solve -3(-8b+7)=3(2b-1)

I cannot say that I am entirely sure of the answer so let me know if it doesn't make sense, but I will try to explain as best as I can nonetheless.

1. The graph of f''(x) represents the graph of the second derivative of f(x). Now, we know that the graph is continuous and decreasing. I think that the most important thing here is to mentally visualise the graph - if it is decreasing and has an x-intercept at x = -3, then we can say the following:

a) for all values of x before -3, f''(x) is positive

b) at x = -3, f''(x) is 0

c) for all values of x after x = -3, f''(x) is negative

2. What this means in terms of the graph f'(x) is the following:

a) for values of x less than -3, the gradient of the graph of f'(x) is positive and becoming less positive as x reaches 0

b) at x = -3, the gradient of the graph of f'(x) is 0

c) for values of x more than -3, the gradient of the graph of f'(x) is negative and becoming more negative as x reaches ∞

With this in mind, maybe try drawing a quick sketch to guide you (I would include one here but I have trouble adding attachments so I hope you'll forgive my lack of one) - it could perhaps look something similar to -(x + 3)^2 (but wouldn't be restricted to this - remember, it is just a visual aid).

3. Now, we need to work from the graph of f'(x) to the graph of f(x).

What we need to notice is that the graph of f'(x) takes the form of a concave down graph - this means that the gradient of the graph of f(x) immediately to either side of x = -3 changes from being either:

a) + >> ++ >> +++ >> ++ >> +

(Here, the number of + symbols signifies the strength of the positive gradient. >> represents an arrow.

So, the gradient starts off less positive, becomes more positives, reaches its peak, and then becomes gradually less positive again - imagine this being represented by f'(x) = -(x + 3)^2 + 5 (again, remember this is just a visual aid) )

b) --- >> -- >> - >> -- >> ---

(Likewise, the number of - symbols signifies the strength of the negative gradient.

So, the gradient starts off very negative, becomes less negative, reaches its peak, and then gradually becomes more negative again - you can see that this is effectively the same pattern as above: there is an increasing trend and then a decreasing trend. You can imagine this as being represented by the graph f'(x) = -(x + 3)^2 - 5)

c) -- >> - >> 0 >> - >> --

(Here, the gradient is negative, becomes less negative, reaches 0, then gradually becomes more negative - again, there is the same increasing trend followed by a decreasing trend. You can imagine this as being represented by the graph f'(x) = -(x + 3)^2)

It is this increasing trend in the gradient up to x = -3 followed by a decreasing trend that is crucial to take note of - this signifies that there is a point of inflection at x = -3. What we must remember here is that a point of inflection is characterised by a change in the curvature of the graph - either from concave up to concave down or from concave down to concave up. In our case, this would be a transition from concave up to concave down as the gradient gradually becomes more positive until it reaches its highest value at x = -3 and then gradually becomes less positive. Thus, we can say that answer B (the graph of f has an inflection point at x = -3) is correct.

Looking at the other answers:

A - The graph of f cannot be always concave down since there is a clear change in the gradient from less positive to more positive to less positive again (if it were always concave down the gradient would just gradually become more negative)

C - A relative minimum is characterised by the fact that the gradient to the left of the minimum is negative, the gradient at the minimum is 0, and the gradient to the right of the minimum is positive. Since this isn't the case for our graph, this is not the correct answer.

D - This is only a viable answer if none of the others are correct; since we have identified B as correct, this is incorrect.

I hope this helped but if you have any questions or problems with my working, please don't hesitate to comment below.

The correct statement about the function is,

⇒ The graph of f is always concave down.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Since, We have to given that;

The graph of f’’(x) is continuous and decreasing with an x-intercept at

x = - 3 .

We know that;

⇒ f(x) is a function then the solutions to the equation f′(x) = 0 gives the maximum and minimum values to f(x)

Hence, The value of  x  gives maximum if f′′(x) is negative and minimum if  f′′(x) is positive.

- Inflection points of the function  f(x) are found the solutions of the equation f′′(x) = 0

- The graph of f'(x) is continuous means that the graph is unbroken line

- The graph of f'(x) decreasing with an x-intercept at x = 2 means f'(2) = 0

- The differentiation of a function equal to zero at the critical point  (minimum or maximum) of the function

Since, f'(x) = 0 at x = 2

Hence, The x-coordinate of the critical point of f(x) is 2

Now,  If the differentiation of the function is decreasing, then the critical point of the function is maximum point.

