D − 37 = 40
D =
Check your solution.
− 37 = 40

The graph is attached and all the sub parts have been answered.

A function is  away of relating a dependent variable to an independent variable .

It is given that

Current weight of Rex at 2 months =6 pounds

Let x represents the age in months of Rex

then a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. is

Let y be the current weight of Rex

then

y = 6 + 9(x -2)

The table  that represents Rex’s current weight, in pounds, as a function of his age, in months

2              6

3              15              

4              24

5              33

6              42

7              51

8              59

The graph is plotted for the given data and attached .

If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old

6 + 9*(12-2)

96 pounds.

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The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

The function is given as:

[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]

To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5

At this domain;

g(x) = -1

So, the value of g(-0.5) is

g(-0.5) = -1

To calculate g(0.3), we make use of the domain -0.5 < x  0.5

At this domain;

g(x) = 0

So, the value of g(0.3) is

g(0.3) = 0

To calculate g(0.5), we make use of the domain 0.5 ≤ x  1.5

At this domain;

g(x) = 1

So, the value of g(0.5) is

g(0.5) = 1

Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

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Answer:

See below

Step-by-step explanation:

129 500     original price

selling price =   2 ( 129 500) - 9000 = 250 000

% change   Questions worded like this are often up for debate as to exactly answer the question

250 000 / 129 500 =  193 %      Selling price was 193% of original price

(250 000 - 129500)/ 129500 =   93 % INCREASE

Answer:

B -o.60

Step-by-step explanation:

34 - 40 = -6.  -6 divide by 10 = -3/5 or - 0.6. So answer is B

The correct option regarding the recursively defined strings is given by:

c) Both i) and ii).

First we start with string 101, we have that:

101 -> 1w -> 10w -> 101

Which belongs to alphabet S.

For string 001, we have that:

001 -> 0w -> 00w -> 001.

Which belongs to alphabet S.

Hence statement c is correct.

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The fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Fractions that are between 12/13 and 19/20 such that:

The numerator(N) is one less than the denominator(D).

N =  D - 1

N = (12, 19)

D = (13, 20)

D = 14, N = 13

D = 15, N = 14

D = 16, N = 15

D = 17, N = 16

D = 18, N = 17

D = 19, N = 18

The fractions that are between 12/13 and 19/20:

N/D = {13/14, 14/15, 15/16, 16/17, 17/18, 18/19}

Thus, the fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6

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Answer:

=8x+14 or

=16x²+56x+49

[tex]\bf{(4x+7)2 }[/tex]

[tex]\bf{=2(4x+7)}[/tex]

[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]

[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]

[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]

The value of this irrational Expression is 40.77 .

An expression is a mathematical statement consisting of variables , constants and mathematical operators.

The expression given is

7√22 +3√7

√22 = 4.69

√7 = 2.65

32.83 + 7.94

40.77

The value of this irrational Expression is 40.77 .

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Answer: 7

Step-by-step explanation:

As tangents drawn from a common external point to a circle are congruent,

Answer:

Step-by-step explanation:

Answer: SAS

Step-by-step explanation:

Since [tex]\frac{BC}{CD}=\frac{AC}{CE}=\frac{1}{2}[/tex], and [tex]\angle ACB \cong \angle DCE[/tex] because they are vertical angles, the triangles are similar by SAS

Answer:

-3 is a zero of the function  False

-1 is a zero of the function  True

1 is a zero of the function   False

2 is a zero of the function  True

4 is a zero of the function   False

The angle θ to the diameter that she should row is; θ = 56.44°

It should be noted that;

a = 90° - θ. Thus;

b = 2θ

For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .

The time required to walk this distance is given by;

t_w = 4θ/5 = 0.8θ

The distance rowed is given by: cos θ = d_r/2.4

d_r = 2.4cos θ while the time needed for it is;

t_r = 2.4cos θ/3.5

t_r = 0.6857θ

Thus, total time is;

T(θ) = t_r + t_w

T(θ) = 0.6857θ + 0.8θ

T(θ) = 1.4857θ

Now we need the critical numbers:

T'(θ) = 1 - 1.2 sin θ

At T'(θ) = 0, we have;

1 - 1.2 sin θ = 0

1/1.2 = sin θ

θ = sin⁻¹(1/1.2)

θ = 56.44°

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Answer:

300 cupcakes

Step-by-step explanation:

[tex]27 = .09c[/tex]

[tex]c = \frac{27}{.09} = \frac{2700}{9} = 300[/tex]

In total, the bakery sold 300 cupcakes on a certain day.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of cupcakes sold that day.

let, 'x' be the total number of cupcakes sold that day.

Therefore, 9% of 'x' is 27 which is,

(9/100)×x = 27.

0.09x = 27.

x = 27/0.09.

x = 300.

So, The number of cupcakes sold that day is 300.

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Answer:

11. always

12. always

13. always

14. never

15. never

16. always

17. always

18. sometimes

19. sometimes

20. never

Step-by-step explanation:

11. A line can be defined by at least two points

12. A plane can be defined by at least three points

13. If two planes intersect, then they form a line at the intersection.

14. If two lines intersect, then they form a point at the intersection (not a segment).

15. A line does not have any endpoints (infinite in both ways).

16. If two planes are not parallel they will always intersect.

17. If two lines are not parallel they will always intersect.

18. Two points are sometimes collinear. It depends on where they are.

19. Two points are sometimes coplanar. It depends on where they are.

20. Ray MN and NM are not the same ray because the end points are different.

The equation for the red graph is f(x)=-x^2.

