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4 years ago

Which of the following is a solution of y - x > -3? (6, 2) (2, 6) (2, -1)

Mathematics

1 answer:

posledela4 years ago

7 0

y - x > -3

(6, 2) → x = 6, y = 2

substitute

2 - 6 = - 4 < -3 NOT

(2, 6) → x = 2, y = 6

substitute

6 - 2 = 4 > -3 CORRECT

(2, -1) → x = 2, y = -1

substitute

-1 - 2 = -3 NOT

Answer: (2, 6)

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Please apply the properties of rational exponents to simplify expressions with radical or rational exponents. Explain the steps

schepotkina [342]

Step-by-step explanation:

Product property

If the bases are the same, you don't multiple them. However, if they are the same, you do multiple for example : (2³ * 2¹ = 2⁴.when the bases are the same) (2³ * 3¹ =6⁴. When the bases are not the same
We add the index.

Quotient property

Same here, if the bases are the same, they stay the way they were
We subtract the index

Power property

Here we multiple the index because of the bracket for example : (9²)²= 9⁴

Negetive exponent property

When ever the index has a negative sign its convected to a fraction, for instance : 9¯² = 1 /9²
Note, when it turns to a fraction th index becomes positive

6 0

3 years ago

PLs help 50 PTS!!!!! PLEASE ILL GIVE BRAINLIEST!!!!!

Nookie1986 [14]

Answer:

$\large\boxed{y=\dfrac{1}{4}x^2-x-4}$

Step-by-step explanation:

The equation of a parabola in vertex form:

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

(h, k) - vertex

The focus is

$\left(h,\ k+\dfrac{1}{4a}\right)$

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of a using $k+\dfrac{1}{4a}$

k = -5

$-5+\dfrac{1}{4a}=-4$ add 5 to both sides

$\dfrac{1}{4a}=1$ multiply both sides by 4

$4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4$

$\dfrac{1}{a}=4\to a=\dfrac{1}{4}$

Substitute

$a=\dfrac{1}{4},\ h=2,\ k=-5$

to the vertex form of an equation of a parabola:

$y=\dfrac{1}{4}(x-2)^2-5$

The standard form:

$y=ax^2+bx+c$

Convert using

$(a-b)^2=a^2-2ab+b^2$

$y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5$

use the distributive property: a(b+c)=ab+ac

$y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4$

3 0

4 years ago

PLEASE HELP!!!! 25 POINTS!!!!

Andrei [34K]

Answer:

0.9562

Step-by-step explanation:

Binomial probability is mathematically expressed as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}$

Given that p=0.18, n=5 , is calculated as:

$P(X\leq 2)=P(0)+P(1)+P(2)\\\\={5\choose 0}0.18^0(1-0.18)^5+{5\choose 1}0.18^1(1-0.18)^4+{5\choose 2}0.18^2(1-0.18)^3\\\\=0.3707+0.4069+0.1786\\\\=0.9562$

Hence, the probability of no more than 2 successes in 5 trials is 0.9562

4 0

3 years ago

A french class has a total of 25 student.The number of males is 7 more than the number of females how many males and how many fe

Lady_Fox [76]

Answer:

16 males and 9 females

Step-by-step explanation:

To solve this we can use a system of equations.

Let's start by naming the number of females x.

The number of males would then be y.

Using these variables, we can set up 2 equations using info provided:

A french class has a total of 25 students, -> x+y=25

The number of males is 7 more than the number of females -> x+7=y

Use substitution to solve.

From the second equation:

x+7=y

Subtract 7 from both sides.

x=y-7

Substitute that into the first equation.

x+y=25

y-7+y=25

Combine like terms.

2y-7=25

Add 7 to both sides.

2y=32

Divide both sides by 2.

y=16

Substitute y=16 into equation 2.

x+7=y

x+7=16

Subtract 7 from both sides.

x=9

Therefore, there are 16 males and 9 females in the french class.

3 0

3 years ago

Read 2 more answers

Given that mCD=20°, find mBC

frosja888 [35]

Answer:

70°

Step-by-step explanation:

$m\widehat {BC} = 90\degree - m\widehat {CD}$

$m\widehat {BC} = 90\degree -20\degree$

$m\widehat {BC} = 70\degree$

5 0

3 years ago