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The roots of the quadratic equation x² - x - 56 = 0 is x = -7 or x = 8

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

x² - x - 56 = 0   be equation (1)

On simplifying the equation , we get

x² - 8x + 7x - 56 = 0

Taking the common terms in the equation , we get

x ( x - 8 ) + 7 ( x - 8 ) = 0

Now , on factorizing the equation , we get

( x + 7 ) ( x - 8 ) = 0

We have two factors which can solve the equation ,

when ( x + 7 ) = 0

Subtracting 7 on both sides of the equation , we get

x = -7

And , when ( x - 8 ) = 0

Adding 8 on both sides of the equation , we get

x = 8

Therefore , the roots of the equation are x = -7 and x = 8

Hence , the quadratic equation is solved

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Answer:

x = 8

x = -7

Step-by-step explanation:

To find the solutions of the quadratic equation x^2 - x - 56 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = -1, and c = -56. Plug these values into the formula and calculate the discriminant (the value inside the square root):

Discriminant (D) = b^2 - 4ac = (-1)^2 - 4(1)(-56) = 1 + 224 = 225

Now, calculate the two possible solutions:

x1 = (-(-1) + √225) / (2(1)) = (1 + 15) / 2 = 16 / 2 = 8

x2 = (-(-1) - √225) / (2(1)) = (1 - 15) / 2 = -14 / 2 = -7

So, the correct solutions to the equation x^2 - x - 56 = 0 are:

x = 8 (x = 0 is not a solution)

x = -7

Answer: B (−5 < x < 3)

Steps

−19 < 3x − 4 < 5

−19 < 3x − 4 and 3x − 4 < 5

x > −5 and x < 3

−5 < x < 3

Number Line

−19 < 3x − 4 < 5 : Solution: − 5 < x < 3

[ Interval Notation: (−5, 3)]

If a < u < b then a < u and u < b

−19 < 3x − 4 : x > −5

3x − 4 < 5 : x < 3

Combine the intervals

Merge Overlapping Intervals

And that equals=

−5 < x < 3

Answer: The ratio 18:26 simplified is 9:13.

Step-by-step explanation:

To simplify the ratio 18:26, we find the greatest common divisor of 18 and 26, and then we divide 18 and 26 by the greatest common divisor.

The greatest common divisor that you can use to simplify 18:26 is 2. Which means the answer to ratio 18:26 simplified is: 9:13

Answer:9/13

explanation: k12

Distributive property is illustrated by the statement given as 4[3+2]=4[3]+4[2]

The distributive property is defined as an expression of the form A(B + C). This property is known by distributive law and applies to subtraction also. This can be solved by a multiplication over addition operation that is written as:

A(B + C) = AB + AC

Distributive property is the sum of two numbers times a third number is equal to the sum of each add end times the third number.

Since the general rule is that:

a(b + c) = ab + ac

Then, 4[3+2]=4[3]+4[2]

Therefore, the given statement elaborates the Distributive property.

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Answer:-12.168

Step-by-step explanation: multiply it regularly, then count how many decimals are after the numbers, in this case, 3. cus it’s 2 after 1.56 and one after 7.8

Answer: x=5

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable (x)

Answer:

3.95 + 0.50 + 4.50 × 2 = 13.45

13.45 × x = 124.70

x = 9

Therefore, she can make 9 shirts.

Rising action and climax are best used to describe the narrative element of Plot.

The rising action of the novel encompasses all the developments of the characters and the dramatic events that build to the eventual climax. The most thrilling section of the story is the climax, which also marks a turning point in the plot or the objectives of the main character.

Rising action in literature refers to all the incidents that take place in a narrative leading up to the climax. The tale moves along thanks to the mounting action, which also heightens the tension and keeps us interested in what happens next. It comes after the first step of exposition in the plot.

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Answer:

$2792.39

Step-by-step explanation:

→ Work out interest rate

( 100 + 5 ) ÷ 100 = 1.05

→ Multiply the amount by the interest rate to the power of 9

1800 × ( 1.05 )⁹ = 2792.39

Answer:

lesser x= -2

greater x= -3/2 or -1.5

Step-by-step explanation:

f(x)=(-x-2)(-2x-3)

-x-2=0

+2 +2

-x=2

-1 -1

x=-2

-2x-3=0

+3 +3

-2x=3

-2 -2

x=-3/2

The zeros of the function are x = -2 and x = -1.5.

The lesser value of x is -2, and the greater value of x is -1.5.

A function's zeros, also known as roots or solutions in mathematics, are the values of the independent variable (typically represented as x) for which the function evaluates to zero. In other terms, a function's zeros are the x-values that make the function equal to zero.

To find the zeros of the function f(x) = (-x - 2) (-2x - 3), we set the function equal to zero and solve for x:

(-x - 2) (-2x - 3) = 0

To find the zeros, we need to consider each factor separately and set them equal to zero:

First factor: -x - 2 = 0

Solving for x, we add 2 to both sides:

-x = 2

Multiplying both sides by -1 to isolate x:

x = -2

Second factor: -2x - 3 = 0

Solving for x, we add 3 to both sides:

-2x = 3

Dividing both sides by -2 to isolate x:

x = -3/2 or -1.5

So, the zeros of the function are x = -2 and x = -1.5.

