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2 years ago

What ordered pair is a solution to 5x -6y = -4 A. (3,-3) B. (3,3) C. (4,4)

Mathematics

1 answer:

Ilia_Sergeevich [38]2 years ago

5 0

Answer:

(4,4)

Step-by-step explanation:

5(4)-6(4)=-4

20-24=-4

-4=-4

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Help with line equations?

Alecsey [184]

First question

$line:~~~~y=x+3$

$curve:~~~~x^2+y^2=29$

now we have to replace the y of curve by the y of line, therefore

$x^2+(x+3)^2=29$

$x^2+x^2+6x+9=29$

$2x^2+6x+9-29=0$

$2x^2+6x-20=0$

we can multiply each member by $\frac{1}{2}$

$\boxed{\boxed{x^2+3x-10=0}}$

Now we have to find the roots of this funtion

$x^2+3x-10=0$

Sum and produc or Bhaskara

Then we find two axis

$\boxed{x_1=2~~and~~x_2=-5}$

now we replace this values to find the Y, we can replace in curve or line equation, I'll prefer to replace it in line equation.

$y=x+3$

$y_1=x_1+3$

$y_1=2+3$

$\boxed{y_1=5}$

$y_2=x_2+3$

$y_2=-5+3$

$\boxed{y_2=-2}$

Therefore

$\boxed{\boxed{P_1(2,5)~~and~~P_2(-5,-2)}}$
_______________________________________________________________

The second question give to us

$y=ax+b$

$P_1(2,13)$

$P_2(-1,-11)$

We just have to replace the value then we'll get a linear system.

point 1

$13=2a+b$

point 2

$-11=-a+b$

then our linear system will be

$\begin{Bmatrix}2a+b&=&13\\-a+b&=&-11\end{matrix}$

I'll multiply the second line by -1 and I'll add to first one

$\begin{Bmatrix}2a+(a)+b+(-b)&=&13+(-11)\\-a+b&=&-11\end{matrix}$

$\begin{Bmatrix}3a&=&24\\-a+b&=&-11\end{matrix}$

$\begin{Bmatrix}a&=&8\\-a+b&=&-11\end{matrix}$

therefore we can replace the value of a, at second line

$\begin{Bmatrix}a&=&8\\-8+b&=&-11\end{matrix}$

$\begin{Bmatrix}a&=&8\\b&=&-11+8\end{matrix}$

$\boxed{\boxed{\begin{Bmatrix}a&=&8\\b&=&-3\end{matrix}}}$

then our function will be

$\boxed{\boxed{y=8x-3}}$

_________________________________________________________________

The third one, we have

$line:~~~~y=3x-4$

$curve:~~~~y=x^2-2x-4$

This resolution will be the same of our first question.

Let's replace the y of curve by the y of line

$3x-4=x^2-2x-4$

$0=x^2-2x-4-3x+4$

therefore

$\boxed{\boxed{x^2-5x=0}}$

now we have to find the roots of this function.

$x^2-5x=0$

put x in evidence

$x*(x-5)=0$

$\boxed{x_1=0~~and~~x_2=5}$

then

$y=3x-4$

$y_1=3x_1-4$

$y_1=3*0-4$

$\boxed{y_1=-4}$

$y_2=3x_2-4$

$y_2=3*5-4$

$y_2=15-4$

$\boxed{y_2=11}$

our points will be

$\boxed{\boxed{P_1(0,-4)~~and~~P_2(5,11)}}$

I hope you enjoy it ;)

5 0

3 years ago

Imagine a pet shelter that has noticed older animals (age 5+) have lower adoption rates. This shelter (which has only cats and d

GenaCL600 [577]

Answer:

(a) The tree diagram is attached as an image

(b) P(NO ∩ D ∩ NA) = 0.27

(d) P(A) = 0.438

(e) P(A|C) = 0.162

(f) P(C|A) = 0.374

Step-by-step explanation:

Let C denote cats and D denote dogs. Then,

P(C) = 40% = 0.4 and

P(D) = 60% = 0.6

Let O denote that an animal is older and NO denote that an animal is not older. Then for Cats,

