The lengths (in inches) of two sides of a regular triangle are given by the expressions 5x+40 and 8x-13. Find the length of a side of a triangle.

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{4x+1}{x^2-4x-12}[/tex] ← factorise the denominator

x² - 4x - 12 = (x - 6)(x + 2)

The fraction can now be expressed as

= [tex]\frac{4x+1}{(x-6)(x+2)}[/tex]

Split the numerator into its 2 parts, that is

= [tex]\frac{4x}{(x-6)(x+2)}[/tex] + [tex]\frac{1}{(x-6)(x+2)}[/tex]

Answer:

[tex]x=18[/tex]

[tex]y=60[/tex]

[tex]z=40[/tex]

Step-by-step explanation:

From the relations stablished in the problem we have the following equation system:

[tex]y-z=20[/tex] (equation 1)

[tex]\frac{1}{2} xy+420=\frac{1}{2}z(x+30)[/tex] (equation 2)

[tex]\frac{y}{y+z} =\frac{x}{30}[/tex] (equation 3)

From equation 1 we can find an expression of [tex]y[/tex] in terms of [tex]z[/tex] which we're going to call equation 4

[tex]y-z=20[/tex]

[tex]y=z+20[/tex] (equation 4)

We can then replace the equation 4 in the equation 2 in order to find an expression of [tex]x[/tex] in terms of [tex]z[/tex]

[tex]\frac{1}{2} xy+420=\frac{1}{2}z(x+30)[/tex]

[tex]\frac{1}{2} (xy+840)=\frac{1}{2}z(x+30)[/tex]

[tex]xy+840=z(x+30)[/tex]

[tex]x(z+20)+840=z(x+30)[/tex] (here we replaced the eq.4)

[tex]xz+20x+840=xz+30x[/tex]

[tex]xz+20x-xz=30z-840[/tex]

[tex]20x=30z-840[/tex]

[tex]10(2x)=10(3z-84)[/tex]

[tex]x=\frac{1}{2} (3z-84)[/tex] (equation 5)

Now, we can replace equations 4 & 5 inside the equation 3 so we can find the value of [tex]z[/tex]

[tex]\frac{y}{y+z} =\frac{x}{30}[/tex]

[tex]\frac{z+20}{z+20+z} =\frac{1}{30}*\frac{1}{2} (3z-84)[/tex]

[tex]\frac{z+20}{2z+20} =\frac{1}{30}*\frac{1}{2} (3z-84)[/tex]

[tex]\frac{z+20}{2(z+10)} =\frac{1}{2}*\frac{1}{30} (3z-84)[/tex]

[tex]\frac{1}{2}*\frac{z+20}{z+10} =\frac{1}{2}*\frac{1}{30} (3z-84)[/tex]

[tex]\frac{z+20}{z+10} =\frac{1}{10} (\frac{3z}{3}-\frac{84}{3})[/tex]

[tex]\frac{z+20}{z+10} =\frac{1}{10} (z-28)[/tex]

[tex]z+20 =\frac{1}{10} (z-28)*(z+10)[/tex]

[tex]10(z+20) =z^{2}+10z-28z-280[/tex]

[tex]10z+200 =z^{2}-18z-280[/tex]

[tex]z^{2}-28z-480=0[/tex]

This is a quadratic equation which has the form [tex]a*z^{2} +b*z+c=0[/tex]

where

[tex]a=1[/tex]

[tex]b=-28[/tex]

[tex]c=-480[/tex]

Then, we can find the solutions to this quadratic equation using the well-know quadatric formula which says that

[tex]z=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^{2}-4ac} }{2a}[/tex]

then, replacing the values of a, b and c we find the values of z

[tex]z_{1}=\frac{-(-28)+\sqrt{(-28)^{2}-4(1)(-480)} }{2(1)}[/tex]

[tex]z_{1}=40[/tex]

[tex]z_{2}=\frac{-(-28)-\sqrt{(-28)^{2}-4(1)(-480)} }{2(1)}[/tex]

[tex]z_{2}=-12[/tex]

We have two possible values of z, but because we're trying to find the measure of trapezoid's height the result shouldn't be negative, so we keep only the positive value of z, then

[tex]z=40[/tex]

Now we may replace this value of z in the equations 4 & 5 in order to find the values of x & y.

