Which function increases the fastest?​

Answer:

(For the first two questions I do believe that you will need a protractor to calculate the angles.)

15) [tex]-(\frac{7\pi }{18} )\\[/tex] measures out to -70° in order to display that the angle would be in quadrant IV (the bottom right quadrant.)

The first image attached shows where the angle should be located.

16) [tex]\frac{\pi }{3}[/tex] is equal to 60° (the line you draw will be in quadrant 1 (the top right quadrant))

17) 350° is [tex]\frac{35\pi }{18}[/tex] or 6.11 (the answer depends on the format the professor wants.)

18) 240° is [tex]-(\frac{4\pi }{3})[/tex] radians or -4.19 (I am rounding to the nearest hundredths place the unsimplified answer is −4.18879020...)

Answer:

a.) y= 75x+25

b.) y= 25x+225

c.) Their account balances will be the same in 4 months and they'll have $325.

Step-by-step explanation:

For A and B: The variable is x which is the amount of months then add the initial amounts without a variable and equal it to y which is the amount in all.

For Rowan, they are saving $75 per month. This is where our variable goes and then we add the intial $25 dollars. The equation is y= 75x+25.

For Reem, they are saving $25 per month. This is where our variable goes and then we add the intial $225 dollars. The equation is y= 25x+225

C. You have to set the equations equal to each other and then solve for x.

75x+25 = 25x+225

Subtract 25 from each side

75x=25x+200

Subtract 25x from each side

50x=200

Divide each side by 50

X=4

For the amount they'll have, just plug 4 into one of the equations.

Rowan : y=75(4)+25

y=325

Reem: y=25(4)+225

y=325

Answer:

Step-by-step explanation:

Area = s^2 =

New Area = (S- 6)(S+6) = S^2 -36, Choice (A)

Hope that helps!

Answer:

Set up an equation using the key terms:

We can consider 60% in our equation to be 60/100 which we later on simplify.

We contemplate that "-Of a blank number(of what number)" means the multiplication of an unknown value, "x".

The resulting of 51 will be what the equation will equal.

Form the equation;

Solve for x:-

60/100x = 51

60/100 can simplify to 0.6 so it will now be,

0.6x = 51

Isolate x by dividing by 0.6 from both sides because the inverse operation of multiplication is division(since 0.6 is being multiplied by x).

÷0.6  ÷0.6

x = 85, therefore 60% of 85 is 51.

Answer:

0

Step-by-step explanation:

1. Distribute:  6x-12 - 6x+12

2. Combine like terms:  0

Answer:

0

Step-by-step explanation:

First you want to do distributive properties, so multiply 2 and -4 by 3. leaving you with 6x-12-6x+12. then we have to combine all the like terms. so you can either add 6x to the negative 6x or take away 6x from the positive 6x. Same with the 12's. so once you've combined all the like terms you should be left with 0. Thus, your answer would be 0.

Step-by-step explanation:

A line can be translated over to form a line. Since the line has the same slope, the only thing different is y intercept. Since a Translation is a rigid transformation, they perseve distance. So this will be true for all lines.

Key Concept: The distance between two parallel lines and is the difference in y intercepts.

10. The y intercept is 7 and -2

So the distance is

[tex]7 - ( - 2) = 9[/tex]

or

[tex] - 2 - 7 = - 9[/tex]

Rember Distance is a scalar, so it is positve.

So we take absolute value of both answer

[tex] |9| = 9[/tex]

[tex] | - 9| = 9[/tex]

So the answer for 10 is 9.

11. The distance is 3 because |4-1|=3 or |1-4|=3 so the distance is 3.

12. The distance is 2

13.The distance is 8.

