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elixir [45]
3 years ago
11

Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12 A coordinate grid with one line labele

d 8 x minus 4 y equals 12. The line passes through a point at (0, negative 3), (1, negative 1) and a point at (1.5, 0). -2 - 2
Mathematics
1 answer:
nydimaria [60]3 years ago
4 0

Answer:

A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2

Step-by-step explanation:

The equation of the given line is 8·x - 4·y = 12

Which gives;

8·x- 12= 4·y

y = 2·x - 3

Given that the line passes through the points (0, -3) and (1, -1), we have;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;

Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2

y - (-3) = 2×(x - 0)

y = 2·x - 3 which is the equation of the given line

For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x  - 6 to have no solution, the slope of the two lines should be equal that is m = 2

Given that the line passes through the point (1.5, 0), we have;

y - 0 = 2×(x - 1.5)  

y = 2·x - 3...................(1)

For the equation, y = m·x  - 6, when m = 2, we have;

y = 2·x  - 6..................(2)

Solving equations (1) and (2) gives;

2·x - 3 = 2·x  - 6, which gives;

2·x - 2·x=  - 3 - 6

0 = 9

Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.

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13. Find the vertex of f(x)=x2 -6x +8 .
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Answer:

  a  (3,-1)

Step-by-step explanation:

The number that "completes the square" is the square of half the x-coefficient, (-6/2)^2 = 9. Rearranging the given function to include the square trinomial, we have ...

  f(x) = x^2 -6x +9 -1 . . . . . . . here, we have 8 = 9 - 1

  f(x) = (x -3)^2 -1 . . . . . . . . . . vertex form

Comparing this to the generic vertex form ...

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2 years ago
PLEASE ANSWER i WILL PUT MOST BRAINLIEST!
galina1969 [7]

Answer:

The correct option is;

c. Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.

Step-by-step explanation:

Here we have the values

μ = 275 mL

275.4

276.8

273.9

275

275.8

275.9

276.1

Sum = 1928.9

Mean (Average), = 275.5571429

Standard deviation, s = 0.921696159

We put the null hypothesis as H₀: μ₁ = μ₂

Therefore, the alternative becomes Hₐ: μ₁ ≠ μ₂

The t-test formula is as follows;

t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}

Plugging in the values, we have,

Test statistic = 1.599292

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4 0
3 years ago
Really need help with this .
lions [1.4K]

Answer:

Step-by-step explanation:

The attached photo shows the diagram of quadrilateral QRST with more illustrations.

Line RT divides the quadrilateral into 2 congruent triangles QRT and SRT. The sum of the angles in each triangle is 180 degrees(98 + 50 + 32)

The area of the quadrilateral = 2 × area of triangle QRT = 2 × area of triangle SRT

Using sine rule,

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QT = r = sin50 × 24.24 = 18.57

Also

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QR = t = sin32 × 24.24 = 12.84

Let us find area of triangle QRT

Area of a triangle

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Area of triangle QRT

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= 118.06

Therefore, area of quadrilateral QRST = 2 × 118.06 = 236.12

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