5
The average rate of change of g(x) between x = 4 and x = 7 is Ē. Which statement must be true?

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1600\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=years\dotfill &3 \end{cases} \\\\\\ A=1600e^{0.014\cdot 3} \implies A \approx 1668.63[/tex]

Answer:

C. n^3 - 16 = 48

[tex]\textsf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4}{25} - \dfrac{-1}{2}}[/tex]

[tex]\textsf{Cross\ multiply and you should see what the result comes}[/tex]

[tex]\mathsf{New\ equation: \dfrac{8}{50} + \dfrac{-25}{50}}[/tex]

[tex]\mathsf{8 - 25 = -17\leftarrow \text{\bf{{NUMERATOR}}}}[/tex]

[tex]\mathsf{50 + 0 = 50\leftarrow \text{\bf{DENOMINATOR}}}[/tex]

[tex]\boxed{\boxed{{\boxed{\textsf{Therefore, your answer is most likely: \boxed{\boxed{{\huge{\mathsf{\bf{\dfrac{-17}{50}}}}}}}}}}}}}\checkmark[/tex]

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

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Answer:

multiplication

Step-by-step explanation:

cuz it says "times greater"

Answer:

It means how may times can the other variable fit into that variable, so you would divide.

- For example: Bob has 6 flowers in his basket, but Sally has only 2 flowers in her basket.

    Q: How many times greater is Bob's basket of flowers than Sally's?

    A: Bob's basket is 3 times greater than Sally's (bc 6/2 = 3, or 2 can fit into 6           three times)

**please mark brainliest!!

Answer:

The answer is 13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

5(3)-2

15-2

13

Answer:

13

Step-by-step explanation:

Substitute 7 for b

6 + 7 = 13

Answer:

It's 13.

Step-by-step explanation:

6+7=13

Answer: 6i

Step-by-step explanation:

Answer:

y = 3x

Step-by-step explanation:

Equation of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

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

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

We are given the following values of the function: f(-1)=-3 and f(2)=6. The points are (-1,-3) and (2,6). The slope is:

[tex]\displaystyle m=\frac{6+3}{2+1}=\frac{9}{3}=3[/tex]

Now find the equation of the line using the second point:

y - 6 = 3 ( x - 2 )

Operating:

y - 6 = 3x - 6

Simplifying:

y = 3x

Answer:

The youth group bought 35 geraniums and 45 daisy plants.

Step-by-step explanation:

We can solve this using a system of equations:

x + y = 80

4x + 6y = 410

X = Geraniums

Y = Daisies

First, let's solve for a variable in the first equation. I am going to solve for y in the first equation:

x + y = 80

y = -x + 80

Now that we have solved for y we can plug that back in to the 2nd equation:

4x + 6(-x + 80) = 410

4x - 6x + 480 = 410

-2x + 480 = 410

-2x = -70

x = 35

Now that we have found the amount of geraniums we can plug it back into the first equation and solve for y:

35 + y = 80

y = 45

Therefore the youth group bought 35 geraniums and 45 daisy plants.

Check:

(35) + (45) = 80

80 = 80

4(35) + 6(45) = 410

140 + 270 = 410

410 = 410

I hope this helps!!

- Kay :)

Answer:

The answer is 7

Step-by-step explanation:

The time is 0 because it wants the depth before the snow melts. -0.5 times 0 is zero plus seven is seven.

Using the  system of equations x+y+z=7200, 0.04x+0.11y+0.14z=805 and z=x+y+200, the value of x=1400,y=2100 and z=3700

Given,

The equations

x+y+z=7200

0.04x+0.11y+0.14z=805

z=x+y+200

Substitute the value of z in the first and second equations

x+y+x+y+200=7200

2x+2y+200=7200

2x+2y=7000

x+y=3500   (1)

Similarly

0.04x+0.11y+0.14(x+y+200)=805

0.04x+0.11y+0.14x+0.14y+28=805

0.18x+0.25y=777

Multiply the equation by  4

0.72x+y=3108   (2)

We have to use elimination method here

Subtract the equation (1) from (2)

x-0.72x=3500-3108

0.28x=392

x=1400

Then,

x+y=3500

1400+y=3500

y=2100

z= x+y+200

z=1400+2100+200

z=3700

Hence, using the  system of equations x+y+z=7200, 0.04x+0.11y+0.14z=805 and z=x+y+200, the value of x=1400,y=2100 and z=3700

Learn more about elimination method here

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Answer:

Step-by-step explanation:

for first,

then solving this we get

Answer:

You still would have $1,000

Step-by-step explanation:

In April, you lost 13% of your fund. So we will subtract it.

In May, you gain 13% back. The rate of change was 0%.

Therefore, you still have $1,000 dollars.

Answer: The answer is that you have $983.

Step-by-step explanation:

Answer:

(-2, -5)

(-1, -2)

(0, 1)

(1, 4)

(2, 7)

Step-by-step explanation:

Substitute x with each number and solve equation.

Answer:

This expression can be written as 53-2m

Step-by-step explanation:

Sometimes it can help to reword the sentence...

2 times Mai's score is being subtracted from 53.

