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Answer: equation: y = 2.5x + 46

slope: 2.5

y intercept: 46

she will be 8 months old by the time she is 66 cm

Step-by-step explanation: the eqation is written in y= mx+b format, where m is the slope and b is the y intercept. You can solve the last part of the problem by using this equation and subbing 66 in for y.

y = 2.5x + 46

66 = 2.5x + 46

20 = 2.5x

8 = x

Answer:

13,586400000000001 per time  

Step-by-step explanation:

Answer:

The roses are sold individualy for $5.00.

Step-by-step explanation:

To find the answer, you divide 90 (the total amount) by 18 (the number of roses). Because we are doing division, you forget about the dollar sign (for now) and do the division. 90➗18=5. Since it is money, it would be $5.00

Answer:

8 smoothies: 4:6

2 smoothies: 1:1.5, etc.

Answer:

There are two stationary points

Note that 1/2 = 0.5

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How to get those answers:

Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing (i.e. it's staying still at that snapshot in time).

Apply the derivative to get:

f(x) = 4x^3 - 3x + 3

f ' (x) = 12x^2 - 3

Then set it equal to zero and solve for x.

f ' (x) = 0

12x^2 - 3 = 0

12x^2 = 3

x^2 = 3/12

x^2 = 1/4

x = sqrt(1/4) or x = -sqrt(1/4)

x = 1/2 or x = -1/2

x = 0.5 or x = -0.5

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Let's do the first derivative test to help determine if we have local mins, local maxes, or neither.

Set up a sign chart as shown below. Note the three distinct regions A,B,C

The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.

The reason why I split things into regions like this is to test each region individually. We'll plug in a representative x value into the f ' (x) function.

To start off, we'll check region A. Let's try something like x = -2

f ' (x) = 12x^2 - 3

f ' (-2) = 12(-2)^2 - 3

f ' (-2) = 45

The actual result doesn't matter. All we care about is whether if its positive or negative. In this case, f ' (x) > 0 when we're in region A. This tells us f(x) is increasing on the interval [tex]-\infty < x < -0.5[/tex]

Let's check region B. I'll try x = 0.

f ' (x) = 12x^2 - 3

f ' (0) = 12(0) - 3

f ' (0) = -3

The result is negative, so f ' (x) < 0 when [tex]-0.5 < x < 0.5[/tex]. The f(x) curve is decreasing on this interval.

The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.

Plug x = -0.5 into the original function to find its paired y coordinate.

f(x) = 4x^3 - 3x + 3

f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3

f(-0.5) = 4

The point (-0.5, 4) is a stationary point. More specifically, it's a local max.

Side note: This is the same as the point (-1/2, 4) when written in fraction form.

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Let's check region C

I'll try x = 2

f ' (x) = 12x^2 - 3

f ' (2) = 12(2)^2 - 3

f ' (2) = 45

The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when [tex]0.5 < x < \infty[/tex]. The function f(x) is increasing on this interval.

Region B decreases while C increases. The change from decreasing to increasing indicates we have a local min when x = 0.5

Plug this x value into the original equation

f(x) = 4x^3 - 3x + 3

f(0.5) = 4(0.5)^3 - 3(0.5) + 3

f(0.5) = 2

The local min is located at (0.5, 2) which is the other stationary point.

The graph and sign chart are shown below.

The local min is located at (0.5, 2) which is the other stationary point.

Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing.

Apply the derivative to get:

f(x) = 4x^3 - 3x + 3

f ' (x) = 12x^2 - 3

Then set it equal to zero and solve for x.

f ' (x) = 0

12x^2 - 3 = 0

12x^2 = 3

x^2 = 3/12

x^2 = 1/4

x = 1/2 or x = -1/2

x = 0.5 or x = -0.5

The first derivative test to help determine if we have local mins, local maxes, or neither.

A = numbers to the left of -0.5

B = numbers between -0.5 and 0.5 excluding both endpoints

C = numbers to the right of 0.5

Thus, The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.

Let's try something like x = -2

f ' (x) = 12x^2 - 3

f ' (-2) = 12(-2)^2 - 3

f ' (-2) = 45

In this case, f ' (x) > 0 when we're in region A.

Let's check region B x = 0.

f ' (x) = 12x^2 - 3

f ' (0) = 12(0) - 3

f ' (0) = -3

The result is negative, so f ' (x) < 0 when f(x) curve is decreasing on this interval.

The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.

Substitute x = -0.5 into the original function to find its paired y coordinate.

f(x) = 4x^3 - 3x + 3

f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3

f(-0.5) = 4

The point (-0.5, 4) is a stationary point, it's a local max.

