What is the length of the hypotenuse to the nearest hundredth place in the diagram
below?
570
4cm
A 2.60
B 6.16
C 4.77
D 7.34

The second option (5n)

["Product" is for multiplication]

Answer: 39210

Step-by-step explanation:

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:

For an equal number of servings, the apples will have six times as much sugar.

Step-by-step explanation:

process of elimination. All the other answer choices are incorrect and this one checks out.

Answer:

b=9

Step-by-step explanation:

54=6b

b=9

(divide by 6 to get b alone)

Answer:

A=2822

Step-by-step explanation:

A+3178=6000

A=6000-3178

A=2822

Answer:

Since f(n + 1) = f(n) - 3, we can also say that f(n - 1) = f(n) + 3.

By which we can say f(n - 3) = f(n) + 9

Since f(4) is 22, then f(1) must be 22 + 9, or 31.

Answer:

[tex]\mathrm{1.}\; m=\mathrm{N/A};\: \mathrm{none}; \: x=14\\\mathrm{2.}\; m=0;\: (0,-5); \:y=-5\\\mathrm{3.}\; m=2;\:(0, -6); \: -2x+y=-6\\[/tex]

Step-by-step explanation:

Problem 1:

Problem 2:

Problem 3:

Answer:

It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.

Step-by-step explanation:

Given that:

Speed of Mr. Chandler = 70 mph

Distance covered in 4 hours = 70 * 4 = 280 miles

Let,

h be the number of hours.

y be the total distance covered.

y = 70h + 280

Speed of Mrs. Chandler = 80 mph

y = 80h

For catching up, the distance would be same.

80h = 70h + 280

80h - 70h = 280

10h = 280

Dividing both sides by 10

[tex]\frac{10h}{10}=\frac{280}{10}\\h=28[/tex]

Hence,

It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.

Answer: x= 3π/2

Hope this helps.... Stay safe and have a great rest of the weekend!!! :D

Answer:

Shirt: $7.5

Sweater: $17.5

Step-by-step explanation:

25/2=12.5

Shirt is 5 less than Sweater

12.5-5=7.5

Add 5 to sweater cost

12.5+5=17.5

Shirt=7.5 Sweater=17.5

17.5+7.5=25

Answer:

210°  

Step-by-step explanation:

To change from radians to degrees, multiply 7π/6 by 180/π

That will give 210°  

Would appreciate a Brainliest if this helped :)

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

For geometric sequences, we find r by dividing one of the terms by the last. So we could do [tex]\frac{1}{\frac{16}{\frac{1}{8}}}[/tex]or [tex]\frac{1}{\frac{8}{\frac{1}{4}}}[/tex] and it'll give us the same result (1/2)

Answer:

B but sorry 4 the time tho

The measure of the trigonometric relation cos 60° = 1/2

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

A = cos 60°

And , cos θ = adjacent / hypotenuse

So , cos 60° = 1/2

Hence , the measure of cos 60° = 1/2

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

#SPJ7

Answer:

4. C: 98 degrees because the angles are consecutive angles

5. E: None of the above

Explanation: 102 degrees because the angles are corresponding angles

6: C: 103 degrees is vertical to angle B and Angle B is corresponding to angle X.

Step-by-step explanation:

Answer:

4. C, 5. E, 6. C

Step-by-step explanation:

4.

Angles x and 82 degrees are supplementary (add up to 180).

x = 180 - 82 = 98

These angles are consecutive interior angles (they're on the inside).

5.

Angles x and 102 degrees are the exact same.

These angles are corresponding angles. So it's none of these, not vertical or alternate interior.

6.

103 degrees is vertical to <b and <b is corresponding to <x.

Hope this helps!

Answer:

[tex]23.1\%[/tex]

Step-by-step explanation:

Stefanie's mixture of 18 grams has a 20% sugar content. Therefore, there are  grams of sugar in her syrup.

John's mixture of 30 grams has a 25% sugar content. Therefore, there are  grams of sugar in her syrup.

Therefore, if they mix their syrups together, there will be 11.1 grams of sugar and 48 total grams of content.

The concentration of sugar in the new mixture is [tex]\frac{11.1}{48}=\fbox{$23.1\%$}[/tex](rounded to one decimal place).

The concentration in the new mixture is 23.1%.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.

Stefanie's 18-gram combination has 20% sugar. As a result, her syrup contains grams of sugar.

John's 30-gram combination contains 25% sugar. As a result, her syrup contains grams of sugar.

As a result, if they combine their syrups, there will be 11.1 grams of sugar and 48 total grams of the substance.

The new combination has a sugar percentage of 11.1/48 = 23.1%. (rounded to one decimal place).

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ2

Answer: 136 ounces

Step-by-step explanation:

Given: The ratio of cranberries and raspberries is 8:9 .

Let quantity of cranberries= 8x , quantity of raspberries = 9x

If quantity of cranberries = 64 ounces

[tex]\Rightarrow\ 8x=64\\\\\Rightarrow\ x=\dfrac{64}{8}\\\\\Rightarrow\ x=8[/tex]

Quantity of raspberries = 9(8) = 72 ounces

Total quantity = 64 ounces  +  72 ounces =  136 ounces

Hence, the total weight of berries purchased=  136 ounces

Answer:

3/3 = 1

Step-by-step explanation:

The slope formula is..

Pick two formulas. Let's do (-5, -2) and (-2, 1)

x1  y1   x2 y2

(-5, -2)   (-2, 1)

[tex]\frac{1-(-2)}{-2-(-5)}[/tex]    =   [tex]\frac{3}{3}[/tex]  = 1

It'll work the same thing for (-2, 1) and (1,4)...

3/3 or 1 is a pattern between the points.

Answer:

30

Step-by-step explanation:

so one of them is 90, one of them is 60

180-150 = 30

so 30

Answer:

1

Step-by-step explanation:

Don't worry I just know

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:

4

Step-by-step explanation:

4 is the coefficient because its infront of the variable

Step-by-step explanation:

If the exchange rate is 1 Euro to 0.80 pounds

So,

30 Euro=0.8×30=24.0=24 pounds.

so,

24 pounds would you spend to purchase something that costs 30 Euros

Answer: Exponential function: [tex]y=12000(1.05)^x[/tex]

Step-by-step explanation:

Exponential function: [tex]y=ab^x[/tex] , a = initial value , x= time,  b= growth factor , b= 1+r , where r=rate of growth.

Given: Initial population = a= 12,000,

rate of growth = r= 5% = 0.05

Then, b=  1+r= 1+ 0.05 = 1.05

Substitute value of a and b in (i), we get

[tex]y=12000(1.05)^x[/tex]

Hence, The required exponential function: [tex]y=12000(1.05)^x[/tex], where x= time.