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ioda
2 years ago
15

Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two clas

ses, and he took a total of 90 minutes Which value of k would cause the system of linear equations 35 x + 14 y = 119 and 5 x + 2 y = k to have an infinite number of solutions?
3
7
17
21
Mathematics
1 answer:
Grace [21]2 years ago
5 0

A system of the equation to be Dependent Consistent System the system must have multiple solutions. The correct option is C.

<h3>What is a System of equation?</h3>

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the system of equations to have infinite number of solutions, the lines of the equations must coincide, therefore, the line must overlap on each other.

For the lines to overlap the equations must be in a ratio. Therefore, the ratio of the left sides of the equations must be equal to the right side,

\dfrac{35x+14y}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac{7(5x+2y)}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac71 = \dfrac{119}{k}\\\\k = 17

Hence, the value of k must be 17, therefore, the correct option is C.

Learn more about System of equation:

brainly.com/question/12895249

#SPJ1

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I NEED HELP PLZ ASAP!!!!! In right triangle ABCD above, x = A. 6 B. 8 C. 6√2 D. 10 E. 13
REY [17]

Answer:

x=6

Step-by-step explanation:

Since this is a right triangle we can use  the Pythagorean theorem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

x^2 + (x+2)^2 = (2x-2)^2

FOIL (x+2)^2 = x^2 +2x+2x+4 = x^2 +4x+4

FOIL (2x-2)^2 = 4x^2 -4x -4x+4 = 4x^2 -8x+4

Replacing these in to the equation

x^2 +x^2 +4x+4 = 4x^2 -8x+4

Combine like terms

2x^2 +4x +4 = 4x^2 -8x +4

Subtract 4 from each side

2x^2 +4x +4-4 = 4x^2 -8x +4-4

2x^2 +4x = 4x^2 -8x

Subtract 2x^2 from each side

2x^2 -2x^2+4x = 4x^2-2x^2 -8x

4x = 2x^2 -8x

Subtract 4x from each side

4x-4x = 2x^2 -8x-4x

0 = 2x^2 -12x

Factor out a 2x

0 = 2x(x-6)

Using the zero product property

2x =0  x-6 =0

x =0  x-6+6 = 0+6

x = 0  c=6

5 0
3 years ago
What is the vertical asymptotes of the function f(x)=x-2/x*2-3x-4
frozen [14]

Answer:

<h2>x = -1 and x = 4</h2>

Step-by-step explanation:

f(x)=\dfrac{x-2}{x^2-3x-4}\\\\\text{DOMAIN}:\\\\x^2-3x-4\neq0\\\\x^2-4x+x-4\neq0\\\\x(x-4)+1(x-4)\neq0\\\\(x-4)(x+1)\neq0\iff x-4\neq0\ \wedge\ x+1\neq0\\\\x\neq4\ \wedge\ x\neq-1\\\\\text{Therefore the vertical asymptotes are:}\\\\x=-1\ and\ x=4.

4 0
3 years ago
X^2-4x+3 factorize into its factors and give me answer I will giv u anda burger
Ghella [55]

Answer:

(x - 3)(x - 1)

Step-by-step explanation:

Consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term.

The factors are - 3 and - 1, since

- 3 × - 1 = + 3 and - 3 - 1 = - 4, hence

x² - 4x + 3 = (x - 3)(x - 1) ← in factored form

6 0
3 years ago
Read 2 more answers
Part 2 HELP PLZ tHIS HARd
natita [175]

You have to find the mean median and mode with the three day period and the four day period and compare them.

I believe that unless I did something wrong, the answer is B!

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6 0
2 years ago
Jeannie is an experienced business traveler, often traveling back and forth from San Francisco to the East Coast several times p
lesya692 [45]

Answer:

The probability that Jeannie will miss her flight because her total time for catching her plane exceeds one hour is 0.0026.

Jeannie should leave her office 55 minutes early.

Step-by-step explanation:

Let <em>X</em> = time it requires Jeannie to catch her plane.

The random variable <em>X</em> is normally distributed, N(46, 5).

Compute the probability that Jeannie will miss her flight because her total time for catching her plane exceeds one hour as follows:

P(X>60)=P(\frac{X-\mu}{\sigma} >\frac{60-46}{5} )\\=P(Z>2.8)\\=1-P(Z

The probability that Jeannie will miss her flight because her total time for catching her plane exceeds one hour is 0.0026.

Now, it is provided that Jeannie has 96% chance of catching her flight if she reaches under <em>x</em> minutes.

That is, P (X < x) = 0.96.

Compute the value of <em>x</em> as follows:

P(X

**Use the <em>z</em>-table to compute the value of <em>z</em>.

The value of <em>z</em> is 1.751.

Compute the value of <em>x</em> as follows:

z=\frac{x-46}{5}\\ 1.751=\frac{x-46}{5}\\x=46+(1.751\times5)\\=54.755\\\approx 55

Thus, Jeannie should leave her office 55 minutes early.

4 0
3 years ago
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