Solve this inequality: 3q + 11 + 8q > 99. A. q > 8 B. q > 1/8 C. q > 88 D. q > 11

Answer:

The value of lesser root is:

                         x=2

Step-by-step explanation:

We are given  a quadratic equation in terms of variable " x " as:

[tex]x^2-6x+8=0[/tex]

We know that for any quadratic equation of the type:

              [tex]ax^2+bx+c=0[/tex]

The roots of x are calculated as:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

      a=1 , b=-6 and c=8

Hence, on solving for roots:

[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]

Hence, we have:

[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]

Hence, the value of lesser root is:

                             x=2

To begin this problem, we need to use the two points that we are given to find the slope of the line. Slope is defined as the change in y values divided by the change in x values, or rise/run, and is represented by the variable m.

m = (y1-y2)/(x1-x2) = (8-0)/(3-6) = 8/(-3) = -8/3

Now, we can use the slope and one of the points from our given values to create an equation of the line in point-slope form.

y = m(x-h) + k, where a point on the line is (h,k)

y = -8/3(x - 3) + 8

Now, we can distribute our slope and simplify through addition.

y = -8/3x + 8 + 8

y = -8/3x + 16

Therefore, your answer is y = -8/3x + 16.

Hope this helps!

Final answer:

The tree's maximum height is not limited to 30 ft but approaches 301 ft. Initially, the tree is 30 ft tall, not 2 ft. To verify the growth between the 5th and 7th years, one must calculate f(5) and f(7). The rate of growth indeed decreases over time.

Explanation:

When analyzing the function f(x) = 301 + 29e^{-0.5x} to understand the growth pattern of a tree, it is apparent that some statements about the tree's growth can be identified as true or false.

Answer:

the answer is c.

Step-by-step explanation:

Answer:

The correct option is c.

Step-by-step explanation:

Given information: The measure of arc AXC is 235°. Let the center of the circle be O.

The sum of all disjoint arcs is 360°. So,

[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]

[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]

[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]

[tex]Arc(AC)=125^{\circ}[/tex]

[tex]\angle AOC=125^{\circ}[/tex]

The measure of arc AC is 125°.

Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.

[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]

[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]

[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]

[tex]\angle ABC=55^{\circ}[/tex]

The measure of angle ABC is 55°. Therefore the correct option is c.

To find the number of sprinkles needed for 60 cookies, determine the number of sprinkles per cookie by dividing 384 by 24, which is 16. Then multiply 16 by 60 to get 960 sprinkles.

The question asks us to calculate the number of sprinkles (p) needed for 60 cookies when a recipe for 24 cookies calls for 384 sprinkles.

To solve this, we start by finding the number of sprinkles per cookie:

Therefore:

Stan would need 960 sprinkles to make 60 cookies.

The box plot that represents the data is option B.

A box plot is known to be a method that is employed to demonstrate the locality and skewness of numerical data. This is carried out graphically and done through the quartiles of the given numerical data.

Rearranging the given data, we have:

112,116, 134, 134, 135, 141, 149, 154, 156, 156

The minimum value after rearranging = 112.

First Quartile, Q1 = 134.

Second Quartile, Q2 or Median = 135+141/2 = 276/2 = 138

Third Quartile, Q3 = 154

Largest figure = 156

The answer is the second figure.

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Answer:

answer is 1 & 3 on edg

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

It is D

Answer:

Option d - [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]      

Step-by-step explanation:

Given : [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]

To find : Use DeMoivre's theorem to evaluate the expression?

Solution :

DeMoivre's theorem state that, for complex number

If [tex]z = r(\cos\theta+ i\sin \theta)[/tex] then [tex]z^n = r^n(\cos n\theta+ i\sin n\theta)[/tex]

We have given,

[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]

On comparing [tex]r=\sqrt3[/tex] and n=4

Applying DeMoivre's theorem,

[tex]=(\sqrt3)^4(\cos 4(\frac{5\pi}{3})+i\sin4(\frac{5\pi}{3}))[/tex]

[tex]=9(\cos (\frac{20\pi}{3})+i\sin(\frac{20\pi}{3}))[/tex]

[tex]=9(\cos (6\pi+\frac{2\pi}{3})+i\sin(6\pi+\frac{2\pi}{3}))[/tex]

[tex]=9(\cos (\frac{2\pi}{3})+i\sin(\frac{2\pi}{3}))[/tex]

We know, the value of

[tex]\cos (\frac{2\pi}{3})=-\frac{1}{2},\sin (\frac{2\pi}{3})=\frac{\sqrt3}{2}[/tex]

[tex]=9(-\frac{1}{2}+i\frac{\sqrt3}{2})[/tex]

[tex]=-\frac{9}{2}+i\frac{9\sqrt3}{2}[/tex]    

Therefore, Option d is correct.

[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]      

The trinomial "10[tex]x^2[/tex] + 7x - 12" is factored by finding two numbers that multiply to -120 and add up to 7, which are 15 and -8. Split the middle term, group, and factor by grouping to get (2x + 3)(5x - 4), which is option A.

To factor the trinomial "10x2 + 7x − 12" completely, you want to find two binomials that, when multiplied together, will give you the original trinomial. To do this, you will need two numbers that multiply to give you the product of the coefficient of the x2 term (which is 10) and the constant term (which is −12), which equals −120, and also add up to the coefficient of the x term (which is 7).

The two numbers that meet these criteria are 15 and −8, since (15)(−8) = −120 and 15 + (−8) = 7. Next, split the middle term of the trinomial using these two numbers:

10x2 + 15x − 8x − 12

Now, group the terms:

(10x2 + 15x) − (8x + 12)

Factor out the greatest common factor from each group:

5x(2x + 3) − 4(2x + 3)

Finally, factor out the common binomial factor:

(2x + 3)(5x − 4)

Therefore, the correct factorization of the trinomial 10x2 + 7x − 12 is (2x + 3)(5x − 4), which corresponds to option A.

By substituting x with 25 in the equation f(x)=35+15x, we find out that Mr. Lewis would earn $410 for working 25 hours.

The function provided is f(x)=35+15x, which represents the amount of money Mr. Lewis earns for working x hours. In the case of Mr. Lewis working for 25 hours, we substitute the value of x with 25 in the equation to calculate his earnings. Therefore, f(25)=35+15(25)=35+375=$410. Hence, Mr. Lewis would earn $410 for working 25 hours.

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It was found that Michael rode 2863 meters.

To find out how many meters Michael rode, we first need to establish the relationship between the distances Cam, Dante, and Michael rode. According to the problem, Cam rode 5 times as far as Dante did. If Cam rode 15.25 kilometers, we first convert this to meters by multiplying by 1000 (since there are 1000 meters in a kilometer):

15.25 km × 1000 = 15250 meters.

Now that we know Cam rode 15250 meters and that this is 5 times the distance Dante rode, we can find Dante’s distance:

15250 meters / 5 = 3050 meters.

Dante rode 3050 meters, which is 187 meters farther than Michael did. To find the distance Michael rode, we subtract 187 meters from Dante’s distance:

3050 meters - 187 meters = 2863 meters.

Therefore, Michael rode 2863 meters.