 5832.

Answer:

2x

Step-by-step explanation:

Solve the equation for a as follows:

First multiply both sides by 2a:

[tex](2a)x=-b[/tex] and then divide both sides by 2x:

[tex]a=-\frac{b}{2x}[/tex]

The denominator will be equal to 2x.

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Given that:-

The value of the denominator will be:-

x    =   -b/2a

From the given information the expression will be written as

a  =  -b / 2x

Therefore the denominator will be equal to 2x.

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Answer:

15092cm^3

Step-by-step explanation:

The total thickness of the strip of metal sheet  would be 2*10=20cm

the new radius of the cylinder would be 9/2+20=24.5cm

Volume of a cylinder: ((pi)r^2)h

the height is 8cm

Volume : (22/7)*24.5^2*8

=15092cm^3

The first attachment is one way that quadrilaterals can be classified. If you've never studied a diagram like this before, it would certainly be mysterious.

There is a little more to it in that a "kite" is not the only kind of quadrilateral with no parallel sides.

Your diagram apparently doesn't recognize the special sorts of trapezoids you might have other than isosceles.

___

The classifications on the first diagram are numbered. The numbers on the second diagram are the way I'd match up the descriptions to the bubbles in your diagram.

Answer:

(B) -8,4

Step-by-step explanation:

Answer:

(-8,4)

Step-by-step explanation:

Given in the picture is a right triangle and a square sharing one commonside

Area of triangle = area of square

ie [tex]1/2 bs = s^2[/tex] (is s is one side of square)

i.e. b = 2s where b = EA

In other words A divides line EB in the ratio 2:1

Using section formula

Coordinates of A=

[tex](\frac{2(-7)+1(-10)}{3} ,\frac{2(2)+1(-8)}{3})\\=(-8, 4)[/tex]

Answer:

  No

Step-by-step explanation:

Not all relations have either an infinite domain or an infinite range. Some have no "end behavior". A sine function, for example, continues to oscillate between -1 and +1 forever.

The graphs of some relations are simply a collection of points, so the "end behavior" would be the points at either extreme of the domain.

The answer is:

The length of the longer side of the rectangle is equal to 45 units.

To solve the problem, we need to use the formula to calculate the perimeter of a rectangle, then, isolate the variable and finally, calculate the length of the longer side.

We can calculate the perimeter of a rectangle using the following equation:

[tex]Perimeter=2Length+2Width\\[/tex]

Let be the length the longer side and the width the short side of the rectangle.

Then, substituting the given information and calculating we have:

[tex]146=2*(3x+3)+2*2x\\146=6x+6+4x\\146-6=10x\\140=10x\\\\x=\frac{140}{10}=14[/tex]

Now, calculating the long side of the rectangle, we have:

[tex]LongSide=3*14+3=45units[/tex]

Hence, we have that the length of the longer side of the rectangle is equal to 45 units.

Have a nice day!

Answer:

False

Step-by-step explanation:

False, because 3 can not be an even number; it's an odd number.  So the condition cannot be satisfied.

One number to the right of the decimal will mean there are two numbers to the left of the decimal.

When rounding to 50 as the nearest ten the number needs to be between 45 and 54.

Using the 3 numbers shown that would be 48.3

Answer:

Los Angeles

Step-by-step explanation:

Los Angeles has the least variability in temperatures.

To determine which location has the least variability in temperatures, we need to calculate the range or variance of the temperatures for both Miami and Los Angeles.

For Miami:

Temperatures: 76 75 83 73606676 81 83 85 83 87 8080 74

To calculate the range, we subtract the minimum temperature from the maximum temperature:

Range = Maximum temperature - Minimum temperature

Range = 87 - 73

Range = 14

For Los Angeles:

Temperatures: 63 62 65 72 67 | 65 | 6565 69 64 64 61 3639 62

Again, to calculate the range, we subtract the minimum temperature from the maximum temperature:

Range = Maximum temperature - Minimum temperature

Range = 72 - 61

Range = 11

Comparing the ranges, we see that Miami has a range of 14, while Los Angeles has a range of 11. Therefore, Los Angeles has the least variability in temperatures.

