What are the 4 ways to solve a quadratic equation?

The 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

n a triangle, the longest side (the hypotenuse) is opposite the largest angle, and the other two sides are opposite the smaller angles. According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side. So, if the longest side of Karen's triangle measures 8 inches, it means that the sum of a and b (the two shorter sides) must be greater than 8 inches. Therefore [tex]a+b > 8 inches[/tex].

For the second part of your question, only one triangle can be drawn with side lengths 3, 5, and 9. The three numbers 3, 5, and 9 form a Pythagorean triple, meaning they can be used as the lengths of the sides of a right triangle. Since the longest side (the hypotenuse) must be greater than the other two sides, the 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

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The area of the frame is 196.73 x²

What is area ?

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.

(15x)^2 = 225x^2

Area of the frame

= π (3x)²

= 28.27 x²

Metal area surrounding the frame

225 x² - 28.27 x²

= 196.73 x²

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]

The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.

Several rules for exponents are

Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!

Dividing the first number by the second using the quotient rule, it would be

= (1.782 × 10⁹) / (8.1 × 10⁶)

= (1.782/8.1) × (10⁹/10⁶)

= 0.22 × 10⁹⁻⁶

= 0.22 × 10³

In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

So,

0.22 × 10³ = 2.2 × 10²

Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².

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Answer:

One number is 5 and the other is 1.

Step-by-step explanation:

Let the numbers be x and y.  Then x + y = 6 and x - y = 4.  We must solve this system of equations:

x + y = 6

x - y = 4

Combining these equations temporarily eliminates y:

x + y = 6

x - y = 4

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

2x     = 10

Then x = 5.  Since x - y = 4,

5 - y = 4

and so y must be 1.

The solution is (5, 1).  One number is 5 and the other is 1.

Step-by-step explanation:

[tex] {x}^{2} + 3x - 5 = 0[/tex]

a =1. b = 3. c = -5

Quadratic equation

[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 \: + \sqrt{ {3}^{2} \: - 4(1)( - 5) } }{2} \\ = \frac{ - 3 \: + \: \sqrt{29} }{2} [/tex]

Note: the plus sign in the quadratic equation should read "+-"

Therefore, the roots of the quadratic equation are

[tex]\frac{ - 3 \: + \: \sqrt{29} }{2} \: \: and \: \: \frac{ - 3 \: - \: \sqrt{29} }{2} [/tex]

Answer:

68%

Step-by-step explanation:

the x & y angles are alternate angles.

The alternate exterior angle theorem states that if two lines are parallel and are intersected by a transversal, then the alternate exterior angles are considered as congruent angles or angles of equal measure.

Here, we have,

from the given figure , we get,

the x & y angles are alternate angles.

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Answer:

88 cm^2

Step-by-step explanation:

one rectangle = perimeter of 28 and times 4 equals 112 but you have to subtract 24 the perimeter of the square  and get your answer

Answer:

56 Cola-flavored gumballs remaining.

Step-by-step explanation:

There are 180 gumballs. Bob purchased 40 gumballs, which leaves 140 gumballs remaining.

There are four flavors. This is the chance (shown as a percentage) of each flavor Bob recieved:

║GR: 4 ⇒ 10%

║CH: 12 ⇒ 30%

║CO: 16 ⇒ 40%

║OR: 8 ⇒ 20%

So, how can we predict the number of Cola flavored gumballs remaining?

[There is a 40% chance of getting a Cola-flavored gumball from the machine. If we find 40% of 140, we can predict that is close to the number of Cola gumballs left in the machine]

║0.40 ⋅ 140 = 56

40% of 140 is 56, so we can predict there are 56 Cola-flavored gumballs remaining.

Answer:

It's the middle option

Step-by-step explanation:

This is an undefined problem

Answer:

x = -3

Step-by-step explanation:

Hi there!

Typically, linear equations would be organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).

However, notice how the two x-coordinates of the given points are the same. They're both -3. This means that this is a vertical line, and vertical lines are organized in this equation: x=d where d is the x-intercept (the value of x when the line crosses the x-axis).

We know that the x-intercept is -3, since all the x-coordinates of the points that a vertical line passes through are the same. Therefore, the equation of this line is x=-3.

I hope this helps!

Answer:

Cost of 500 g of standard pack = € 7.50

Cost of 1 g of standard pack = 7.50/500

Cost of 100 g of standard pack = 7.50/500 ×100

= 7.50/5

= € 1.50

Hope it helps uh dear

They have 0.875 pounds of gummy each

Just divide by 2

Answer: John is 29 years old and Jane is 36 years old.

Step-by-step explanation:

There are many parts to this problem, so let's start by defining John as x and Jane as y.

