Which congruence criteria is met in the following scenario?

SAS
SSS
None, because SSA is not a triangle congruence criteria.
ASA
AAS

Answer:

1a 2dm²= 20000mm² 3dm²=30000mm²

b 18898.8194926 m²

c 0.0054 km²= 540000 dm²

d 1.21931784007 km²

2a 30dm²=3000cm²=300000mm²

b 560cm²=56000mm²

c 7.31cm²=731mm²

Answer: The slope is -1 because this equation is already in y=mx+b so we dont have to apply the y2-y1 over x2-x1 formula you can easily identify the slope when its in y=mx+b because the slope always has a x after the number for example: 4x

Answer:

It is the coefficient of the x, when the y is isolated. In this case it is -1.

[tex]\underline{\bf{Given \:equation:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow ax^2+by+c=0[/tex]

[tex]\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.[/tex]

[tex]\sf We\:know,[/tex]

[tex]\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}[/tex]

[tex]\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}[/tex]

[tex]\underline{\large{\bf Identities\:used:-}}[/tex]

[tex]\boxed{\sf (a+b)^2=a^2+2ab+b^2}[/tex]

[tex]\boxed{\sf (√a)^2=a}[/tex]

[tex]\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}[/tex]

[tex]\boxed{\sf \sqrt{\sqrt{a}}=a}[/tex]

[tex]\underline{\bf Final\: Solution:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}[/tex]

[tex]\bull\sf Apply\: Squares[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}[/tex]

[tex]\bull\sf Put\:values[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}[/tex]

[tex]\bull\sf Simplify[/tex]

[tex]\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}[/tex]

[tex]\underline{\bf More\: simplification:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}[/tex]

[tex]\underline{\Large{\bf Simplified\: Answer:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}[/tex]

The value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Roots of a quadratic equation

Given the quadratic equation ax² + bx + c, the sum and product  of the roots are expressed as:

Get the value of the radical expression [tex]\sqrt{\alpha } +\sqrt{\beta } [/tex]

Taking the square of the expression will give:

Take the square root of both sides:

[tex]\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\ \sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\[/tex]

Substitute the product and the sum values into the expression to have:

[tex]\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Hence the value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Learn more on the roots of equation here: https://brainly.com/question/25841119

Answer: the

Step-by-step explanation: your so broke you cant even afford lunch

Step-by-step explanation:

Given,

the radius(r)of the cone's base = 8 cm

the height(h)of the cone = 8 cm

then the volume of cone

= 1/3 πr²h

= (1/3×22/7×8²×8 (substituting the value of r and h )

=(1/3×22/7×64×8)cm³

=(12544/21)cm³

=597.333cm³(ans)

If you face any doubt related to the solution please ask me

The volume of the cone is 536.38 cubic cm if the radius of the cone is 8 cm and the height of the cone is 8 cm.

The volume of a cone is the amount of space possessed by a cone in a three-dimensional plane. A cone contains a circular base, which suggests the base is made of a radius and diameter.

The volume can be defined as a three-dimensional space enclosed by an object or thing.

The formula for the volume of the cone,

[tex]\rm V=\dfrac{1}{3} \pi r^2h[/tex]

r = radius of the circular base

h= perpendicular height of the cone

Here, r = 8 cm

h = 8 cm

So the volume of the given cone will be,

[tex]\rm V=\dfrac{1}{3} \pi r^2h\\\\\\=\dfrac{1}{3}\times\dfrac{22}{7}\times8^2\times8\\\\\\[/tex]

V  = 536.38 cubic m

Volume =536.38 cubic cm

Thus, the volume of the cone is 536.38 cubic cm if the radius of the cone is 8 cm and the height of the cone is 8 cm.

To know more about the cone please follow:

brainly.com/question/16394302

#SPJ2

Using function concepts, it is found that:

A function f(x) has an inverse if, and only if:

[tex]f(a) = f(b) \leftrightarrow a = b[/tex]

In this problem:

To learn more about the use of graphs to verify if a function is invertible, you can take a look at https://brainly.com/question/13160937

Answer:

(2,-5)

Step-by-step explanation:

See attachment

One can also solve this by calculation:

y=2x-9

y=-2x-1

-

Rearrange either equation to find x.  I'll use the first:

y=2x-9

2x = y+9

x = (y+9)/2

Now use this value of x in the second equation:

y =  -2x-1

y =-2((y+9)/2)-1

y = (-2y-18)/2)-1

y = -y -9 - 1

2y = -10

y = -5

Now use -5 for y in the rearranged equation:

y =  -2x-1

-5 =  -2x-1

-2x = -4

x = 2

Solution is (2,-5)

But the question wants a graph solution, which is also fun when you use DESMOS.

