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2 years ago

If x+y = -10 and x-y = 2 what is the value of x

Mathematics

1 answer:

-BARSIC- [3]2 years ago

7 0

Answer:

x = -4

Step-by-step explanation:

The solution to a "sum and difference" system of equations can be found by adding the equations together.

(x +y) +(x -y) = (-10) +(2)

2x = -8 . . . . . . simplify

x = -4 . . . . . . . divide by 2

_____

Additional comment

y = -6, though this question did not ask that value.

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Find the equation of the line that passes thru (-1,-5) and is parallel to 3x+y=-5. Show work.

sertanlavr [38]

Answer:

$y=-3x-8$

Step-by-step explanation:

slope-intercept form:

$y=mx+b$

Start with the given equation, and to find the slope, convert it to slope-intercept form by solving for y.

$3x+y=-5$

In this case, all you need to do is subtract 3x from both sides.

$y=-3x-5$

Here, the slope is -3. The slope of a parallel line will also be -3.

Now, we have 3 known variables. We have the slope and the x and y of a known point. Use those 3 knowns to solve for the 1 unknown, the y-intercept.

$y=mx+b\\-5=(-3)(-1)+b\\-5=3+b\\-8=b\\b=-8$

Finally, with the slope and the y-intercept, you can write the equation of the line:

$y=-3x-8$

3 0

3 years ago

Write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)

dsp73

Answer:

f(x) = -19/9(x + 3)² + 5

Step-by-step explanation:

Given the vertex, (-3, 5) and the point, (0, 14):

Use the following quadratic equation formula in vertex form:

f(x) = a(x - h)² + k

where:

(h, k) = vertex

a = determines whether the graph opens up or down, and makes the graph wide or narrow.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for a:

f(x) = a(x - h)² + k

14 = a(0 + 3)² + 5

14 = a(3)² + 5

14 = a(9) + 5

Subtract 5 from both sides:

-14 - 5 = 9a

-19 = 9a

Divide both sides by 9 to solve for a:

-19/9 = 9a/9

-19/9 = a

Therefore, the quadratic function in vertex form is:

f(x) = -19/9(x + 3)² + 5

Please mark my answers as the Brainliest, if you find this helpful :)

5 0

2 years ago

Twelve people are given two identical speakers, which they are asked to listen to for differences, if any. Suppose that these pe

ruslelena [56]

Answer:

0.0537

Step-by-step explanation:

This follows a binomial distribution with : n

Number of trials 'N' = 12 ; Probability of success (difference between speakers) 'p' = 1/2 or 0.5 ; Probability of failure (no difference b/w speakers) = 1/2 or 0.5 ; No of success 'r' = 3

P (X = 3) = $N C r. (p)^r.(q)^(n-r)\\$

= 12C3 (0.5)^3 (0.5)^9

0.0537

7 0

3 years ago

What is the value of the expression (−2 4/5)÷(−1.4)

AysviL [449]

Answer:

Step-by-step explanation:

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%2F7%7D%7B7%5Csqrt%7B10%7D%2F2%20%7D" id="TexFormula1" title="\frac{3/7}{7\sqrt{10}

VashaNatasha [74]

Multiply the numerator and denominator by 7×2 = 14 to eliminate the denominators of those fractions:

$\dfrac{\dfrac37}{\dfrac{7\sqrt{10}}2}\times\dfrac{14}{14}=\dfrac{3\times2}{7\sqrt{10}\times7}=\dfrac6{49\sqrt{10}}$

Rationalize the denominator by multiplying both numerator and denominator by √10:

$\dfrac6{49\sqrt{10}}\times\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac{6\sqrt{10}}{49(\sqrt{10})^2}=\dfrac{6\sqrt{10}}{49\times10}=\dfrac{6\sqrt{10}}{490}$

Lastly, cancel the common factor of 2 in both the numerator and denominator (which comes from 6 = 2×3 and 490 = 2×245):

$\dfrac{6\sqrt{10}}{490}=\dfrac{3\sqrt{10}}{245}}$

8 0

2 years ago