Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Solve Using The Quadratic Formula. Show All Work. Write Each Solution In Simplest Form. No Decimals.

Answers

Answer 1

Given:

The given quadratic equation is:

[tex]12a^2+9a+7=0[/tex]

To find:

The solution for the given quadratic equation in simplest form by using the quadratic formula.

Solution:

Consider a quadratic equation is defined as [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:

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

The given quadratic equation is:

[tex]12a^2+9a+7=0[/tex]

We have, [tex]a=12,b=9,c=7[/tex]. Using the quadratic formula, we get

[tex]x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}[/tex]

[tex]x=\dfrac{-9\pm \sqrt{81-336}}{24}[/tex]

[tex]x=\dfrac{-9\pm \sqrt{-255}}{24}[/tex]

[tex]x=\dfrac{-9\pm i\sqrt{255}}{24}[/tex]              [tex][\because \sqrt{-a}=i\sqrt{a}][/tex]

The solutions of the given equations are [tex]x=\dfrac{-9-i\sqrt{255}}{24}[/tex] and [tex]x=\dfrac{-9+i\sqrt{255}}{24}[/tex].

Hence, the correct option is B.


Related Questions

•25 POINTS•

-A
-B
-C

Answers

Answer:

SaS

Step-by-step explanation:

The answer is c-sas

62 less than j i need to know this answer immediately please

Answers

Answer:

62>j

Step-by-step explanation:

mrk me brainliest plz

4
Drag each option to the correct location on the image.
Match the expenses to their respective categories.
Need
tuition and fees
staple foods
Want
Lamborghini
vacation
lavish wedding

Answers

Answer:

NEED:

Tuition and Feesstaple foods

WANT:

VacationLamborghini Lavish Wedding

Step-by-step explanation:

Right on Plato! <3

Have a wonderful day!

The needs listed are tuition and fees and staple foods, while the wants are a vacation, a Lamborghini, and a lavish wedding.

The listed needs and wants reflect different aspects of a person's life and priorities. "Tuition and Fees" and "Staple Foods" are necessities that are essential for a person's survival and well-being.

On the other hand, "Vacation," "Lamborghini," and "Lavish Wedding" are desires that are often seen as luxury items or experiences. While having wants is normal and human, it is important to understand that not all wants can be fulfilled, and it is equally important to prioritize needs over wants. Having a balanced approach to spending, budgeting, and financial planning can help ensure that both needs and wants can be met in a sustainable manner.

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The degrees of freedom for a contingency table with 10 rows and 11 columns is
O 100 O 110 O 21 O 90

Answers

Essentially, a contingency table with 10 rows and 11 columns has (D) 90 degrees of freedom.

What is a contingency table?

A contingency table is a matrix-form table that shows how often different combinations of variables appear.

It's really popular in survey research, business intelligence, engineering, and scientific research. Basically, a contingency table with 10 rows and 11 columns has 90 degrees of freedom.

They are also sometimes known as two-way frequency tables and are used to show how often different combinations of variables occur.

A contingency table gives you an idea of how two variables relate to each other.

It displays one categorical variable along the rows and another categorical variable along the columns. It can help point out any interactions between them.

Therefore, essentially, a table with 10 rows and 11 columns has (D) 90 degrees of freedom.

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Complete question:

The degrees of freedom for a contingency table with 10 rows and 11 columns are:

A. 100

B. 110

C. 21

D. 90

Meri is making birdhouses. Each birdhouse uses 58 yard of wood. What is the total length of wood Meri will need to make 12 birdhouses? Drag each of the numbers from the box to complete and solve the equation. Each number will be used once

Answers

Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.

Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:

length of wood per birdhouse x number of birdhouses = total length of wood

So, in this case, we can substitute the given values in the formula:

58 yards x 12 birdhouses = 696 yards

This means Meri needs 696 yards of wood to make 12 birdhouses.

This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.

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Help please! I need to know if it’s a function or not!! Thank you!