P(O) = 20% = 0.2 and

P(NO) = 1 - 0.2 = 0.8

Similarly, for Dogs,

P(O) = 10% = 0.1 and

P(NO) = 1 - 0.1 = 0.9

Let A denote that an animal is adopted and NA denote that an animal is not adopted. For older cats,

P(A) = 5% = 0.05 and

P(NA) = 1 - 0.05 = 0.95

Similarly, for older dogs,

P(A) = 10% = 0.1 and

P(NA) = 1 - 0.1 = 0.9

For cats that are not older,

P(A) = P(NA) = 0.5

For dogs that are not older

P(A) = P(NA) = 0.5

(a) We can illustrate this information using a tree diagram as shown in the image attached. The first stage represents whether the animal is a cat or a dog. Then, they are classified as older or not older and then they are classified according to if they are adopted or not.

(b) We need to compute the probability that the selected animal is not older and a dog and is not adopted i.e. P(NO ∩ D ∩ NA). For this we will use the tree diagram and trace out the path D to NO to NA. We need this sample point hence, we will multiply all three probabilities and find out the answer.

P(NO ∩ D ∩ NA) = (0.6)*(0.9)*(0.5)

P(NO ∩ D ∩ NA) = 0.27

(c) Now, we need to compute P(O ∩ C ∩ A). So, using the tree diagram, we will trace out the route from C to O to A and multiply these three probabilities to get our answer.

P(O ∩ C ∩ A) = 0.4 * 0.2 * 0.05

P(O ∩ C ∩ A) = 0.004

(d) To compute the probability that a randomly chosen animal is adopted, we need to see the combinations in our tree diagram where we find adopted (A). The possible combinations can be: (C, O, A), (C, NO, A), (D, O, A) and (D, NO, A). So, the probability of adopted is:

P(A) = (C, O, A) + (C, NO, A) + (D, O, A) + (D, NO, A)

= 0.4*0.2*0.05 + 0.4*0.8*0.5 + 0.6*0.1*0.1 + 0.6*0.9*0.5

= 0.002 + 0.16 + 0.006 + 0.27

P(A) = 0.438

(e) Now, we are given that the chosen animal is a cat and we need to compute the probability that it is adopted. So, from the tree diagram, we can see that a cat who is oler can be adopted (C, O, A) and a cat who is not older can also be adopted (C, NO, A). These two sample points make up that probability that a cat is adopted. So,

P(A|C) = (C, O, A) + (C, NO, A)

= 0.4*0.2*0.05 + 0.4*0.8*0.5

= 0.002 + 0.16

P(A|C) = 0.162

(f) P(C|A) = P(C∩A)/P(A)

Now this can hold true for older as well as not older cats. We will consider both and add them.

P(C|A) = P(C∩A)/P(A) (older cats) + P(C∩A)/P(A) (not older cats)

= (0.4*0.2*0.05)/0.438 + (0.4*0.8*0.5)/0.438

= 0.004/0.438 + 0.16/0.438

= 0.009132 + 0.36529

P(C|A) = 0.374

8 0

3 years ago

PLEASE HELP! BRAINLIEST! So desperate

steposvetlana [31]

Answer:

B= A = 68

Step-by-step explanation:

ACE = BCD similar triangles. Similar triangles have equal angles.

A=B

C=C

D=E

This means if we can find angle B, we know angle A

BCD is a triangle so it equals 180 degrees

B+C+D = 180

B + 74+38 = 180

Combine like terms

B +112 = 180

Subtract 112 from each side

B +112-112 = 180-112

B = 68

Since we know angle B, we know angle A

B= A = 68

4 0

3 years ago

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There is a rectangular prism with the volume of 30 X 17 X 45 X 9. What is the volume

STatiana [176]

You have too many numbers we only need 3

8 0

2 years ago

Which of the following is a composite number? A. 91 B. 29 C. 139 D. 13

alexdok [17]

91 is a composite number because has more than 3 factors, which include 13 and 7. Hope this helped!

4 0

2 years ago