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3 years ago

Three more than a certain number is 12 less than four times a number

Mathematics

1 answer:

k0ka [10]3 years ago

4 0

Answer1.7 Step-by-ste explipcación:

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Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

choli [55]

Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

$y=x^{2}-2x-3$

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

4 0

3 years ago

Here are two paint mixtures: • 3 cups of white and 4 cups of blue. • 6 cups of white and 8 cups of blue. Both mixtures make the

lesantik [10]

Answer:

The mixture that is an equivalent ratio is:

1.5 white 2 blue

Step-by-step explanation:

a) Data and Calculations:

Mixtures of the same color because they are in equivalent ratios:

3 cups of white and 4 cups of blue: equivalent ratio = 0.75: 1 (75%) since 3/4 = 75%

6 cups of white and 8 cups of blue. equivalent ratio = 0.75: 1 (75%) since 6/8 = 75%

Other mixtures:

5 cups white 6 blue: equivalent ratio = 0.83: 1 (83%) since 5/6 = 83%

1 white 1 1/2 blue: equivalent ratio = 0.67: 1 (67%) since 1/1.5 = 67%

4 white 3 blue: equivalent ratio = 1: 75 (1.33%) since 4/3 = 1.33%

1.5 white 2 blue: equivalent ratio = 0.75: 1 (75%) since 1.5/2 = 75%

Therefore, the mixture with equivalent ratio as the initial mixtures is 1.5 while 2 blue.

4 0

2 years ago

The product of 3 and a number x is 2/3 .

FrozenT [24]

Rewritten 3x = 2/3

then x = (2/3)/3
therefore x = 0.22

So I don’t think any of them is right

7 0

3 years ago

Read 2 more answers

Can someone please help

Andreas93 [3]

Answer:

x = 13

Step-by-step explanation:

→ Remember the amount of degrees a triangle sums to

180°

→ Make an equation

8x - 44 + 8x - 44 + 8x - 44 = 180

→ Simplify

24x - 132 = 180

→ Add 132 to both sides

24x = 312

→ Divide both sides by 24

x = 13

4 0

2 years ago

Read 2 more answers

Write an equation of the line that passes through (4,-2) and is parallel to y=1/2x -7

myrzilka [38]

Answer:

5 x - 6 y - 8 = 0.

Step-by-step explanation:

6 0

2 years ago