Answers

Answer:

The table represents a function and the slope is -1/2

Step-by-step explanation:

Here, we want to know if the given table is a function

For a relation to be a function, no two y values have same x value

however, 2 x values can have same y value

Looking at the table, we can conclude that what we have is a function

To find the slope, we select any two points and apply the slope formula

m = (y2-y1)/(x2-x1)

(x1,y1) = (6,-2)

(x2,y2) = (-2,2)

m = (2 -(-2))/(-2-6) = 4/-8 = -1/2

Find the domain and range of the function graphed below. PLEASE SHOW YOUR WORK!!

Answers

The domain and range of the function on the graph are:

D: [-2, 1)R: [0, 4]

How to find the domain and range of the function below?

Remember that for any function y = f(x), we define the domain as the set of possible inputs (possible values of x) and the range is the set of the possible outputs of the function (possible values of y).

To find the domain we need to look at the horizontal axis. The minimum is at x = -2 with a colored circle, so x = -2 belongs to the domain.

The largest value is at x = 1, now with an open circle, then this value does not belong to the domain. Thus the domain is:

D: [-2, 1)

For the range we need to look at the vertical axis, the minimum is at zero and the maximum at 4, then the range is:

R: [0, 4]

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Given the expression 7p + 5q + 4p - 2q, what is the result of combining the like terms?

14pq

11p + 3q

11p + 7q

12p + 2q

Answers

Answer:

11p+3q

Step-by-step explanation:

Help i dont get this

Answers

substitute the place of the X

help me please I’ll give BRAINLYIST. A person runs 1 mile in
in 1/2 hour. The
person's speed is miles per hour

Answers

Answer:

since speed is miles per hour it would be s=1/1/2 so it would be 2mph

The ratio of boys to girls at a local sports club is 3 to 1. If there are 45 girls, how many boys are
there?

Answers

Answer: 135 boys

Step-by-step explanation:

Multiply 3*45 since you know the number of boys is 3 times more than the number of girls.

Angles A and B are complementary. If mL A = 2x + 22 and mL B = 46 . Solve for x to find the measure of L and A

Answers

Answer:

x = 11

m∠A = 44°

Step-by-step explanation:

Complimentary angles total 90

(2x + 22) + 46 = 90

Subtract 46 from both sides

2x + 22 = 44

Subtract 22 from both sides

2x = 22

Divide both sides by 2

x = 11

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

m∠A = 2x + 22

m∠A = 2(11) + 22

m∠A = 44°

Answer:

x = 11

∡A = 44°

Step-by-step explanation:

2x+22 + 46 = 90

2x + 68 = 90

2x = 22

x = 11

∡A = 2(11)+22 = 44°

if the center of a circle is (-5, -8) and contains the point (16, 68) what is the equation ?

Answers

Answer:

[tex](x+5)^2+(y+8)^2=6217[/tex]

Step-by-step explanation:

Hi there!

Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at (h,k) and r is the radius

1) Plug the center of the circle into the equation

Center: (-5,-8)

[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-(-8))^2=r^2\\(x+5)^2+(y+8)^2=r^2[/tex]

2) Determine r²

Plug in the given point (16,68)

[tex](x+5)^2+(y+8)^2=r^2\\(16+5)^2+(68+8)^2=r^2\\(21)^2+(76)^2=r^2\\441+5776=r^2\\6217=r^2[/tex]

Therefore, r² is equal to 6217. Plug this back into [tex](x+5)^2+(y+8)^2=r^2[/tex]:

[tex](x+5)^2+(y+8)^2=6217[/tex]

I hope this helps!

What’s the gcf of 18 and 36

Answers

Answer: 18

Step-by-step explanation:

18*1=18

18*2=36

Mark invests $1500 in an account that pays 5.7% interest compounded continuously. Assuming no deposits or withdrawals are made, how much money will be in the account after 10 years?​

Answers

Answer:

$2,611.21

Step-by-step explanation:

A = P(1 + r/n)^nt

A = 1500(1 + 0.057/1)¹⁰

A = 1500(1.057)¹⁰

A = 1500(1.740803988528..)

