Draw and use algebra tiles to solve the equation.

2x - 3 = 5

Answer:

x ∈ [-0.369, 0.678]

Step-by-step explanation:

To prove - [tex]\sqrt[4]{1 + 2x}[/tex] ≈ 1 + [tex]\frac{1}{2}[/tex] x

As given , f(x) = [tex]\sqrt[4]{1 + 2x}[/tex]

As we know that the linear approximation can be defined as :

L(x) = f(a) + f'(a)(x-a)             .........(1)

Now,

We have to show that at a = 0 , equation (1) satisfies

Now,

f(0) = [tex]\sqrt[4]{1 + 0}[/tex] = 1

Also,

f'(x) =

[tex]\frac{d}{dx} (\sqrt[4]{1 + 2x} ) = \frac{1}{4}(1 + 2x)^{\frac{1}{4} - 1}\frac{d}{dx}(1 + 2x) ) \\ = \frac{1}{4}(1 + 2x)^{\frac{-3}{4} } (2)\\ = \frac{1}{2}(1 + 2x)^{\frac{-3}{4} }\\[/tex]

∴ we get

f'(x) = [tex]\frac{1}{2}(1 + 2x)^{-\frac{3}{4} }[/tex]

⇒f'(0) = [tex]\frac{1}{2}[/tex]

Now, equation (1) becomes

L(x) = f(0) + f'(0)(x-0)

     = 1 + [tex]\frac{1}{2}[/tex] (x)

⇒ [tex]\sqrt[4]{1 + 2x}[/tex] ≈ 1 + [tex]\frac{1}{2}[/tex] x

Hence verified.

Now,

|[tex]\sqrt[4]{1 + 2x}[/tex] - (1 + [tex]\frac{1}{2}[/tex] x ) | ≤ 0.1

⇒ -0.36893 ≤ x ≤ 0.67766

⇒x ∈ [-0.369, 0.678]

Answer:

(-1,1)

Step-by-step explanation:

4x+2x+3=-3

6x+3=-3

6x=-6

x=-1

y=2(-1)+3

y=-2+3

y=1

Answer:

It is 4/5

Step-by-step explanation:

hope it helps ^^

Answer:

³/2 (1.5)

Step-by-step explanation:

∆DEF was enlarged to get ∆ABC. The scale factor would be:

The ratio of any of the side length of ∆ABC to the corresponding side length of ∆DEF.

Thus,

BC:EF = 12:8

= 12/8

= 3/2 = 1.5

Scale factor from ∆DEF to ∆ABC is ³/2 or 1.5

Answer:

100 degrees.

Step-by-step explanation:

The missing angle on the bottom triangle is equal to 80 degrees because a triangle's interior angles add up to 180deg.

Think of that middle angle between angle 1 and the two triangles as a full 360deg. Since VAT (Vertical Angle Theorem) suggests that vertical angles are equal, 160deg of that 360deg are taken up by the missing angles in the triangles. That leaves 200deg to split between angle 1 and its equal vertical angle, which means angle 1 is 1/2 of 200, or 100deg.

Answer:

[tex]\$498.75[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the original price of the item. We can set up the following equation:

[tex]x\cdot (1-0.2)=399[/tex].

Solving for [tex]x[/tex], we get:

[tex]x\cdot 0.8=399,\\x=\frac{399}{0.8},\\x=\fbox{$\$498.75$}[/tex].

Answer:

Step-by-step explanation:

In a survey of first graders, their mean height was 51.6 inches with a standard deviation of 3.6 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?

54.03 inches

48.57 inches

48.00 inches

49.17 inches

Answer:

[tex]\displaystyle no[/tex]

Step-by-step explanation:

UT is shorter than WT, therefore you cannot use it on this triangle.

I am joyous to assist you at any time.

Answer:

-(1/2)

Step-by-step explanation:

Slope is the Rise/Run

Going from left to right for (2, -6), (-4,-3):

Rise = (-3 - (-6)) = 3

Run = (-4, -2) = -6

Slope = Rise/Run = 3/-6 = -(1/2)

Using proportions, it is found that the proportional equation for t in terms of d that matches the context is:

[tex]t = 42d[/tex]

Elizabeth practices the piano 1470 minutes in 5 weeks, hence, each day, consdering a week has 7 days, the amount of time she practices is:

[tex]a = \frac{1470}{35} = 42[/tex]

Hence, the proportional equation, considering t the time in minutes and d the number of days, is:

[tex]t = 42d[/tex]

You can learn more about proportions at https://brainly.com/question/24372153

Answer:

46

Step-by-step explanation:

First you need to solve.. So put 3x - 10 and 2x + 1 together as one equation.

It should look like this:

3x - 10 = 2x + 1

Now you just need to solve it.

1) First you add 10 on both sides.

3x - 10 = 2x + 1

   + 10 =    + 10

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

     3x = 2x + 11

2) Then you subtract 2x on both sides.

     3x = 2x + 11

   - 2x =- 2x + 11

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

      x = 11

3) Now you plug in 11 for x.

