Answer:
x = 1, y = 6
or
x = 5, y = 2.
Step-by-step explanation:
y=x2−7x+12
y=−x+7
Substitute for y in the first equation:
- x + 7 = x^2 - 7x + 12
x^2 - 7x + x + 12 - 7 = 0
x^2 - 6x + 5 = 0
(x - 1)(x - 5) = 0
x = 1, 5.
When x = 1, y = -1 + 7 = 6.
when x = 5, y = -5+7 = 2.
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
An example of a domain that can be illustrated from the information given will be D(x) = 32.
<h3>Domain and range</h3>
An example based on the information given is "A gas tank in John's car can hold 20 gallons of gas and the car gets 32 miles for every gallon".
John fills up the tank and then goes on a trip. In this case, the distance that will be travelled on one tank will be:
D(x) = 32x
In the above function, it should be noted that the number of gallons can be from 0 to 20. Since he gets 32 miles per gallon, the car can travel 640 miles.
In this case, the domain is the number of gallons that can be used. The number of miles will be the range.
Learn more about domains on:
brainly.com/question/2264373
In order to figure out what N is you have to isolate it by dividing by 50 on both sides as shown below:
Data:
l and m are parallel lines
QR and ST are perpendicular in R
Angle 1 is 63°
The angle formed by perpendicular lines is a right angle (90°)
Angles 1 and 3 are alternate angles: angles that occur on opposite sides of a transversal line that is crossing two parallel.
Alternate angles are congruent, have the same measure.
The sum of the interior angles of a triangle is always 180°. In triangle QRT:
Use the equation above to find the measure of angle 2:
Then, the measure of angle 2 is 27°
