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The function g(x) = ∛(x -3) is positive at the interval x > 3

Given g(x) = ∛(x -3), on what interval is the function positive?

The function is given as:

g(x) = ∛(x -3)

Set the radicand to positive

x - 3 > 0

Add 3 to both sides

x > 3

Hence, the function is positive at the interval x > 3

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Answer:

opotion has not correct answer

answer is 15.

Answer:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

Step-by-step explanation:

[tex]\left(\sqrt{3}\right)\left(\sqrt[5]{3}\right)=\sqrt[10]{3^7}\quad[/tex]

(√3)([tex]\sqrt[5]{3}[/tex]) = √3 · [tex]\sqrt[5]{3}[/tex]

{√3 = [tex]3^{\frac{1}{2}}[/tex]}                 {radical rule: [tex]\sqrt{x}=x^1^/^2[/tex]}

[tex]\sqrt3[/tex][tex]\sqrt[5]{3}[/tex] =  [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex]

{[tex]\sqrt[5]{3}[/tex] = [tex]3^{\frac{1}{5}}[/tex]}                  {radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex]}

 [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex] =   [tex]3^{\frac{1}{2}}[/tex] · [tex]3^{\frac{1}{5}}[/tex]     {exponent rule:  [tex]a^x*a^y=a^x^+^y[/tex]}

                (1/2 + 1/5 = 5/10 + 2/10 = 7/10)

              [tex]=3^\frac{7}{10}[/tex]        {opposite of radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex] ;  [tex]x^\frac{a}{b}=\sqrt[b]{x^a}[/tex]}

             = [tex]\sqrt[10]{3^7}[/tex]

so, the simplified version of this equation can either be written as:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

hope this helps!!

(I can't clearly see the last option, but if it's either of these, then it's correct)

Answer:

24

Step-by-step explanation:

7 hours = 420 mins (7×60)

420-60=360 (time taken for lunch)

15mins=one ride

360÷15=24 rides

Answer:

search it up ok that's all you can do

Answer:

4

Step-by-step explanation:

4 is the intersecting point which states p intersect q giving both tennis and basketball players

Using the slope concept, it is found that the change of elevation for a car at the end of the 5 mile drive is of 0.3672 miles.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(4.2º) = h/5

h = 5 x tan(4.2º)

h = 0.3672.

The change of elevation for a car at the end of the 5 mile drive is of 0.3672 miles.

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Answer:

a=10w +50

Step-by-step explanation:

a= amount

w= weeks

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Work Shown:

x = number of quarters

3x = number of dimes

0.25x = value of just the quarters, in dollars

0.10(3x) = 0.30x = value of just the dimes, in dollars

0.25x+0.30x = 0.55x = total value in dollars

0.55x = 9.35

x = (9.35)/(0.55)

x = 17

Alison has 17 quarters and 3x = 3*17 = 51 dimes

17 quarters = 17*0.25 = $4.25

51 dimes = 51*0.10 = $5.10

17 quarters + 51 dimes = $4.25 + $5.10 = $9.35

The answers are confirmed.

Answer:

d(v) =2.15v^/25.116

Step-by-step explanation:

Answer:

first 1  is .39
second one is C

Step-by-step explanation:

We need to prove

[tex]\frac{\tan A+\sin A}{\tan A-\sin A}=\frac{\sec A+1}{\sec A-1}[/tex]

[tex]\text{LHS}=\frac{\tan A+\sin A}{\tan A-\sin A}\\\\=\frac{\frac{\sin A}{\cos A}+\sin A}{\frac{\sin A}{\cos A}-\sin A}\\\\=\frac{\sin A+\sin A \cos A}{\sin A-\sin A \cos A}\\\\=\frac{\sin A(1+\cos A)}{\sin A(1-\cos A)}\\\\=\frac{1+\cos A}{1-\cos A}\\\\=\frac{1+\frac{1}{\sec A}}{1-\frac{1}{\sec A}}\\\\=\frac{\sec A+1}{\sec A-1}\\\\ =\text{RHS}[/tex]

Answer:

Adjacent sides are in the ratio 5 : 12

That means,

Let length = 12x and breadth = 5x

Perimeter = 34

2(l+b) = 34

12x + 5x = 17

17x = 17

x = 1

Lenth =12 cm

Breadth = 5 cm

By Pythagorean theorem

The length of the diagonal of rectangle = 13 cm

If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get

[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]

Integrate both sides:

[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]

Use the initial condition to solve for [tex]C[/tex] :

[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]

Then the particular solution to the initial value problem is

[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]

(A)

Answer:

Domain & Range are both all real numbers.

Step-by-step explanation:

i

If this was a traditional parabola, the range would be y<=4. However, the arrow on the left going back up means eventually y will go to both positive & negative infinity.