A = 2611.205982792..

A ≈ $2,611.21

______________________

Where A is the total amount including interest, P is the initial amount or principle, r is the rate, n is how many times it is compounded per year, and t is the time in years.

4/5 + 3/4= asap PLEASEEE

Answers

31/20 or 1 11/20 they the same

The graphs of lines f an g are shown on the grid. Write a system of equations to represent this graph.

Answers

The Equation of line F is y= -9/2x  + 59/2.

The Equation of line G  is y = 1/10 x .

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

For Line F:

slope = -9 /2

and, Equation of line F as

y - (-2) = -9/2 (x -(7))

y + 2= -9/2( x- 7)

y = -9/2x + 63/2 -2

y= -9/2x  + 59/2

For Line G:

Slope = (0 -(1))/ ( 0-(10))

slope = 1/10

and, Equation of line G as

y - (1) = 1/10 (x -10)

y-1 = 1/10 x - 1

y = 1/10 x

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Multiply.
Your answer should be a monomial in standard form.
{(4z^3)(-3z^3)}=(4z
3
)(−3z
3
)

Answers

The required simplified expression as a monomial is given as -12[z⁶].

What is a polynomial function?

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,

Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]

Thus, the required simplified expression as a monomial is given as -12[z⁶].

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the diffrence between the roots of the equation 2x^2-5x+c=0 is 0.25 find c

Answers

Answer:

c = 3.09375

Step-by-step explanation:

Standard for of quadratic equation:

ax² + bx + c = 0

We have

2x² - 5x + c = 0

Sum of the roots

x₁ + x₂ = - b/a = -(-5)/2 = 2.5

Product of the roots

x₁x₂ = c/a = c / 2

We have:

x₁ - x₂ = 0.25

The square of the above is:

(x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂

Substitute known values and solve for c:

0.25² = (2.5)² - 4(c/2) 2c = 6.25 - 0.06252c = 6.1875c = 3.09375

Answer:

c = 3.09375

Step-by-step explanation:

Factored form of a quadratic equation

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

a is the leading coefficient[tex]r_1[/tex] and [tex]r_2[/tex] are the roots

Given quadratic:

[tex]2x^2-5x+c=0[/tex]

Therefore, the leading coefficient is:

[tex]\implies a=2[/tex]

Substitute the value of a into the formula:

[tex]\implies y=2(x-r_1)(x-r_2)[/tex]

Expand:

[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]

Compare the coefficients of x:

[tex]\implies -(2r_2+2r_1)=-5[/tex]

[tex]\implies 2r_2+2r_1=5[/tex]

[tex]\implies r_2+r_1=2.5[/tex]

If the difference between the roots is 0.25 then:

[tex]\implies r_2-r_1=0.25[/tex]

Add the two root equations to eliminate r₁:

[tex]\implies 2r_2=2.75[/tex]

[tex]\implies r_2=1.375[/tex]

Substitute the found value of r₂ into one of the root equations and solve for r₁:

[tex]\implies 1.375-r_1=0.25[/tex]

[tex]\implies r_1=1.375-0.25[/tex]

[tex]\implies r_1=1.125[/tex]

As c = 2r₁r₂ then:

[tex]\implies c=2(1.125)(1.375)[/tex]

[tex]\implies c=3.09375[/tex]

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60% of the animals at a pet shop are dogs. If there are 42 dogs at the shop, then how many animals are there altogether?
25
70
45
50​

Answers

Answer:

70

Step-by-step explanation:

The formula for this question is

60/100 * x = 42

Look carefully at how this is written. You have so many pets (x) in the shop.

60 % of them are dogs. But that 60% we are told is also how many animals are dogs and that is 42.

So you have two facts meaning the same thing.