Answer:

51

Step-by-step explanation:

3n means 3 × n

substitute n = 17 into the expression

3n = 3 × 17 = 51

Answer:

9.42 years (= 113 months)

Step-by-step explanation:

Use the compound rate interest formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

[tex]\implies 7850=5000(1+\frac{0.048}{12})^{12t}[/tex]

[tex]\implies 7850=5000(1.004)^{12t}[/tex]

[tex]\implies \dfrac{7850}{5000}=(1.004)^{12t}[/tex]

[tex]\implies 1.57=(1.004)^{12t}[/tex]

Take natural logs:

[tex]\implies \ln1.57=\ln(1.004)^{12t}[/tex]

[tex]\implies \ln1.57=12t\ln(1.004)[/tex]

[tex]\implies t=\dfrac{\ln 1.57}{12 \ln1.004}[/tex]

[tex]\implies t=9.42\textsf{ years (nearest hundredth)}[/tex]

[tex]\implies t=113 \textsf{ months}[/tex]

Answer:

22 years

Step-by-step explanation:

suppose his present age is x years

After 2 years, father's age (x+24+2) years and son will be (x+2). now x = 22 years is the answer if u solve it.

The present age of the son is 22 years .

Let us assume that the present age of the son is x years . Therefore according to question, we can say that the present age of his father will be x + 24 years. Then after two years, the age of the man will be twice the age of his son , i.e:

[tex] \quad\dashrightarrow\quad \sf {(x + 24) + 2 = 2 ( x + 2 ) }[/tex]

[tex] \quad\dashrightarrow\quad \sf { x + 26 = 2x + 4}[/tex]

[tex] \quad\dashrightarrow\quad \sf {2x -x = 26 - 4 }[/tex]

[tex] \quad\dashrightarrow\quad \underline{\sf {x = 22 }}[/tex]

Hence, the present age of the son is 22 years.

Answer:

C. 22/5

Step-by-step explanation:

4x5=20

20+2=22

Answer:

C. 22/5

When making an improper fraction you must first multiply the denominator with the whole number in this case that would be 4 and 5

4*5=20

Then just add the numerator

20+2=22

And bring it back over the denominator

22/5

There you go your improper fraction.

Step-by-step explanation:

We are given with a limit and we need to find it's value so let's start !!!!

[tex]{\quad \qquad \blacktriangleright \blacktriangleright \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}}[/tex]

But , before starting , let's recall an identity which is the main key to answer this question

Consider The limit ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}}[/tex]

Now as directly putting the limit will lead to indeterminate form 0/0. So , Rationalizing the numerator i.e multiplying both numerator and denominator by the conjugate of numerator

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}\times \dfrac{\sqrt{x}+\sqrt{3\sqrt{x}-2}}{\sqrt{x}+\sqrt{3\sqrt{x}-2}}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-\sqrt{3\sqrt{x}-2})(\sqrt{x}+\sqrt{3\sqrt{x}-2})}{(x^{2}-4^{2})(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Using the above algebraic identity ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x})^{2}-(\sqrt{3\sqrt{x}-2})^{2}}{(x-4)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-(3\sqrt{x}-2)}{(x-4)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}+2}{\{(\sqrt{x})^{2}-2^{2}\}(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}-2}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , here we need to eliminate (√x-2) from the denominator somehow , or the limit will again be indeterminate ,so if you think carefully as I thought after seeing the question i.e what if we add 4 and subtract 4 in numerator ? So let's try !

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}-2+4-4}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(x-4)+2+4-3\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , using the same above identity ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)+6-3\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)+3(2-\sqrt{x})}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , take minus sign common in numerator from 2nd term , so that we can take (√x-2) common from both terms

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)-3(\sqrt{x}-2)}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , take (√x-2) common in numerator ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)\{(\sqrt{x}+2)-3\}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Cancelling the radical that makes our limit again and again indeterminate ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\cancel{(\sqrt{x}-2)}\{(\sqrt{x}+2)-3\}}{\cancel{(\sqrt{x}-2)}(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}+2-3)}{(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-1)}{(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , putting the limit ;

[tex]{:\implies \quad \sf \dfrac{\sqrt{4}-1}{(\sqrt{4}+2)(4+4)(\sqrt{4}+\sqrt{3\sqrt{4}-2})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{2-1}{(2+2)(4+4)(2+\sqrt{3\times 2-2})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+\sqrt{6-2})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+\sqrt{4})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+2)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(4)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{128}}[/tex]

[tex]{:\implies \quad \bf \therefore \underline{\underline{\displaystyle \bf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}=\dfrac{1}{128}}}}[/tex]

We can transform the limand into a proper rational expression by substitution.

