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4 years ago

7

Which quadratic equation has the roots -1+4i and -1-4i

1 answer:

AysviL [449]4 years ago

6 0

Answer:

C

Step-by-step explanation:

Solve the quadratic in answer choice C using the quadratic formula:

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$ .

Here a=1, b=2, and c=17.

Substitute and you'll have:

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-2+/-\sqrt{(-2)^2-4(1)(17)} }{2(1)}=\frac{-2+/-\sqrt{4-68}}{2)}$

$\frac{-2+/-\sqrt{-64} }{2}=\frac{-2+/-8i }{2}=-1+/- 4i$

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The volume of an oblique pyramid with a square base is V units3 and the height is h units.Which expression represents the area o

melamori03 [73]

Answer: a) $\dfrac{3V}{h}\ units^2$

Step-by-step explanation:

We know that the volume of an oblique pyramid is given by :-

$\text{Volume}=\dfrac{1}{3}\text{(Base Area x height) }$

If the volume of an oblique pyramid with a square base is V units³ and the height is h units.

Then, we have

$V=\dfrac{1}{3}\text{(Base Area x h) }$

Multiply 3 on both sides , we get

$3V=\text{(Base Area x h) }$

Divide both sides by h , we get

$\dfrac{3V}{h}=\text{Base Area }$

i.e. $\text{Base Area }=\dfrac{3V}{h}\ units^2$

Hence, the expression represents the area of the base of the pyramid = $\dfrac{3V}{h}\ units^2$

Hence, the correct answer is a) 3 v/h units^2

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3 years ago

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The city of Orlando’s building a dog park in downtown Orlando dog park will be triangular shaped as shown on the coordinate plan

kiruha [24]

Answer:

Perimeter of the dog park = 15.4 yards

Step-by-step explanation:

Coordinates of the vertices of the given triangle are,

P(1, 2), Q(1, 6), R(-4, 2)

Since distance between the two points $(x_1, y_1)$ and $(x_2,y_2)$ is,

d = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Length of PQ = $\sqrt{(1-1)^2+(2-6)^2}$

PQ = 4

Length of PR = $\sqrt{(1+4)^2+(2-2)^2}$

PR = 5

Length of QR = $\sqrt{(1+4)^2+(6-2)^2}$

QR = $\sqrt{25+16}$

= $\sqrt{41}$

= 6.4 yards

Therefore, perimeter of the given triangle = PQ + QR + PR

= 4 + 6.4 + 5

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4 0

4 years ago

Write a rule for the function whose graph can be obtained from the given parent function by performing the given transformations

kati45 [8]

ANSWER

$g(x) = {(x + 5)}^{3} + 4$

EXPLANATION

Given the parent function:

$f(x) = {x}^{3}$

If we shift the graph of f(x), 5 units to the left, then the new rule is

$x \to \: {(x + 5)}^{3}$

If we again, shift this graph upward by 4 units, then the completely transformed function will have the rule,

$x \to \: {(x + 5)}^{3} + 4$

Or

$g(x) = {(x + 5)}^{3} + 4$

7 0

3 years ago

Jerry has a miniature model of a boat. He knows that the boat is 3 3/4 inches wide and 5 1/2 inches long. What is the actual len

FromTheMoon [43]

Width of the miniature model = $3\frac{3}{4}$ inches

Length of the miniature model = $5\frac{1}{2}$ inches

The actual width of the boat = 15 feet

Let us find the actual length of the boat.

Write it in a proportion form.

width of model : length of model : : width of actual : length of actual

$$\Rightarrow 3\frac{3}{4}:5\frac{1}{2}::15:x$

$$\Rightarrow\frac{15}{4}:\frac{11}{2}::15:x$

$$\Rightarrow\frac{\frac{15}{4}}{\frac{11}{2}} =\frac{15}{x}$

Do cross multiplication.

$$\Rightarrow{\frac{15}{4}x =15\times\frac{11}{2}$

$$\Rightarrow{\frac{15}{4}x =\frac{165}{2}$

$$\Rightarrow x =\frac{165}{2}\times{\frac{4}{15}$

⇒ x = 22

Hence the actual length of the boat is 22 feet.

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4 years ago

A tank had 6 liters of water. The tank had a small hole in its base through which water leaked out at a constant rate. The tank

Mariana [72]

Based on the given problem above, if we analyze it, we are going to look for the graph which with coordinates (0,6) which represents starting out with 6 gallons, and ending at (4,0). So, the graph that best represents this situation would be the first graph on the top left. Hope this answers your question. Have a great day!

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3 years ago

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