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3 years ago

Enter the equation in standard form. y − 6 = −(x + 4)

Mathematics

1 answer:

worty [1.4K]3 years ago

3 0

<h3>Answer: x + y = 2</h3>

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Work Shown:

y - 6 = -(x + 4)

y - 6 = -x - 4

y = -x - 4 + 6 ..... adding 6 to both sides

y = -x + 2

y + x = 2 .... adding x to both sides

x + y = 2

The equation is in standard form Ax+By = C, with A = 1, B = 1, and C = 2.

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Find the equation of the line through point (5,1) and perpendicular to 5x−y=−3. Use a forward slash (i.e. "/") for fractions (e.

IRINA_888 [86]

Y = -1/5x + 2

A line perpendicular to another line has an opposite reciprocal slope. What opposite means is that you flip the sign (from - to + or from + to -) and reciprocal means that you flip the numerator and denominator (so if line A is perpendicular to line B and line As slope is -3, line Bs slope would be 1/3).

First find the slope of 5x - y = -3
Add y to both sides
5x = y - 3
Add 3 to both sides
y = 5x + 3

So the slope of the line is 5. That means the slope of of the perpendicular line is -1/5.

Plug the slope of the perpendicular line and the point (5, 1) into point slope form to solve the equation

y - y1 = m(x - x1)
y - 1 = -1/5(x - 5)
y - 1 = -1/5x + 1
y = -1/5x + 2

3 0

2 years ago

A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

1 year ago

WILL GIVE A BRAINLIEST PLEASE HELP!!!

kaheart [24]

A(n) = a₁.(r)ⁿ⁻¹, where a₁ = 1st term, r= common ratio and n, the rank

In the formula given a₁ = 5, r = 3/2 and n = 6 (we have to find the 6th term value).

a₆ = 5.(3/2)⁶⁻¹ = 5.(3/2)⁵ = 1215/32 (answer C)

7 0

3 years ago

Using the points [164,166]and[173,174] find the slope

Lana71 [14]

Answer:

8/9

Step-by-step explanation:

The equation to find a slope is y2-y1/x2-x1=m. (m is the slope)

174-166/173-164

8/9

So the slope is 8/9.

8 0

3 years ago

You want to buy a camera. The retail price is $75. The camera is on sale for 15% off . What is the sale price of the camera?

ludmilkaskok [199]

Answer:

$63.75

Step-by-step explanation:

15% off

Get percentage of retail price

1-0.15 = .85

0.85 = 85%

The sale price is 85% of the retail price

Multiply

0.85 * 75

$63.75

7 0

2 years ago