What are the roots of the function y = 4x2 + 2x – 30? To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of .
Next, factor the trinomial completely. The equation becomes .
Use the zero product property and set each factor equal to zero and solve. The roots of the function are .

Answer:

We are given,

The transformed function is [tex]f(x)=\sqrt{x+1}-5[/tex].

So, we can see that,

The parent function is [tex]f(x)=\sqrt{x}[/tex].

Then, we have,

The parent function is translated 1 units to the left to give [tex]\sqrt{x+1}[/tex].

Then, it is translated 5 units downwards to give the function  [tex]\sqrt{x+1}-5[/tex].

Hence, we have,

The parent function f(x) = √x has been shifted 1 unit left and 5 units down

The parent function of a square root function is represented as:

[tex]f(x) = \sqrt x[/tex]

When the function is shifted 1 unit left, we have the following equation

[tex]f(x) = \sqrt {x + 1}[/tex]

When the function is shifted 5 units down, we have the following equation

[tex]f(x) = \sqrt {x + 1} - 5[/tex]

Hence, the parent function f(x) = √x has been shifted 1 unit left and 5 units down

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90-7 =83 degrees

height = 3 miles

divide 3 by the cos of 83 degrees

3/cos(83) = 24.6165

rounded to nearest mile = 25 miles

Answer:

Correct option is A.          

Step-by-step explanation:

Given the following functions we have to choose the option which illustrates a change in amplitude.

Multiplying a sine or cosine function by a constant changes the graph of the parent function i.e results in change in the amplitude of function. Amplitude is the measure of distance from the sinusoidal axis to the maximum or the minimum.

Option A:  y = 3cos4x

The parent function is f(x) = cos x.

The amplitude of function changes from 1 to 3.

Option B:  y = 1+sinx

The parent function is f(x) = sin x

The amplitude remains same i.e 1

Option C: y = -2-cos(x - pi)

Here also remains same.

Option D: y = tan 2x

The tangent function does not have an amplitude because it has no maximum or minimum value.

Hence, correct option is A.

Answer:

y= 3cos4x

Step-by-step explanation:

divide 64 by 3.2 to get x

64/3.2 = 20

 x = 20

Answer: [tex]\text{Area}=9.8\ \text{square centimeter}[/tex]

Step-by-step explanation:

Given: The height of the triangle h= 3.0 cm

The base corresponding to the given height b= 6.5 cm

We know that the area of a triangle is given by :-

[tex]\text{Area}=\frac{1}{2}bh\\\\\Rightarrow\text{Area}=\frac{1}{2}(3)(6.5)\\\\\Rightarrow\text{Area}=\frac{19.5}{2}\\\\\Rightarrow\text{Area}=9.75\approx9.8\ \text{square centimeter}[/tex]

Answer:

Option (B) is correct.

To prove

As given the epression in the question is given by

[tex]= 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex]

Now simplify the above

Terms are written as

[tex]\sqrt{8} = \sqrt{2\times 2\times 2} = 2 \sqrt{2}[/tex]

[tex]\sqrt{18} = \sqrt{3\times 3\times 2} = 3 \sqrt{2}[/tex]

Put in the above expression.

[tex]= 5\times 2 \sqrt{2} -3 \sqrt{2} - 2 \sqrt{2}[/tex]

[tex]= 10 \sqrt{2} -5 \sqrt{2}[/tex]

[tex]=5 \sqrt{2}[/tex]

[tex]Therefore\ the\ expression\ 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\ is\ equivalent\ to\ 5 \sqrt{2} .[/tex]

Answer:

 32,760 is the correct answer, the first person is wrong! Took the test and this is it!

Step-by-step explanation:

The solution of the given quadratic equation is x = 1.37, - 1.37.

"A quadratic equation is an algebraic equation of the second degree in any variable."

Given quadratic equation:

9x² = 17

⇒ x² = (17 / 9)

⇒ x = ± √(17 / 9)

⇒ x = ± (√17) / 3

⇒ x = 1.37, - 1.37

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Final answer:

Yes, a segment can have more than one bisector. A bisector divides a segment into two equal parts.

