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2 years ago

If r is the midpoint of qs rs=2x-4, st= 4x-1 and rt = 8x-43 find qs

Mathematics

1 answer:

sammy [17]2 years ago

6 0

Answer:

$QS=68\ units$

Step-by-step explanation:

step 1

Find the value of x

we know that

r is the midpoint of qs

QR=RS

QS=QR+RS------> QS=2RS -----> equation A

RT=RS+ST ----> equation B

see the attached figure to better understand the problem

Substitute the given values in the equation B and solve for x

$8x-43=(2x-4)+(4x-1)$

$8x-43=6x-5$

$8x-6x=43-5$

$2x=38$

$x=19$

step 2

Find the value of RS

$RS=2x-4$

substitute the value of x

$RS=2(19)-4$

$RS=34\ units$

step 3

Find the value of QS

Remember equation A

QS=2RS

$QS=2(34)=68\ units$

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2 years ago

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Joline is solving the equation 0 = x2 – 5x – 4 using the quadratic formula. Which value is the negative real number solution to

katen-ka-za [31]

Answer:

- 0.7

Step-by-step explanation:

We are given the general quadratic formula, as " $x = -b \frac{+}{-} \sqrt{(b^2-4ac)} / 2a$ . " This can be represented by two separate formula's, which will come in handy when determining the positive and negative roots of the equation ( and here we need the negative root ):

1 ) $x = - b+ ( \sqrt{b^2-4ac} ) / 2a$ ,

2 ) $x = - b- ( \sqrt{b^2-4ac} ) / 2a$

We know that a = 1, b = - 5, and c = - 4 from the equation " $0 = x^2 - 5x - 4$ " ( which can be rewritten in the form $0 = ax^2 + bx + c$ ). Therefore, simply plug in these values into the quadratic formula to receive two solutions:

$x = 5 + ( \sqrt{( - 5 )^2 - 4( 1 )( - 4 )} ) / 2( 1 ),\\x = 5 + ( \sqrt{25 + 16} ) / 2,\\x = 5 + \sqrt{41} / 2,\\x = ( About ) 5.7$ - This is our positive solution

__________

$x = 5 - ( \sqrt{( - 5 )^2 - 4( 1 )( - 4 )} ) / 2( 1 ),\\x = 5 - ( \sqrt{25 + 16} ) / 2,\\x = 5 - \sqrt{41} / 2,\\x = ( About ) - 0.7$ - And this is our negative solution

You can see that - 0.7 is the negative real number solution to Joline's quadratic equation!

4 0

2 years ago

Jeremy opens a chocolate shop in the city. He pays $1,500 a month for rent and maintenance of the shop. The price of raw materia

KATRIN_1 [288]

Amount of money paid by Jeremy as rent and maintenance of shop per month = $1500
Cost of raw materials and manufacturing per month = $6000
Total cost that Jeremy has to spend per month = (1500 + 6000) dollars
      = 7500 dollars
Number of individual chocolates sold = 2400
Number of chocolates sold in boxes = 50 boxes
   = (12 * 50) chocolates
   = 600 chocolates
Then
Total number of chocolates sold by Jeremy = 2400 + 600
   = 3000
Now
Price of each chocolate = 7500/3000 dollars
   = 75/30 dollars
   = 5/2 dollars
   = 2.5 dollars
Price of 600 chocolates = 600 * (5/2) dollars
   = 300 * 5 dollars
   = 1500 dollars
Price of 12 chocolates = (1500/600) * 12
   = 15 * 2
   = 30 dollars
Then
We can say that each box of chocolate should be sold at $30. All the loose chocolates should be sold at $2.5 each.

8 0

2 years ago

The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches. Use the Empiric

maks197457 [2]

Answer: c)[50,60]

Step-by-step explanation:

The Empirical rule says that , About 68% of the population lies with the one standard deviation from the mean (For normally distribution).

We are given that , The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches.

Then by Empirical rule, about 68% of the heights of students lies between one standard deviation from mean.

i.e. about 68% of the heights of students lies between $\text{Mean}\pm\text{Standard deviation}$

i.e. about 68% of the heights of students lies between $55\pm5$

Here, $55\pm5=(55-5, 55+5)=(50,60)$

i.e. The required interval that contains the middle 68% of the heights. = [50,60]

Hence, the correct answer is c) (50,60)

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2 years ago

Complete the square to rewrite y = x2 - 6x + 15 in vertex form. Then state

love history [14]

Since $x^2$ is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.

So, if we think of 15 as 9+6, we have

$x^2-6x+9+6 = (x-3)^2+6$

Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).

Since the leading coefficient is 1, the parabola is facing upwards (it's U shaped), so the vertex is a minimum.

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2 years ago