Learn more about Range of data here:

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Answer:

  f(-2) = 3

Step-by-step explanation:

The graph goes through the point (-2, 3), indicating the value of f(x) is 3 when x=-2.

Answer:

  A)  -12

Step-by-step explanation:

The point of intersection on the graph is (-6, -6). That is the solution to the system of equations. The sum of the solution values is ...

  (-6) +(-6) = -12

Answer:

A

Step-by-step explanation:

The solution to the system of equations is at the point of intersection of the 2 lines, that is

(- 6, - 6) ⇒ A = B = - 6, thus

A + B = - 6 + (- 6) = - 6 - 6 = - 12 → A

Answer:

a. $51,458

Step-by-step explanation:

Answer:

the correct answer is option A

Step-by-step explanation:

given,

Health insurance payment = $1,825

Life insurance per year = $ 93

paid off per year =   $2,860

monthly gross pay is = $3,890

Miguel's  get paid yearly =health insurance + life insurance + paid time off

                                        = 1825 + 93 + 2860

                                        = $ 4778

his monthly gross pay = $ 3,890

his yearly  gross pay =  $ 3,890 ×12

                                   = $ 46,680

hence total job benefit =  $ 46,680 + $ 4778

                                      = $51,458

so , the correct answer is option A

Answer:

I believe you mean what square number that is less than 100 has the most factors.  

The square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.  

1 obviously only factors to 1*1.

4, 9, 25, and 49 are square of prime numbers. If we call the original number n and the root p (for prime) each of them can only be factored as 1*n or p*p. example: 1*4, 2*2 .We can eliminate those.  

16 and 81 are not only squares, but the fourth power of a prime (2 and 3) respectively. They can be factored as 1*n, (p^3)*p, or (p^2*p^2). Example: 1*16, 8*2, or 4*4.

But 36 is 2*2*3*3 as it’s prime factoring. This allows us to find more combinations of factors: 1*36, 2*18, 4*9, 12*3, or 6*6.

Final answer:

The largest even square number smaller than 100 is 64, which is the square of 8.

Explanation:

To find an even square number smaller than 100, we can look at the squares of the even numbers less than 10, since 10² (which is 10 times 10) equals 100. Squaring each even number from 2 to 8, we get the following even square numbers: 2²=4, 4²=16, 6²=36, and 8²=64. Among these, 64 is the largest even square number that is less than 100.

Answer:

Step-by-step explanation:

Any side to side movement of a function will be reflected inside a set of parenthesis with the x.  For example, if the function was a parabola, the parent graph could be, very simply,

[tex]y=x^2[/tex]

Side to side movement would make the equation look like this:

[tex]y=(x-h)^2[/tex]

where h is the x coordinate of the vertex.

Up or down movment would make the equation look like this:

[tex]y=x^2+k[/tex] for movement upwards, or

[tex]y=x^2-k[/tex] for movement downwards.  The k represents the y coordiante of the vertex in this parabola.

Because our function has NO numbers inside the parenthesis with the f(x), but it has a -1 after, we are moving the parent graph of this function, whatever it is, down one from its starting position.

The transformation from the graph of a function f(x) describes the graph of f(x) - 1 is a vertical shift down by 1 unit

From the question, we have the following parameters that can be used in our computation:

The function f(x)

Also, we have

The function f(x) - 1

Subtracting a value from a function means that the function is shifted down

In this case, the subtracted value is 1

This means that f(x) - 1 is a vertical shift down by 1 unit from f(x)

[tex]2e^x=14\\e^x=7\\x=\ln 7[/tex]

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric sequence:

# U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

  between each two consecutive terms  and n is the position of the

  number in the sequence

- Ex: U5 = ar^4  ,  U7 = ar^6  ,  U10 = ar^9  ,  U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term  U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

Answer:

B edge

Step-by-step explanation:

Answer:

  20

Step-by-step explanation:

The ratio of rise to run is 5:2, so if the run is 8, the rise is correspondingly 4 times as much:

  rise : run = 5 : 2 = 20 : 8

A similar right triangle would be created by a run of 8 and a rise of 20.

