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3 years ago

Write the quadratic equation y= x^2 -6x = 7 in vertex form.

Mathematics

1 answer:

lapo4ka [179]3 years ago

7 0

Answer:

(x - 3)² - 16 = 0

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Subtract 7 from both sides

x² - 6x + 7 = 0 ← in standard form

with a = 1, b = - 6

Given a quadratic in standard form then the x- coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$ = - $\frac{-6}{2}$ = 3

Substitute x = 3 into the equation for y

y = 3² - 6(3) - 7 = 9 - 18 - 7 = - 16 ⇒ (h, k) = (3, - 16)

y = (x - 3)² - 16 = 0

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What is the volume of the cylinder

kogti [31]

Answer:

Step-by-step explanation:

Volume of the figure = Volume of cylinder + Volume of cone

Note: A cone having the same radius and height as cylinder have a volume (1/3) of cylinder

Volume of cone=(1/3)*96=32

Volume of the figure = 32+96=128

5 0

3 years ago

Could someone help here, thankyou!

ludmilkaskok [199]

Answer:

x = 6 cm

Step-by-step explanation:

Given ratio of sides of similar figures = a : b , then

ratio of areas = a² : b²

Here ratio of areas = 5 : 45 = 1 : 9 , so

ratio of sides = $\sqrt{1}$ : $\sqrt{9}$ = 1 : 3

Thus side of B is 3 times side of A

x = 3 × 2 = 6 cm

3 0

3 years ago

What is the slope of the line passing through the points (-1,-7) and (-9, -2) ?

Dominik [7]

The equation for slope is:
(y2 - y1) / (x2 - x1)

-2 -(-7) = 5
-9 -(-1) = -8

Slope of the line:

5/-8 or -5/8

7 0

3 years ago

Read 2 more answers

Which shapes can be drawn with two opposite angles equal to 105°

sertanlavr [38]

Answer:

see the explanation

Step-by-step explanation:

we know that

A shape with two opposite angles equal to 105° could be a quadrilateral, a parallelogram, a rhombus or a trapezoid

Because

A quadrilateral: A quadrilateral is a four-sided polygon. The sum of the interior angles in any quadrilateral must be equal to 360 degrees

If the quadrilateral have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

$360^o-2(105^o)=150^o$

A parallelogram: A Parallelogram is a flat shape with opposite sides parallel and equal in length. Opposite angles are congruent and consecutive angles are supplementary

If the parallelogram have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

$180^o-105^o=75^o$

A rhombus: A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel. Opposite angles are congruent and consecutive angles are supplementary

If the Rhombus have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

$180^o-105^o=75^o$

A trapezoid: A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel

If the trapezoid have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

$360^o-2(105^o)=150^o$

4 0

3 years ago

Middle School: Math (10 Points)

sasho [114]

1) Our marbles will be blue, red, and green. You need two fractions that can be multiplied together to make 1/6. There are two sets of numbers that can be multiplied to make 6: 1 and 6, and 2 and 3. If you give the marbles a 1/1 chance of being picked, then there's no way that a 1/6 chance can be present So we need to use a 1/3 and a 1/2 chance. 2 isn't a factor of 6, but 3 is. So we need the 1/3 chance to become apparent first. Therefore, 3 of the marbles will need to be one colour, to make a 1/3 chance of picking them out of the 9. So let's say 3 of the marbles are green. So now you have 8 marbles left, and you need a 1/2 chance of picking another colour. 8/2 = 4, so 4 of the marbles must be another colour, to make a 1/2 chance of picking them. So let's say 4 of the marbles are blue. We know 3 are green and 4 are blue, 3 + 4 is 7, so the last 2 must be red.
The problem could look like this:

A bag contains 4 blue marbles, 2 red marbles, and 3 green marbles. What are the chances she will pick 1 blue and 1 green marble?

You should note that picking the blue first, then the green, will make no difference to the overall probability, it's still 1/6. Don't worry, I checked

2) a - 2% as a probability is 2/100, or 1/50. The chance of two pudding cups, as the two aren't related, both being defective in the same packet are therefore 1/50 * 1/50, or 1/2500.

b - 1,000,000/2500 = 400
400 packages are defective each year

5 0

3 years ago