MATHEMATICS HIGH SCHOOL

Identify all factors of the expression 12x^2-14x-6

Answers

Answer 1
Answer:

Let's solve this by using the quadratic formula:

(-b+-√(b^2-4ac) )/(2a)


Note that we only use the coefficients so a=12, b=-14, and c=-6.

Plug values in the quadratic equation:

\frac{ -  ( - 14)± \sqrt{ {( - 14)}^(2) - 4(12)( - 6) } }{2(12)}

And so by evaluating those values we obtain:

(14+-√(484) )/(24)=(14+-22)/(24)  \n\n

Now we have two answers which are our factors one where we add another where we subtract and so:

First factor:

(14+22)/(24)=(36)/(24)=(3)/(2)


Second Factor:

(14-22)/(24)=(-8)/(24)=-(1)/(3)


And so your factors are

(3)/(2),-(1)/(3)

meaning that those are your roots/x-intercepts.

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-4 (5x - 1)+ -11 (2x + 4)

Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used. A table titled Bleach Solution showing Cups, Bleach concentration, and Total. The first row shows 10 percent Bleach with 5, 0.10, and 0.5. The second row shows, 25 percent bleach, with x, 0.25, and 0.25 x. The third row shows Mixture, with 5 plus x, 0.20, and 3. What is the value of x? 1 3 10 24 Mark this and ret

Answers

Answer: 10

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Is an isosceles triangle. What is the length of RT? Round to the nearest hundredth.Enter your answer in the box

Answers

Answer:

9.33

Step-by-step explanation:

Find the diagram attached, to get the length of RT, we will use the pythagoras theorem as shown:

Hyp² = opp²+adj²

Hyp = 11

Adj = 6

Opposite = RT

Substitute into the formula

11² = opp²+6²

Opp² = 11²-6²

Opp² = 121-36

Opp² = 85

Opp = 9.22

Hence the measurel RT to nearest hundredth is 9.22

transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts.

Answers

The\ vertex\ form\ of\ y=ax^2+bx+c:y=a(x-h)^2+k\n\nwhere\ h=(-b)/(2a)\ and\ k=f(h)=(-(b^2-4ac))/(4a)\n-----------------------------\n\ny=-2x^2-12x-10\n\na=-2;\ b=-12;\ c=-10\n\nh=(-(-12))/(2(-2))=(12)/(-4)=-3\n\nk=f(-3)=-2(-3)^2-12(-3)-10=-2\cdot9+36-10=-18+26=8\n\ntherefore:y=-2(x-(-3))^2+8\to\boxed{y=-2(x+3)^2+8}\leftarrow The\ vertex\ form


y-intercept\to f(0)=-2(0^2)-12(0)-10=\boxed{-10}\leftarrow y-intercept


x-intercept\ if\ y=0\n\n-2x^2-12x-10=0\ \ \ \ \ |divide\ both\ sides\ by\ (-2)\nx^2+6x+5=0\nx^2+x+5x+5=0\nx(x+1)+5(x+1)=0\n(x+1)(x+5)=0\iff x+1=0\ or\ x+5=0\n\n\boxed{x=-1\ or\ x=-5}\leftarrow x-intercept
y=-2x^2-12x-10
to find the x value of the vertex find the axis of symmetry which is
-b/2a
=12/2(-2)
=-3
to find the y value of the vertex sub the axis of symmetry back into the original equation. 
y=-2(-3)^2-12(-3)-10
y=8
vertex=(-3,8)
to put it into vertex form use y=a(x-h)^2 +k where h and k are the x and y values of the vertex respectively. 

y=-2(x--3)^2 +8
y=-2(x+3)^2+8

to find the x intercept let y=0

-2x^2-12x-10=0
x^2+6x+5=0 
use quad formula and you will get 
x=-5 and -1

to find the y intercept let x=0

y= -2(0)^2-12(0)-10
y=-10

A relation is:A.) the output (y) values of the relation

B.) the input (x) values of the relation

C.) a set of points that pair input values with output values

D.) x and y values written in the form (x,y)

Answers

D. X and y values written in the form of (x,y)
the answer would be D since x,y is a function

A merchant buys an old carpet for $25.00. He spends $15.00 to have it restored to goodcondition and then sells the rug for $50.00. What is the percent profit on his total
investment?

Answers

The percent profit on his total 20%.

What is Unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

  • Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
  • Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Cost of old carpet =$25

He spends $15.00 to have it restored

So, he spend= 25+ 15 = 40

He sells it at = $50

Profit= 50-40 = 10

Profit %= P/ CP * 100

Profit % = 10/ 25 * 100

Profit %=  25% on CP

and, P% on selling price= 10/50* 100 = 20%

Learn more about profit percent here:

brainly.com/question/14411361

#SPJ5
$25-how much it cost
+$15- restored
Total of $35 spend
$50 earned
- 35 what he spend
Total of 15$
To get the percent u divide 35 by 50=0.7 x100
The profit is 70%

Help me please!! asap!

Answers

The equation represent the situation is:

First let x be number of small apartment

Since the total apartment is 18

Then number of large apartment is 18 – x

So the equation is:

17,600 = 800x + 1200(18-x)

Simplifying

17,600 = 800x + 21,600 – 1200x

400x = 4000

X = 10
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