1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Firlakuza [10]
2 years ago
9

Please answer and show work/explain.

Mathematics
1 answer:
MrRissso [65]2 years ago
3 0

Answer:

5. x = { -13/2, 13/2 }

6. x = { (-5/4)±(<em>i</em>√(23)/4) }

7. x = { 1 - √7, 1 + √7 }

8. z = { -9<em>i </em>,9<em>i </em>}

Step-by-step explanation:

Most quadratic equations can be graphed with the help of their x-intercepts. These x-intercepts, also known as zeroes or solutions, can be found by solving the quadratic equation. In a quadratic equation, when x is isolated, what x equals to is considered the solutions of the equation.

There are four main methods of solving quadratic equations: factoring, using the quadratic formula, using the square root method, and completing the square. I will try to solve each of these eqautions with one of the four methods.

5. 4x^2 - 169 = 0 (The Square Root Method)

<u>Quadratic equations have a standard form of ax^2 + bx + c = 0, where a, b, and c are constants. The square root method can be used if b = 0. The first step of the square root method is to make ax^2 = c. We do that by adding 169 to both sides.</u>

4x^2 = 169

<u>We then divide both sides by 4 to isolate x^2.</u>

x^2 = 169/4

<u>To get x by itself we square root both sides. </u><em><u>When doing so, the c becomes ±c because both squaring a positive and negative number gets a positive result.</u></em>

x = ±√(169/4)

<u>We then use the quotient property of square roots to make solving x much easier.</u>

x = ±(√169/√4)

x = ± 13/2

x = { -13/2, 13/2 }

6. 2(x^2) + 5x = -6 (The Quadratic Formula)

<u>The quadratic formula is a derived form of the standard form of a quadratic equation:</u>

x = (-b±√(b^2-4ac))/2a

<u>To use it, we first have to find the a, b, and c in this equation. To do this we must change this into equation into standard form by adding 6 on both sides.</u>

2(x^2) + 5x + 6 = 0

<u>Now we know that a = 2, b = 5, and c = 6. We will now subsitute this into the quadratic formula and solve for x.</u>

x = (-5±√(5^2-4*2*6))/2*2

x = (-5±√(25-48))/4

x = (-5±√(-23))/4

x = (-5/4)±(√(-23)/4)

<u>The square root of -1 is said to be </u><u><em>i</em></u><u>, an imaginary number. The square root of -23 is √(23)*√(-1) or </u><u><em>i</em></u><u>√(23).</u>

x = { (-5/4)±(<em>i</em>√(23)/4) }

I<u>f don't know imaginary numbers yet or still consider answers with negative square roots as not real, then just say that the equation has no real solutions. </u>

<u />

7. x^2 - 6 = 2x (Completing the Square)

<u>Some expressions can be factored so that it multiplies by itself. If we have (a+b)(a+b), it is said to be a perfect square trinomial, where it equals a^2 + 2ab + b^2. The same can be said for (a-b)(a-b), which equals a^2 - 2ab + b^2. Completing the square helps us use this idea to solve quadratic equations.</u>

<u>First, we need to get the quadratic formula into a^2 + bx = c form. So we mush add 6 and subtract 2x on both sides.</u>

x^2 - 2x = 6

<u>Now, in order to make a perfect square trinomial, we consider the b constant. We must add (b/2)^2 to both sides to make sure that we can have this. Only simplify the inside of the parantheses for the first (b/2)^2.</u>

x^2 - 2x + (2/2)^2 = 6 + (2/2)^2

x^2 -2x + (1)^2 = 7

<u>Now that we have a^2 - 2ab + b^2, we can change that to (a-b)^2.</u>

(x-1)^2 = 7

<u>Now look at this! It went from a completing the square problem to a square root method problem. Since we know how to solve this kind of problem, let's do it.</u>

x-1 = ± √7

x = 1 ± √7

x = { 1 - √7, 1 + √7 }

8. z^2 + 81 = 0 (The Square Root Method)

z^2 = -81

z = ±√-81

z = ±(√81*√-1)

z = ±9<em>i</em>

z = { -9<em>i </em>,9<em>i </em>}

<em />

<u>Sadly, there's no example of the factoring method, so I'll make one myself.</u>

BONUS. z^2 - 81 = 0 (Factoring)

<u>First, we make the equation into the form of (x+?)(x+?) = 0.</u>

(x+?)(x+?) = 0.

<u>In the FOIL method, (x+a)(x+b) = x^2 + x(a+b) + ab. What this means is that these two unknown factors add and multiply together to get the b and c constants of the quadratic equation respectively. So, on in the case of b equaling 0 and c equaling -81, we have to ask ourselves this: What two numbers multiply to get -81 and add to get 0? </u>

<u>First, consider the multiplicants: -1 and 81, 1 and -81, -3 and 27, 3 and -27, -9 and 9. Out of all of these, only -9 and 9 fit. </u>

(x+9)(x-9) = 0.

<u>Separate these two into their own equations equal to 0 and solve them.</u>

x + 9 = 0 => x = -9      

x - 9 = 0 => x = 9

x = { -9, 9}

You might be interested in
Determine the total cost or selling price to the nearest cent $65 video game ; 25% discount?
kodGreya [7K]

Answer:

48.75$

Step-by-step explanation:

the difference is  about 16.25$

6 0
3 years ago
Find the length of the third side. If necessary, round to the nearest tenth. 25 20 ​
Komok [63]

Answer:

15

Step-by-step explanation:

using \: pythagoras \: theorem \\ let \: the \: unknown \: side = x \\ 25 {}^{2}  = x {}^{2}  + 20 {}^{2}  \\ 625 = x {}^{2}  + 400 \\ x {}^{2}  = 625 - 400 \\ x {}^{2}  { = 225} \\ x =  \sqrt{225}   \\ x = 15 \\ lenght \: of \: the \: third \: side = 15

3 0
2 years ago
How do you substract two digits for example 60-4 only by the operator plus(+)? only digets &gt;=0 are allowed​
Olegator [25]

Answer:

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtraction is signified by the minus sign (−). For example, in the adjacent picture, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, the difference of 5 and 2 is 3, that is, 5 − 2 = 3. Subtraction represents removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.

Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is also not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Because 0 is the additive identity, subtraction of it does not change a number. Subtraction also obeys predictable rules concerning related operations such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.

Performing subtraction is one of the simplest numerical tasks. Subtraction of very small numbers is accessible to young children. In primary education, students are taught to subtract numbers in the decimal system, starting with single digits and progressively tackling more difficult problems.

In advanced algebra and in computer algebra, an expression involving subtraction like A − B is generally treated as a shorthand notation for the addition A + (−B). Thus, A − B contains two terms, namely A and −B. This allows an easier use of associativity and commutativity.

5 0
3 years ago
Find the distance between each of the following pairs of points. (1,5) and (2,3)
Lapatulllka [165]

Answer:

The distance is 2.2360....

Step-by-step explanation:

Hope this helps! Have an Amazing day!!

3 0
3 years ago
Read 2 more answers
JK and LM are straight lines. Find /NOK.<br> ( help me pls)<br>​
VashaNatasha [74]

Answer:

NOK = 58

Step-by-step explanation:

Given

JOM = 108

LON = 50

Required

Find NOK

From the attached triangle, we have:

LOK = JOM =108 --- Corresponding angles

And

LOK = LON + NOK

Substitute for LOK and LON

108= 50+ NOK

Make NOK the subject

NOK = 108 - 50

NOK = 58

8 0
3 years ago
Other questions:
  • Which shows a correct order to solve this story problem? The bus driver's route is 77.8 miles long on each of the first four day
    15·2 answers
  • Find an equivalent ratio where the total number of students is 250
    14·1 answer
  • -4.66666666667 as a fraction
    14·1 answer
  • Find the value of x. Write an equation and<br> solve, showing ALL work.
    8·1 answer
  • Plsss help if you can! I will mark you brainliest, give thanks, and 5 stars, and friend invite if you are correct!!
    15·2 answers
  • Slope between(-1,-6) and (2,-12)
    11·2 answers
  • A shipping company charges a $6.50 flat fee for a package, plus a fee based on the weight of the package. The
    11·1 answer
  • For each triangle check all that apply
    14·1 answer
  • What is the slope of the line that contains the<br> points (-6, 1) and (4,-4)?
    9·2 answers
  • Pls help will give brainliest
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!