Three copies of this rectangle were connected along a side to make a larger rectangle. What could the perimeter of the new rectangle be? Consider all possibilities.

Work Shown:

-1 < x+3 < 5

-1-3 < x+3-3 < 5-3 ... subtract 3 from all sides

-4 < x < 2

Answer:

[tex]\displaystyle f'(x)=-\frac{2}{x^{{}^{3}\!/\!{}_{2}}}[/tex]

Step-by-step explanation:

We have the function:

[tex]\displaystyle f(x)=\frac{4}{\sqrt x}[/tex]

And we want to find the derivative using the limit process.

Recall that the definition of a derivative is:

[tex]\displaystyle \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Therefore, by substitution:

[tex]\displaystyle \lim_{h \to 0}\frac{\dfrac{4}{\sqrt{x+h}}-\dfrac{4}{\sqrt x}}{h}[/tex]

First and foremost, we can move the constant factor outside of the limit:

[tex]\displaystyle =\lim_{h \to 0}\frac{4\left(\dfrac{1}{\sqrt{x+h}}-\dfrac{1}{\sqrt x}\right)}{h}\\ \\=4\lim_{h \to 0}\frac{\dfrac{1}{\sqrt{x+h}}-\dfrac{1}{\sqrt x}}{h}[/tex]

Next, we can multiply everything by (√(x + h)(√x) to eliminate the fractions in the denominator. Therefore:

[tex]\displaystyle =4\lim_{h \to 0}\frac{\dfrac{1}{\sqrt{x+h}}-\dfrac{1}{\sqrt x}}{h}\left(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x}\right)[/tex]

Distribute:

[tex]\displaystyle =4\lim_{h \to 0}\frac{\left({\sqrt{x+h}\sqrt x}\right)\dfrac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\dfrac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}[/tex]

Distribute and simplify:

[tex]\displaystyle =4 \lim_{h\to 0}\frac{\sqrt x-\sqrt{x+h}}{h(\sqrt{x+h}\sqrt{x}) }[/tex]

Next, we can multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x + h)). Thus:

[tex]\displaystyle = 4\lim_{h\to 0}\frac{\sqrt x-\sqrt{x+h}}{h(\sqrt{x+h}\sqrt{x}) }\left(\frac{\sqrt x +\sqrt{x+h}}{\sqrt x +\sqrt{x+h}\right)}[/tex]

Simplify:

[tex]\displaystyle =4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\ \\ \\ =4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})} \\ \\ \\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}[/tex]

Cancel like terms:

[tex]\displaystyle =4 \lim_{h \to 0} -\frac{1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}[/tex]

Now, we can use direct substitution. Hence:

[tex]\displaystyle \Rightarrow4 \left( -\frac{1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})}\right)[/tex]

Simplify:

[tex]\displaystyle =4\left( -\frac{1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})}\right) \\ \\ \\ =4\left( -\frac{1}{(x)(2\sqrt{x})}\right)[/tex]

Multiply:

[tex]\displaystyle =- \frac{4}{2x\sqrt{x}}[/tex]

Reduce and rewrite:

[tex]\displaystyle =-\frac{2}{x(x^{{}^{1}\! / \! {}_{2} \!})}[/tex]

Simplify:

[tex]\displaystyle =-\frac{2}{x^{{}^{3}\!/\!{}_{2}}}[/tex]

Therefore:

[tex]\displaystyle f'(x)=-\frac{2}{x^{{}^{3}\!/\!{}_{2}}}[/tex]

Answer:

16.16 is 16% of 101

Step-by-step explanation:

Hope this helps!

