1. What is the value of x? Show your work to justify your answer.


2. What is the value of the exterior angle? Show your work to justify your answer.

Answer:2.6

Step-by-step explanation:

Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6

Answer:2.6

Step-by-step explanation:

Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6

Answer:

18

Step-by-step explanation:

Since this is an isosceles triangle, sides AB and sides AC are equal

AB=AC

8x-4 = 5x+11

Subtract 5x from each side

8x-5x-4 = 5x-5x+11

3x-4 = 11

Add 4 to each side

3x-4+4 = 11+4

3x=15

Divide by 3

3x/3 =15/3

x=5

We want to find BC

BC= 4x-2

Since x=5

BC = 4(5) -2

BC = 20-2

BC =18

Answer:

D. 7

Step-by-step explanation:

In synthetic division, the first # in the division bracket (2)  is dropped, and the number outside the bracket is multiplied with it to find 4. Then, -2 and 4 are added to get 2. Again, 2 x 2=4. 3+4=7.

Simplified version: Drop, multiply, add, multiply, add till you reach the last term.

The synthetic division problem hasn't been stated in this query, making it impossible to ascertain the missing number. Synthetic division is a mathematical methodology used to simplify polynomial division by binomial. The correct problem should be offered for accurate guidance.

Unfortunately, the provided synthetic division problem was not included in your question so I'm unable to solve for the missing number. In general, synthetic division is a method used in algebra to divide a polynomial by a binomial. I would suggest you to verify the problem and restate your question providing all necessary details. Then I would gladly help you solve the missing number in the synthetic division.

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Answer:

0.1

Step-by-step explanation:

Base Case: plug in n = 1 (the smallest positive integer)

If n = 1, then 3n-2 = 3*1-2 = 1. Square this and we see that (3n-2)^2 = 1^2 = 1

On the right hand side, plugging in n = 1 leads to...

n*(6n^2-3n-1)/2 = 1*(6*1^2-3*1-1)/2 = 1

Both sides are 1. So that confirms the base case.

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

Inductive Step: Assume that

1^2 + 4^2 + 7^2 + ... + (3k-2)^2 = k*(6k^2-3k-1)/2

is a true statement for some positive integer k. If we can show the statement leads to the (k+1)th case being true as well, then we will have sufficiently proven the overall statement to be true by induction.

1^2 + 4^2 + 7^2 + ... + (3k-2)^2 = k*(6k^2-3k-1)/2

1^2 + 4^2 + 7^2 + ... + (3k-2)^2 + (3(k+1)-2)^2 = (k+1)*(6(k+1)^2-3(k+1)-1)/2

k*(6k^2-3k-1)/2 + (3(k+1)-2)^2 = (k+1)*(6(k^2+2k+1)-3(k+1)-1)/2

k*(6k^2-3k-1)/2 + (3k+3-2)^2 = (k+1)*(6k^2+12k+6-3k-3-1)/2

k*(6k^2-3k-1)/2 + (3k+1)^2 = (k+1)*(6k^2+9k+2)/2

k*(6k^2-3k-1)/2 + 9k^2+6k+1 = (k+1)*(6k^2+9k+2)/2

(6k^3-3k^2-k)/2 + 2(9k^2+6k+1)/2 = (k*(6k^2+9k+2)+1(6k^2+9k+2))/2

(6k^3-3k^2-k + 2(9k^2+6k+1))/2 = (6k^3+9k^2+2k+6k^2+9k+2)/2

(6k^3-3k^2-k + 18k^2+12k+2)/2 = (6k^3+9k^2+2k+6k^2+9k+2)/2

(6k^3+15k^2+11k+2)/2 = (6k^3+15k^2+11k+2)/2

Both sides simplify to the same expression, so that proves the (k+1)th case immediately follows from the kth case

That wraps up the inductive step. The full induction proof is done at this point.

Answer:

5 pages

Step-by-step explanation:

30 sticker and 6 stickers on each page

30 divided by 6 = 5

Answer:

He puts stickers on 5 pages.

Answer:

b=2A-2a

Step-by-step explanation:

First you subtract a to the other side.

Then you divide by 2.

