Brainliest if correct

Solve the following quadratic equations by completing the square. y^2-14y+48=0

NISA [10]

Answer:

y = 6 or 8

Step-by-step explanation:

1. Subtract the constant:

y^2 -14y = -48

2. Add the square of half the y-coefficient:

y^2 -14y +49 = -48 +49

Write as a square, if you like:

(y -7)^2 = 1

3. Take the square root:

y -7 = ±√1 = ±1

4. Add the opposite of the constant on the left:

y = 7 ±1 = 6 or 8

The solution is y = 6 or y = 8.

5 0

3 years ago

This diagram shows triangles ABC and PQR.

Stels [109]

Answer:

<h3>A reflection across the line x=3, a reflection across the x-axis and a dilation with a scale factor of 2, because each side is double.</h3><h3>Step-by-step explanation:</h3>

We know that the first transfomration is a rotation 90° clockwise.

Notice that vertex R is at the same horizontal coordinate than vertex C, which means the second transformation must include a reflection across the line x=3, a reflection across the x-axis and a dilation with a scale factor of 2, because each side is double.

6 0

3 years ago

How would you do a,b,c,and d

I am Lyosha [343]

a) You are told the function is quadratic, so you can write cost (c) in terms of speed (s) as

... c = k·s² + m·s + n

Filling in the given values gives three equations in k, m, and n.

$28 = k\cdot 10^2+m\cdot 10+n\\21=k\cdot 20^2+m\cdot 20+n\\16=k\cdot 30^2+m\cdot 30+n$

Subtracting each equation from the one after gives

$-7=300k+10m\\-5=500k+10m$

Subtracting the first of these equations from the second gives

$2=200k\\\\k=\dfrac{2}{200}=0.01$

Using the next previous equation, we can find m.

$-5=500\cdot 0.01+10m\\\\m=\dfrac{-10}{10}=-1$

Then from the first equation

[tex]28=100\cdot 0.01+10\cdot (-1)+n\\\\n=37[tex]

There are a variety of other ways the equation can be found or the system of equations solved. Any way you do it, you should end with

... c = 0.01s² - s + 37

b) At 150 kph, the cost is predicted to be

... c = 0.01·150² -150 +37 = 112 . . . cents/km

c) The graph shows you need to maintain speed between 40 and 60 kph to keep cost at or below 13 cents/km.

d) The graph has a minimum at 12 cents per km. This model predicts it is not possible to spend only 10 cents per km.

4 0

3 years ago

What is the first step in solving the equation x2 – 16/25 = 0?

Keith_Richards [23]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-(16/25)=0

Step by step solution :Step 1 : 16 Simplify —— 25 Equation at the end of step 1 : 16 (x2) - —— = 0 25 Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 25 as the denominator :

x2 x2 • 25 x2 = —— = ——————— 1 25

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x2 • 25 - (16) 25x2 - 16 —————————————— = ————————— 25 25 Trying to factor as a Difference of Squares :

2.3 Factoring: 25x2 - 16

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5
Check : 16 is the square of 4
Check : x2 is the square of x1 

Factorization is : (5x + 4) • (5x - 4)

Equation at the end of step 2 : (5x + 4) • (5x - 4) ——————————————————— = 0 25 Step 3 :When a fraction equals zero : 3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

(5x+4)•(5x-4) ————————————— • 25 = 0 • 25 25

Now, on the left hand side, the 25 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
(5x+4) • (5x-4) = 0

Theory - Roots of a product :

3.2 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.3 Solve : 5x+4 = 0

Subtract 4 from both sides of the equation :
 5x = -4
Divide both sides of the equation by 5:
 x = -4/5 = -0.800

Solving a Single Variable Equation :

3.4 Solve : 5x-4 = 0

Add 4 to both sides of the equation :
 5x = 4
Divide both sides of the equation by 5:
 x = 4/5 = 0.800

x = 4/5 = 0.800
 x = -4/5 = -0.800

3 0

3 years ago

Read 2 more answers

When ABC was dialed by a scale factor of 2, centered at the origin, the result was its image A'B'C' shown on the coordinates pla

sweet-ann [11.9K]

Answer:

Step-by-step explanation:

In dilation, the image and the original are similar, in that they are the same shape but not necessarily the same size. They are not congruent because that requires them to be the same shape and the same size, which they are not (scale factor is 2)

vertices of ABC are A(-2,2), B(-2,3), and C(1,2)

If we multiply by 2 from original to image,

then from image to original we divide by 2

4 0

3 years ago