After a baby was born, she began to gain weigh at a rate of 2 pounds per month. The weight of the baby at birth was 8 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.

Answer:

[tex]\frac{x+6}{x-1}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x^2-3x-54}{x^2-10x+9}[/tex] ← factorise both numerator and denominator

= [tex]\frac{(x-9)(x+6)}{(x-9)(x-1)}[/tex] ← cancel (x - 9) on numerator/ denominator

= [tex]\frac{x+6}{x-1}[/tex] ← x ≠ 1

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[tex] \frac{ {x}^{2} - 3x - 54 }{ {x}^{2} - 10x + 9 } = \frac{(x - 9)(x + 6)}{(x - 9)(x - 1)} = \frac{x + 6}{x - 1} \\ [/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

1)

I think you should start off by solving the function equal to the given growth.

[tex]f(m) = 5.98[/tex]

[tex]3(1.09) {}^{m} = 5.98[/tex]

[tex]1.09 {}^{m} = \frac{5.98}{3} [/tex]

[tex]1.09 {}^{m} = 1.9933[/tex]

[tex]m \times ln(1.09) = ln(1.9933) [/tex]

[tex]m = \frac{ ln(1.9933) }{ ln(1.09) } = 8 [/tex]

It is sufficient to plot the exponential growth over the domain m [0,8]

2)

The y-intercept in this case represents the growth achieved at the beginning when m=0.

Before the experiment started::

3)

I'm not really sure about this one,but i think it's supposed to be solved according to this eq,,

[tex]c = \frac{f(8) - f(2)}{8 - 2} [/tex]

Note that c is the average rate of change.

Find f(2) first by substituting 2 in f(m)

f(2)=3(1.09)²=3.5643

[tex]c = \frac{5.98 - 3.5643}{ 8 - 2} [/tex]

[tex]c = \frac{2.4157}{6} = 0.4026[/tex]

average growth=0.4026 cm/month

Answer:

I don't think you provided the whole question...

Step-by-step explanation:

Answer:

Area of a triangle is 100 in²

Height of triangle is 10 in .

we have been asked to find the length of its base .

Formula Used to Find length of its base

☯[tex] \bf\: Area \: of \: triangle \: = \dfrac{1}{2} \times base \: \times height \: [/tex]

Put the given value we obtain

[tex] \rm \implies \: 100 = \dfrac{1}{2} \times base \: \times 10 \\ \\ \rm \implies \: 100 = \dfrac{1}{ \cancel2} \times base \: \times \cancel{10} \\ \\ \rm \implies \: 100 = base \: \times 5 \\ \\ \rm \implies \: base \: = \dfrac{100}{5} \\ \\ \rm \implies \: base \: = \cancel\dfrac{100}{5} \\ \\ \rm \implies \: base \: = 20 \: inch[/tex]

So, the length of its base is 20 inch .

The base length of the triangle with the given values of area and length of height to the nearest inch 20in.

A triangle is a two-dimensional shape with three edges and three vertices.

The area of a triangle is expressed as;

A = (1/2) × base × height

Given the data in the question;

We substitute our given values into the expression above.

A = (1/2) × base × height

100in² = (1/2) × Base × 10in

100in² = 0.5 × 10in × Base

100in² = 5in × Base

Base = 100in² / 5in

Base = 20in

Therefore, the base length of the triangle with the given values of area and length of height to the nearest inch 20in.

Learn more on area of traingle here: https://brainly.com/question/11952845

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[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{2 positives (+) equals positive}\\\large\textsf{2 negatives (-) equals negative}\\\large\textsf{1 negative (-) \& 1 positive (+) equals negative}\\\large\textsf{1 positive (+) \& 1 negative (-) equals negative}[/tex]

[tex]\large\text{According, to your equation you have 2 POSITIVES and even your}\\\large\text{symbol is a positive, so this means your result will turn out to be a positive}[/tex]

[tex]\large\textsf{46.2 + 112.3}\\\rightarrow\large\large\textsf{46.20 + 112.30}\\\rightarrow\large\textsf{158.50}\\\\\large\text{Thus, your equation answer is: \boxed{\mathsf{158.50}}}\\\\\\\\\huge\textbf{Your overall is: \boxed{\mathsf{Positive}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

(-2,0) and (2,0)

Step-by-step explanation:

These are the zeroes because they are the x-intercepts of the graph / they are the points where the line crosses the x-axis

Answer:

b. divide both sides by 5/7 or multiply both sides by 7/5

125 = 40 + 15w

W = number of weeks

6 weeks is 125 = 40 + 15(16) 

15(16) is 90 so 90 + 40 = 130

So the inequality would be w >= 6

To be more precise because 6 weeks is $130 and not $125, divide 85 (money still needed) by 15 to get the decimal 5.66…, so it would be w >= 5.66…

Answer:

I believe the better deal would be,

Seven packs of gum for $4.00.

