Solve each system by substitution. -5x + 3y = 3 and -4x + y = 1

1 answer:

5 0

$\left\{\begin{array}{ccc}-5x+3y=3\\-4x+y=1&|\text{add 4x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-5x+3y=3\\y=4x+1&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to the first equation}\\\\-5x+3(4x+1)=3\qquad\text{use distributive property}\\\\-5x+(3)(4x)+(3)(1)=3\\\\-5x+12x+3=3\qquad\text{subtract 3 from both sides}\\\\7x=0\qquad\text{divide both sides by (-5)}\\\\\boxed{x=0}\\\\\text{Substitute the value of x to}\ (*):\\\\y=4(0)+1\\y=0+1\\\boxed{y=1}\\\\Answer:\ x=0\ and\ y=1.$

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Given f(x) = x^2-2x+5<br> Find f(-2)

lbvjy [14]

Answer:

Step-by-step explanation:

f(x) = x² - 2x + 5

Yo find f(-2) substitute the value of x that's - 2 into f(x) that is for every x in f (x) replace it with - 2

So we have

f( - 2) = (-2)² - 2(-2) + 5

= 4 + 4 + 5

= 8 + 5

We have the final answer as

Hope this helps you

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3 years ago

Choose one of the theorems about chords of a circle and state it using your own words. Create a problem about chords that uses t

Mazyrski [523]

Answer:

Step-by-step explanation:

1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.

2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.

3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.

A radius that meet the chord at center C, and divides it into two equal parts.

So that;

AC = CB = 5 units

Applying Pythagoras theorem to ΔOCB,

OC = d, CB = 5 units and OB = 13 units

$13^{2}$ = $5^{2}$ + $d^{2}$