Since,  f'(x) is decreasing

Hence, The critical point of the f(x) is maximum point

That means the slope of curve is negative

Hence,  The graph of f is concave down at x = 2

Thus, The correct answer is the graph of f is always concave down.

Learn more about the function visit:

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Answer:

#5: 180 paperclips in total.

#6: 126 stamps in total.

#7: Elena should give Lucy 15 colored pencils.

Step-by-step explanation:

This explanation solves each question by setting a single unknown, [tex]x[/tex].

Let [tex]x[/tex] the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

Antonio gives [tex]30[/tex] paperclips to Abby. After that,

Abby now possess twice as many paperclips as Antonio does. In other words,

[tex]2(x - 30) = x + 30[/tex].

By the distributive property:

[tex]2x - 60 = x + 30[/tex].

Substract [tex]x - 60[/tex] from both sides

[tex]x = 30 - (-60) = 90[/tex].

Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.

Similarly, let [tex]x[/tex] be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

After Emily gives [tex]42[/tex] stamps to Jasmine:

Jasmine now possesses twice as many stamps as Emily does. In other words,

[tex]2(x-42) = x+42[/tex].

[tex]x = 42 + 2\times 42 = 126[/tex].

Jasmine used to possess 126 stamps. Now she possesses [tex]126 + 42 = 168[/tex] stamps after receiving [tex]42[/tex] stamps from Emily.

Let the number of pencils that Elena needs to give to Lucy be [tex]x[/tex].

Initially:

After Elena gives [tex]x[/tex] pencils to Lucy:

Elena should now possess four more pencils than Lucy does. In other words,

[tex]\underbrace{60 - x}_{\text{Elena's}} = \underbrace{(26 + x)}_{\text{Lucy's}} +4[/tex].

[tex]2x = 30[/tex].

[tex]x = 15[/tex].

Answer:

minimum = 30,  Q1 = 36, median = 50.5,  Q3 = 80, and maximum = 91.

Step-by-step explanation:

We are given the following data set for the exam scored of 8 students in a math course and we are to find the five number summary:

51, 91, 46, 30, 36, 50, 73, 80

Step 1: For that, we first need to rearrange in an ascending order:

30, 36, 46, 50, 51, 73, 80, 91

Step 2: Now we will spot the smallest and largest number in the data.

Smallest number: 30

Largest number: 91

Step 3: Finding the median (middle number) now:

Median = 50+51/2 = 50.5

Step 4: Placing parenthesis around the number before and after the median values:

(30, 36, 46) 50, 51 (73, 80, 91)

Find Q1 (median in the lower half of the data) and Q3 (median for the upper half of data):

Q1 = 36

Q3 = 80

Five step summary:

minimum = 30,  Q1 = 36, median = 50.5,  Q3 = 80, and maximum = 91.

Answer:

Minimum = 30, Maximum = 91, Median = 50.5, Q₁ = 36, Q₃ = 80

Step-by-step explanation:

We have to find the five-number summary of the given data represents the semester exam scores of 8 students in a math course.

The five-number summary includes 5 items:

1. The minimum

2. Q₁ (First quartile)

3. Median

4. Q₃ (Third quarlile)

5. The maximum

First we put the numbers in ascending order (lowest to highest)

30, 36, 46, 50, 51, 73, 80, 91

Now find the minimum and maximum from your data set.

Minimum = 30 and Maximum = 91

Now find the median, median is the middle number. But we have 50, 51 two middle numbers so we take the median of those numbers =

Median = [tex]\frac{(50+51)}{2}[/tex] = 50.5

Median = 50.5

Now place parenthesis around the numbers before and after the median values

30, 36, 46, 50, 51, 73, 80, 91

Median of lower half of the data Q₁ = 36

Median of upper half of the data Q₃ = 80

Five-number summary found

Minimum = 30, Maximum = 91, Median = 50.5, Q₁ = 36, Q₃ = 80

Answer: 15 represents where Jerry is after the elevation dropped 25 meters and then rose 40 meters.

Answer:

15 represents that Jerry hiked up 15 meters from his starting position.