Explanation:

Yes, a segment can have more than one bisector. A bisector of a segment is a line, segment, ray, or plane that divides the segment into two equal parts. Each bisector intersects the segment at its midpoint. Since the definition of a bisector doesn't specify uniqueness, there can be infinitely many bisectors of a given segment, especially in a two-dimensional plane.

For example, if you have a horizontal line segment, you could have one vertical bisector that divides it in the middle, but you could also have an infinite number of bisectors at various angles that also pass through the midpoint. Thus, there are multiple bisectors for any given line segment. Thus, consider two points A and B on a straight line segment AB. According to geometric principles, you can draw a perpendicular bisector that would be unique in the sense that it's the only line that both bisects AB and is perpendicular to it

Final answer:

The height difference between Amersham station (147 meters above sea level) and Waterloo station (21 meters below sea level) is 168 meters.

Explanation:

To find the height difference between Amersham station, which is the highest station in the London Tube at 147 meters above sea level, and Waterloo station, the lowest at 21 meters below sea level, we simply add the two values together, treating the below sea level as a negative altitude.

147 meters (Amersham altitude above sea level) + (-21 meters) (Waterloo altitude below sea level) = 168 meters.

Therefore, the height difference between Amersham and Waterloo stations is 168 meters.

Answer:

Option B.[tex]\sqrt[6]{200}[/tex]

Step-by-step explanation:

The given expression is ∛5.√2 and we have to find the product.

In this question ∛5 can be written as [tex]5^{\frac{1}{3} }[/tex] and [tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]

We know to multiply these terms we should have the same powers of both the terms.

Now we will convert these terms to the terms having same powers.

first term [tex]5^{\frac{1}{3}}=5^{(\frac{1}{3}).(\frac{2}{2})}[/tex]

=[tex]5^{\frac{2}{6}}[/tex]

=[tex]25^{\frac{1}{6}}[/tex]

Second term √2 = [tex]2^{\frac{1}{2}}[/tex]

= [tex]2^{(\frac{1}{2}).(\frac{3}{3})}[/tex]

= [tex]2^{\frac{3}{6}}[/tex]

= [tex]8^{\frac{1}{6}}[/tex]

Now we multiply these terms

[tex]25^{\frac{1}{6}}.8^{\frac{1}{6}}[/tex]

= [tex]200^{\frac{1}{6} }[/tex]

Therefore option B is the answer.

Answer with explanation:

⇒Consider a Non Zero Rational Number = 2, 3, [tex]\frac{2}{3}[/tex], 53,....

The decimal Expansion of Rational number is Either terminating or  Non Teminating repeating.

⇒ Irrational Number = π, √2,√7,...

The decimal Expansion of Irrational number is Non terminating Non repeating.

⇒Product of a non-zero rational number and an irrational number

  =2 ×√2 or 3 × √2 or 3 π

are all Irrational number.

In terms of decimals:

                     (c)⇒a non-repeating, non-terminating decimal=(Irrational Number)

Option C

Answer:

34 inches.

Step-by-step explanation:

Answer:

c) -16 ≤ x < 5

Step-by-step explanation:

The given function is f(x) = -3x + 2 and domain is  -1 < x ≤ 6

The maximum value of the domain is 6 and the minimum value of the domain is -1.

To find the range, plugin the maximum and minimum value of the domain.

Plug in x = 6 in the given function, we get

f(6) = -3(6) + 2 = -18 +2 = -16

f(-1) = -3(-1) + 2 = 3 + 2 = 5

So the range is -16 ≤ x < 5

Answer:

that persons work is correct im pretty sure

Step-by-step explanation:

The total distance between the two women would simply be the sum of the hypotenuse formed by the triangular path they created.

For each women:

c^2  = a^2 + b^2

c^2 = 3^2 + 4^2

c^2 = 9 + 16

c^2 = 25

c = 5 m

Therefore the distance between the two is:

distance between the two women = 2 * c

distance between the two women = 10 m