We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.

We also know that John is 7 years younger than Jane, which gives x=y-7.

Luckily, we have x defined for us, so we can directly substitute that into our equation.

[tex](y-7)+y=65[/tex]         [combine like terms]

[tex]2y-7=65[/tex]                [add both sides by 7]

[tex]2y=72[/tex]                      [divide both sides by 2]

[tex]y=36[/tex]

Now we know that y=36, we can plug that into either equations to find x.

[tex]x+36=65[/tex]                [subtract both sides by 36]

[tex]x=29[/tex]

This concludes that John is 29 years old and Jane is 36 years old.

Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).

A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.

For example, assigning a value to the wrong variable may cause a many of unexpected program errors.

These errors can be programmer mistakes or sometimes machine less memory to load the code.

if(x>=5) {

// program

}

else if(x==5) {

//program

}

else(x<=5) {

//program

}

they all do not give any error.

x=5 gave an error because it is value assigning to 5.

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Answer:

20.7 yd(rounded)

21 yd (exact)

Step-by-step explanation:

Since it goes 7 wide, do 7 x1/3 = 2.3 The 1/3rd comes from measurement given.

The length is 3 x 1/3 = 1 yd., so each level is 2.3 (repeating).

Since the height is 9, 9x2.3  = 20.7 yds (rounded)

If you want to be exact, 2.3333333333 x 9 = 21 (exact)

Answer:

n=13

Step-by-step explanation:

When multiplying two numbers with the same base, add the exponents

[tex]8^{9} *8^{4} =8^{13}[/tex]

When dividing two numbers with the same base, subtract the exponents[tex]\frac{(8^{n})^{3}}{8^{2} } =(8^{n})^{3-2}=(8^{n})^{1}=8^{n}[/tex]

So

[tex]8^{13} =8^{n}[/tex]

The bases are the same, so you can cancel them

13=n

n=13

A. ∠F corresponds to ∠F' is True.

B. Segment EE' is parallel to segment FF' is False.

C. The distance from point D' to the origin is One-third the distance of point D to the origin is True.

D. The measure of ∠E' is One-third the measure of ∠E is False.

E. △DEF ~ △D'E'F' is True.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given:

As triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'.

and, The center of dilation = (0, 0)

Also, Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).

Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)

A) ∠F corresponds to ∠F'. ( True)

B) Segment EE' is parallel to segment FF'. (False)

As they intersect each other at the origin.

C) The distance from point D' to the origin is One-third the distance of point D to the origin.    ( True)

Now, the length of DE

D = √(-9-0)² + (-9-0)²

D = 9√2

and, length of D'E'

D = √(-3-0)² + (-3-0)²

D = 3√2

Thus, DE / D'E' =  3√2/  9√2 = 1/3

D) The measure of ∠E' is One-third the measure of ∠E. ( False)

E)  △DEF ~ △D'E'F'.  ( True)

As they are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

Example of perfect square trinomial is: x² + 6x + 9 it is expressed as

(x + 3)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Example:

  x² + 6x + 9

= x² + 3x + 3x + 9

= (x +3) (x + 3)

= (x + 3)²

so, this is a perfect square trinomial.

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Answer:

100

Step-by-step explanation:

hope this helps

Answer:

I'm pretty sure the answer is B.

Step-by-step explanation:

so you multiply 3x4 and get 12. Then you multiply 5x11 and get 55. last but not least multiply 12 and 55 and get 660 so yeah hope it helps

Explanation:

When solving a function, you plug in the given [tex]x[/tex]-value (what's inside the parentheses next to the [tex]g[/tex] or [tex]f[/tex]) into the corresponding equation (what [tex]f(x)[/tex] and [tex]g(x)[/tex] are set equal to).

Before starting the worksheet, take a simpler example:

Given the function [tex]h(x) = x + 2[/tex],

the following work solves for [tex]h(3)[/tex].

[tex]h(3) = 3 + 2[/tex]

[tex]h(3) = 5[/tex]

Essentially, to solve for the value of a function for a given [tex]x[/tex]-value, simply plug in that value in for [tex]x[/tex] and simplify the resulting expression.

Onto problem 14 from the given worksheet:

We are given [tex]f(x) = 3x + 2[/tex] and are asked to solve for [tex]f(4)[/tex].

Hence, all we have to do is plug [tex]4[/tex] in for [tex]x[/tex]:

[tex]f(4) = 3(4) + 2[/tex]

[tex]f(4) = 12 + 2[/tex]

[tex]f(4) = 14[/tex]

You can apply this concept to the rest of the problems.

