If K is the midpoint of HJ, HK equals x+6, and HJ equals 5x-6, then KJ equals?

Answers

Answer 1

Answer: Hello,

5x-6=2(x+6)
==>3x=6
==>x=2
==>KJ=HK=x+6=8

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Find the equation of the line that is parallel to y=3x-2 and that contains the points ( 2,11)
One of the two positive integers is 5 less than the other. If the product of the two integers is 24, find the integers.
Jana bought a car for $4200 and later sold it for a 30% profit. How much did Jana sell the car for?
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What percentage did you tip if your lunch was $5 and you left $1

Answers

well 20% of $5 is $1 so u paid a 20% tip

The owner of a discount clothing store ordered six belts and eight hats for $140. Aweek later, at the same prices, he bought nine belts and six hats for $132. Find the
price of a belt and a hat.

Answers

Let b = the price of the belt
h = the price of the hat
Equation 1
6b + 8h = 140
Equation 2
9b + 6h = 132
Multiply equation 1 by 1.5
1.5(6b + 8h = 140)
9b +12h = 210
Subtract by equation 2
9b-9b +12h-6h = 210-132
6h = 78
h = 13
Substitute h = 13 in equation 1
6b + 8*13 = 140
6b = 140 - 104
6b = 36
b = 6
The price of the hat is $13.00 each
The price of the belt is $6.00 each

A pro football team has 36,000 season ticket holders. Then the team wins the championship and the number of season ticket holders increases by 9,000. What is the percent of change in season ticket holders?20%
25%
33.3%
75%

Answers

Given:
36,000 season ticket holders (base number)
9,000 increase in season ticket holders.

9,000 / 36,000 = 0.25
0.25 * 100% = 25%

The percentage change is an increase of 25%.

36,000 + 9,000 = 45,000 new number of season ticket holders.

Identify the factors of 13m-2n

Answers

Answer:

The factors of $13m$ are 13 and $m$ .

The factors of $2n$ are 2 and $n$ .

Step-by-step explanation:

We are asked to determine the factors of the given expression $13m-2n$ .

We know that factor is a number or quantity such that when multiplied with another number or quantity produces a given number or expression.

Since 13 is a prime number, so the factors of $13m$ are 13 and $m$ .

Since 2 is a prime number, so the factors of $2n$ are 2 and $n$ .

the factors of 13m are 13 and m and it goes the same with 2n hope that helps.

**I need to find out what the vertex , axis of symmetry, maximum or minimum, and the domain and range for function f(x)=-(x-3)^2+2 HELP ME I DONT UNDERSTAND!!

Answers

Notice that the given equation is a parabola.

a) VERTEX
We need to find out where the parabola opens. You can predict the equation by tabulating any values of x and f(x). The table is shown:
x f(x)
_____
0 -7
1 -2
2 1
3 2
4 1
5 -3
As you plot it, the parabola opens downward. The vertex is (3,2) because that is the maximum point. The rest of the values are lesser than 2.
However, there is an easier technique to find the opening parabola and vertex rather than you plot it.

b) AXIS OF SYMMETRY
The axis of symmetry is a line that divides the parabola into two congruent halves. There is a formula for the axis of symmetry which is x = -b/2a.
Note: That is only applied if the parabola opens upward or downward and their axis of symmetry is a vertical line.
To get a and b, arrange the given equation first.
f(x) = -(x - 3)^2 + 2
= -(x^2 - 6x + 9) + 2
= -x^2 + 6x - 7 + 2
= -x^2 + 6x -5
The general form of the quadratic equation is ax^2 + bx + c. Setting a = -1, b = 6, c = -5, the axis of symmetry is
x = -6/(2*-1) = 3.

But anyway, you find it out the table above. We know that the coordinate of the vertex is (3,2). For instance, that is x = 3.

c) MAXIMUM or MINIMUM
Remember that the maximum refers to a vertex where the parabola opening downward. Otherwise, it is a minimum if the parabola opens upward. The maximum or minimum must have a certain value.
We know the answer will be a maximum. Since the axis is symmetry is a vertical line, the value for a maximum is 2.

d) DOMAIN and RANGE
Based on the given equation, the domain will be (-∞, ∞) because all values of x, the parabola continually spreads out.
The range will be (-∞, 2] because the maximum point is 2 and the rest of the values goes negative.

1. x=1/(root3-root2). find rootx-(1/rootx) 2. if x=[root(a+2b)+root(a-2b)]/[root(a+2b)-root(a-2b]. show that bx^2-ax+b=0

Answers

Answer with explanation:

Ques 1)

$x=(1)/(√(3)-√(2))$

Now we are asked to find the value of:

$√(x)-(1)/(√(x))$

We know that:

$(√(x)-(1)/(√(x)))^2=x+(1)/(x)-2$

Also:

$x=(1)/(√(3)-√(2))$ could be written as:

$x=(1)/(√(3)-√(2))* (√(3)+√(2))/(√(3)+√(2))\n\n\nx=(√(3)+√(2))/((√(3))^2-(√(2))^2)$

since, we know that:

$(a+b)(a-b)=a^2-b^2$

Hence,

$x=(√(3)+√(2))/(3-2)\n\n\nx=√(3)+√(2)$

Also,

$(1)/(x)=√(3)-√(2)$

Hence, we get:

$(√(x)-(1)/(√(x)))^2=√(3)+√(2)+√(3)-√(2)-2\n\n\n(√(x)-(1)/(√(x)))^2=2√(3)-2\n\n\n√(x)-(1)/(√(x))=\sqrt{2√(3)-2}$

Hence,

$√(x)-(1)/(√(x))=\sqrt{2√(3)-2}$

Ques 2)

$x=(√(a+2b)+√(a-2b))/(√(a+2b)-√(a-2b))$

on multiplying and dividing by conjugate of denominator we get:

$x=(√(a+2b)+√(a-2b))/(√(a+2b)-√(a-2b))* (√(a+2b)+√(a-2b))/(√(a+2b)+√(a-2b))\n\n\nx=((√(a+2b)+√(a-2b))^2)/((√(a+2b))^2-(√(a-2b))^2)\n\n\nx=((√(a+2b))^2+(√(a-2b))^2+2√(a+2b)√(a-2b))/(a+2b-a+2b)\n\n\nx=(a+2b+a-2b+2√(a+2b)√(a-2b))/(4b)\n\n\nx=(2a+2√(a^2-4b^2))/(4b)\n\n\nx^2=((2a+2√(a^2-4b^2))/(4b))^2\n\n\nx^2=((2a+2√(a^2-4b^2))^2)/(16b^2)$

Hence, we have:

$x^2=(4a^2+4(a^2-4b^2)+8a√(a^2-4b^2))/(16b^2)\n\n\nx^2=(4a^2+4a^2-16b^2+8a√(a^2-4b^2))/(16b^2)\n\n\n\nx^2=(8a^2-16b^2+8a√(a^2-4b^2))/(16b^2)\n\n\nbx^2=(8a^2-16b^2+8a√(a^2-4b^2))/(16b)\n\n\nbx^2=(8a(a+√(a^2-4b^2))-16b^2)/(16b)\n\n\nbx^2=(8a(a+√(a^2-4b^2)))/(16b)-(16b^2)/(16b)\n\n\nbx^2=(a(a+√(a^2-4b^2)))/(2b)-b\n\n\nbx^2=ax-b\n\n\ni.e.\n\n\nbx^2-ax+b=0$

1. x = 1/ ( $√(3) - √(2))$ = $√(3)+ √(2)$ ;
( $√(x) -1/ √(x) )^(2) = x + 1/x - 2 =$ =

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