Therefore, the lesser value of x is -2, and the greater value of x is -1.5.

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how many movies were there?

Answer:

Relative frequency

Step-by-step explanation:

Re

the simplest form of the given expression is 3n+2.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

-n + (-4) - (-4n) + 6

= -n + (-4) + 4n + 6

= 3n -4 +6

= 3n+2

Hence the simplest form of the given expression is 3n+2.

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Answer:

  d.  45°

Step-by-step explanation:

You want to know which from your list is a standard elbow angle.

An elbow is a pipe fitting that is used to change the direction of piping. Elbows can be used together to produce an offset and/or a change in the plane of the piping.

Standard elbow angles commonly are 90°, 45°, and, less commonly, 22.5°. The greater the angle, and/or the smaller the bend radius, the more resistance to flow it has.

The best choice of answer here is 45°.

__

Additional comment

The typical elbow has the same kind of threads on both sides. A "street elbow" has male threads on one side and female threads on the other side.

Elbow joints are not necessarily threaded. They may also be soldered, welded, or compression joints.

Answer:

Renee spent 1/2 of the time she spent landscaping pulling weeds, which is 1/2 * 1/8 = 1/16 of the day. Therefore, Renee spent 1/16 of the day pulling weeds.

The LCM is

( x − 1 ) ( x + 2) ( x + 3)

Remember that you can find the LCM between two expressions by multiplying them, and then dividing it with their GCF.

Answer:

The 95% CI for the true average porosity of a certain seam is (4.52, 5.18).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.77}{\sqrt{21}} = 0.33[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.33 = 4.52.

The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.33 = 5.18

The 95% CI for the true average porosity of a certain seam is (4.52, 5.18).

9514 1404 393

Answer:

  $970

Step-by-step explanation:

If we assume that the $1295 selling price of the first color television was paid to Camarena, and that he had no costs other than the ones described, then his profit was ...

  $1295 -25 -300 = $970

Answer:

0.9659

Step-by-step explanation:

sin 7π/12 = sin 105° = 0.9659

Answer:

The correct answer is sqr root of 6 + sqr root of 2 over/ 4. =)

Step-by-step explanation:

The number of positive 10 digit numbers that can be made using seven ones and three zeros is; 28

We want to find the number of positive 10 digit numbers that can be made using seven ones and three zeros.

Now, the leftmost position digit cannot be 0 and as such it is 1, due to the fact that there are no other possibilities.

The rightmost position therefore must be 0 in order to fill the need for an even number.

Thus, we have 8 remaining positions that we need to fill with six ones and two zeros using an arbitrary manner.

This means that we can place two digits of zero among 8 positions by using combination formula as;

⁸C₂ = 8!/(2! * 6*)

= 28 different ways

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is b because he has been a great friend of the object of his cow and he is very good about the fact he has been coughing all night long time is a force of the object to do the work and to be a good man and

Answer:

he will do 34 the next month

Answer:

4704 in²

Step-by-step explanation:

We are given that,

We are asked to to find the surface area of the cube.

Surface area generally refers to total surface area .

[tex]\bigstar \: \boxed{\sf {Surface \; Area_{(Cube)} = 6a^2 }} \\ [/tex]

→ Surface area of cube = 6 × (28)² in²

→ Surface area of cube = 6 × 784 in²

→ Surface area of cube = 4704 in²

[tex] \therefore [/tex] Surface area of cube is 4704 in².

Answer:

I think 34880.

Step-by-step explanation:

34880 I AM NOT SURE

Answer:

Option (3)

Step-by-step explanation:

Volume of the cylinder = 40 ft³

Since, volume of a cylinder is given by the expression,

V = [tex]\pi r^{2}h[/tex]

Here, r = radius of the circular base

h = Height of the cylinder

40 = [tex]\pi r^{2}h[/tex]

[tex]h=\frac{40}{\pi r^2}[/tex] ------(1)

Volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex]

By substituting the value of 'h' from equation (1)

Volume of the cone = [tex]\frac{1}{3}\pi r^{2}(\frac{40}{\pi r^{2} } )[/tex]

                                 = [tex]\frac{1}{3}(40)[/tex] ft³

Therefore, Option (3) will be the correct option.

Answer:

False

Step-by-step explanation:

The slope in the graph is not negative.

The correct equation for the graph would be [tex]y = \frac{3}{2} x+3[/tex]

Answer:

38.5

Step-by-step explanation:

The formula for the area of the circle is [tex]\pi rx^{2} \\[/tex].

Since you have the diameter and you're told to use 3.14 as pi, all you need to do is to substitute.

The diameter is also 2 times the size of the radius so you divide 7 by 2.

So [tex](3.14)(3.5)^{2} = 38.5[/tex]