SO it will be b=2A-2a which is your answer

Answer:

Correct choice is D

Step-by-step explanation:

Consider the quadratic expression [tex]5x^2 + 7x + 2.[/tex]

First, find the discriminant:

[tex]D=7^2-4\cdot 5\cdot 2=49-40=9.[/tex]

Now find the roots of the quadratic expression [tex]5x^2 + 7x + 2:[/tex]

[tex]x_{1,2}=\dfrac{-7\pm \sqrt{9}}{2\cdot 5}=\dfrac{-7\pm 3}{10}=-1,\ -0.4.[/tex]

Then

[tex]5x^2 + 7x + 2=5(x-(-1))(x-(-0.4))=5(x+1)(x+0.4)=(x+1)(5x+2).[/tex]

Answer: 5

Step-by-step explanation:

Let x represent the number, then

x² + x = 30

x² + x - 30 = 0      

(x + 6) (x - 5) = 0

x + 6 = 0   x - 5 = 0

 x = -6        x = 5

    ↓

not valid since the restriction is that x > 0 (a positive number)

So, x = 5

Answer:

Amount of gas that can be hold by Joe's tank = 16 gallons.

Step-by-step explanation:

Given that Joe's gas tank is 1/4 full. After he buys 6 gallons of gas, it is 5/8 full. Now we need to find about how many gallons can Joe's tank hold.

So let's find change that happened after filling the gas.

Change = (5/8 full) - (1/4 full)

Change = (5/8 - 1/4)  full

Change = (5/8 - 2/8)  full

Change = (5 - 2)/8  full

Change = 3/8  full

So that means 3/8 full happens in 6 gallons

then 1 full will happen in 6/(3/8) gallons = 6*(8/3) gallons = 48/3 gallons = 16 gallons

So the amount of gas that can be hold by Joe's tank = 16 gallons.

Let the initial savings at first be = x

Given ratio is [tex]\frac{5}{4}[/tex] and after donating $40 to charity, the ratio becomes [tex]\frac{13}{10}[/tex]

Hence, the relation becomes:

[tex]\frac{5x-40}{4x-40}=\frac{13}{10}[/tex]

[tex]10(5x-40)=13(4x-40)[/tex]

= [tex]50x-400=52x-520[/tex]

[tex]-2x=-120[/tex] or

[tex]2x=120[/tex]

[tex]x=60[/tex]

So , Dave's saving at first was 5x = 5*60 = $300

and Sam's saving at first was 4x = 4*60= $240

Answer:

Proof

Step-by-step explanation:

Recall the identity [tex]\sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)[/tex].

Consider [tex]\sin(a + b) = k\sin(a - b)[/tex]. We firstly apply the above identity to reach

[tex]\sin(a)\cos(b) + \cos(a)\sin(b) = k(\sin(a)\cos(b) - \cos(a)\sin(b))[/tex].

By expanding the bracket on the right we obtain

[tex]\sin(a)\cos(b) + \cos(a)\sin(b) = k\sin(a)\cos(b) - k\cos(a)\sin(b)[/tex] and so

[tex]\cos(a)\sin(b) + k\cos(a)\sin(b) = k\sin(a)\cos(b) - \sin(a)\cos(b)[/tex] and so

[tex](1+k)\cos(a)\sin(b) = (k-1)\sin(a)\cos(b)[/tex] and so

[tex](k+1)\frac{\cos(a)}{\sin(a)}= (k-1)\frac{\cos(b)}{\sin(b)}[/tex] and finally

[tex](k+1)\cot(a)= (k-1)\cot(b)[/tex].

Final answer:

Using the sum and difference identities for sine, we can manipulate the equation sin(a+b) = k sin(a-b) to prove the trigonometric identity (k-1)cotb = (k+1)cota as required.

Explanation:

To solve the given trigonometric identity, we must show that if sin(a+b) = k sin(a-b), then (k-1)cotb = (k+1)cota. First, let's utilize the sum and difference identities for sine:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

Substitute these into the original equation:

sin(a)cos(b) + cos(a)sin(b) = k(sin(a)cos(b) - cos(a)sin(b))

Now, distribute the k on the right side and arrange terms:

sin(a)cos(b)(1-k) = cos(a)sin(b)(1+k)

Divide both sides by sin(b)cos(b) to isolate cot(a) and cot(b):

(1-k) cot(b) = (1+k) cot(a)

This proves the identity as required. Notice that the cotangent function is the reciprocal of the tangent function, which is the ratio of sine to cosine.