Complete Question

The complete question is shown on the first and  second uploaded image

Answer:

The correct option is the first and the last option

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  10

   The null hypothesis is  [tex]H_o :  \mu_d  =  0[/tex]

   The alternative hypothesis is  [tex]H_a :  \mu_d  >  0[/tex]

    The test statistics is  [tex]t \approx 6.537[/tex]

   The level of significance is  [tex]\alpha  = 0.05[/tex]

Generally the p-value is mathematically represented as

    [tex]p-value  =  P(t >  6.537 )[/tex]

From z-table  [tex]P(t >  6.537 ) = 0[/tex]

So  

   [tex]p-value  =  0[/tex]

From the value obtained we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis that the true mean difference between the number of units sold after the billboard was placed and the number of units sold before the billboard was placed is equal to zero

Thus we conclude that

Based on the results of the hypothesis test, there is not enough evidence at the level of significance(0.05) to suggest that the true mean difference between the number of units sold after the billboard was placed and the number of units sold before the billboard was placed is greater than zero    

Answer:

Step-by-step explanation:

the resistors which connected in series

equivalent resistance = R1 +R2 + R

is the relationship between the resistors connected in series.

For parallel connection

R1 = 2ohm

R2 = 3ohm

R3 = 6ohm

for equivalent resistance (Rt)

1/Rt = 1/R1 + 1/R2 + 1/R3

1/Rt = 1/2 + 1/3 + 1/6

1/Rt = (3 + 2 + 1)/6 = 6/6 =1/1

Rt = 1 ohm

equivalent resistance = 1 ohm

Answer:

105°

Step-by-step explanation:

FEG+EFG=FGN (Exterior angle of a triangle= 2 interior opposite angles)

FEG+35°=140°

FEG=140-35

FEG= 105

Step-by-step explanation:

We are here given that a point B is between A and C . Also ,

And we would like to calculate the length of BC . For figure refer to the attachment. From figure we can see that ,

[tex]\rm:\implies AC = AB + BC [/tex]

Substitute the respective values,

[tex]\rm:\implies 21 = 2x + 3x + 1[/tex]

Add like terms ,

[tex]\rm:\implies 21 = 5x +1 [/tex]

Subtract 1 on both sides,

[tex]\rm:\implies 21-1 = 5x [/tex]

Simplify,

[tex]\rm:\implies 20=5x [/tex]

Divide both sides by 5,

[tex]\rm:\implies \blue{ x = 4}[/tex]

Now consider ,

[tex]\rm:\implies BC = 3x+1 [/tex]

Plug in the value of x found above ,

[tex]\rm:\implies BC= 3(4)+1[/tex]

Simplify,

[tex]\rm:\implies BC = 12+1[/tex]

Add,

[tex]\rm:\implies \underline{\boxed{\blue{\rm{ \quad BC \quad =\quad 13\quad }}}}[/tex]

And we are done !

Answer:

+ BC = AC

x + 2x+1 = 22

3x +1 = 22

3x = 21

x = 7

AB = 7

BC = 2*7+1 = 14 + 1 = 15

15 - 2

13

Options:

Rotation of 180° about point B

Rotation of 90° about point b

Reflection over the x-axis

Translation down 2 units

Answer:

Rotation of 180° about point B

Step-by-step explanation:

Considering coordinates of point B

Assume the coordinates of the line at point B is (x,y)

i.e. [tex]B = (x,y)[/tex]

First, we need to determine the slope at point B

Taking coordinates about the origin.

The slope of B is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (0,0)[/tex] --- origin

[tex](x_2,y_2) = (x,y)[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes

[tex]m = \frac{y - 0}{x - 0}[/tex]

[tex]m = \frac{y}{x}[/tex]

Taking the options one after the other:

Option A.

When rotated by 180°, the resulting coordinates of B would be

[tex]B' = (-x,-y)[/tex]

Taking the slope of B'

The slope of B is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (0,0)[/tex] --- origin

[tex](x_2,y_2) = (-x,-y)[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes

[tex]m = \frac{-y - 0}{-x - 0}[/tex]

[tex]m = \frac{-y}{-x}[/tex]

[tex]m = \frac{y}{x}[/tex]

Notice that the slope of B and B' is the same;

[tex]m = \frac{y}{x}[/tex]

Hence:

Rotation of 180° about point B  answers the question

There's no need to check for other options

Answer: A) -10 ≤ x ≤ 10 , -10 ≤ y ≤ 10

Step-by-step explanation:

Answer:

Parallelogram means opposite sides equal and parallel to each other

So

Done!