Use 'M' for Mai's score:

53-2m

Answer:

17,070

Step-by-step explanation:

Continue to move the decimal point to the right, and it adds a zero when the decimal places are all taken.

Answer:

10,070

Step-by-step explanation:

so 10 to the power of three is 1 with three 0s

so 1000

remember 10 cubed is 10 times 10 times 10 that equals 1000

then 1000 times 17.07 is 17070

this is a 2 step equation

Answer:

Five less than twelve times a number is represented by  12n - 5

Expressing word problems as Equations

Let the unknown nmber be represented as n

Such that twelve times the  number will be represented as 12 n

There fore Five less than twelve times the  number becomes 12n - 5

Answer:

As far as I can see, yes it is correct.

Answer:

6800

Step-by-step explanation:

Answer:

Sry but i hope u have great christmas and get all the gifts you wnated.

Step-by-step explanation:

Answer:

I will give you the link below to a PDF that one of my young friends made for someone who had this exact question.

Step-by-step explanation:

The appropriate domain for this situation is [tex]\{t : 0 \leq t \leq 1.5\ \& \: t \in \mathbb R \}[/tex] (that means t can be any real number and between 0 and 1.5 (both endpoints included)

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

For this case, we have  only those values of 't' as appropriate value, which are from t = 0 till the time when ball hits the ground, since after that the height will be constantly 0, but the height function will give negative values which doesn't model the situation correctly.

Thus, those values of t for which the equation [tex]h(t) = -16t^2 + 24t[/tex] correctly models the real world situation are said to be appropriate values of domain of this function.

The time when the ball will reach the ground will be when the height will be 0, thus,:

[tex]0 = -16t^2 + 24t\\2t^2 - 3t = 0\\(2t-3)(t) = 0\\t = 0, t = 3/2 = 1.5 \: \rm sec[/tex]

The height is 0 when ball starts going up(t=0), and when t = 1.5 the ball reaches ground.

Thus, the appropriate domain for modelling the situation is values of t in the interval [0, 1.5] (both endpoints are inclusive, as shown by big bracket).

Learn more about appropriate domain here:

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The distance between the bottom of the ladder and the ground's surface is 24.7 feet.

Given that a is the ground, b is the building, and c is the ladder.

Also the ground is perpendicular to the building, the ladder, the building, and the ground form a right triangle.

Therefore, the Pythagorean theorem can be applied as follows:

c² = a² + b²

According to the information in the problem, c is 30 feet, b is 17 feet, and we solve for a as follows:

(30 ft)² = a² + (17 ft)²

900 ft² = a² ₊ 289 ft²

900 ft² ₋ 289 ft² = a²

611 ft² = a²

a² = 611 ft²

a = √611 ft²

a = 24.71

rounding off to nearest tenth, so a = 24.7

Hence the bottom of the ladder is 24.7 feet far away from the base of the ground.

Learn more about Pythagorean problems here:

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Your question is incomplete. Please find the missing content here.

A 23-foot ladder is placed against a building. If the top of the ladder will lean against the building 17-feet high, how far away from the base of the building is the bottom of the ladder located?

Answer:

I think the second one!

Step-by-step explanation:

Note: Consider the below figure attached with this question.

Given:

[tex]a=3\sqrt{3}[/tex]

To find:

The value of b.

Solution:

In a right angled triangle,

[tex]\tan \theta = \dfrac{Perpendicular}{Base}[/tex]

For the given right angled triangle,

[tex]\tan \theta = \dfrac{a}{b}[/tex]

[tex]\tan (30^\circ) = \dfrac{3\sqrt{3}}{b}[/tex]

[tex]\dfrac{1}{\sqrt{3}} = \dfrac{3\sqrt{3}}{b}[/tex]

On cross multiplication, we get

[tex]1\times b=3\sqrt{3}\times \sqrt{3}[/tex]

[tex]b=3(3)[/tex]

[tex]b=9[/tex]

Therefore, the value of b is 9.

Answer:

(2x+5)(3x-2)

Step-by-step explanation:

6x²+11x-10

6x²+15x-4x-10

3x(2x+5)-2(2x+5)

(2x+5)(3x-2)

Answer:

The steps are :

[tex] {tan}^{2} θ - {cot}^{2} θ = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]

[tex]RHS = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]

[tex]RHS = (1 + {tan}^{2} θ)(1 - \frac{1}{ {tan}^{2} θ} )[/tex]

[tex]RHS = (1 + {tan}^{2} θ)( \frac{ {tan}^{2}θ - 1}{ {tan}^{2} θ} )[/tex]

[tex]RHS = - \frac{(1 + {tan}^{2}θ)(1 - {tan}^{2} θ)}{ {tan}^{2} θ}[/tex]

[tex]RHS = - \frac{(1 - {tan}^{4} θ)}{ {tan}^{2} θ} [/tex]

[tex]RHS = \frac{ {tan}^{4} θ - 1}{ {tan}^{2}θ } [/tex]

[tex]RHS = {tan}^{2} θ - \frac{1}{ {tan}^{2}θ } [/tex]

[tex]RHS = {tan}^{2} θ - {cot}^{2} θ[/tex]

[tex]RHS = LHS (proven)[/tex]