Answer:

20

Step-by-step explanation:

Answer:

55510

Step-by-step explanation:

Answer:

A) 10

Step-by-step explanation:

The value of 8 in 2781 is in the tens place value.

The value of 8 in 948 is in the ones place value.

Note that the tens place value is x10 greater than the ones place value.

A)10 is your answer, for:

8 x 10 = 80

~

Answer:

A) 10

Step-by-step explanation:

The value of the 8, in 2781, is 10 times the value of the 8, in 948.

Answer:

2/15

Step-by-step explanation:

There is a 4/10 probability that she chooses blue the first time, but the second time it is a 3/9 chance because she didn't put the marble back so there are 9 marbles in total, 3 blue ones.

4/10 x 3/9 = 2/5 x 1/3 = 2/15

I hope this helps :)

Edit: Messed up the multiplication, whoops!

[tex]|\Omega|=10\cdot9=90\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{90}=\dfrac{2}{15}[/tex]

Answer: Option A

[tex]h(x) = -0.01 (x-150) (x + 4)[/tex]

Step-by-step explanation:

The javelin will have reached its maximum horizontal distance when it touches the ground.

Then the maximum horizontal distance occurs when the height h (x) is equal to zero.

So we must equal h(x) to zero and solve the equation for x.

Therefore the form that is most useful to determine the horizontal distance that the javelin covers is the one that is factored. Because it allows us to find the zeros of the quadratic function more easily

[tex]h(x) = -0.01 (x-150) (x + 4) = 0[/tex]

[tex]-0.01 (x-150) (x + 4) = 0[/tex]

The equation is equal to zero when [tex]x = 150[/tex] or when [tex]x = -4[/tex]

Therefore the solution is [tex]x = 150[/tex].

The horizontal distance that covers the javelin is 150 feet

Answer:

The answer is A

Step-by-step explanation:

I am 100% sure cuz I just did the test:)

[tex]n,n+1[/tex] - two consecutive integers

[tex]n+n+1=-7\\2n=-8\\n=-4\\n+1=-3[/tex]

-4 and -3

Answer:

  After you swap the top two descriptions on the right, everything matches  straight across.

Step-by-step explanation:

1. The circle described is the incircle, circumscribed by the polygon.

2. When the tangent line separates the centers of the circles to which it is tangent, it is called an internal tangent.

3. An external tangent will be parallel to or will intersect the line joining circle centers at a point not between any of those centers.

4. A tangent to a circle is coplanar with the circle and intersects it in exactly one point.

Answer:

A

Step-by-step explanation:

Answer:

The equation is: y = 5x - 268

Explanation:

We are given that:

At 73°F, the chirp is 97 times per minute .........> first point is (73, 97)

At 80°F, the chirp is 132 times per minute .......> second point is (80, 132)

The general equation of the linear line is:

y = mx + c

where m is the slope and c is the y-intercept

1- getting the slope:

The slope can be calculated using the following rule:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substitute with the given points to get the slope as follows:

[tex]m = \frac{132 - 97}{80 - 73} = 5[/tex]

The equation, now, became:

y = 5x + c

2- getting the y-intercept:

To get the y-intercept, use any of the given points and substitute in the rule we got in part 1. I will use the point (80, 132)

Therefore:

y = 5x + c

132 = 5(80) + c

c = 132 - 5(80) = -268

The equation, therefore, is:

y = 5x - 268

Hope this helps :)