Step-by-step explanation:

the average rate of change is

(f(x2) - f(x1)) / (x2 - x1)

(a)

(f(4) - f(-6)) / (4 - -6) = (3 - 1) / (4 + 6) = 2 / 10 = 1/5

(b)

(f(2) - f(-2)) / (2 - -2) = (-1 - -3) / (2 + 2) = (-1 + 3) / 4 = 2/4 = 1/2

Applying the equation for the area of the trapezoid, it is found that the height is of 10 cm.

The area of a trapezoid is half the multiplication of the sum of the bases and the height, that is:

[tex]A = \frac{h}{2}(b_1 + b_2)[/tex]

For this problem, we have that: [tex]A = 205, b_1 = 20, b_2 = 21[/tex], hence:

[tex]A = \frac{h}{2}(b_1 + b_2)[/tex]

[tex]205 = \frac{h}{2}(20 + 21)[/tex]

[tex]20.5h = 205[/tex]

[tex]h = \frac{205}{20.5}[/tex]

[tex]h = 10[/tex]

The height is of 10 cm.

To learn more about area of a trapezoid, https://brainly.com/question/9918120

Answer:

The height of trapezoid is 10 cm.

Step-by-step explanation:

Given :

To Find :

Using Formula :

[tex]{\star{\small{\underline{\boxed{\sf{\red{Area_{(Trapezoid)} = \dfrac{1}{2} \Big(b_1 + b_2\Big)h}}}}}}}[/tex]

Solution :

Substituting all the given values in the formula to find height of trapezoid :

[tex]{\dashrightarrow{\small{\sf{Area_{(Trapezoid)} = \dfrac{1}{2} \Big(b_1 + b_2\Big)h}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \Big(20 + 21\Big)h}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \Big( \: 41 \: \Big)h}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{1}{2} \times 41 \times h}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{205 = \dfrac{ 41}{2}\times h}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{h = 205 \times \dfrac{2}{41}}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{h = \cancel{205} \times \dfrac{2}{\cancel{41}}}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{h =5 \times 2}}}}[/tex]

[tex]{\dashrightarrow{\small{\sf{h =10 \: cm}}}}[/tex]

[tex]{\star{\small{\underline{\boxed{\frak{\pink{h =10 \: cm}}}}}}}[/tex]

Hence, the height of trapezoid is 10 cm.

[tex]\rule{300}{1.5}[/tex]

Answer:

32 degrees

a triangle is = to 180 degrees

Answer:

Step-by-step explanation:

Other correct expressions:

t = r/s

s = r/t

------------------

Choices

1)  t = s/r   No

2) t = rs     No

3)  s =r/t    Yes

4)  s = rt    No

The equation that is equivalent to the given equation is [tex]s = r/t[/tex] and this can be determined by using the arithmetic operations.

Given :

Equation is [tex](r = st)[/tex].

The following steps can be used in order to determine the equation that is equivalent to the given equation:

Step 1 - Write the given equation.

[tex]r = st[/tex]    --- (1)

Step 2 - The arithmetic operations can be used in order to determine the equation that is equivalent to the given equation.

Step 3 - Now, divide 't' on both sides in the equation (1).

[tex]\dfrac{r}{t} = \dfrac{st}{t}\\\\\\dfrac{r}{t}=s[/tex]  

Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/11897796

[tex] (\frac{x + 1}{x} ) ^{2} \\ = \frac{ {(x + 1)}^{2} }{ {x}^{2} } \\ = \frac{ (x + 1)(x + 1) }{ {x}^{2} } \\ = \frac{ {x}^{2} + 2x + 1}{ {x}^{2} } [/tex]

Hope you could get an idea from here.

Doubt clarification- use comment section.

Answer:

25.93%

Step-by-step explanation:

Percent change formula is [tex]\frac{(V_2-V_1)}{|V_1|}[/tex]x 100

v2 = value 2

v1 = Value 1

now you substitute in.