Answer:

  c  Lee

Step-by-step explanation:

The coordinates of the community center are both negative. They place it 2 units left and 3 units up from Lee's house in the 3rd quadrant.

Answer:

(Cosx-Cos³x)/Sinx=SinxCosx

Step-by-step explanation:

sin3x−cos3x

=sinxsin2x−cosxcos2x

=sinx(1−cos2x)−cosx(1−sin2x)

=sinx−sinxcos2x−cosx+cosxsin2x

=sinx−cosx+(sinx−cosx)sinxcosx  

=(sinx−cosx)(1+sinxcosx

Answer:

34%

Step-by-step explanation

34% (I believe)

Answer:

What is the probability and odd for 7/16​

There is a 30.43 percent of a particular outcome and 69.57 percent of another outcome.

Answer:

OB

-2 multiply by a -2 is a - 4 which is a numerator then

3 doesn't change cause it is a denomenator

thus your final answer is a -4/3

Answer: 3 + 10i

Step-by-step explanation:

Complex numbers follow the same rules that real numbers do when it comes to addition and subtraction. Removing the parenthesis we have:

[tex]5+6i-2+4i[/tex]

Combine the real parts, then combine the complex parts:

[tex]3+10i[/tex]

Answer:

There!!

Step-by-step explanation:

mark me brainliest!!

Answer:

88 m

Step-by-step explanation:

Given,

Radius ( r ) = 14

Formula : -

Circumference of circle = 2π4

Circumference of circle

= 2 x 22 / 7 x 14

= ( 2 x 22 x 14 ) / 7

[ 14 = 2 x 7 ]

= ( 2 x 22 x 2 x 7 ] / 7

= 2 x 22 x 2

= 88 m

Note : -

The value of π = 22 / 7.

EXPLANATION:

To convert degrees to radians, multiply by π / 180 °

since a full circle is 360° or 2π radians.

240°⋅π / 180° radians

Cancel the common factor of 60

4 × π / 3 radians

Combine 4 and π / 3.

4π / 3 radians

HOPE ITS HELPS !!!!!

The coordinates of the points on unit circle at the given angle 240 degrees is[tex](\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )[/tex]

[tex]radians= (degrees)[/tex]×[tex]\frac{\pi }{180}[/tex]

x=rcosθ

y=rsinθ           (where r is the radius of  circle for unit circle r=1)

According to the question

we have

θ = 240 degrees and, r =1

so,  240 degrees = 240×[tex]\frac{\pi }{180}[/tex]

⇒240 degrees = [tex]\frac{4\pi }{3}[/tex]   (in radians)

Therefore, the coordinates of the points on unit circle at angle [tex]\frac{4\pi }{3}[/tex] is calculated as

[tex]x=(1)cos\frac{4\pi }{3}[/tex]                    (for unit circle r=1)

[tex]x=\frac{-1}{2}[/tex]

And,

[tex]y=(1)sin\frac{4\pi }{3}[/tex]                 (for unit circle r=1)

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

Hence, the coordinates of the point on unit circle at angle 240 degrees is [tex](\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )[/tex]

Learn more about coordinates of the point on circle here:

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Answer:

A.)

-2, -1, 0, 1, 2, 3, 4, 5, 6

Step-by-step explanation:

mark me brainliest!!

Answer:

f(x+2)+6 = 4^(x+2)+6

Step-by-step explanation:

(The power is to the x+2) Hope this helps!:)

Answer:

The width of the rectangle is equal to 5 and the length is equal to 13

Step-by-step explanation:

Perimeter of rectangle = (Length + Width) ×2

Perimeter of rectangle = (13 + 5) ×2

Perimeter of rectangle = 36

The length of the rectangle is 13, which is 3 more than two times the width, if the width is 5

5 (Width) ×2 = 10

10 +3 = 13 (Length)

Answer:

Step-by-step explanation:

The Pythagorean theorem relates side lengths in right triangles. It tells you the square of the hypotenuse is equal to the sum of the squares of the sides.

__

  8.8² + x² = 11²

  x² = 121 -77.44 = 43.56

  x = √43.56 = 6.6 . . . inches

__

  6.6² +10² = y²

  43.56 +100 = y² = 143.56

  y = √143.56 ≈ 11.982

  y ≈ 12.0 . . . inches