Answer:

See proof below

Step-by-step explanation:

Consider triangle with midpoints D, E, F of the sides BC, AC and AB, respectively.  If D, E and F are midpoints  of the sides BC, AC and AB, then

Triangle ABC is equilateral triangle, then

If AB=BC=AC, then EA=CE=FA=BF=DC=DB.

By SAS theorem, ΔFAE≅ΔDCE≅ΔEBD.

Congruent triangles have congruent corresponding sides, then

EF=FD=DE. This means that triangle DEF is equilateral.

Answer:

2 lbs  9 oz

Step-by-step explanation:

Lets line up the ounces and pounds and subtract

  5 lb. 10 oz.

− 3 lb. 1 oz.

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

2 lbs  9 oz

The result of subtraction of 5 lb. 10 oz. − 3 lb. 1 oz.  is: 2 lbs  9 oz.

Here, we have,

given that,

5 lb. 10 oz. − 3 lb. 1 oz.

so, we have to subtract them.

Lets line up the ounces and pounds and subtract

 5 lb. 10 oz.

− 3 lb. 1 oz.

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

2 lbs  9 oz

Hence, The result of subtraction of 5 lb. 10 oz. − 3 lb. 1 oz.  is: 2 lbs  9 oz.

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Answer:

$780

Step-by-step explanation:

The initial sum of money borrowed was $750

at a simple interest rate of 8%

Dan pays the money back in 6 months

The amount of money Dan has to pay back his brother including the interest in 6 months' time.

The total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.

The total interest that is to be paid back can be calculated using the formula

where P is the prinicipal amount of money we begin with (in this case $750), r is the rate of interest (in this case 8%) and t is the time period (in this case, 6 months or 1/2 of a year).

(Note that we must take the value of t in years if the interest is annual interest and that is why we use t = 1/2 = 0.5 instead of t = 6).

So, by simple calculation we can find interest to be paid as

the interest accrued is $30

To find the total sum to be paid back, we add the initial sum or pricipal amount to the interest we have calculated above i.e.,

the total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.

Answer:

1/6 = 3/18

1/9 = 2/18

Step-by-step explanation:

The common denominator for 6 and 9 is the smallest number that they both go into, which is 18.  We need to multiply 6 by 3 to get 18 and multiply 9 by 2 to get 18

1/6 *3/3 = 3/18

1/9 *2/2 = 2/18

Answer:

the pair would be 3/18 and 2/18

Divide 260 and 156 to get 5/3, or 1 2/3. Multiply by 100 to get 166.(6). (6) means repeating forever. For example 1.(3)=1.333333333....

Answer: there is an app that helps you with this stuff. but are you solving for x or y

Step-by-step explanation:

Answer:

In quadrant I   x is positive , y is positive

In quadrant II   x is negative , y is positive

In quadrant III   x is negative , y is negative

In quadrant IV  x is positive , y is negative

Step-by-step explanation:

In quadrant I   x is positive , y is positive

In quadrant II   x is negative , y is positive

In quadrant III   x is negative , y is negative

In quadrant IV  x is positive , y is negative

How I remember, I and II quads have a positive y

                             I and IV quads have a positive x

Answer:

D - it uses data entered in certain cells to calculate values for other cells

Step-by-step explanation:

A-p-e-x approved

Final answer:

The jogger runs a total distance of 224 meters, which includes running along the width and length of the park and taking a shortcut diagonally across the park.

Explanation:

To calculate the total distance the jogger runs, we must add the distances from each leg of the jogger's path. Starting from the southeast corner, the jogger runs the width of the park (28 meters) to the west, and then the length of the park (96 meters) to the north, reaching the northwest corner. The shortcut from the northwest corner directly back to the southeast corner, where her car is parked, is the hypotenuse of the resulting right-angled triangle. To find the length of this hypotenuse, we use the Pythagorean theorem (a² + b² = c²), where the sides of the rectangle serve as 'a' and 'b'.