[tex]\frac{68-54}{|54|}[/tex]x 100

[tex]\frac{14}{54}[/tex]x100

0.259259x100

= 25.9259% or 25.93%

Answer:

the first option i think

Step-by-step explanation:

If earth did not tilt and orbited in an upright position around the sun, there would be minor variations in temperatures and precipitation throughout each year as Earth moves slightly closer and farther away from the sun. Basically, we would not have any seasons.

Answer:

Assuming you're saying the earth is flat in hence scenerio it would be hotter or. Colder depending how far the sun's placement is from the earth

Step-by-step explanation:

Closer to sun warmer you are

Shift in moon causes water drought or water rise

Answer:

Here you go...

Step-by-step explanation:

You have 4, and you have 5.

You have 4+2 and you have 5+1

So, you take a 1 from the 2 in the first problem, which gives u 4+1 that equals 5.

Therefore, if u put the first equation in a simpler form then you get 5+1 with the other equation. So it would look like 5+1=5+1.

FURTHERMORE, 4+2= 5+1 (because you simplify 2 into a 1).

So. 5+1 equals 5+1. (which is common sense... 5+1= 6.)

Step-by-step explanation:

Some expressions that are equivalent to this is: 1 - 1/5; 2 - 1  1/5; 3 - 2  1/5; etc.

Answer:

the variables mean (1)

Step-by-step explanation:

you need to divide

Answer:

equals y<5?

Step-by-step explanation:

i dont think this will help but i hope it does help

Answer:

The First Table

Step-by-step explanation:

All values can be said to be directly proportional to one another being multipled by 3.

Given that the total amount of land in acres is 538

The problem statements requires us to divide the total amount of land into 34 places, the number of whole parts is 15 acres

Mathematically we have

538/34 = 15.823

But we are required to return the whole parts, therefore, let us ignore the values that comes after the decimal point. we have 15

Learn more about division of numbers:

https://brainly.com/question/17220365

Answer:

by getting the solution

Step-by-step explanation:

Answer:

  1.728×10¹⁵

Step-by-step explanation:

You may recall from 3rd grade that multiplying by 10 adds a zero to the right of a number (moves the decimal point 1 place to the right).

An exponent is used to signify repeated multiplication. These facts together are used to translate to/from scientific notation.

  10 = 1 × 10

  100 = 1 × 10 × 10 = 1 × 10²

__

Continuing in like fashion, 5.4×10⁸ represents 5.4 × (1 followed by 8 zeros).

Similarly, 3.2×10⁶ = 3.2 × (1 followed by 6 zeros)

The product will be ...

  (5.4×10⁸)×(3.2×10⁶) = (5.4×3.2) × (1 followed by 8+6 = 14 zeros)

  = 17.28 × 10¹⁴

  = (1.728 × 10) × 10¹⁴ . . . moving the decimal point so there's 1 digit to its left

Adding that extra zero into the count we already have, this becomes ...

  = 1.728×10¹⁵

_____

Additional comment

Your scientific or graphing calculator will have a mode for showing numbers in scientific notation. You can enter these numbers directly into your calculator and have it show you the result in scientific notation.

Or, you can use a spreadsheet with appropriate output cell formatting.

Answer:

1.728×10¹⁵ is the answer

Answer:

w is 22.5°

See solution in the photo

Answer:

22.5⁰

Step-by-step explanation:

<Q = <S = 5w⁰

<R + <S = 180 (Linear pair)

3w + 5w = 180

8w = 180

w = 180/8

w = 22.5⁰

Answer:

y=3

Step-by-step explanation:

m=0

b=3

[tex]\dfrac{10}{12} = \dfrac{10 \times \tfrac 12 }{12 \times \tfrac 12} =\dfrac{5}6[/tex]

Answer:

Step-by-step explanation:

Conclusion:

Therefore, the simplified form of 10/12 is 5/6.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

i think original price Php656.25

Step-by-step explanation:

original price Php x

80%x = 575

x = 575×100/80

x = 656.25

original price Php656.25

Answer:

what is that i dont answering this sorry

81/1000

hope this helps!

Answer:

i think 2²m² is answer. you are correct, my sweetie !

Answer:

c)

[tex] {2}^{2} {m}^{2} [/tex]

Step-by-step explanation:

2 × 2 =4 it can also be written as 2^2( 2 squared) which also equals 4

same with m