(2,6) after a reflection in the x axis

(-2,-6) after a reflection in the y axis

Step-by-step explanation:

this is the ans in my view

Answer:

t = d/V

Step-by-step explanation:

V = d/t

Multiply each side by t

Vt = d/t *t

Vt = d

Divide each side by V

Vt/V = d/V

t = d/V

Answer:

x= c - b / A

please look at the step by step explanation to better understand :)

Step-by-step explanation:

subtract b from the left side and right side

so you are left with Ax = c - b

divide what number c - b is by A

and you are left with x= c - b / A

Answer:

wow sry this is a tuff one :(

Step-by-step explanation:

Answer:

your welcome it has to be c

Answer:

I honestly dont know

Step-by-step explanation:

Use a calculator for algebra srry if this answer is useless

Answer:

Step-by-step explanation:

GIRL! You should add diagrams to these types of questions. It would really help

That 10cm does not mean point C is 10cm. It means the line AB is 10 cm in total.

And since point C is the midpoint, which means that point C cuts the line AB in half, that makes AC = 5cm

Answer:

the answer is fjdixekd

Answer:

a) (-2, -1)

b) (-3, 0) and (-1, 0)

Step-by-step explanation:

The turning point is the same as the vertex of the graph.

The vertex would be (-2, -1).

The zeros of the equation would be where the graph crosses the x-axis when y = 0.

The roots would be (-3, 0) and (-1, 0).

Answer:

t=28/3

Step-by-step explanation:

Id this helped feel free to send thanks and give brainliest so I can continue to help people around the brainly community.

The area is the measure of a space delimited by a contour that is called perimeter. In some cases, the term surface or area is often used interchangeably, but the former refers to space, while the latter refers to its measurement. That is, area is the measurement of a surface.

Obtaining the measurements of its sides,

The sides are:

Each of these sides measures a certain amount, for that, which is multiplied.

To calculate the area: multiply the given value of the base by the value of the height, and divide by 2.

Answer:

Step-by-step explanation:

What we are expected to solve for that the problem did not expressly state is most likely the number of hours that you could ride for an amount of $65.

firstly we need to model the inequality (equation) for this scenario.

the constant fee= $3 additional fee for helmet

[tex]3+15n\leq 65\\\\[/tex]

We can now solve for n since the above inequality satisfies the condition presented in the problem statement.

 [tex]3+15n\leq 65\\\\15n\leq65-3\\\\ 15n\leq 62[/tex]

Divide both sides by 15 to find n

[tex]n\leq 62/15\\\\n\leq 4hrs -8min[/tex]

Answer:

She would receive $10.05 cents back

Step-by-step explanation:

Add 6.75, 1.45, and 1.75. You would get 9.95. Then, you would subtract $20.00 by $9.95, getting 10.05 as change.

Hope this helps!

Answer:

5.55

Step-by-step explanation:

The cost of the 3.4 pounds of trail mix is:

STEP 1:

multiply number of pounds purchased by price per pound

= 3.4 pounds * $4.25 per pound

= $14.45 total cost

STEP 2:

subtract total cost of purchase (step 1) from amount she gave cashier ($20.00)

= $20.00 - $14.45

= $5.55 amount received back from cashier

Answer: 29

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5x the base

Answer:

100 vasos

Step-by-step explanation:

Sabemos que usando la conversión de unidades SI

1 litro = 1000 mililitros

En la pregunta se nos dice que:

Necesitamos trasvasar 20 litros de leche utilizando vasos de 200 mililitros de capacidad.

Por lo tanto,

1 litro = 1000 mililitros

20 litros =

20 litros × 1000 mililitros / 1 litros

= 20.000 mililitros de leche que hay que transferir.

Dado que estamos usando vasos con capacidad de 200 mililitros, la cantidad de vasos necesarios

= 20.000 mililitros de leche / 200 mililitros

= 100 vasos

Por tanto, se necesitan 100 vasos de 200 mililitros de capacidad para trasvasar 20 litros de leche que se encuentran en un barril de 200 litros a una jarra de 25 litros de capacidad.

Answer:

The correct option is;

The number of items for each shopper

Step-by-step explanation:

Quantitative data are data that are the result of a measurement and are therefore the numerical value assigned as an attribute of an item based on measurement. Examples of quantitative data are, the weights or heights of items, the count of an item and other similar measurable data

Discrete data are data to which are assigned specific unique numerical values

Data that is obtained by counting of a number of items are quantitative discrete data

Therefore, of the options, the one that is a discrete quantitative variable is the number of items for each shopper as it is countable which makes it quantitative and it carries a unique number, which makes it countable.