Multiply the equation by 100

100 * 60/100 *x = 42 * 100

60x = 4200    

Divide by 60

x = 4200/60

x = 70

The total number of animals was 70

Write the answer to 3^4 x 3^7
(i) in the form 3^x
(ii) as an integer

Answers

Answer:

I)3^4 x 3^7=3^4+7(b/c the base is similar)

3^4 x 3^7=3^11

Ii) first 3^4=3x3x3x3=81

3^7=2187

then 81 x 2187=177147

Enter the fraction as a decimal and a percent
2
5
The decimal representation is
The percent representation is

Answers

Answer:

Percent is 40%

the decimal is .40

Step-by-step explanation:

1/5 = 20%/.20

So if 1/5 is 20% 2/5 should just have 20% more resolving in 40% or .40

What is simple negation give 5 examples?

Answers

Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .

Examples of negation are ,

The negation of P is ∼P.The negation of A ^ B^ C is ∼( A ^ B ^ C ).The negation of A is ∼( A ).The negation of Y ^ VB is ∼( Y ^ VB ).The negation of 6 ^ 7is ∼( 6 ^ 7).

Logical operations are performed to check the trueness of an expression.

These are generally Boolean expressions or algebraic functions.

A negation of a basic assertion is made by  inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.

Under negation, what was true becomes false and the vice - versa.

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Evaluate: Percents Benita answered 85% of the test questions correctly. If she answered 9 questions incorrectly, how many questions were on the test?


It is urgent. ​

Answers

Answer:

60

Step-by-step explanation:

What is the equation of the line in slope-intercept form that has a slope of 6 and a y-intercept of 1/2


- I have struggled with this for an hour
-I have been taking tutoring and still need help -it's just not clicking

Answers

Answer: y = 6x + 1/2

Given the information, use the slope-intercept formula to help you find the equation

1. The slope-intercept formula is y = mx + b. M represents the slope in this equation and b represents the y-intercept. This means you just need to replace m and b with the information they’ve given you. So replace m with 6 and b with 1/2. This should look like y = 6x + 1/2.

What is not a polynomial class 10?

Answers

A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.

As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.

There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.

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cual es la raiz cuadrada de 94?

Answers

Answer:

9.7(aproximado)

Step-by-step explanation:

Aquí,

[tex] \sqrt{94} [/tex]

= 9.69......

= 9.7(aproximado)

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 121 kilograms. A
delivery of 6 large boxes and 2 small boxes has a total weight of 136 kilograms. How much does each type of box weigh?
Weight of each large box: [kilogram(s)
Weight of each small box: kilogram(s)
?

Answers

Answer:

136 yhdiby8sruygftdtuggdyubh

Answer:

Weight of each large box: 18.25kg

Weight of each small box: 13.25kg

Step-by-step explanation:

For this question, we have two unknowns, but we can solve them as we are given two equations.

If we use the variables 'L' for Large and 'S' for small, we  an write out the information given to us as equations:

3L + 5S = 121

6L + 2S = 136

Now we can solve these simultaneous equations by multiplying one of them by a constant so that one of the variable co-efficients are the same so we can cancel them. We can see here that we can easily double the first equation which would result in both having 6L:

2(3L + 5S) = 2(121)

=> 6L+10S=242

Now that we have one term which is the same, we can subtract one equation from the other:

  6L+ 10S = 242

- (6L + 2S = 136)

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

=>0L + 8S = 106

Now we can solve for S:

8S/8 = 106/8

S = 13.25

And use this value of S to solve for L:

3L + 5(13.25) = 121

3L + 66.25 = 121

3L + 66.25 - 66.25 = 121 - 66.25

3L = 54.75

3L/3 = 54.75/3

L = 18.25

Hope this helped!

Express the number in standard form
1.028×10^9

Answers

Answer:

1.028 × 10⁹

= 1028000000

How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/2^5.5^8 ?

Answers

There are seven zeroes  located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).

Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.

Let P=1/(2^5.5^8)

Multiplying and dividing the numerator by 2^3

P= 2^3/(2^5.5^8.2^3)

P=8/(2^8.5^8)

P=8/10^8

P=0.00000008

The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.

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