Let y = √x. Then as x approaches 4, y will approach √4 = 2. So

[tex]\displaystyle \lim_{x\to4}\frac{\sqrt x - \sqrt{3 \sqrt x - 2}}{x^2 - 16} = \lim_{y\to2} \frac{y - \sqrt{3y-2}}{y^4 - 16}[/tex]

Now let z = √(3y - 2). Then as y approaches 2, z will approach √(3•2 - 2) = 2 as well. It follows that y = (z² + 2)/3, so that

[tex]\displaystyle \lim_{y\to2} \frac{y - \sqrt{3y-2}}{y^4-16} = \lim_{z\to2} \frac{\frac{z^2+2}3 - z}{\frac{(z^2+2)^4}{81}-16} \\\\ = \lim_{z\to2} \frac{27(z^2+2)-81z}{(z^2+2)^4 - 1296} \\\\ = 27 \lim_{z\to2} \frac{z^2 - 3z + 2}{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280}[/tex]

Plugging z = 2 into the denominator returns a value of 0, which means z - 2 divides z⁸ + 8z⁶ + 24z⁴ + 32z² - 1280 exactly. Polynomial division shows that

[tex]\dfrac{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280}{z-2} \\\\ = z^7+2z^6+12z^5+24z^4+72z^3+144z^2+320z+640[/tex]

and it's easy to see that the numerator is also divisible by z - 2, since

[tex]z^2 - 3z + 2 = (z - 1) (z - 2)[/tex]

So, we can eliminate the factor of z - 2 and we're left with

[tex]\displaystyle 27 \lim_{z\to2} \frac{z^2 - 3z + 2}{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280} = 27 \lim_{z\to2}\frac{z-1}{z^7+\cdots+640}[/tex]

The remaining limand is continuous at z = 2, so we can evaluate the limit by direct substitution:

[tex]\displaystyle 27 \lim_{z\to2}\frac{z-1}{z^7+\cdots+640} = \frac{27}{3456} = \boxed{\frac1{128}}[/tex]

gallon = pint *0.125

gallon = pint / 8
0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+

0.125+0.125+0.125+0.125+0.125 = 2

16 would be the answer I believe, maybe I'm wrong, double check.

Answer:

5 1/3 pints

Step-by-step explanation:

1 pint is 1/8gal and u need to find how many pints in 2/3 gal so it'll be 2/3 ÷ 1/8 which is 5 1/3

Answer: 3.33

Step-by-step explanation:

6x-2= 20

    +2= +2

Add two to both sides

6x=22

÷ 6= ÷6

Divide both sides by 6

x= 3.33 OR x= 22/6 simplified = 11/3

What you do to one side you do to the other to make the equation balanced.

Answer:

Step-by-step explanation:

6x - 2 = 20

Add 2 to both sides

6x - 2 + 2 = 20 + 2

          6x = 22

Divide both sides by 6

         [tex]\dfrac{6x}{6}=\dfrac{22}{6}\\\\\\x =\dfrac{11}{3}\\\\\\x = 3\dfrac{2}{3}[/tex]

Answer for x should be 7

x = 7

Step-by-step explanation:

Hi there! if you don't understand any part make sure to ask me :D

Answer:

so

Step-by-step explanation:

it is 5 pounds your welcome

The bigger measurement is 5 lbs.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Given two measurements.

75 ounces and 5 lbs.

We have the conversion formula,

1 lbs = 16 ounces

5 lbs = 5 × 16 = 80 ounces

80 ounces is greater than 75 ounces

5 lbs is greater than 75 ounces.

Hence the measurement which is bigger is 5 lbs.

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Answer:

B

Step-by-step explanation:

(4 , 9) and (0, 5)

4 is x1, 9 is y1, 0 is x2, 5 is y2

formula:

slope = y2 - y1/ (underline is fraction line btw ;) )

             x2 - x1

5 - 9

0 - 4

So the answer is B

Answer:

A) SSS

Step-by-step explanation:

Two of the similarities are given to you. The last one will be the hypotenuse, which is congruent based on the reflexive property of congruence.