Answer:

12 is the correct answer

Answer:

x<2 or x ≥ 15/2

Step-by-step explanation:

Answer:

(f-g)(x) = 7x+5

Step-by-step explanation:

Given that,

f(x)=2x+2 and g(x) =-5x-3

To Find:

Solution:

[tex](f - g)(x)[/tex]

Re-write as:

Now substitute the values on the polynomial/function:

Simplify using this order:BPEMDAS

Hence,(f-g)(x) = 7x+5.

The Correct Question is ......

Question :

Choose the simplified form of  the fifth term of  ⁶C₄ (2x)² (-y²)⁴

Answer: D. 60x²y⁸ is the simplified form of the fifth term of the

expansion ⁶C₄ (2x)² (-y²)⁴.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

According to the Given Expression,

⁶C₄ (2x)² (-y²)⁴

The value of the combination can be written as,

[tex]= [\frac{6!}{4!(6-4)!} ] (2x)^{2} (-y^{2})^{4}[/tex]

= 15 (4x²)  (-y²)⁴

The value of y can be written as,

= 15 (4x²)  y⁸

= 60 x²y⁸

Therefore,

The value of the expression ⁶C₄ (2x)² (-y²)⁴ is 60x²y⁸.

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Answer:

If the denominators are equal for all of the fractions, you can simply look at the numerator and order them. If the denominators aren't equal, you'll have to find the lcm (lowest common multiple), for example, if we have the fractions 3/6 and 1/4, we would find the lcm of 6 and 4, which is 12 and multiply the numerators accordingly. So the fractions would then become 6/12 and 3/12, this makes it easier for you to figure out their order from least to greatest.

Goodluck for your finals :)

Answer:

8/7

Step-by-step explanation:

-convert the mixed fractions into improper fractions

-find the LCD (least common denominator)

-solve!

-65/7-(-73/7)

8/7

mixed number form: 1 1/7

hope this helps!!

Answer:

8/7

Step-by-step explanation:

The inequality which represents the situation is; |x - 7| < 20 and the solution is; 27 > x > -13.

Since the number is less than 20 units away from.the number 7 on the number line, it follows.from interpretation that the inequality is;

|x - 7| < 20

Hence; x-7 < 20; x < 27

Or

-x + 7 < 20

-x < 13

x > -13

Hence, the solution of the inequality is; 27 > x > -13.

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Answer: C: 5

Step-by-step explanation:

An equation is formed of two equal expressions. The given equation is not true.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The complete question is: Check whether the given equation is true or not?cos2pi/7+cos4pi/7+cos8pi/7=1/8.

To know if the given equation, [tex]cos\dfrac{2\pi}{7}+cos\dfrac{4\pi}{7}+cos\dfrac{8\pi}{7}=\dfrac18[/tex] is true or not, both the sides of the equation are needed to be solved separately.

The value of [tex]cos\dfrac{2\pi}{7}+cos\dfrac{4\pi}{7}+cos\dfrac{8\pi}{7}[/tex] when simplified is equal to -0.5, or the value can be written as -(1/2).

Since the right side of the equation is equal to -1/2, while the right side of the equation is 1/8. Thus, the given equation is not true.

Hence, the given equation is not true.

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a) the correct expression for the perimeter of the shape is B

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{First Inequality :} [/tex]

[tex]\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 2x - 10 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 10 + 4 > x + 2x[/tex]

[tex]\qquad \tt \rightarrow \: - 6 > 3x[/tex]

[tex]\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x[/tex]

[tex]\qquad \tt \rightarrow \: - 2 > x[/tex]

[tex]\qquad \tt \rightarrow \: \therefore x < - 2[/tex]

[tex] \textsf{Second Inequality :} [/tex]

[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)[/tex]

[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24[/tex]

[tex]\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 36 < 9x[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{36}{9} < x[/tex]

[tex]\qquad \tt \rightarrow \: 4 < x[/tex]

[tex]\qquad \tt \rightarrow \: \therefore x > 4[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

6/12 or 1/2 or 50% or 0.5

Step-by-step explanation:

You have two 6-sided dice, and there are 3 odd numbers on each.

So, you put 6 on top, (the total number of odd outcomes) and 12 on the bottom. (12 total outcomes for both dice.) This simplifies to 1/2 or 50% or .5.

The true statement is Peter walks at a rate of 13 over 4 miles per hour.

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases. When the hour Peter walks increases, the distance he walks also increases.

Here are the options:

Peter walks at a rate of StartFraction 4 over 13 EndFraction miles per hour.

Peter walks at a rate of 4 miles per hour.

Peter walks at a rate of StartFraction 13 over 4 EndFraction miles per hour.

Peter walks at a rate of 13 miles per hour.

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Step-by-step explanation:

please mark me as brainlest

Answer:

-92/35

Step-by-step explanation:

-3 + 4/7 - 1/5 =

-21/7 + 4/7 - 1/5 =

-(21*5) / (7*5) + (4*5)/(7*5) - (1*7)/(5*7) =

-105/35 + 20/35 - 7/35 =

-105+20-7 / 35 = -92/35