Step-by-step explanation:

It is given that Jerry hiked downhill to a valley where the elevation dropped 25 meters below his starting position. Then, he hiked up to a hill that was 40 meters higher than the valley.

Hiked downhill = 25 meters

Hiked up = 40 meters

The given equation is

[tex]-25+40=15[/tex]

Here, hiked downhill represented by negative sign and hiked up represents by positive sign.

So, positive 15 represents that Jerry hiked up 15 meters from his starting position.

Answer:

C

Step-by-step explanation:

Given

S = lw + 0.5Ph ( subtract lw from both sides )

S - lw = 0.5Ph ( divide both sides by 0.5h )

[tex]\frac{S-lw}{0.5h}[/tex] = P → C

Answer:

c

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{\frac{7}{5}})~\hspace{10em} slope = m\implies \cfrac{6}{19} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\cfrac{7}{5}=\cfrac{6}{19}[x-(-1)]\implies y-\cfrac{7}{5}=\cfrac{6}{19}(x+1)[/tex]

Answer:

Option D. 108 g

Step-by-step explanation:

we know that

The density is equal to the mass divided by the volume

D=m/V

Solve for the mass m

m=D*V

we have

D=2.7 g/cm³

V=40 cm³

substitute

m=(2.7)(40)=108 g

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

[tex]-5x+(-2)=-2x+4[/tex]

[tex]-5x+(-2)+5x=-2x+4+5x[/tex]  (according to first step)

[tex]-2= 3x+4[/tex]

[tex]-2+(-4)=3x+4+(-4)[/tex]        (according to second step)

[tex]-6=3x[/tex]

[tex]\frac{-6}{3}[/tex]=[tex]\frac{3x}{3}[/tex]  (according to third step)

[tex]-2=x[/tex]

[tex]x=-2[/tex]

hence the solution of the given equation is  [tex]x=-2[/tex]

Answer:

The answer is negative two.

Step-by-step explanation:

sorry i'm very late but this answer might help other people.

hope you have a good day.

:)

2root 21

Opp^2 =hyp^2 - adj^2

Opp=root 10^2-4^2

Opp=root 100-16

Opp =root 84

AB=2root21 or 9.165

Answer:

(1, −3) (3, −5)

Slope = Y2 -Y1 / X2 - X1

Slope = -5 --3 / 3 -1

Slope = -2 / 2

Slope = -1

Step-by-step explanation:

Answer:

zeros

x=0  

x=4 with multiplicity 2

Step-by-step explanation:

We need to solve x^3-8x^2+16x=0

Notice each term has a factor of x in common in x^3-8x^2+16x so we can factor it as x(x^2-8x+16)

Now x^2-8x+16 is a quadratic where a=1... We can see if it is factorable by looking for two numbers that multiply to be 16 and add up to be -8 which is -4 and -4

So you have x^3-8x^2+16x=0 is equivalent to x(x-4)(x-4)=0 (this one is in factored form).

x=0

x=4 (multiplicity 2 since you had the factor that is came from occurring twice)

ANSWER

[tex]- \frac{2}{3} [/tex]

EXPLANATION

The given given equation is

[tex]2y - 3x = 8[/tex]

We need to rewrite this equation in the slope-intercept form:

[tex]y = mx + b[/tex]

We add 3x to both sides.

[tex]2y - 3x + 3x=8 + 3x[/tex]

[tex] \implies \: 2y = 3x + 8[/tex]

We divide through by 2 to get,

[tex]y = \frac{3}{2}x + 4[/tex]

The slope of this line is

[tex]m = \frac{3}{2} [/tex]

Let the slope of the line perpendicular to this line be 'n' .

Then the product of the slopes of two perpendicular lines is always negative 1.

[tex]m \times n = - 1[/tex]

[tex] \implies \: \frac{3}{2} n = - 1[/tex]

[tex]\implies \: \frac{2}{3} \times \frac{3}{2}n = - 1 \times \frac{2}{3} [/tex]

[tex]n = - \frac{2}{3} [/tex]

Therefore the slope of the new line is

[tex] - \frac{2}{3} [/tex]

Answer:

C) -2/3

Step-by-step explanation:

2y-3x=8

2y=3x-8

Divide 2 from each number to get:

y=3/2-4

The opposite reciprocal of 3/2 is -2/3

Remember the f(x) is the same thing as y so...

y = -3x + 5

y = -1

To solve this plug -1 in for y in the equation y = -3x + 5 and solve for x

-1 = -3x + 5

-6 = -3x

2 = x

When f(x) is -1 then x is 2

Hope this helped!

