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3 years ago

The equation

Mathematics

2 answers:

Vilka [71]3 years ago

4 0

Answer: B

Step-by-step explanation: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.

The final answer is B.

hammer [34]3 years ago

3 0

Answer: B

Step-by-step explanation:

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The standard form of the equation of a parabola is y= x2 - 6x + 14.

Bas_tet [7]

<h3>Option C</h3><h3>The vertex form of the equation is:</h3>

$y = (x - 3)^2 + 5$

Solution:

The vertex form of equation is given as:

$y = a(x- h)^2 + k$

Where, (h, k) is the vertex

Given that,

$y = x^2 - 6x + 14$

We have to find the vertex form of equation

Step 1:

Complete the square for $x^2 - 6x + 14$

$\text{ Use the form } ax^2 + bx + c \text{ to find values of a, b, c }$

a = 1

b = -6

c = 14

Consider the vertex form of a parabola.

$a(x + d)^2 + e ----- eqn 1$

Substitute the values of a and b into following:

$d = \frac{b}{2a}\\\\d = \frac{-6}{2 \times 1}\\\\d = -3$

Find the value of "e" using following formula:

$e = c - \frac{b^2}{4a}\\\\e = 14 - \frac{(-6)^2 }{4 \times 1}\\\\e = 14 - 9\\\\e = 5$

Substitute the values of a, d, e in eqn 1

$y = 1(x -3)^2 + 5\\\\y = (x - 3)^2 + 5$

Thus vertex form form is found. Option C is correct

3 0

3 years ago

Can you solve this problem so that you can explain me as best as possible to understand the problem?

Alchen [17]

Answer:

Answer: 2

Step-by-step explanation:

$\frac{2}{3} (4 \frac{1}{6} - \frac{7}{6} ) \\$

express the mixed fraction into proper fraction:

${ \boxed{4 \frac{1}{6} = \frac{(6 \times 4) + 1}{6} = \frac{25}{6} }}$

then solve simplify:

$= \frac{2}{3} ( \frac{25}{6} - \frac{7}{6} ) \\$

solve the bracket:

$= \frac{2}{3} ( \frac{25 - 7}{6} ) \\ \\ = \frac{2}{3} ( 3)$

then simplify:

$= \frac{2 \times 3}{3} \\ \\ = 2$

6 0

3 years ago

20pts PLS EXPLAINN for brainliest

Inga [223]

inequality is C D A

6 0

4 years ago

HELP ASAP!! WILL MARK AS BRAINLIEST IF ANSWERED NOW!!!!

tiny-mole [99]

Answer: She should blend 98 lbs of high-quality beans.

She should blend 72 lbs of cheaper beans

Step-by-step explanation:

Let x represent the number of pounds of high quality beans that she should blend.

Let y represent the number of pounds of cheaper beans that she should blend.

She needs to prepare 170 lbs of blended coffee beans. This means that

x + y = 170

She plans to do this by blending together a high-quality bean costing $4.75 per pound and a cheaper bean at $2.00 per pound. The blend would sell for $3.59 per pound. This means that the total cost of the blend would be 3.59×170 = $610.3. This means that

4.75x + 2y = 610.3 - - - - - - - - - -1

Substituting x = 170 - y into equation 1, it becomes

4.75(170 - y) + 2y = 610.3

807.5 - 4.75y + 2y = 610.3

- 4.75y + 2y = 610.3 - 807.5

- 2.75y = - 197.2

y = - 197.2/-2.75 = 71.9

y = 72 pounds

x = 170 - y = 170 - 71.9

x = 98.1

x = 98 pounds

4 0

3 years ago

PLEASE HELP ME!!!!!!!!! 75/w=150/100

allsm [11]

Answer:

The answer is 75/50

Step-by-step explanation:

7 0

3 years ago

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