Let's calculate the hypotenuse:

a = 28 m (width)

b = 96 m (length)

c = √(a² + b²) = √(28² + 96²)

c = √(784 + 9216)

c = √10000

c = 100 m

Now, we sum up all the distances:

28 m (west along the width)

96 m (north along the length)

100 m (shortcut diagonally)

Total distance = 28 m + 96 m + 100 m = 224 meters

Answer:  The answer is:  "  [tex]\frac{7}{80}[/tex] " .

_________________________________________________

Step-by-step explanation:

__________________________________________________

Given:  " 8 [tex]\frac{3}{4}[/tex] % "  ;  Convert this to a "fraction" .

__________________________________________________

Start with the:  " 8  [tex]\frac{3}{4}[/tex] "  portion:

Start with the:  " [tex]\frac{3}{4}[/tex] "  portion :

Note:  " [tex]\frac{3}{4}[/tex] " ;

                           =  3/4 ;

                           =  3 ÷ 4 ;  {use calculator} ;

                           =  0.75  .

_________________________________________________

Or;  recognize, from experience, that:  "3/4" = " 0.75 " .

_________________________________________________

Or:  Calculate as follows:

          →  " [tex]\frac{3}{4}[/tex]  = [tex]\frac{?}{100}[/tex] " ;  

          →   Solve for the:  "(?)" value:

__________________________________________________

Consider the "denominator" portions:

         →  " 4 * {what value?} = 100 " ;

         →  100/4 = 100 ÷ 4  = 25 ;  

         →  So:  " 4 * {25}  = 100 ;

Now, consider the "numerator" portions:

         →  " 3 * {25}  = "{?}" ;

         →  " 3 * {25}  = " 75 " ;

__________________________________________________

Now, we can rewrite the expression;

           & replace the "{?}" — with:  " 75 " ;  as follows:

__________________________________________________

The original expression:

          →  " [tex]\frac{3}{4}[/tex]  = [tex]\frac{?}{100}[/tex] " ;  

Rewrite as:

          →  " [tex]\frac{3}{4}[/tex]  = [tex]\frac{75}{100}[/tex] " ;  

_______________________________________________

Note:  " [tex]\frac{75}{100}[/tex] "  ;

                       =   75 / 100  =  75 ÷ 100 ;  

          →   Use calculator:   = 0.75 ;

_______________________________________________

                               Or:  75 ÷ 100 = ? ;

     →  Note:  when dividing by "100" ; we take the original value, and move that number backward "2 (two) decimal spaces".  We move "backward" because we are "dividing" (not "multiplying") ; and we move 2 (two) decimal spaces because:  " 100" has 2 (two) zeros.

     →  " 75 ÷ 100  =  75.  ÷  100  =  .75  ;

                               →  Write as:  " 0.75.

_______________________________________________

So:  " 8 [tex]\frac{3}{4}[/tex]  "  ;

          =  8  +  [tex]\frac{3}{4}[/tex]  ;

          =   8  + 0.75 ;

         =   8.75  .

_______________________________________________

So:  " 8 [tex]\frac{3}{4}[/tex] % " ;  

          =  8.75 % ;

_________________________________________

Note that " % " ;  refers to parts per hundred;  or:  "divided by 100" ;

_______________________________________________

       →  So:   " 8.75 % " ;

                  = 8.75 / 100 = 8.75 ÷ 100 ;  

       →  Use calculator; to get:  " 0.0875 " .

_______________________________________________

Or:  " 8.75 ÷ 100 " ;   →  As aforementioned, when dividing by "100" ;

                                   we move the decimal point "backward 2 (two) spaces:

      →   " 8.75 ÷ 100  =  .0875 ;

                          →  Write as:  " 0.0875 " .

_______________________________________________

Now, let us convert this value to a "fraction value" ;

    →  We have:  " 0.0875 ;

We look at the last consecutive non-zero digits:  "875" .

   →  How many decimal spaces backward from "875" ;  specifically, the digit, "5" ;  are there (counting backward; to the actual decimal point)?

