I need help on this please

Mathematics

1 answer:

Mazyrski [523]3 years ago

7 0

Answer: B, 2.4 Units
Explanation: Since the two triangles are similar, the lengths of the triangles are equal in ratio. This equates to:
AB/DE = AC/DF
since the value of AB/DE IS 5/3, the ratio between AC and DF are the same.
Substitute the ratio with the values of AC and DF, and you will get the value of DF.
If you don't understand feel free to look at my workings

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Instructions: Given the vertex, fill in the vertex form of the quadratic function..

miskamm [114]

Answer:

$\implies y=(x-2)^2-6$

Step-by-step explanation:

Vertex form of a quadratic equation:

$y=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

Given vertex: (2, -6)

⇒ h = 2 and k = -6

Substitute the values of h and k into the formula:

$\implies y=a(x-2)^2+(-6)$

$\implies y=a(x-2)^2-6$

As we have not been given a value for the constant $a$ , assume this is 1.

Therefore, the vertex form of the quadratic function with vertex (2, -6) is:

$y=(x-2)^2-6$

Learn more about vertex form here:

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2 years ago

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A total of $6000 was invested, part of it at 3% interest and the remainder at 8%. If the total yearly interest amounted to $380,

Nastasia [14]

$ 2000 is invested at 3 % interest and $ 4000 is invested at 8 % interest

Solution:

Given that, total of $6000 was invested

Let "x" be the amount invested at 3 % interest

Then, (6000 - x) is the amount invested at 8 % interest

Given that,

The total yearly interest amounted to $380

Then, we can frame a equation as:

$x \times 3 \% + (6000 - x) \times 8 \% = 380$

Solve the above expression for "x"

$x \times \frac{3}{100} + (6000-x) \times \frac{8}{100} = 380\\\\0.03x + (6000-x) \times 0.08 = 380\\\\0.03x + 480 - 0.08x = 380\\\\-0.05x = -100\\\\\text{Divide both sides by -0.05 }\\\\x = 2000$