~

Answer:

$320

Step-by-step explanation:

If $38.40 is 12%, then 1% is 38.40 ÷ 12.

⇒ 1% = 38.40 ÷ 12 = $3.20

Simply multiply 3.2 by 100 to get 100%:

⇒ 3.2 x 100 = $320

Answer:

60 degrees

Step-by-step explanation:

It measures 60 degrees

Tip: the wider the angle, the bigger the degree.

Hope this helps!

D.

[tex]22 - 8 \sqrt{5} [/tex]

Answer:

y - int = 7

Step-by-step explanation:

y = -3/4x + 7

Answer:

i think the intercept is (0,7) im not sure, sorry if its not.

Step-by-step explanation:

Answer:

nonlinear increasing

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Cos3A= Sin2A ........ (i)\\\\Cos3A= Cos (90-2A)\\\\3A= 90-2A\\\\5A= 90\\\\A= 18\\\\[/tex]

Now,

Putting the value of A to find the value,

[tex]From (i)\\Cos(3x18) = Sin (2x18)\\Cos54= Sin36\\0.5877= 0.5877 \\LHS=RHSProved .[/tex]

Answer:

Cos3A= Sin2A ........ (i)

Cos3A= Cos (90-2A)

3A= 90-2A

5A= 90

A= 18

from (i)

Cos(3×18) = Sin (2×18)

Cos54= Sin36

0.5877= 0.5877 proved .

Step-by-step explanation:

Step-by-step explanation:

the height from the right angle in a right-angled triangle is the square root of the product of the segments of the Hypotenuse the height is splitting it into.

so,

x = sqrt(7×9) = sqrt(63) = 3×sqrt(7)

Answer:

The y axis is a vertical line

Step-by-step explanation:

Y axis is up

The sum of the terms of the given sequence will be 648.

An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value.

The given sequence is representing an arithmetic sequence.

Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6

3 - (-3) = 3 + 3 = 6

Since last term of the sequence is 81.

By the explicit formula of an arithmetic sequence, we can find the number of terms of this sequence.

[tex]\rm T_n= a+(n-1)d\\\\[/tex]

Where a = first term of the sequence, d = common difference.

Substitute all the values in the formula

[tex]\rm T_n= a+(n-1)d\\\\ 81 = -9 + 6(n - 1)\\\\ 81+9 =6(n-1)\\\\90=6(n-1)\\\\ n-1=\dfrac{90}{6}\\\\n-1=15\\\\n = 15+1\\\\n=16[/tex]

Now we know the sum of an arithmetic sequence is represented by

[tex]\rm S_{16}=\dfrac{16}{2}[-9+(16-1)6]\\\\S_{16}=8 [-9+15\times 6]\\\\S_{16}=8 [-9+90}\\\\S_{16} = 8 \times 81\\\\S_{16}=648[/tex]

Hence, the sum of the terms of the given sequence will be 648.

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Answer: 3.5 ft cubed.

Step-by-step explanation:

width*length*height Multiply all the numbers to find the volume.

It will be easier to change the fractions to decimals first.

Answer:

(3x+2)(3x−2)

Step-by-step explanation:

a^2−b^2=(a+b)(a−b)

where a=3x and b=2

(3x+2)(3x−2)

Answer:

i believe its a

Step-by-step explanation:

Collision is the type of insurance can be waived (refused) if a driver feels that his/her car is not worth insuring.

Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury.

Collision insurance covers the cost of repairing or replacing a driver's car if it is damaged in an accident.

It is typically optional and not required by law.

If a driver feels that the value of their car is low and that the cost of collision insurance is not worth the potential benefit, they may choose to waive (refuse) this type of coverage.

Comprehensive insurance covers damage to a driver's car from causes other than an accident, such as theft, vandalism, or natural disasters. Liability insurance covers damages and injuries that a driver causes to others in an accident.

Uninsured motorist insurance covers damages and injuries to a driver if they are hit by an uninsured or underinsured driver.

Hence, collision is the type of insurance can be waived (refused) if a driver feels that his/her car is not worth insuring.

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