3x - 10 = 2x + 1

Like this:

3(11) - 10 = 2(11) + 1

33 - 10 = 22 + 1

23 =23

So C to E and E to A = 23

To get from C to A just add 23 + 23 which is 46. And that is ur answer.

Answer:

it is 46

Step-by-step explanation:

First you need to solve.. So put 3x - 10 and 2x + 1 together as one equation.

It should look like this:

3x - 10 = 2x + 1

Now you just need to solve it.

1) First you add 10 on both sides.

3x - 10 = 2x + 1

  + 10 =    + 10

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

    3x = 2x + 11

2) Then you subtract 2x on both sides.

    3x = 2x + 11

  - 2x =- 2x + 11

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

     x = 11

3) Now you plug in 11 for x.

3x - 10 = 2x + 1

Like this:

3(11) - 10 = 2(11) + 1

33 - 10 = 22 + 1

23 =23

So C to E and E to A = 23

To get from C to A just add 23 + 23 which is 46. And that is ur answer.

you can slove this in this way if want more explansion ask me

Hey there!

The length of the hypotenuse is about 11 centimeters.

To solve this, we use the formula [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse leg and [tex]a[/tex] and [tex]b[/tex] are the other sides. So we can plug the numbers in to the formula:

[tex]5^2 + 10^2 = c^2[/tex]

Now we get the squares of 5 and 10:

[tex]25 + 100 = c^2[/tex]

Add 25 and 100:

[tex]125 = c^2[/tex]

Take the square root from both sides:

[tex]11.18033... = c[/tex]

The length of the hypotenuse is about 11 centimeters.

Hope it helps and have an amazing day!

The length of Hypotenuse = 11.18 cm

In mathematics, the Pythagoras theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Given,

In right angle ΔABC

AB = 5 cm

BC = 10 cm

AC = ?

By the Pythagoras theorem,

AC² = AB² + BC²

AC² = 5² + 10²

AC² = 25 + 125

AC = √125 = 11.18

Hence, 11.18 cm is the length of Hypotenuse AC .

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ2

Answer:

0.32 yes mhmmmhmhmhwididididurruuidididi

Answer:

70 miles / hour

Step-by-step explanation:

d = 175 miles

t = 2.5 hours

r = d/t

r = 175 / 2.5

r = 70 miles / hour

Answer:

daaaaaaaaaa

Step-by-step explanation:

ssdddsss

Answer:

if it's out of 100 it would be 55

Step-by-step explanation:

Answer:

D 55%

Step-by-step explanation:

I am assuming that the "45" is 45$ so then we do 100%-45$=55% But, if the "45" is 1 in 45, then the answer is 1-1/45=44/45 which rounds to 98%. That isn't any of the answers, so should be 55%

Answer:

waste

Step-by-step explanation:

Try to think of something that doesn't involve energy and you won't get very far. Even thinking—even thinking about energy!—needs some energy to make it happen. In fact, everything that happens in the world uses energy of one kind or another. But what exactly is energy?

Energy is a bit of a mystery. Most of the time we can't see it, yet it is everywhere around us. Revving car engines burn energy, hot cups of coffee hold energy, street lights that shine at night are using energy, sleeping dogs are using energy too—absolutely everything you can think of is using energy in one way or another. Energy is a magical thing that makes other things happen. Everything in the world is either energy or matter ("stuff" around us) and even matter, when you really get down to it, is a kind of energy!

Answer:

the volume will be doubled if the height is doubled

hope it helps you

Answer:

do we answer all of them are just one

Answer:

Step-by-step explanation:

Given

[tex]Badwater = -282ft[/tex]

[tex]Telescope\ Peak = 11043ft[/tex]

The position of badwater is negated because it is below sea level

The interpretation of the question, is to calculate the distance between the two given points.

This is calculated as:

[tex]Difference = Telescope\ Peak - Badwater[/tex]

[tex]Difference = 11043ft - (-282ft)[/tex]

Open bracket

[tex]Difference = 11043ft+282ft[/tex]

[tex]Difference = 11325ft[/tex]

Hence, the distance between both is 11325ft

Answer:

Step-by-step explanation:

7x - 382 = 3x - 161

4x - 382 = -161

4x = 221

x = 55.25

please pic the photo correct ly

Answer:22.2%

thank me later

Answer: Brazil produces 9,428,400 sugar.

Step-by-step explanation:

That is the answer because 9.7% of 97,200,000 is 9,428,400.

Step-by-step explanation:

Given that,

The side of a square field = 70 m

The dimensions of a rectangular field with length 90m and breadth 60m.

The distance covered by the person on square field is given by :

P = 4×side

= 4×70

= 140 m

The distance covered by the person on a rectangular field is given by :

P = 2(l+b)

= 2(90+60)

= 2×150

= 300 m

Hence, a person will cover more distance in the rectangular field.

Answer: 4.5 cups

Step-by-step explanation:

2:10

4:20

half of a cup would be 5 pancakes

so, 4.5 cups of flour will make 25 pancakes.