~Just a girl in love with Shawn Mendes

[tex]\bf (1-2i)^2\implies (1-2i)(1-2i)\implies 1-2i-2i+(2i)^2 \\\\\\ 1-4i+(2^2i^2)\implies \stackrel{\textit{recall }i^2=-1}{1-4i+(4\cdot -1)}\implies 1-4i-4\implies \boxed{-3-4i}[/tex]

Answer:

2/14

Step-by-step explanation:

i tried my best

Answer:

Part 1) [tex]f(-3)=21[/tex]

Part 2) [tex]g(3)=9+21r[/tex]

Step-by-step explanation:

Part 1) Find the value of f(-3)

we have

[tex]f(x)=-6x+3[/tex]

we know that

f(-3) is the value of the function f(x) for x=-3

so

substitute the value of x=-3 in the function to find f(-3)

[tex]f(-3)=-6(-3)+3[/tex]

[tex]f(-3)=18+3[/tex]

[tex]f(-3)=21[/tex]

Part 2) Find the value of g(3)

we have

[tex]g(x)=3x+21r[/tex]

we know that

g(3) is the value of the function g(x) for x=3

so

substitute the value of x=3 in the function to find g(3)

[tex]g(3)=3(3)+21r[/tex]

[tex]g(3)=9+21r[/tex]

The solution for the given equation is x = ±√y-11.

This can be done by moving every term with the required variable to the other side and equating it.

The given equation is: y = x^2 +11

We can rewrite this equation in terms of y.

This can be done as shown below:

y = x^2 +11

⇒ y -11  = x^2

⇒ ±√y-11 = x

⇒ x = ±√y-11

The given equation is rewritten in terms of y.

The equation written in terms of y is x = ±√y-11.

Therefore, the solution for the given equation is x = ±√y-11.

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Answer:

Part 1) The vertex is the point (0.50,2.50)

part 2) [tex]y=-58[/tex]

Step-by-step explanation:

we have

[tex]y=-2x^{2} +2x+2[/tex]

Part 1) Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y-2=-2x^{2} +2x[/tex]

Factor the leading coefficient

[tex]y-2=-2(x^{2} -x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]y-2-0.50=-2(x^{2} -x+0.25)[/tex]

[tex]y-2.50=-2(x^{2} -x+0.25)[/tex]

[tex]y-2.50=-2(x-0.50)^{2}[/tex]

[tex]y=-2(x-0.50)^{2}+2.50[/tex] -----> equation in vertex form

The vertex is the point (0.50,2.50)

Part 2) Find the value of y for x=6

substitute the value of x in the equation

[tex]y=-2(6)^{2} +2(6)+2[/tex]

[tex]y=-72 +12+2[/tex]

[tex]y=-58[/tex]

[tex]\sin\theta=-1\\\theta=-\dfrac{\pi}{2}+2n\pi, n\in\mathbb{Z}[/tex]

Answer: 270

Step-by-step explanation:sin 270 = -1

Answer:

5 nickels

Step-by-step explanation:

You can setup and solve a system of equations, or you can solve by trial and error until you get the correct answer.

Here is the solution by trial and error.

If all 20 coins are quarters, the value is 20 * $0.25 = $5

That is too much value.

Let's try 16 quarters. 16 quarters are worth 16 * $0.25 = $4.

That is the correct value, but it is only with quarters, and only 16 of them.

We need fewer quarters than 16.

Try 12 quarters: 12 * $0.25 = $3.00

The number of nickels is: 20 - 12 = 8

8 nickels are worth 8 * $0.05 = $0.40

12 quarters and 8 nickels are worth $3.00 + $0.40 = $3.40

There are 20 coins, but the value is too low.

The number of quarters is between 12 and 16.

Try 14 quarters and 6 nickels:

14 * $0.25 + 6 * $0.05 = $3.50 + $0.30 = $3.80

We are closer to $4 but not there yet.

Try 15 quarters and 5 nickels.

15 * $0.25 + 5 * $0.05 = $3.75 + $0.25 = $4

The total value is $4 and there are 20 coins. This is the answer.

