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3 years ago

Which of the following points satisfies the inequality x ≥ -3? (select all that apply) a(0, -2) b(-3, 4) c(-4, 2) d(5, -5)

Mathematics

1 answer:

VladimirAG [237]3 years ago

8 0

Answer:

a, b, d

Step-by-step explanation:

For the inequality x ≥ -3 . . .

a(0, -2) . . . 0 ≥ -3, true

b(-3, 4) . . . -3 ≥ -3, true

c(-4, 2) . . . -4 ≥ -3, FALSE

d(5, -5) . . . 5 ≥ -3, true

Points a, b, d satisfy the inequality.

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Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?

densk [106]

Answer:

$A.\ y = x^2 - 6x + 13$ is the correct answer.

Step-by-step explanation:

We know that vertex equation of a parabola is given as:

$y = a(x-h)^2+k$

where $(h,k)$ is the vertex of the parabola and

$(x,y)$ are the coordinate of points on parabola.

As per the question statement:

The parabola opens upwards that means coefficient of $x^{2}$ is positive.

Let $a = +1$

Minimum of parabola is at x = 3.

The vertex is at the minimum point of a parabola that opens upwards.

$\therefore$ $h = 3$

Putting value of a and h in the equation:

$y = 1(x-3)^2+k\\\Rightarrow y = (x-3)^2+k\\\Rightarrow y = x^2-6x+9+k$

Formula used: $(a-b)^2=a^{2} +b^{2} -2\times a \times b$

Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.

Comparing $y = x^2 - 6x + 13$ and $y = x^2-6x+9+k$

13 = 9+k

k = 4

Please refer to the graph attached.

Hence, correct option is $A.\ y = x^2 - 6x + 13$

3 0

2 years ago

Read 2 more answers

Rename the decimal numbers as a fraction. 1.0.15 2.0.37. 3.0.5 4. 1.38 5.0.4

olasank [31]

Answer:

See image

Step-by-step explanation:

You put One-place decimals over ten and then simplify.

You put Two-place decimals over 100 and then simplify. See image.

6 0

2 years ago

Solve the equation: .2x(.7x-5)+0.2=1.4(x-1.6)

Ilia_Sergeevich [38]

9514 1404 393

Answer:

x = 8/7

Step-by-step explanation:

.2(.7x-5)+0.2=1.4(x-1.6) . . . . given

Eliminating parentheses, we have ...

0.14x -1 +0.2 = 1.4x -2.24

1.44 = 1.26x . . . . . . . add 2.24-0.14x to both sides

x = 1.44/1.26 . . . . . . divide by the coefficient of x

x = 8/7 . . . . . . . . . . .simplify the fraction

As a repeating decimal, the value of x is ...

$x=1.\overline{142857}$

However, the notation 1.(142857) is usually reserved for the case where the contents of parentheses are being multiplied by the factor in front. You would need to consult your instructions to see how the decimal version of the answer should be entered. (Quite often, rounding is suggested.)

_____

Additional comment

The equation in the text of your question is different from the one in the picture. We have answered for the one in the picture. The text asks for the solution of a quadratic. Those two solutions are approximately 1.085 and 16.057.

6 0

2 years ago

Read 2 more answers

5/8 9/x the figures are similar find x

Drupady [299]

5/8 9/x

Cross multiply

9x8=72
5×x=5x

Rewrite the equation

72 = 5x

Divide by 5

72÷5=14.4

So, x=14.4

8 0

3 years ago

If 4x-1=X, Find 30x a) 10 b) 40 C) 12 d)11 How do you solve this?

cestrela7 [59]

Answer:

(a)

Step-by-step explanation:

Given

4x - 1 = x ( subtract x from both sides )

3x - 1 = 0 ( add 1 to both sides )

3x = 1 ( multiply both sides by 10 )

30x = 10 → (a)

3 0

2 years ago