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2 years ago

11

Find the slope of the line containing the pair of points (-6,4) and (3. - 3) The slope of the line is (Simplify your answer. Typ

e an integer or a fraction.)

1 answer:

Pie2 years ago

6 0

Answer:

-0.7777777777778.

Step-by-step explanation:

I think as a fraction it's -77/100

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The length of a rectangle is 5959 inches greatergreater than twice the width. if the diagonal is 2 inches more than the length,

lorasvet [3.4K]

Length: 2w + 59

width: w

diagonal: (2w + 59) + 2 = 2w + 61

Length² + width² = diagonal²

(2w + 59)² + (w)² = (2w + 61)²

(4w² + 118w + 3481) + w² = 4w² + 122w + 3721

5w² + 118w + 3481 = 4w² + 122w + 3721

w² + 118w + 3481 = 122w + 3721

w² - 4w + 3481 = 3721

w² - 4w - 240 = 0

a = 1, b = -4, c = -240

w = $[-(b) +/- \sqrt{(b)^{2} - 4(a)(c) }]/2(a)$

= $[-(-4) +/- \sqrt{(-4)^{2} - 4(1)(-240) }]/2(1)$

= $[4 +/- \sqrt{(16 + 960) }]/2$

= $[4 +/- \sqrt{(976) }]/2$

= $[2 +/- 4\sqrt{(61) }]/2$

= $1 +/- 2\sqrt{(61) }$

since width cannot be negative, disregard 1 - 2√61

w = 1 + 2√61 ≈ 16.62

Length: 2w + 59 = 2(1 + 2√61) + 59 = 2 + 4√61 + 59 = 61 + 4√61 ≈ 92.24

Answer: width = 16.62 in, length = 92.24 in

7 0

2 years ago

Eva payrolls for on a number cube and the number of cubes roll 24 times then what is a reasonable prediction for the number of s

Allushta [10]

Answer:

The reasonable prediction for successful rolls is 4.

Step-by-step explanation:

Assuming the rolling cube is a fair 6 sided cube, so the probability of success of one roll is given as

$P(Success)=\dfrac{Number\ of\ successful\ events}{Number\ of\ total\ events}$

$P(Success)=\dfrac{1}{6}$

The total success is given as

$P(Total\ Success)=P(Success)\times Number\ of\ events$

For 24 rolls it is given as

$P(Total\ Success)=P(Success)\times Number\ of\ events\\P(Total\ Success)=\dfrac{1}{6}\times 24\\P(Total\ Success)=4$

So the reasonable prediction for successful rolls is 4.

3 0

2 years ago

Could someone please explain I keep getting the wrong answer

Naddika [18.5K]

Of course! so basically for each value of x, for example -6, plug it into the equation. so for -6 do -2/3(-6)+7. hope this helps!

3 0

2 years ago

The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

2 years ago

Solve for x using the diagram

liraira [26]

Its bh 5 time 7 = 35 is ur hight

6 0

2 years ago