Let's check region C x = 2

f ' (x) = 12x^2 - 3

f ' (2) = 12(2)^2 - 3

f ' (2) = 45

The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when The function f(x) is increasing on this interval.

Susbtitute this x value into the original equation

f(x) = 4x^3 - 3x + 3

f(0.5) = 4(0.5)^3 - 3(0.5) + 3

f(0.5) = 2

Hence, The local min is located at (0.5, 2) which is the other stationary point.

Learn more about equations here;

https://brainly.com/question/10413253

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Answer:

(x - 10)(x + 2)

Step-by-step explanation:

We are looking for two things that multiply together to give us

x^2 - 10x - 20

These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)

We know the first term in the binomial has to be x, because x times x is x^2.

And then we are looking for two numbers that multiply to -20 but also add up to -8.

-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)

Answer:

Option C

Step-by-step explanation:

x² - 8x - 20

x² - (10x - 2x) - 20

x² - 10x + 2x - 20

x(x - 10) + 2(x - 10)

(x - 10)(x + 2)

Hence

Option C is correct

Answer:

32

Step-by-step explanation:

180 - 148 = 32

I hope this helps!

Answer:

4 * 4 ÷ 4 = 4

8 ÷ (2*2) = 2

Step-by-step explanation:

[tex]4 * 4 \div4\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\4 * 4 \div4\\\\4 * 1\\\\\boxed{4}[/tex]

==============================

[tex]8 \div (2*2)\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\8 \div (2*2)\\\\8 \div 4\\\\\boxed{2}[/tex]

I hope this helps.

Answer: 4.8

Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8

Answer: 219

Step-by-step explanation:

[tex] \frac{(7 {x}^{2} {y}^{4} ) ^{2} }{49 {x}^{6} {y}^{5} } \\ = \frac{ {7}^{2} {x}^{2 \times 2} {y}^{4 \times 2} }{49 {x}^{6} {y}^{5} } \\ = \frac{49{x}^{4} {y}^{8} } {49 {x}^{6} {y}^{5}} \\ = {x}^{4 - 6} {y}^{8 - 5} \\ = {x}^{ - 2} {y}^{3} \\ = \frac{y ^{3} }{ {x}^{2} } [/tex]

Answer:

[tex] \frac{y ^{3} }{ {x}^{2} } [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

(1) x+6

Step-by-step explanation:

Possible rational zeroes include ±1, ±2, ±3, ±4, ±6, ±12

Check each answer choice with synthetic division:

1 | 1 9 16 -12

 __1_10_26

    1 10 26 | 14

-2 | 1  9   16 -12

   __-2_-14_-4

      1  7   2  | -16

-6 | 1 9     16 -12

    __-6_-18_12

      1  3   -2  | 0

Therefore, x+6 is a factor of the polynomial

Answer:

(1) x+6

Step-by-step explanation:

[tex]\\ \sf\longmapsto y=2x-x^2[/tex]

[tex]\\ \sf\longmapsto 2x-x^2=0[/tex]

[tex]\\ \sf\longmapsto x^2-2x=0[/tex]

[tex]\\ \sf\longmapsto x(x-2)=0[/tex]

[tex]\\ \sf\longmapsto x=0,2[/tex]

⇒ y=2x−x2

⇒ 2x - x² = 0

⇒ x² - 2x = 0

⇒ x ( x - 2 ) = 0

⇒ x = 0, 2

Answer:

y = 2x - 7

Step-by-step explanation:

lmk if you want an explanation

Answer:

112.81 miles

Step-by-step explanation:

304.6 divided by 2.7

Answer:

i thinks its

the unot rate for the 1st company is 2,86

Step-by-step explanation:

Answer: 92,700

Step-by-step explanation:

9,270,000 / 100 = 92,700

Answer:

6

Step-by-step explanation:

im not sure but I think 6 is the answer

Answer:

25

Step-by-step explanation:

x = the number

2x - 7 = 43

    +7      +7

-----------------

2x = 50

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2        2

x = 25

Answer:

hi the answer to your question should be 50 miles

Step-by-step explanation:

hope this helps have a great day!

[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]

Answer:

  8

Step-by-step explanation:

It appears your table includes points (4, 9) and (7, 33). The average rate of change on the interval is the slope of the line between these two points:

  m = (y2 -y1)/(x2 -x1)

  m = (33 -9)/(7 -4) = 24/3 = 8

The average rate of change is 8.

Answer:

1/9

Step-by-step explanation:

Answer:

y=3x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=3(x-(-3))

y+5=3(x+3)

y=3x+9-5

y=3x+4

Answer:

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 6 inches for a patio if the concrete costs $42.00 per cubic yard?

Step-by-step explanation:

I HOPE THIS HELPS

Answer:

The first one

Step-by-step explanation:

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the one triangles are said to be congruent.