Find the missing side

Find the values a, b, and c to substitute into the quadratic formula.

Notice how there are a, b, and c. Everything is left of the equal sign, leaving 0 on the right.

ax² + bx + c = 0

Notice how there are a, b, and c too, just like in standard form. After we find standard form, we can substitute a, b and c values into the quadratic formula.

[tex]\displaystyle{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} }[/tex]

Here are the steps we will follow:

Move everything to the left while keeping both sides equal.

x² + 1 = 2x – 3                 Equation from the question

x² + 1 + 3 = 2x – 3 + 3     Add three to both sides.

x² + 1 + 3 = 2x                 -3 + 3 cancels out to 0.

x² + 4 = 2x                      Simplify.

x² + 4 – 2x = 2x – 2x     Subtract 2x from both sides.

x² + 4 – 2x = 0                No numbers on the right side is the same as 0.

x² – 2x + 4 = 0                Rearrange to follow ax² + bx + c = 0.

Find a, b, and c from standard form.

ax² + bx + c = 0         Standard form

x² – 2x + 4 = 0           No number attached to x² means a = 1.

a = 1,  b = –2,  and  c = 4

Substitute a = 1, b = –2, and c = 4 into the quadratic formula.

[tex]\displaystyle{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} }[/tex]    

Here is how our formula set up should look:

[tex]\displaystyle{x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(1)(4)}}{2(1)} }[/tex]

Let's compare formula set up to the options in the question.

The denominator is 2(1). So, the answer is not option B.

Inside the square root, it says –4(1)(4). So, the answer is not option D.

This leaves us with either option A or option C.

Before the ±, it says –(–2). When simplified, –(–2) is 2.

Option C has –2. So, the answer is not option C.

Inside the square root, it says (–2)², which is equal to 2².

When solving exponents of negative numbers,

The exponent 2 is even.

(–2)² = 4

∵ (–2)² = 4 and 2² = 4

∴ (–2)² = 2²

(–2)² is the same as 2².

Therefore, the answer is option A.

Answer:

24.85 mph

Step-by-step explanation:

I hope you have a great day:)

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

         What is -4x+2>26?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

First subtract 2 on both sides, which results in

-4x>24

Now, divide by -4 on both sides:

x<-6

The inequality sign changed because we divided both sides by a negative number.

So the values of x less than -6 will make this inequality true (will satisfy the inequality).

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

Answer:

For rectangulasr prism

a. [tex]72cm^3[/tex]

b. [tex]108cm^{3}[/tex]

Step-by-step explanation:

For rectangulasr prism

a. Equation: Volume = length x width x height

length: 6cm

width: 4cm

height: 3cm

Volume = 6cm x 4cm x 3cm

Volume = 24cm x 3cm

b. Equation: A = 2[(width x length) + (height x length) + (heigth x width)]

A = 2[(4cm x 6cm) + (3cm x 6cm) + (3cm x 4cm)]

A = 2[(24cm) + (18cm) + (12cm)]

A = 2[(24cm) + (30cm)]

A = 2[(54cm)]

Answer: [tex]i\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{-5}=\sqrt{(-1)(5)}=\sqrt{-1} \sqrt{5}=\boxed{i\sqrt{5}}[/tex]

Answer:

Step-by-step explanation:

Comment

(Fans who received a baseball) = 2500

Total number of seats in Yankee Stadium = 50086

P(those who got a baseball) = 2500 / 50086

Answer P(Those who got a baseball) = 0.04991 rounded.

Answer:

38

Step-by-step explanation:

add 189+115 = 304

then 304÷8 =38

Answer:

314.16cm²

Step-by-step explanation:

please mark me as brainliest.hope this helps

Answer:

Step-by-step explanation: Parts of a circle.

Radius - the side of one slice of pizza

minor arc - The arc formed by the outer side of 3 or less slices of pizza

Diameter - the slice of pizza from side to side that passes through the center

Major arc - The arc formed by the outer side of 5 to 7 slices of pizza

semi circle - 4 slices of pizza or half of the whole pizza

Pairs:

angle BAC - Inscribed angle

Line IE - Secant

Segment AC - Chord

Arc FH - Minor arc

Angle HGF - Circumscribed angle

The complete sentences are:

A secant line is a straight line that passes through two points on a circle. The section of the line that connects two separate circle points is known as a chord. Every secant line defines a distinct chord, and each chord is in its own unique secant line.

Given:

We have circle with center O.

Now, <BAC is inside the circle.

So, <BAC is an  Inscribed angle.

then, IE is a secant as it is intersecting circle at two points

then, AC id a chord

then, Arc FH is a minor arc

and, <HGF is an Circumscribed angle as it is outside the circle.

Learn more about secant & chord here:

https://brainly.com/question/19008587

#SPJ5

Answer:

4 +311/59 answer IsD ong I know

Answer:

a.......4880

Step-by-step explanation:

b.......180 per year

Answer:

CF is a diagonal through the interior of the cube.

Reason:

The domain is the set of allowed x inputs.

The graph shows an open hole at x = 7, meaning that 7 itself isn't part of the domain. But any value smaller than this will be part of the domain. So that's why we go for x < 7.

The value x = -1 is allowed since we have a closed endpoint for one of the pieces here.

The arrow pointing to the left indicates that piece goes on forever in that direction.

Answer:

x < 7

Step-by-step explanation:

The domain of the function is less than 7 as indicated by the open dot. (a closed dot indicates ≥ or ≤)

At x = -1, it is part of the domain because there is at least one closed dot indicating it is part of the domain.

The domain of the function is :

Answer:

mean: 106900

median: 8500

mode: 7,000, 8,000, and 11,000

Step-by-step explanation:

To calculate mean, add them all together and divide the number of how many numbers it has. For median make out the sequence from small to large. For this one is 5,000, 7, 000, 7,000, 8,000, 8,000, 9,000, 10,000, 11,000, 11,000, 1,000,000. The middle is between 8,000 and 9,000 so find it's middle number. The mode is the number that appears the most. In this case 7,000, 8000, 11,000 all appeared twice so they are the mode.

Answer:

Brother has $6

I have $18

Step-by-step explanation:

To answer - you have to write the equation out. Money I have is (3x) and Brother's money is x. :)

Answer:

So basically there are the letters V, U , T, and S on each corner right? If you remove the X and cross in the middle, the shape of V, U, T, and S gives you a parallelogram. A parallelogram is a shape that has two pairs of parallel sides. The lines V and U are parallel to the lines S and T. The same goes for lines V and S; they are parallel to U and T.

Step-by-step explanation:

I hope this helped! I tried to explain the best as I could..

The quadrilateral which can be considered  as a "Parallelogram" or "Not necessarily a parallelogram. are second and fourth figure.

"The correct figures are (b) and (d)

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).

        Here the adjacent angle are given equal.

Learn more about parallelogram here:

https://brainly.com/question/14708246

#SPJ1

Answer:

6[tex]\sqrt{17}[/tex] or 24.738634

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the sides. We will only need to find the length of AB and AD, as AB = DC and AD = BC.

The picture shows the Pythagorean theorem being used to find AB and AD.

AB = [tex]\sqrt{17}[/tex]

AD = [tex]\sqrt{68}[/tex]

Now we can find the perimeter

2([tex]\sqrt{17}[/tex]) + 2([tex]\sqrt{68}[/tex]) = 6[tex]\sqrt{17}[/tex]

Answer:

The coefficient of x is 2.

Step-by-step explanation:

1) Add the numbers

7y + 4x + 4 - 2x + 8

7y + 4x + 12 - 2x

2) Combine like terms

7y + 4x + 12 - 2x

7y + 2x + 12

3) Rearrange items

7y + 2x + 12

2x + 7y + 12

Answer:

option b, 205

Step-by-step explanation:

Each dot on the line plot represents a different length of the ribbon,

To find the total length of the ribbon you add all the different length that was cut,

3(11.5) + 5(12) + 1(12.5) + 2(13.5) + 4(14) + 1(15)

34.5 + 60 + 12.5 + 27 + 56 + 15 = 205

205

hope it helps...!!!

thx for points

Answer:

Ash has 58 flowers in total

Step-by-step explanation:

Given:

-  buys 5 bunches

- each bunch contains 10 flowers

- 8 more flowers from his yard.

