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3 years ago

What is the solution to the system of equations? y = –5x + 3 y = 1

2 answers:

7 0

Ok so we know that y=1 so we can simply sub in the value of y into the equation :

y = -5x +3

1 = -5x +3

Move the -5x to the LHS ( Left-hand-side ) therefore it changes sign as well move 1 to the RHS ( Right-hand-side ) it also changes sign.

5x = 3 - 1

5x = 2

x = 2/5

x = 0.4

Hope this helps :).

neonofarm [45]3 years ago

7 0

Y=-5x+3

y=1
Replacing for the first equation;
1=-5x+3
-5x=-2
x= $\frac{2}{5}$
x=0.4

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Nataliya [291]

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2 years ago

A population is estimated to have a standard deviation of 9. We want to estimate the population mean within 2, with a 99% level

cupoosta [38]

Answer:

The sample required is $n = 135$

Step-by-step explanation:

From the question we are told that

The standard deviation is $\sigma = 9$

The margin of error is $E = 2$

Given that the confidence level is 99% then the level of significance is mathematically evaluated as

$\alpha = 100-99$

$\alpha = 1 \%$

$\alpha = 0.01$

Next we will obtain the critical value $\frac{\alpha }{2}$ from the normal distribution table(reference math dot armstrong dot edu) , the value is

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58$

The sample size is mathematically represented as

$n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2$

substituting values

$n = [ \frac{ 2.58 * 9 }{2} ]^2$

$n = 135$

3 0

2 years ago

Solve for x in the equation.

labwork [276]

Answer:

The solution is $\displaystyle x=1\pm \sqrt{47}$ . Fourth option

Explanation:

Solve for x:

$2x^2+3x-7=x^2+5x+39$

Move all the terms from the right to the left side of the equation, a zero in the right side:

$2x^2+3x-7-x^2-5x-39=0$

Join all like terms:

$x^2-2x-46=0$

The general form of the quadratic equation is:

$ax^2+bx+c=0$

Solve the quadratic equation by using the formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In our equation: a=1, b=-2, c=-46

Substituting into the formula:

$\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}$

$\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}$

$\displaystyle x=\frac{2\pm \sqrt{188}}{2}$

Since 188=4*47

$\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}$

Take the square root of 4:

$\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}$

Divide by 2:

$\displaystyle x=1\pm \sqrt{47}$

First option: Incorrect. The answer does not match

Second option: Incorrect. The answer does not match

Third option: Incorrect. The answer does not match

Fourth option: Correct. The answer matches exactly this option

8 0

2 years ago

The sum of the angle measures of a polygon with n sides is 1800. find n

Lilit [14]

The summation of the angle measures of a polygon is given by:
180(n - 2).
Thus, we need to find: 1800 = 180(n - 2)
10 = n - 2
n = 12

Therefore, the shape is a dodecagon, and the number of sides it has is 12.

5 0

3 years ago

First Identify the Angle relationship, then solve for x.

aleksley [76]

Answer:

Corresponding Angles Theorem

x = -5

Step-by-step explanation:

Since they are corresponding angles, they are equal to each other.

x + 105 = 100

x = -5

3 0

2 years ago