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Katen [24]
3 years ago
8

What relationship does the vertex of the parabola always have with the x-intercepts?

Mathematics
1 answer:
ipn [44]3 years ago
8 0

Answer:

<h3>The solutions to the equation are called the roots of the function</h3>

Step-by-step explanation:

<h3> These are the same roots that are observable as the x -intercepts of the parabola. Notice that, for parabolas with two x -intercepts, the vertex always falls between the roots.</h3>

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10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x
ddd [48]
Rationalizing the denominator, simply means "getting rid of that pesky root at the bottom", and we do so by simply multiplying it by something to take it out, of course, we multiply the bottom, we have to also multiply the top,

\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}

\bf \cfrac{4\sqrt{28350x}}{189x}\qquad &#10;\begin{cases}&#10;28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\&#10;\qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\&#10;\qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\&#10;\qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\&#10;\qquad 2\cdot (45)^2\cdot 7\\&#10;\qquad 14\cdot 45^2&#10;\end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x}&#10;\\\\\\&#10;\cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}
4 0
3 years ago
A sequence is defined recursively by the following rules: f(1)=3f(n+1)=2⋅f(n)−1 Which of the following statements is true about
Radda [10]

Answer:

f(2)=5

f(5)=33

Step-by-step explanation:

The given formula, that recursively defines the sequence is

f(1) = 3 \\ f(n + 1) = 2f(n) - 1

When n=1, we obtain;

f(1+ 1) = 2f(1) - 1 \\ f(2) = 2 \times 3 - 1 \\ f(2) = 6 - 1 \\ f(2) = 5

When n=2, we get:

f(2+ 1) = 2f(2) - 1 \\ f(3) = 2 \times 5 - 1 \\ f(3) = 10 - 1 \\ f(3) = 9

When n=3,

f(3 + 1) = 2f(3) - 1 \\ f(4) = 2f(3) - 1 \\ f(4) = 2 \times 9 - 1 \\ f(4) = 18 - 1 \\ f(4) = 17

When n=4

f(4 + 1) = 2 f(4) - 1 \\ f(5) = 2 \times 17 - 1 \\ f(5) = 34 - 1 \\ f(5) = 33

When n=5,

f(6) = 65

4 0
3 years ago
A car drives 195 miles in 3 hours and 15 mins.<br> what is the average speed of the car?
maria [59]

Answer:

one mile per hour

Step-by-step explanation:

4 0
2 years ago
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A table costs Rs 720 to make. He sells it for Rs 920. What percentage of profit did he earn?
jenyasd209 [6]

Answer:

27 7/9%

Step-by-step explanation:

Take the selling price and subtract the cost

920 -720 = 200

Divide it by the cost

200/720

.27777777

Change to percent form

27.777777%

27 7/9%

3 0
3 years ago
Read 2 more answers
There are 18 sweets in a packet. 8 of the sweets are mint what fraction of the sweets are not mint
Tcecarenko [31]
10/18 because 18-8=10 and the total amount is 18 so the fraction is 10/18
6 0
2 years ago
Read 2 more answers
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