Answer:

D. 4x + y ≥ 4

Step-by-step explanation:

Answer:

- ANTIFRAGILE -

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

가시밭길 위로 riding, you made me boost up (ah-ah-ah-ah)

거짓으로 가득 찬 party 가렵지도 않아

내 뒤에 말들이 많아, 나도 첨 듣는 내 rival

모두 기도해 내 falling 그 손 위로 I'ma jump in

Yes, gimme that

걸어봐 위엄 like a lion

눈빛엔 거대한 desire (nan-na-na-eh)

더 부어 gasoline on fire

불길 속에 다시 날아 rising (nan-na-na-eh)

잊지 마, 내가 두고 온 toe shoes

무슨 말이 더 필요해?

무시 마, 내가 걸어온 커리어

I go to ride 'til I die, die

더 높이 가줄게

내가 바랐던 세계 젤 위에 (ah-ah)

떨어져도 돼

I'm anti-fragile, anti-fragile (ah-ah)

난 지금 on my way

갖다버려 줘 너의 fairy tale (ah-ah)

Now you know my name

I'm anti-fragile, anti-fragile

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

Lovey, lovey, lovey

Dovey, dovey, dovey

멋대로 정하네 나란 애에 대해

I don't know what to say, I can't feel it

뜨거운 관심은 환영, 귀여운 질투는 go ahead

줄 달린 인형은 no thanks 내 미랠 쓸 나의 노래

Yeah, gimme that

걸어봐 위엄 like a lion

눈빛엔 거대한 desire (nan-na-na-eh)

더 부어 gasoline on fire

불길 속에 다시 날아 rising (nan-na-na-eh)

잊지 마, 내가 두고 온 toe shoes

무슨 말이 더 필요해?

무시 마, 내가 걸어온 커리어

I go to ride 'til I die, die

더 높이 가줄게

내가 바랐던 세계 젤 위에 (ah-ah)

떨어져도 돼

I'm anti-fragile, anti-fragile (ah-ah)

난 지금 on my way

갖다버려 줘 너의 fairy tale (ah-ah)

Now you know my name

I'm anti-fragile, anti-fragile

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

We can break it baby

Rock it, twist it, lock it baby

All I know is you can't chain me

'Cause I'm gonna break out

Gonna, gonna break out, out

We can break it baby

Rock it, twist it, lock it baby

All I know is you can't chain me

'Cause I'm gonna break out

Gonna, gonna break out, out (whoa-uh-oh-oh!)

더 높이 가줄게

내가 바랐던 세계 젤 위에 (ah-ah)

떨어져도 돼

I'm anti-fragile, anti-fragile (ah-ah)

난 지금 on my way

갖다버려 줘 너의 fairy tale (ah-ah)

Now you know my name

I'm anti-fragile, anti-fragile

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

- song by Le Sserafim

- song title : anti fragile

- stan Le Ssefarim for a better life <3

xoxo

Step-by-step explanation:

To solve complex fractions there are two methods -

1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.

2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.

What is a complex fraction?

A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.

There are two ways to solve a complex fraction -

Method 1 : Take an example - (1/3-1/4)/(1/8+1/2)

Step 1 - If necessary, combine the denominator and numerator into a single fraction.

Add the numerator -

=1/3-1/4

=(4-3)/12

=1/12

Add the denominator -

=1/8+1/2

=(1+4)/8

=5/8

Combine back to form a complex fraction -

=(1/12)/(5/8)

Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.

Step 3: Simplify the rational expression if necessary.

=(1/12)×(8/5)

=8/60

=2/15

Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]

Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.

(x^2-25)=(x+5)(x-5)

The denominator of the denominator’s fraction  has the following factor -

(x-5)

Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -

(x+5)(x-5)

By multiplying the LCD by the numerator and denominator -

=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]

=(2x+1)/(2x+1)(2x-1)(x+5)

Step 2 - Simplify the rational expression if necessary.

=(2x+1)/(2x+1)(2x-1)(x+5)

=1/(2x-1)(x+5)

Therefore, there are two methods to solve complex fractions.

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Answer:

$6.23

Hope this helps! :)

The residual of the given situation is 0.8

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.

Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,

Finding the actual value,

y = 0.66 × 75 + 33.3

y = 82.8

The predicted value = 82

Residual = actual y value − predicted y value

Therefore,

Residual = 82.8-82 = 0.8

Therefore, y = 0.8

Hence, the residual of the given situation is 0.8

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Answer:

92°

Step-by-step explanation:

We can say that the angle that is of x degrees is an inscribed angle because its vertex is on the circle and its sides are made up of rays. When you have an inscribes angle, it measures exactly half the angle it intercepts. In this case that angle is 184°. So, because of this we can say:

x = 184° / 2

x = 92°