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3 years ago

What is the solution to 5x-8y=-45 9x-8y=49

Mathematics

1 answer:

Paladinen [302]3 years ago

6 0

Answer:

$\large\boxed{x=\dfrac{47}{2},\ y=\dfrac{325}{16}\ or\ x=23.5,\ y=20.3125}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}5x-8y=-45\\9x-8y=49&\text{change all signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}5x-8y=-45\\-9x+8y=-49\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=-94\qquad\text{divide both sides by (-4)}\\\\.\qquad\dfrac{-4x}{-4}=\dfrac{-94}{-4}\\\\.\qquad \boxed{x=\dfrac{47}{2}=23.5}\\\\\text{Put the value of}\ x\ \text{to the first equation}\\\\5(23.5)-8y=-45\\\\117.5-8y=-45\qquad\text{subtract 117.5 from both sides}$

$-8y=-162.5\qquad\text{divide both sides by (-8)}\\\\\dfrac{-8y}{-8}=\dfrac{-162.5}{-8}\\\\y=\dfrac{1625}{80}\\\\\boxed{y=\dfrac{325}{16}=20.3125}$

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F(x) = 5x^3+ 2x^2 - 90x - 36. finding all zeros by factoring and explaining the steps

ella [17]

Answer:

f(x)=5x^3-2x^2-90x-36=0

=x^2(5x-2)-18(5x-2)=(x^2-18)(5x-2)=0

x^2-18=0/5x-2=0

x^2=18=x=9√2

5x-2=0

x=2/5

zeros are 9√2,2/5

8 0

3 years ago

If AC = 3, BC = 5, and AB = 7, find AD: 2 5/8 4 1/5 4 3/8 11 2/3

Vesna [10]

Answer:

1. $2\frac{5}{8}$

Step-by-step explanation:

We can see that CD is angle bisector, So we will use angle bisector theorem which states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

We can set up an equation as:

$\frac{AC}{AD}=\frac{BC}{BD}$

Upon substituting our given values we will get,

$\frac{3}{AD}=\frac{5}{(7-AD)}}$

Cross multiplying our equation we will get,

$5AD=3*(7-AD)$

$5AD=21-3AD$

$5AD+3AD=21$

$8AD=21$

$AD=\frac{21}{8}$

$AD=2\frac{5}{8}$

Therefore, the length of AD is $2\frac{5}{8}$ units and 1st option is the correct choice.

6 0

3 years ago

Write y=x^2+16x−7 in vertex form. Then identify the vertex.

WARRIOR [948]

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Step-by-step explanation:

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

(h , k) are the coordinates of the vertex point
a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
$h=\frac{-b}{2a}$
k is the value of y when x = h

∵ y = x² + 16x - 7

∵ y = ax² + bx + c

∴ a = 1 , b = 16 , c = -7

∵ $h=\frac{-b}{2a}$

∴ $h=\frac{-16}{2(1)}$

∴ h = -8

To find k substitute y by k and x by -8 in the equation above

∵ k is the value of y when x = h

∵ h = -8

∴ k = (-8)² + 16(-8) - 7 = -71

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 1 , h = -8 , k = -71

∴ y = (1)(x - (-8))² + (-71)

∴ y = (x + 8)² - 71

∵ (h , k) are the coordinates of the vertex point

∵ h = -8 and k = -71

∴ The vertex is (-8 , -71)

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Learn more:

You can learn more about quadratic equation in brainly.com/question/9390381

#LearnwithBrainly

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Which coordinate point is a solution to the linear equation? (The graph counts by 1s)

Harman [31]

Answer:

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adoni [48]

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3 years ago