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lana66690 [7]
3 years ago
5

The ordered pair (a,b) satisfies the inequality y>x+3. Which statement is true ?

Mathematics
1 answer:
nordsb [41]3 years ago
3 0

Answer:The correct option is(C). b is greater than 3.

Step-by-step explanation:

 Given that the ordered pair (a, b) satisfied the following inequality :

We are to select the TRUE statement from the given options.

Since the ordered pair (a, b) satisfies inequality (i), so we have

Therefore, b is greater than 3.

Thus, the correct option is (C). b is greater than 3.

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Write the equation of the line that passes through 7, 0 and is parallel to y = -3x + 4​
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Answer:

y = - 3x + 21

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes , then

y = - 3x + c ← is the partial equation

To find c substitute (7, 0 ) into the partial equation

0 = - 21 + c ⇒ c = 0 + 21 = 21

y = - 3x + 21 ← equation of parallel line

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3 years ago
Two urns contain white balls and yellow balls. The first urn contains 2 white balls and 7 yellow balls and the second urn contai
Romashka [77]

-- The first urn has 9 balls in it all together, and 2 of them are white.
If you don't peek, then the prob of pulling out a white ball is  2/9 .

-- The second urn has 13 balls in it all together, and 3 of them are white.
If you don't peek, then the prob of pulling out a white ball is  3/13 .

-- The probability of being successful BOTH times is

        (2/9) x (3/13)  =  ( 6/117 )  =  about  0.0513  or  5.13% (rounded) 
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What Shape is generated when Triangle ABC is rotated around the vertical line through B and C
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The shape that is generated is a Cone.

A triangle, when rotated about one of it's side will generate a solid in a form of a Cone. The cone could be a hollow one or a solid filled one, depending on the properties of the triangle being rotated.
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Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -
GaryK [48]

Consider all parabolas:

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y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

2.

y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

3.

y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

4.

y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

5.

y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

6.

y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

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3 years ago
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lidiya [134]
X=6 and x=1

You can find your zeros by determining what you have to plug into the function in order for it to equal zero

If we plug in 6, for example we’d get (6-6)(x-1)

Simplified this is 0(x-1)

Anything times 0 is 0, so this is one of our zeros.

Same goes for x-1, we just need to plug in 1 for it to equal 0

Therefore there are zeros at x=1 and x=6 :))
7 0
3 years ago
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