5 bunches times 10 flowers plus the 8 more flowers from the garden

F = 10(5) + 8

F = 50 + 8

F = 58

Answer:

Ash has 58 flowers in all

Step-by-step explanation:

Y representing = bunches of flowers  

F representing =  the flower  

1. Y=10f      

2. Y=10f                    5 x 10 = 50

3. Y=10f                   50 + 8 = 58

4. Y=10f      

5. Y-10f                      

                         f = 58

Answer:

A square is sometimes a rectangle, but a rectangle is never a square.

Answer:

  A.  Consecutive sides have opposite reciprocal slopes

Step-by-step explanation:

A rectangle is a special case of parallelogram, in which the diagonals bisect each other and are the same length, and all angles are right angles. In order to prove a quadrilateral is a rectangle, it can be shown to be a parallelogram, but one or the other of these additional characteristics must be proven.

__

A. Consecutive sides have opposite reciprocal slopes

Sides with opposite reciprocal slopes will be perpendicular. That is, the angle between them will be a right angle. If all pairs of consecutive sides meet at right angles, the figure must be a rectangle.

B. All sides are congruent

A rhombus is a quadrilateral in which all sides are congruent. It will only be a rectangle if the diagonals are the same length, or, equivalently, adjacent sides meet at right angles.

C. Opposite sides are parallel

A parallelogram will have opposite sides parallel. It will only be a rectangle if the diagonals are the same length, and/or adjacent sides meet at right angles.

D. Consecutive sides are congruent, opposite sides are not.

This seems a contradiction, as opposite sides are consecutive to the same side. (For example, sides AB and CD are both consecutive to side BC.) If we take this to mean that there are two pairs of consecutive congruent sides, then the figure may be a kite, but isn't necessarily a rectangle unless the other conditions are met.

_____

Additional comment

If sides are horizontal and vertical, the slope of the vertical sides is "undefined." It cannot be shown to be the opposite reciprocal of the slope of the horizontal sides.

Answer:

E empty set

Step-by-step explanation:

The answer is empty at

a) The difference between the temperatures is 5°c.

b) We will see that at midday, the temperature is 12°C.

We know that at midnight the temperature was T = -8°C, and at 5am the temperature was T' = -3°C.

a) First we want to find the difference between the temperatures, we can compute that directly:

T' - T = -3°C - (-8°C) = 5°C

This means that the temperature increased 5°C in that time interval.

b) At midday, the temperature was 9°C higher than at 5am, this means that:

T'' - T' = 9°C

T'' - 3°C = 9°C

Now we can solve this for T''

T'' = 9°C + 3°C = 12°C

At midday, the temperature is 12°C.

If you want to learn more about temperature.

https://brainly.com/question/25290815

#SPJ1

Answer:

  x = 20

Step-by-step explanation:

The problem tells you the relationship between time, distance, and speed. Use the given relations to find the total journey time.

__

  total time = Journey A time + Journey B time

  total time = (distance A)/(speed A) + (distance B)/(speed B)

  total time = 15/x +6/(x+4) = 1 . . . . . using the given values

Multiplying by x(x+4) we have ...

  15(x +4) +6(x) = (x)(x +4)

  21x +60 = x² +4x

  x² -17x -60 = 0 . . . . . rearrange to standard form

  (x -20)(x +3) = 0 . . . . factor the equation

  x = 20  or  x = -3 . . . values of x that satisfy the equation

We know the speed must be positive, so x = -3 is an extraneous solution.

The value of x is 20 (km/h).

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$99.931\\ r=rate\to 14\%\to \frac{14}{100}\dotfill &0.14\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (99.931)(0.14)(5)\implies I\approx 70[/tex]