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3 years ago

Write the equation of the line perpendicular to y=4/3x+1 that passes through the points (-8, 4).

Mathematics

1 answer:

Murrr4er [49]3 years ago

3 0

Answer:

The equation is;

y = -3/4x + 12

Step-by-step explanation:

The general form for the equation of a straight line is;

y = mx + b

where m is the slope and b is the y-intercept

With respect to this question;

4/3 is the slope and 1 is the intercept

If two lines are perpendicular, then the product of their slopes is -1

Mathematically;

4/3 * m2 = -1

m2 = -3/4

So to find the equation of this second line, we use the point slope form

This is;

y-y1 = m(x-x1)

y-4 = -3/4(x + 8)

y- 4 = -3/4x + 8

y = -3/4x + 12

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From a bowl containing five red, three white, and seven blue chips, select four at random and without replacement. Compute the c

snow_lady [41]

Answer:

The probability is $\frac{5}{9}$

Step-by-step explanation:

Let A be the event of one red, zero white, and three blue chips,

And, B is the event of at least three blue chips,

Since, A ∩ B = A (because If A happens that it is obvious that B will happen )

Thus, the conditional probability of A if B is given,

$P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}=\frac{P(A)}{P(B)}$

Now, red chips = 5,

White chips = 3,

Blue chips = 7,

Total chips = 5 + 3 + 7 = 15

Since, the probability of one red, zero white, and three blue chips, when four chips are chosen,

$P(A)=\frac{^5C_1\times ^3C_0\times ^7C_3}{^{15}C_4}$

$=\frac{5\times 35}{1365}$

$=\frac{175}{1365}$

$=\frac{5}{39}$

While, the probability that of at least three blue chips,

$P(B)=\frac{^8C_1\times ^7C_3+^8C_0\times ^7C_4}{^{15}C_4}$

$=\frac{8\times 35+35}{1365}$

$=\frac{315}{1365}$

$=\frac{3}{13}$

Hence, the required conditional probability would be,

$P(\frac{A}{B})=\frac{5/39}{3/13}$

$=\frac{65}{117}$

$=\frac{5}{9}$

4 0

3 years ago

Which expression shows the resuit of applying the distributive property to 12(5y+4)

Alex Ar [27]

Answer:

60y+48

Step-by-step explanation:

Multiply both terms inside the parentheses by 12

6 0

3 years ago

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If one leg of a right triangle has a measure of 7 cm and the other leg has a measure of 9 cm, what is the measure of the hypoten

KonstantinChe [14]

Answer:

11.4

Step-by-step explanation:

using the hypotenuse formula,7 to the second power plus 9 to the second is 130 after you would find the square root of 130 which is 11.401754251 but rounded is 11.4

3 0

4 years ago

A 3-D printer is used to produce plastic models of crayons, which will be used as part of a larger model. The dimensions of the

Zolol [24]

Answer:

30295 $mm^3$

Step-by-step explanation:

V of pencil = V of cone + V of cylinder

let's find V of cone first (you can do cylinder first but I'm getting the hard stuff out first)

V cone = $\frac{1}{3} \pi r^{2} h$

now plug known values in

$\frac{1}{3}(36)(9)(3.14) =339.12 \\$ $mm^{3}$

now cylinder

V cyl. = $\pi r^{2} h$

plugging known values

= $(3.14)(6^2)(64) = (3.14)(36)(64)$ = 7234.56 $mm^3$

add the two values together to find the volume of the crayon

339.12 + 7234.56= 7573. 68 $mm^3$

rounding to nearest millimeter: 7574 $mm^3$

5 0

3 years ago

Which expression is equal to 4 (2+3) ? 1. 2+12 2. 4+5 3. 8+3 4. 8+12

allsm [11]

4. 8+12=20

4 (2+3)
First you add 2+3 and get 5
Next, since the 5 is now in the parentheses, it indicates that you have to multiply
Finally, 5 times 4=20

5 0

3 years ago

Read 2 more answers