The question is an incomplete graph of a function is missing

For a complete question refer to the graph attached below

we have [tex]g(x)=4-x^2[/tex]

The vertex of the function g(x) is the point (0,4)

The vertex of the function f(x) is the point (0,0)

This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.

So, the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

The translation is 4 units down

The equation of the function f(x) is

[tex]f(x)=g(x)-4[/tex]

[tex]f(x)=(4-x^2)-4[/tex]

[tex]f(x)=-x^2[/tex]

Therefore, The answer is f(x)=-x^2

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The graph is shown in the attached image.

Answer:

[tex] \boxed{f(6) =2 4}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = x² - 2x[/tex]

Solution:

ATP,it is that x = 6. So substitute 6 on the function.

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

Simplifying using PEMDAS,we obtain:

[tex]f(6) = 6 \times 6- 12[/tex]

[tex]f(6) = 36 - 12[/tex]

[tex] \boxed{f(6) =2 4}[/tex]

Hence,f(6) = 24.

The graph of [tex]\mathbf{y=\sin{3x}}[/tex] is given by,

Here given the function is [tex]y=\sin{3x}[/tex]

when [tex]x=0\Rightarrow y=\sin{3\times 0}=\sin0=0[/tex], then it passes through the origin (0,0).

When [tex]x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1[/tex]

Since we know that, [tex]-1\leq\sin{x}\leq1,\forall x[/tex], then the function has maximum height at [tex]x=\frac{\pi}{6}[/tex].

Again when [tex]x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0[/tex], again the function is 0.

So clearly the function is the Oscillating function with a maximum value of the function as 1 and a minimum value of the function as -1.

Range of the oscilaltion of the function = 1-(-1) = 1+1 = 2

Using graphing calculator we get the graph of function [tex]y=\sin3x[/tex],

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Here....

The length is given 15 feet and the width is 12 feet...Now let's find the Perimeter..

Perimeter = 2 ( l + b )

= 2 ( 15 + 12 )

= 2 × 27

= 54 feet

[tex]...[/tex]

:)...

Answer:

Step-by-step explanation:

[tex]x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}[/tex]

Answer:

yes

Step-by-step explanation:

the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.

the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).

so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.

but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.

there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).

but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.

Answer:

(-2, 1)

Step-by-step explanation:

You can read the solution from graph. The solution is where the two lines intersect. That happens in point (-2, 1).

---

Alternative:

If you want to be sure, you can alway double check by solving the system of equations.

First equation: [tex]y = \frac{1}{2}x + 2[/tex]

Second equation: [tex]y = -\frac{1}{2}x[/tex]

Substituting y in first equation with y from second.

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

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

Adding [tex]\frac{1}{2}x[/tex] on both sides.

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

[tex]0 = 1x + 2[/tex]

[tex]0 = x + 2[/tex]

[tex]-2 = x[/tex]

Substituting x with -2.

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

[tex]y = -\frac{1}{2}(-2)[/tex]

[tex]y = 1[/tex]

As you see you get the same result as from reading the graph, (-2, 1).

Answer:

  no

Step-by-step explanation:

In order for one number (A) to be a factor of another (B), the exponents of the primes in the prime factorization of A cannot exceed those of the prime factorization of B.

__

  A = 2^14 × 3^20

  B = 2^12 × 3^22

The exponent of the factor 2 in A is 14, which exceeds the exponent of the factor 2 in B (12). Therefore, A cannot be a factor of B.

  (3^20)(2^14) is not a factor of (3^22)(2^12)

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

[tex]\qquad \tt \rightarrow \: Acceleration_{dog} = 0[/tex]

____________________________________

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

A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.

And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0

Henceforth, Acceleration of dog is 0 as well.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer: Acceleration = 0 ✅

Step-by-step explanation:

Hii, let me help you out! (:

Acceleration means "change in speed (which is also known as velocity, V, in physics) per a specific amount of time.

Part 1 is Successfully completed!

                                              ↪

Now let's focus on finding the acceleration of the dog.

Like I said above, [tex]\sf Acceleration=change\;in\;speed\;per\;a\;specific\;amount\;of\;time[/tex]

Well, we are provided with the information that the dog's speed is constant. This means that it doesn't change. So the dog keeps on moving at a speed of 8 m/s. This means that its speed doesn't change, so the change in speed is 0. And this means that its acceleration is 0.

Voila! There's our answer, cheers! (:

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Answer:

1/2 cup of chocolate chips

Step-by-step explanation:

Given ratio:

Let x be the unknown amount of chocolate chips:

[tex]\implies \sf \dfrac{1}{3}:2=x:3[/tex]

[tex]\implies \sf \dfrac{\frac{1}{3}}{2}=\dfrac{x}{3}[/tex]

Cross multiply:

[tex]\implies \sf 3 \cdot \dfrac{1}{3}=2 \cdot x[/tex]

[tex]\implies \sf 1=2x[/tex]

[tex]\implies \sf x=\dfrac{1}{2}[/tex]

Therefore, 1/2 a cup of chocolate chips will be needed for 3 cups of flour.

Let that be x

Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)

Step-by-step explanation:

Reflecting over y = x maps (x,y) onto (y,x).