Please show me how to solve for Xsquared - 21.75X = -15.75. I have the solution but do not know how to solve it.

Answers

Answer 1

Answer: $x^2-21.75x=-15.75 \nx^2-21.75x+15.75=0$

Use the quadratic formula:
$x^2-21.75x+15.75=0 \n \na=1 \n b=-21.75 \n c=15.75 \n b^2-4ac=(-21.75)^2-4 * 1 * 15.75=473.0625-63=410.0625 \n \nx=(-b \pm √(b^2-4ac))/(2a)=(-(-21.75) \pm √(410.0625))/(2 * 1)=(21.75 \pm 20.25)/(2) \nx=(21.75-20.25)/(2) \ \lor \ x=(21.75+20.25)/(2) \nx=(1.5)/(2) \ \lor \ x=(42)/(2) \nx=(15)/(20) \ \lor \ x=21 \nx=(3)/(4) \ \lor \ x=21 \n\boxed{x=(3)/(4) \hbox{ or } x=21}$

$(x-5)/(x^(2) +3x-40)$

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to $x-5$ later):

$x^(2) +3x-40$

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that $x^(2)$ has an exponent of 2. When variables are multiplied, the exponents are added, meaning that $x*x=x^(2)$ . (Or $x^(1) + x^(1) =x^(2)$ , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

$x^(2) +3x-40 = (x+)(x-)$

Next, let's look at the factors of 40:

1 and 40 2 and 20 4 and 10 5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

$8-5=3$

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in $3x$ . Therefore, $8(-5)=-40$ .

$x^(2) +3x-40 = (x+8)(x-5)$

Now let's go back to our original equation and substitute our old expression with the new one:

$(x-5)/((x+8)(x-5))$

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a $(1)/(1)$ .

$(x-5)/((x+8)(x-5))$ = $(1)/(x+8)$

Therefore, your simplified answer is $(1)/(x+8)$ !

Here's the whole process:

$(x-5)/(x^(2) +3x-40) \n\n(x+?)(x-?)\n\n40:\n1, 40\n2, 20\n4, 10\n5, 8\n\n8-5=3 \n(8x-5x=3x)\n\n(x+8)(x-5)\n\n(x-5)/((x+8)(x-5))=(1)/(x+8) \n\n(1)/(x+8)$

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

The vertices of a quadrilateral ABCD are A(-3, 4), B(-4, 1), C(-7, 2), and D(-7, 6). The vertices of another quadrilateral EFCD are E(-10, 1), F(-11, 4), C(-7, 2), and D(-7, 6). Which conclusion is true about the quadrilaterals?Their corresponding diagonals are equal.

The measures of their corresponding angles are not identical.

The lengths of their corresponding sides are unequal.

Their shapes and sizes are not identical.

Answers

"Their corresponding diagonals are equal" is the one conclusion among the following choices given in the question that is true about the quadrilaterals. The correct option among all the options that are given in the question is the first option. I hope that this is the answer that has actually come to your help.

demetri invested money in two different stocks. After one year, he recieved a letter that summarized the performance of the stocks graphically. Demetri observed that the growth of each stock was the same. Which equation shows the translation of the graph of stock B to that of stock A?

Answers

Answer: C

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Ln(x + 1) − ln(2) = 1

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Answer:

The answer to your question is: x = 4.44

Step-by-step explanation:

Data

ln(x + 1) − ln(2) = 1

In (x + 1)/2 = 1

(x + 1) / 2 = e¹

x + 1 = 2 (2.7183)

x = 5.44 - 1

x = 4.44

Mario paid $44.25 in taxi fare from the hotel to the airport. the cab charged $2.25 for the first mile plus $3.50 for each additional mile. how many miles was it from the hotel to the airport

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The distance from the hotel to the airport was 12 miles.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

From the information given, the taxi fair is equal to the initial cost of first mile added to the result of multiplying the cost per mile for the number of miles, which is:

t=2.25+3.50x, where:

t is the b

x is the number of miles

Now, you can replace t with 44.25 and solve for x to find the miles:

44.25=2.25+3.50x

42 = 3.5x

x = 42/3.5

x = 12

Therefore, the distance from the hotel to the airport was 12 miles.

Please show me how to solve for Xsquared - 21.75X = -15.75. I have the solution but do not know how to solve it.

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$(x-5)/((x+8)(x-5))$ = $(1)/(x+8)$