15 quarters and 5 nickels works.

Answer: 5 nickels

Answer:

(0, 5)

Step-by-step explanation:

At the time the ball is thrown time t = 0

The corresponding height at t = 0 is 5 ft

This is the point (0, 5) on the graph

Answer: Option A.

Step-by-step explanation:

The surface area of a right rectangular prism can be calculated with this formula:

[tex]SA = 2(wl + lh + hw)[/tex]

Where "w" is the width. "l" is the lenght and "h" is the height.

We know that:

[tex]w=6in\\l=9in\\h=18in[/tex]

Knowing this values, we can substitute them into the formula.

Therefore we get that the surface area of a right rectangular prism is this:

[tex]SA = 2[(6in)(9in) + (9in)(18in) +(18in)(6in)][/tex]

[tex]SA=648in^2[/tex]

This matches with the option A.

Answer:

14

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = 3x² + 1 - (1 - x) = 3x² + 1 - 1 + x = 3x² + x

(f - g)(2) = 3(2)² + 2 = 12 + 2 = 14

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]\frac{1}{2}x-2y > -6[/tex]

Isolate the variable y

[tex]-2y > -6-\frac{1}{2}x[/tex]

Divide by -2 both sides

[tex]y < 3+\frac{1}{4}x[/tex]

The solution of the inequality is the shaded area below the dashed line [tex]y = 3+\frac{1}{4}x[/tex]

To plot the inequality find the intercepts

The y-intercept is the point (0,3)  (value of y when the value of x is equal to zero)

The x-intercept is the point (-12,0) (value of x when the value of y is equal to zero)

Plot the intercepts

Drawn the dashed line

shaded the region below the dashed line

The graph in the attached figure

Answer:

I think it is    D.

I could be wrong though, my apologies if I am :(

Answer:

c. $11.80

Step-by-step explanation:

If Elizabeth has an APR of 14.61%, how much will her July finance charge be?

a. $9.97

b. $12.62

c. $11.80

d. $10.80

Answer:

A

Step-by-step explanation:

Since we are given self defining variables, h is obviously referring to the plant's height and y is referring to the plant's years or age.

Then, since a plant's height is 1.4 times its age, age multiplied by 1.4 should be the plants height.

The equation would come out to [tex]h=1.4y[/tex]

Answer:

The m∠D is 98° ⇒ answer D

Step-by-step explanation:

* Lets revise some facts in the circle

- The quadrilateral is inscribed in a circle if its four vertices lie on the

  circumference of the circle

- It is called a cyclic quadrilateral

- Every two opposite angles in it are supplementary means the

  sum of their measures is 180°

∵ ABCD is inscribed in a circle

∴ ABCD is a cyclic quadrilateral

∵ ∠A and ∠C are opposite angles in the cyclic quadrilateral ABCD

∴ ∠A and ∠C are supplementary

∴ m∠A + m∠C = 180°

∵ m∠A = 64°

∵ m∠C = (9x - 1)°

∴ 64 + (9x - 1) = 180 ⇒ simplify

∴ 63 + 9x = 180 ⇒ subtract 63 from both sides

∴ 9x = 117 ⇒ divide both sides by 9

∴ x = 13

- Lets find the measure of ∠B

∵ m∠B = (6x + 4)°

∵ x = 13

∴ m∠B = 6(13) + 4 = 78 + 4 = 82°

- Lets find the measure of ∠D

∵ ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD

∴ ∠B and ∠D are supplementary

∴ m∠B + m∠D = 180°

∵ m∠B = 82°

∴ 82° + m∠D = 180° ⇒ subtract 82° from both sides

∴ m∠D = 98°

* The m∠D is 98°

Answer:

D on plato

Step-by-step explanation:

I just took this test and the ones that say answer E is correct is WRONG it is not correct.

Answer:

120 tiny cubes

Step-by-step explanation:

Find the volume of both the tiny cubes and the big cube. Then we will take big volume cube and divide it by tiny cube volume.

So big cube has volume (5/3*4/3*2)=40/9 cm^3

Tiny cube volume is (1/3*1/3*1/3)=1/27 cm^3

(40/9) divided by (1/27)

is the same as 40/9 time 27=40(27)/9=40(3)=120

Answer:

120

Step-by-step explanation: