Solve each question with the quadratic formula
6a² + 10 = 0


I know the answer but I'm not to sure how imaginary roots work. I would really appreciate if someone could explain how imaginary roots work! :)

Answers

Answer 1

Answer:

[tex]\boxed{\sf a=\cfrac{\sqrt{15i} }{3}}[/tex]

[tex]\boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}[/tex]

Step-by-step explanation:

[tex]\sf 6a^2 + 10 = 0[/tex]

We'll solve this equation using The Quadratic Formula:

[tex]\boxed{\sf \frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]

[tex]\sf 6a^2 + 10 = 0[/tex]

Substitute 6: a, 0: b, 10: c

[tex]\longmapsto\sf a=\cfrac{0\pm\sqrt{0^2-4\times 6\times 10} }{2\times 6}[/tex]

→ Square 0

→ Multiply -4 * 6= -24

→ Multiply -24 * 10 = -240

[tex]\longmapsto\sf a=\cfrac{0\pm\sqrt{-240} }{2\times 6}[/tex]

→ Take the square root of -240:

Multiply 2 * 6= 12

Now, Separate solutions:

[tex]\longmapsto\sf a=\cfrac{0\pm 4\sqrt{15i} }{12}[/tex]

Now, Separate solutions:

First, solve the equation when ± is plus:

[tex]\longmapsto \boxed{\sf a=\cfrac{\sqrt{15i} }{3}}[/tex]

___

Now, solve it when ± is minus:

[tex]\longmapsto \boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}[/tex]

__________________________________________

Answer 2

[tex]\sf\longmapsto 6a^2+10=0[/tex]

a=6b=0c=10

[tex]\sf\longmapsto a=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex](This a is root of equation)

[tex]\sf\longmapsto a=\dfrac{-0\pm\sqrt{0^2-4(6)(10)}}{2(6)}[/tex]

[tex]\sf\longmapsto a=\dfrac{\pm\sqrt{-240}}{12}[/tex]

[tex]\sf\longmapsto a=\dfrac{\pm\sqrt{240}i}{12}[/tex]

[tex]\sf\longmapsto a=\dfrac{\pm 4√15i}{12}[/tex]

[tex]\sf\longmapsto a=\dfrac{\pm √15i}{3}[/tex]

[tex]\sf\longmapsto a=\dfrac{\pm √3√5i}{3}[/tex]

[tex]\sf\longmapsto a=\pm\dfrac{√5i}{\sqrt{3}}[/tex]

[tex]\sf\longmapsto a=\pm\sqrt{\dfrac{5}{3}}i [/tex]

What is i?

i stands for iota.

[tex]\sf\longmapsto i=\sqrt{-1}[/tex]


Related Questions

BRAINLIEST
Please solve at least one of these problems. I would love it if you could do all of them but I know you probably won’t have time for it. Ty!

Answers

Answer:

Step-by-step explanation:

How do you write 1841.66666667 as money? Where does the 7 go?

Answers

Answer:

We write it as $1841.67 (Rounded)

Step-by-step explanation:

The 7 will round up to the hundredths (0.01) place.

Hoped this helped.

Solve the word problems below: When I woke up today morning, the temperature was 24 o C. Every two hours, it gets warmer by 1o C. Write an equation to represent this linear relationship.

Answers

Answer:

n + 23

24,25,26,27,28,29,30,...

The area of a triangular sail is given by the expression 1/2 bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 12 inches and h = 7 inches?

Answers

42 square inches.

Step-by-step explanation:

A = 1/2 b × h

A = 1/2 x 12 x 7

A = 6 × 7

A = 42

Pls help me asap!! Only answer if u know the correct answer! Thanks! :)

Answers

The answer is 168 feet tall!

I hope this helps, please tell me of you want a step by step, I can give one. :)

test again Add.

3/8+3/8

Answers

Answer:

3/4 or 0.75

Step-by-step explanation:

[tex] \frac{3 }{8} + \frac{3}{8} [/tex]

transform the equation

[tex] \frac{3 + 3}{8} [/tex]

calculate

[tex] \frac{6}{8} [/tex]

simplify

[tex] \frac{3}{4} [/tex]

or 0.75

paisley’s mom buys a car using a loan . she repays the loan by paying $22.032 in 48 equal monthly payments . how much is each payment ?

Answers

Answer: $459 each month

Step-by-step explanation:

Paisley's mom is paying the loan of $22,032 in 48 equal monthly payments.

In order to find how much each month's payment would be you divide the loan by 48.

22,032 ÷ 48 = 459

Paisley's mom would need to pay $459 each month for 48 months to pay off her loan.

A xerox machine makes scale copies of the pages in your math book. If the copy comes out the exact same size as the original,what do you think the scale factor is?

Answers

If the copy made by Xerox's machine is same size as the original, the scale factor will be 1.

Recall:

The scale factor = dimension of new copy / dimension of original copy.

Let's assume that one of the dimension of the original copy is 4 inches.

If the new copy is of exact same size as the original copy, therefore the new copy will still have a dimension of 4 inches.

Thus:

Scale factor = 4/4 = 1

Therefore, if the copy made by Xerox's machine is same size as the original, the scale factor will be 1.

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please dont give a useless answer

Answers

Answer:

[tex]\frac{7}{10} ,0.7[/tex]

Reasoning:

Do the inverse of adding 4/5 to isolate and find a.

[tex]1\frac{1}{2} - \frac{4}{5} =\frac{7}{10}[/tex]

Decimal Form:

[tex]1.5-0.8=0.7[/tex]

Answer:

  a = 0.7 = 7/10

Step-by-step explanation:

Subtract 4/5 from both sides.

  a + 4/5 = 1 1/2

  a + 0.8 = 1.5

  a + 0.8 -0.8 = 1.5 -0.8 . . . . subtract 4/5 from both sides

  a = 0.7 = 7/10

_____

If you like, you can solve this a couple of other ways:

1) Solve it as an integer problem.

  10a +8 = 15 . . . . . . multiply the given equation by 10 to clear fractions

  10a = 7 . . . . . . . . subtract 8

  a = 7/10 . . . . . . divide by 10

2) Use a common denominator

  a +8/10 = 1 5/10

  a = 1 5/10 -8/10 . . . . . subtract 8/10

  a = 15/10 -8/10 = (15 -8)/10 = 7/10 . . . . . convert to improper fraction

__

Additional comment

It is a good idea to get comfortable working with numbers in any form in which they are presented: decimal, fraction, mixed number, scientific notation, percentage. Knowing how to convert between forms is essential.

GIVING BRAINLIEST!! (ignore the answer i put i accidentally clicked on it) A line passes through the point (-2, 7) and has.a slope of -5.
What is the value of a if the point (a, 2) is also on the line?

Answers

the answer is -1 just believe me

miss tan has 20 boys and 15 girls in her English class.What percent of the student are girls?

Answers

Step-by-step explanation:

it's 42.85 percent that you can say 42 or maybe 43

What is the mass of 64 mL of a liquid with a
density of 2.7 g/mL?

Answers

Answer:

172.8

Step-by-step explanation:

to get density its mass over volume so if you mutiply volume by density you get the mass

SHOW WORK, please!!!!!!
A pineapple is 7 times as heavy as an orange. The pineapple also weighs 870 grams more than the orange.
What is the total weight in grams for the pineapple and orange?

Answers

Answer:

1015 g and 145 g

Step-by-step explanation:

Let pineapple  = x, orange = y

A pineapple is 7 times as heavy as an orange:

x = 7y

The pineapple also weighs 870 grams more than the orange:

x = y + 870

Compare the two equations above:

7y = y + 8706y = 870y = 870/6y = 145

Find the value of x:

x = y + 870 = 145 + 870 = 1015

[tex]\huge \bf༆ Answer ༄[/tex]

Weight of pineapple :

[tex] \boxed{ \sf1015 \: g}[/tex]

Weight of Orange :

[tex] \boxed{ \sf145 \: g}[/tex]

[tex]꧁  \:  \large \bf{ Kaul } \: ꧂[/tex]

At which root does the graph of f(x) = (x + 4)(x + 7,5) cross the x-axis?
-7
-4
4
7

Answers

Answer:

Answer: -7

Step-by-step explanation:

The roots at which the graph of f(x) =(x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] cross the x axis are -4 and -7.

What is Root of Equation?

In mathematics, a root is a solution to an equation that is usually stated as a number or an algebraic formula.

A quadratic equation's roots are the variable values that fulfil the equation. They are also referred to as "solutions" or "zeroes" of the quadratic equation.

We have If(x) = (x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] cross the x-axis then y = f(x) = 0.

Now, if f(x) = 0

then (x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] = 0

Now, calculating in separate the value of x as

x +4 =0 and x+ 7= 0

x = -4 and x = -7

Thus, the roots cross x axis at -4 and -7.

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CAN SOMEONE HELP ME PLEASE ASAP!

Answers

Answer:

2 and 3

Step-by-step explanation:

20/12 = 1.6666666

15/9 = 1.6666666

find the length of segment AB

Answers

11x-9=6x+11
11x= 6x+20
5x=20
x=4
So plug in 4 to AB 11(4)-9

The coordinates of the vertices of △PQR are P(1, 4), Q(2, 2), and R(−2, 1). The coordinates of the vertices of △P′Q′R′ are P′(−1, 4), Q′(−2, 2), and R′(2, 1).

Which statement correctly describes the relationship between △PQR and △P′Q′R′?

1. △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a translation 2 units to the left, which is a rigid motion.

2. △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.

3. △PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′.

4. △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the x-axis, which is a rigid motion.

no links please

Answers

Answer:

the Answer is:

△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

I got 100% on the quiz

The two triangles ΔPQR and ΔP'Q'R' are congruent.

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

The statement that correctly describes the relationship between △PQR and △P′Q′R′ is:

2. △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.

From the attached graph we can observe that the given Triangle PQR is reflected across the y-axis.

In this case, a translation, a reflection across the x-axis, but a reflection across the y-axis can map △PQR onto △P′Q′R′. Therefore, the two triangles are congruent.

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The difference between two integers is 6. The sum of their sqaures is a minimum. Find the 2 integers.
Answer with explanation gets brainliest.​

Answers

Answer:

3 and - 3

Step-by-step explanation:

Let the numbers are x and y.

Their difference is:

x - y = 6

Sum of their squares:

S = x² + y²

Substitute y = x - 6 into sum equation:

S = x² + (x - 6)² =      x² + x² - 12x + 36 =      2x² - 12x + 36

We observe this is a quadratic expression. It has minimum value at vertex, which is when x = -b/2a or:

x = - (-12/2*2) = 3

Then the value of y is:

y = x - 6 = 3 - 6 = - 3

What is 100,000×1,000,000

Answers

Answer:

100,000 × 1,000,000 = 1.E11

Answer:

100000000000

Step-by-step explanation:

find the measure of angle y, 38,41,19

Answers

If this is DMS then the answer is 38.68861111 degrees

What is the solution to the equation 3/4y+1/4=1+y , given the replacement set {−4, −3, −2} ?

−4
−3
−2

Answers

Answer:

-3

Step-by-step explanation:

Solution of the equation is y = -3.

What is the solution of the equation?

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation.

Given expression (3/4)y+1/4= 1+y.

simplify each term,

(3/4)y + 1/4 = 1+y

Move all terms not containing y to the right side of the equation,

(3/4)y - y = 1-1/4

(-1/4)y = 3/4

Since  both side of the expression has the same denominator, the numerators must be equal.

y = -3

Solution of the equation is y = -3.

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A glue company needs to make some glue that it can sell for $120 per barrel. It wants to use 150 barrels of glue worth $100 per barrel, along with some glue worth $150 per barrel and glue worth $190 per barrel. It must use the same number of barrels of $150 and S190 glue. How much of the $150 and $190 glue will be needed? How many barrels of $120 glue will be produced

Answers

4860 i think that is the answer

A fisherman has 420 crabs. He sold one tenth of the crabs for a party. Then he sold two-thirds of the remaining crabs to a restaurant. The fisherman estimates that he has 232 crabs left. How far off is the fisherman's estimate?

Answers

Answer:

The answer I'd 28464835383637533

April's unpaid balance is $200.15. Her APR is 15% and she has $80.50 in new transactions. What is her new balance?

Answers

Based on the information given the new balance is $283.15.

Using this formula

New balance=Principal+ [Principal ×(APR/12)]+New transaction

Where:

Principal=$200.15

APR=15%

New transaction=$80.50

Let plug in the formula

Let plug in the formula

New balance=$200.15+($200.15×(0.15/12)+$80.50

New balance=$200.15+$2.50+$80.50

New balance=$283.15

Inconclusion  the new balance is $283.15.

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Help plzz

Tap the word that "they" refers to.

Answers

Answer:Frogs

I think so…If it’s wrong and you can tell me and I’ll try correct it

Hope its correct!

;)

Have a great day!

Can someone please help solving for x

Answers

Answer:

x=6.7

Step-by-step explanation:

In relation to the given angle, we are given the triangle's opposite side and hypotenuse. Therefore, we use the sine function to set up a proportion and solve for x:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]sin(31^\circ)=\frac{x}{13}[/tex]

[tex]13sin(31^\circ)=x[/tex]

[tex]x=13sin(31^\circ)[/tex]

[tex]x\approx6.7[/tex]

So, the opposite side is about 6.7 inches

21. Paul has $900 to invest in a savings account that has an annual interest rate of 1.8%, and a money market account that pays 4.2% per year. Write a polynomial for the interest he will earn in one year if he invests x dollars in the savings account.

Answers

The polynomial that gives the interest earned after a year will have variables, exponents and constants that are joined by operators.

The interest earned after one year is 0.018·x

Reasons:

The amount Paul has to invest = $900

The annual interest rate from the savings account = 1.8%

The amount the money market account pays per year = 4.2 %

Required: The polynomial for the interest Paul earned by investing x dollars in the savings account.

Solution:

The interest earned is found using the compound interest formula as follows;

[tex]\displaystyle A = \mathbf{P \cdot \left(1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]

Where;

A = The amount in the account after one year

P = The original amount invested = x

r = The interest rate offered on the investment = 1.8% = 0.018

t = The time of the investment = 1 year

n = The number of times of application of the interest per period = Once per year

Which gives;

Interest = Amount earned = A - P

Therefore;

[tex]\displaystyle Interest, \ I = \mathbf{P \cdot \left(1 + \frac{r}{n} \right)^{n \cdot t} - P}[/tex]

Plugging in the values gives;

[tex]\displaystyle I = x \cdot \left(1 + \frac{0.018}{1} \right)^{1 \times 1} - x = x \cdot 1.018^1 - x = 1.018 \cdot x - x = 0.018 \cdot x[/tex]

The polynomial equation is therefore;

Interest, I = 0.018·x

Using the simple interest formula, we have;

[tex]\displaystyle Interest = \mathbf{\frac{P \times r \times t}{100}}[/tex]

Which gives;

[tex]\displaystyle Interest = \frac{x \times 1.8 \times 1}{100} = 0.018 \cdot x[/tex]

Interest earned by investing in the savings account for one year, I = 0.018·x

The polynomial representing the interest earned is I = 0.018·x

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what is the x intercept

Answers

Answer:

The answer is B

Is the relation a function? Explain

Answers

Answer:

No, does not pass the vertical line test

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

A function is a relation in which that one x-value (input) is related to exactly one y-value (output). For relations shown on graphs, we can use the vertical line test.

Since the line would intercept at 2 points in the graph at one point, it is not a function.

Hope this helps.

how do I find a slope that does not have zero as a point of origin​

Answers

Answer:

See answer below.

Step-by-step explanation:

Pick any two ordered pairs that is on the given graph line.

The  Slope = (the change in the y-values)/(the change in the x-values) or

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