Answer:

The number of items for each shopper

Step-by-step explanation:

give the other guy brainliest

Answer:

6x²-8x-8

Step-by-step explanation:

[tex](3x - 2)(2x + 4)[/tex]

[tex]3x \times 2x = 6 {x}^{2} \\ 3x \times 4 = 12x \\ - 2 \times 2x = - 4x \\ - 2 \times 4 = - 8[/tex]

[tex]6 {x}^{2} + 12x - 4x - 8 \\ 6 {x}^{2} + 8x - 8[/tex]

Answer:

(3x-2)(2x+4)

= 6x^2+8x-8

Step-by-step explanation:

Answer:

(a). The value of y is 6.

(b). The value of RS and ST are 33 and 31.

Step-by-step explanation:

Given that,

RS = 5y+3

ST=4y+7

RT=64

(a). We need to calculate the value of y

Using given data

[tex]RS+ST=RT[/tex]

Put the value into the formula

[tex]5y+3+4y+7=64[/tex]

[tex]9y=64-10[/tex]

[tex]y=\dfrac{54}{9}[/tex]

[tex]y=6[/tex]

(b). We need to calculate the value of RS

Using equation of RS

[tex]RS=5y+3[/tex]

Put the value of y

[tex]RS=5\times6+3[/tex]

[tex]RS=33[/tex]

We need to calculate the value of ST

Using equation of ST

[tex]ST=4y+7[/tex]

Put the value of y

[tex]ST=4\times6+7[/tex]

[tex]RS=31[/tex]

Hence, (a). The value of y is 6.

(b). The value of RS and ST are 33 and 31.

Answer:

The number cupcakes Ms. Ciervo can make using the [tex]9 \frac{2}{3}[/tex] teaspoons of vanilla is 29.

Step-by-step explanation:

The information provided is:

Compute the number cupcakes Ms. Ciervo can make using the [tex]9 \frac{2}{3}[/tex] teaspoons of vanilla as follows:

Amount of vanilla required for one cupcake = [tex]\frac{1}{3}[/tex] teaspoons

Total amount of vanilla available [tex]9 \frac{2}{3}[/tex] teaspoons.

[tex]\text{number of cupcakes}=\frac{\text{total amount}}{\text{amount required for 1 cupcake}}[/tex]

                               [tex]=\frac{9\frac{2}{3}}{\frac{1}{3}}\\\\=\frac{29}{3}\div\frac{1}{3}\\\\=\frac{29}{3}\times \frac{3}{1}\\\\=29[/tex]

Thus, the number cupcakes Ms. Ciervo can make using the [tex]9 \frac{2}{3}[/tex] teaspoons of vanilla is 29.

Answer:

C

Step-by-step explanation:

A: (16 - 12)² = 4² = 16 (Incorrect)

B: -|-4| = -(4) = -4 (Incorrect

C: (96 ÷ 8) - 2³ = 12 - 8 = 4 (Correct)

Answer:

2

Step-by-step explanation:

First do whats in the parenthesess

it will look like this

2+5-5=2 the 5's cancel eachother out so your left with 2

Answer:

Step-by-step explanation:

3x+4=31

subtract 4 on both sides That gives you

3x=27

now divide 27 by 3

that gives you X=9

———————————————-

3(2x+1)

you distribute 3 into the parentheses

so 3 x 2x is 6x 3x1 is 3

so its 6x+3

————————————————

1/2(16x-8)=2(x+16)

first you distribute 1/2 into the parentheses on the left side and distribute 2 into the parentheses on the right

which gives you 8x-4=2x+32

then you combine like terms 8x+2x is 10x and -4+32 is 28

so you answer to this one is 10x+28

Answer:

For this question if you need proper help in video format, tthen watch the video of MIND YOUR DECISIONS