  →  0.0875 .  →  The answer is:  "4 (four)" ;  which are: 5, 7, 8, and 0 " .

                               {Refer to digits in "bold font".}.

_______________________________________________

So, this value:  " 0.0875 " ;  

          →  is equal to:  " 875 " ÷ { 1 followed by 4 [four] zeros } ;

_______________________________________________

                               =  " 875 ÷ 10000 " ;

                               = " 875 ÷ 10,000 " ;

_______________________________________________

  Using a calculator:

       " 875 ÷ 10,000 "  = " [tex]\frac{875}{10,000}[/tex] " ;

______________________________________________

                                    = " [tex]\frac{7}{80}[/tex] " .

______________________________________________

The answer is: "  [tex]\frac{7}{80}[/tex] " .

______________________________________________

Hope this is helpful to you!

       Best wishes to you!

______________________________________________

8 3/4% as a fraction in simplest form is 7/80.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a percentage is any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In this exercise and scenario, we would convert the given percentage 8 3/4% into a fraction by dividing as follows;

8 3/4% = 8% + 0.75%

8% + 0.75% = 8.75%

8.75/100

Multiply both sides by 100, we have:

Fraction: 875/10000 = 7/80.

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Answer:

The null and alternative hypotheses are:

[tex]H_{0}: \mu = 170[/tex]

[tex]H_{a}: \mu >170[/tex]

Under the null hypothesis, the test statistic is:

[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

         [tex]=\frac{180-170}{\frac{35}{\sqrt{225}} }[/tex]

         [tex]=\frac{10}{2.33}[/tex]

         [tex]=4.29[/tex]

Now, we have to find the right tailed z critical value at 0.10 significance level. Using the standard normal table, we have:

[tex]z_{critical} = 1.28[/tex]

Since the test statistic is greater than the z critical value, we therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the university students weigh more than the population.

Answer:

3.10 miles

Step-by-step explanation:

1k = 0.62 miles

5x.62= 3.10

Kyle will run approximately 3.11 miles in a 5K marathon. This calculation is performed by first converting the 5K race distance into meters and then into miles, rounding the result to the nearest hundredth place.

The subject of this question is conversions between different units of distance, specifically kilometers to miles. To help Kyle with this, first, we need to convert the kilometers into meters. Since 1 kilometer equals 1000 meters, therefore, 5 kilometers will be 5000 meters.

Then, remembering that 1 mile is approximately 1609.34 meters, we can divide the total meters by the conversion factor for meters to miles. Therefore, the conversion from meters to miles is as follows: 5000 meters / 1609.34 meters/mile = 3.11 miles.

So, if Kyle is running a 5K marathon, he will be running approximately 3.11 miles. This answer has been rounded to the nearest hundredth place as per your instructions.

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Answer:

0 And 12

Step-by-step explanation:

0 + 12 = 12

But 0 is 12 away from 12. hope i helped :)

Answer:

0 and 12

Step-by-step explanation:

0+12=12

12-0=12

Answer:

x = -11, -11/5, -1, -1/5, 1/5, 1, 11/5,11

Step-by-step explanation:

The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + d

Your polynomial is  

f(x) = 5x³ + 7x + 11

a = 5; d = 11

p/q = Factors of d/Factors of a

Factors of d = ±1, ±11

Factors of a = ±1, ±5

Potential roots are x = ±1/1, ±1/5, ±11/1, ±11/5

Putting them in order, we get the potential roots

x = -11, -11/5, -1, -1/5, 1/5, 1, 11/5, 11

(There are no rational roots. There is one irrational root and two imaginary roots.)

Answer:

Third choice "The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4." is the correct answer.

Step-by-step explanation:

We know that partitioning a directed line segment into a ratio of 1:3 means that we are dividing the given line segment into two parts whose first part is 1 times the of some quantity while the another part is 3 times of the same quantity. So basically we are comparing part to part in by ratio. And total number of parts in the whole will be just sum of both so we get 1+3=4

Hence choice (3) is correct answer.

"The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4."

Answer:

it is C

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4." is the correct answer.