MATHEMATICS HIGH SCHOOL

What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?

Answers

Answer 1

Answer:

Answer: The required discriminant of the given quadratic equation is 8.

Step-by-step explanation: We are given to find the discriminant of the following quadratic equation :

$-x^2+4x-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the discriminant of a quadratic equation of the form $ax^2+bx+c=0,~a\neq 0$ is given by

$D=b^2-4ac.$

In the given quadratic equation, we have

a = -1, b = 4 and c = -2.

Therefore, the discriminant of the given quadratic equation is

$D=b^2-4ac=4^2-4*(-1)*(-2)=16-8=8.$

Thus, the required discriminant of the given quadratic equation is 8.

Answer 2

Answer: The discriminant is the b^2 - 4ac part of the quadratic formula. So you plug in the numbers you should have 4^2 - (4)(-1)(-2) to give you the answer 8

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Show how square root 5 can be represent on number line?

Answers

What they do is basically put it between the square root of 4 and 9, so that's 2 and 3.

Compare using <, >, or =.
7/9_____4/9

Answers

< is the answer , trust me

Think of fractions like a pizza pie, the more parts it's cut into the less everyone will have. 7/9 is smaller than 4/9 because of the remainder of what would be left over if this was actual pie.

7/9 is less than (the first symbol) 4/9

Naomi deposited money into a savings account that is compounded quarterly at an interest rate of 6%. she thinks this quarterly rate is the same as a monthly interest rate of 1.25%. Is Naomi right? If so, explain why and show how you got your answer. Is Naomi incorrect? if so, explain the mistake in her reasoning, give the correct monthly interest rate, and show how you got your answer.

Answers

answer is attached below

Of 10 students surveyed in a school , 7 picked Summer as their favorite season. If the school has 350 students. How many can be expected to perfer summer?

Answers

Answer:

The expected number of students to prefer summer=245

Step-by-step explanation:

Step 1

Determine the number of students that prefer summer as their favorite season, and the sample size

number that prefer summer=7

sample size=10

Step 2

Determine the probability of a student picking summer as their favorite season as shown;

Probability=number that prefer summer/sample size

Probability=7/10=0.7

Step 3

Determine the total number of students out of the total population that can be expected to prefer summer as follows;

Expected number of students=probability×total number of students

where;

probability=0.7

total number of students=350

replacing;

Expected number of students=(0.7×350)=245

The expected number of students to prefer summer=245

Write a function for the situation described and find the value after 5 years. A $12,500 car depreciates 9% each year. please show work i'm stuck on this problem

Answers

Y=12500(0.91)^x --> x=5 --> 7,800.40 just did this study guide too :)

I am about to fail this math class. I would like to verify that my answers are right. Please help.Find the distance from the given point to the vertical axis.
(7, −6)

Determine the value of k such that the points whose coordinates are given lie on the same line.
(k, 0), (0, −1), (10, −11)

Find the slope of the line containing the given points.
P1(5, −9), P2(1, 7)

Find the equation of the line that passes through the midpoint of the line segment between
P1(4, 1) and P2(−2, 3) and has slope of 3.
Let y be the dependent variable and let x be the independent variable.

Find the equation of the line that contains the given point and has the given slope.
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Suppose a ball is being twirled at the end of a string and the center of rotation is the origin of a coordinate system. If the string breaks, the initial path of the ball is on a line that is perpendicular to the radius of the circle. Suppose the string breaks when the ball is at the point whose coordinates are P(3, 9). Find the equation of the line on which the initial path lies

During one month, a homeowner used 500 units of electricity and 100 units of gas for a total cost of $331. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.

Answers

Answer:

1) 7 2) (-1,0) 3) m=-4 4) y=3x-4 5) y=x+6 6)

g(x)=-1/3x+10 7) y= $0.36

Step-by-step explanation:

These questions are all about Cartesian Geometry.

1) The Distance from point (7,-6) to vertical axis (0,-6) is measured with a straight line, between point (7,-6) and nearer point (0,-6)

d=|7-0|=7

2) To determine the value of k, let's determine the function with the two known points: (0, −1), (10, −11).

$m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(-11+1)/(10-0)\Rightarrow m=-1\n-11=-1*(10)+b\therefore b=-1\Rightarrow f(x)=-x-1\nf(k)=-k-1\n0=-k-1\therefore k=-1$

So (k,0)=(-1,0)

3) To find the slope of the line, we must apply that formula used above.

$m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(7+9)/(1-5)\Rightarrow m=(16)/(4)=-4$

4) To find the equation of the line which the midpoint (2,2) since Midpoint is given by

$Midpoint=((x_(1)+x_(2))/(2)+(y_(1)+y_(2))/(2))\n$

And the slope is 3, then m=3. Notice the formula is the same to calculate the slope, but we will only pick one point. Since (2,2) ∈ to the function let's use this point, as initial value (x0,y,0)

$m(x-x_(0))=y-y_(0)\n3(x-2)=y-2\n3x-6=y-2\Rightarrow 3x-y=6-2\Rightarrow -y=4-3x\Rightarrow y=3x-4$

5) Similarly to the previous one:

$m(x-x_(0))=y-y_(0)\n(x-0)=y-6\nx=y-6\Rightarrow -y=-x-6\Rightarrow y=x+6$

6) A ball being twirled. The center of the rotation is the origin of Coordinate System (0,0) when the string breaks at point (3,9)

If the line was straight from the origin to point (3,9) $m=(9-0)/(3-0)\Rightarrow m=3\therefore 9=3(3)+b\Rightarrow b=0\Rightarrow f(x)=3x$

But the point (3,9) ∈ to a tangent line to the circumference described by the twirling.

Since it is perpendicular instead of m=3 it is -1/m i.e. -1/3, also the circumference intercepts the y-axis in ≈10

g(x)=-1/3x+10

7) In this case, we must also find the function.

x=units of electricity, y=units of gas |

500x+100y=331

400x+250y=326

The cost per unit of gas is y. Finding out the unit value for y

$100y=331-500x\rightarrow y=(331-500x)/(100)\n500x=331-100y\nx=(331-100y)/(500)\n400((331-100y)/(500))+250y=326\n52.96-80y+250y=326\Rightarrow y=(9)/(25) \,and \,x=(59)/(100)$

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