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2 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

Leto [7]2 years ago

5 0

Answer:

(x, y) = (8, -1)
(x, y) = (7, 10.5)

Step-by-step explanation:

1. You can use the expression for y to substitute into the first equation:

2x +4(1/4x -3) = 12

2x +x -12 = 12 . . . . . . eliminate parentheses

3x = 24 . . . . . . . . . . . add 12; next divide by 3

x = 8 . . . . . matches choice C

2. You can use the expression for y to substitute into the second equation:

x -2(2x -3.5) = -14

-3x +7 = -14 . . . . . . eliminate parentheses

21 = 3x . . . . . . . . . . add 3x+14; next divide by 3

7 = x . . . . . matches the third choice

_____

When the answer choices are sufficiently different, you only need to find one value to determine which is the correct choice. (If you want to check your work further, you can substitute the other answer value into the two equations to see if it works.)

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In ∆ABC, m∠ACB = 90°, m∠A = 40°, and D ∈ AB such that CD is perpendicular to side AB. Find m∠DBC and m∠BCD.

podryga [215]

Answer: ∠B = 50°

∠BCD = 40°

<u>Step-by-step explanation:</u>

ACB is a right triangle where ∠A = 40° and ∠C = 90°.

Use the Triangle Sum Theorem for ΔABC to find ∠B:

∠A + ∠B + ∠C = 180°

40° + ∠B + 90° = 180°

∠B + 130° = 180°

∠B = 50°

BCD is a right triangle where ∠B = 50° and ∠D = 90°.

Use the Triangle Sum Theorem for ΔBCD to find ∠C:

∠B + ∠C + ∠D = 180°

50° + ∠C + 90° = 180°

∠C + 140° = 180°

∠C = 40°

8 0

3 years ago

What can be the next step please helppppppppppppp

stepladder [879]

Answer:

Statement: Triangle ACD is congruent to Triangle BCD

Reason: SSA (Side, Side, Angle)

8 0

2 years ago

Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. In a random sample of 12 drivers driving between 1

Lesechka [4]

Answer:

(a) 0.28347

(b) 0.36909

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

$P(x=r)=^nC_rp^rq^{n-r}$

(a) Exactly two will be drunken drivers.

$P(x=2)=^{12}C_{2}(0.2)^{2}(0.8)^{12-2}$

$P(x=2)=66(0.2)^{2}(0.8)^{10}$

$P(x=2)=\approx 0.28347$

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

$P(x=3\text{ or }x=4)=P(x=3)\cup P(x=4)$

$P(x=3\text{ or }x=4)=P(x=3)+P(x=4)$

Using binomial we get

$P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}$

$P(x=3\text{ or }x=4)=0.236223+0.132876$

$P(x=3\text{ or }x=4)\approx 0.369099$

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

$P(x\geq 7)=1-P(x$

$P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]$

$P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]$

$P(x\leq 7)=1-[0.9961]$

$P(x\leq 7)=0.0039$

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

$P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)$

$P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315$

$P(x\leq 5)=0.9806$

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

5 0

2 years ago

??????((((((((??????????

mart [117]

Answer:

G. 17.3

solution:

5 0

2 years ago

If y2 = x3 + 2, which statement is true? The equation is a function at all values of x. The equation is not a function. The equa

tatyana61 [14]

Answer:

The equation is not a function.

Step-by-step explanation:

We are given that

$y^2=x^3+2$

$y=\pm\sqrt{x^3+2}$

Function: It is mapping between the values of two sets A and B.

Each element of A has unique value in set B.

By definition of function

In given function

y has no unique value for each value of x.

Substitute x=0

$y=\pm \sqrt{0+2}=\pm \sqrt 2$

Hence, it is not a function.

6 0

3 years ago