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ValentinkaMS [17]

3 years ago

12

Olivia was baking. The recipe called for seven cups of flour and three cups of sugar.she already put two cups of flour. How many

more cups of flour does she need

1 answer:

ANEK [815]3 years ago

8 0

She needs 5 cups of flour and 3 cups of sugar.

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Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

<em>Solved</em>

7 0

4 years ago

Read 2 more answers

Which of the following functions is graphed below?

pishuonlain [190]

Answer: B

The piece wise functions first part says: x is less than it equal to one and has a vertical shift down 4. which would mean the circle is closed and shaded down.

The second part of the function says x is greater than one and has a vertical shift up 3. This would mean it is an open circle and is shaded up.

7 0

3 years ago

Write the expression in standard form<br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B3-15i%7D" id="TexFormula1" title="\

valentina_108 [34]

<em>Answer:</em>

<em>7/78 - 35/78i</em>

<em>Step-by-step explanation:</em>

<em>A complex number is a real number, an imaginary number or a number with both real and imaginary number. Its standard form is: </em>

<em>a + bi </em>

<em> </em>

<em>For the expression, 7/ 3-15i </em>

<em> </em>

<em>(7/ 3-15i) (3+15i) </em>

<em>21 - 105i / (234) </em>

<em>7/78 - 35/78i </em>

4 0

3 years ago

Ashley use 3 yards of ribbon to wrap these presents how many feet and rub it did actually how many inches did she

Alchen [17]

Answer:

108 inches

Step-by-step explanation:

one yard = 36 inches

multiply 36 by 3

4 0

4 years ago

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Which choice represents the number of cookies Rhianna must sell for 35 cents each to make more than $15. A) 0.035x > 15 B) 0.

Tanya [424]

0.35x > 15 <=== ur inequality

7 0

3 years ago

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