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IrinaK [193]
2 years ago
15

The value of y varies directly with x, and y= -10 when x=40. Identify the value of y when x=-5

Mathematics
1 answer:
scoray [572]2 years ago
8 0

Answer:

y = 1.25

Step-by-step explanation:

Use the direct variation equation y = kx, and solve for k:

y = kx

-10 = k(40)

-0.25 = k

So, the equation is y = -0.25x. Solve for y when x = -5

y = -0.25x

y = -0.25(-5)

y = 1.25

So, y = 1.25 when x = -5

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3 years ago
If Pentagon ABCDE was dilated to create Pentagon A'B'C'DE', what rule was used?
svetlana [45]

Answer:

<em>B</em> (x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)

Step-by-step explanation:

<u>Dilations</u>

Given a point A(x,y) and a scale factor k the dilated image of A, called A' is calculated as A'=(kx,ky), assuming the same scale factor is applied in both axes.

The pentagon ABCDE was dilated to create pentagon A'B'C'D'E'. To find the dilaton rule used, we must find two clear points where the coordinates of both axes can be easily read from the graph.

Point C(-2,0) maps to C'(-5,0). This gives us the scale factor for the x-axis of -5/(-2)= 5/2.

The y-coordinate of E is 2 and the y-coordinate of E' is 5. This gives us the same scale factor for the y-axis of 5/2.

Thus, the rule to dilate the pentagon is:

B \mathbf{(x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)}

5 0
3 years ago
Which equation has the solutions x=1+/- 5?
nikitadnepr [17]

Answer:

x^{2} -2x-4=0

Solving Steps

Use the quadratic formula

x=\frac{-(-2)(+/-)\sqrt{(-2)^2-4*1*(-4)} }{2*1}

Multiply / Remove the parentheses / Evaluate

x=\frac{2(+/-)\sqrt{4+16} }{2}

Calculate

x=\frac{2(+/-)\sqrt{20} }{2}

Separate the solutions

x=\frac{2(+/-)2\sqrt{5} }{2} \\x=\frac{2-2\sqrt{5} }2}

Simplify

x=1+\sqrt{5} \\x=1-\sqrt{5}

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2 years ago
Assessment items What is the quotient? 1 5/8 ÷(−1 3/5 )
Solnce55 [7]

We need convert the mixed numbers to improper fractions.

1\dfrac{5}{8}=\dfrac{1\cdot8+5}{8}=\dfrac{8+5}{8}=\dfrac{13}{8}\\\\1\dfrac{3}{5}=\dfrac{1\cdot5+3}{5}=\dfrac{5+3}{5}=\dfrac{8}{5}

Divide the number by a fraction, this is the same as multiply this number by the reciprocal of the fraction:

1\dfrac{5}{8}\div\left(-1\dfrac{3}{5}\right)=-\dfrac{13}{8}\div\dfrac{8}{5}=-\dfrac{13}{8}\cdot\dfrac{5}{8}=-\dfrac{(13)(5)}{(8)(8)}=-\dfrac{65}{64}\\\\\boxed{1\dfrac{5}{8}\div\left(-1\dfrac{3}{5}\right)=-1\dfrac{1}{64}}

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Step-by-step explanation:

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