[tex]y=z+20[/tex] (equation 4)

[tex]y=40+20[/tex]

[tex]y=60[/tex]

[tex]x=\frac{1}{2} (3z-84)[/tex] (equation 5)

[tex]x=\frac{1}{2} (3(40)-84)[/tex]

[tex]x=18[/tex]

So we've found the values of x, y, and z.

[tex]x=18[/tex]

[tex]y=60[/tex]

[tex]z=40[/tex]

Answer:

  1

Step-by-step explanation:

Three points define 1 plane.

Answer:

The answer is plane 1

Step-by-step explanation:

Planes X and Y and points J, K, L, M, and N are shown.

Answer: I believe the answer would be 100 because there are or should be more than 100 M&M's in the jar.

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

we know that

If two figures are congruent, then the corresponding sides and the corresponding angles are congruent

In this problem, the corresponding sides are congruent, but the corresponding angles are not congruent

therefore

The square ABCD and the rhombus GHIJ are not congruent

Two Geometrical Shape are Congruent, only when

 1. Corresponding sides are equal

 2. Corresponding Interior as well as Exterior Angles are equal.

 3. Areas are equal.

⇒Square ABCD and Rhombus GHIJ, have length of their Corresponding side equal , but their interior angles are not equal.

So,⇒ Square ABCD NOT≅ to Rhombus GHIJ

Answer:

  d.  (4,3,6,2)

Step-by-step explanation:

The list of second numbers of the ordered pairs is the range.

___

The second number of the first pair is 4; the second number of the second pair is 3. The only 4-number answer choice containing these two numbers is (d). You don't even have to work the whole problem to make the proper choice.

Answer:

12 nickels, 37 dimes and 22 pennies

Step-by-step explanation:

Let

x ----> the number of nickels

y ----> the number of dimes

z ----> the number of pennies

we know that

1 nickel=$0.05

1 dime=$0.10

1 pennies=$0.01

so

0.05x+0.10y+0.01z=4.52 -----> equation A

y=3x+1 ----> equation B

z=x+10 ----> equation C

substitute equation B and equation C in equation A and solve for x

[tex]0.05x+0.10(3x+1)+0.01(x+10)=4.52 0.05x+0.30x+0.10+0.01x+0.10=4.52\\0.36x+0.20=4.52\\ 0.36x=4.52-0.20\\x=4.32/0.36\\x=12\ nickels[/tex]

Find the value of y

[tex]y=3(12)+1=37\ dimes[/tex]

Find the value of z

[tex]z=12+10=22\ pennies[/tex]

Answer:Boys=5,girls =2

Step-by-step explanation:

Let b be the no of boys and g be the no of girls

Therefore

Sam has twice as many brothers as sisters

2g=b-1

b-2g=1--------------1

Amanda has five times as many brothers as sisters

5(g-1)=b

5g-b=5----------------2

using (1) & (2) we get

g=2

b=5

There are 5 boys and 2 girls in Sam and Amanda's family. We determined this by setting up equations based on the clues provided and solving for the number of brothers and sisters.

To solve the riddle of how many boys and girls are in Sam and Amanda's family, we must first establish two equations based on the information provided:

Now we solve these two equations.

From the second equation, b = 5s - 5. Substituting this into the first equation:

(5s - 5) - 1 = 2s

Simplifying, we get:

5s - 6 = 2s

Now we solve for 's':

5s - 2s = 6

3s = 6

s = 2

There are 2 sisters. Substituting 's = 2' into b = 5(s - 1), we get:

b = 5(2 - 1)

b = 5

There are 5 brothers. But since we are including Sam in the total, there are 4 boys excluding Sam.

In conclusion, the family consists of 5 boys and 2 girls.

Answer:

a) C(x) = 1.33 + 0.097x

b) Fixed Initial cost =  $1.33

c) C(1200) = $ 117.73

Step-by-step explanation:

a) Let's first define our x variable and y variable as:

x: Number of cups of coffee produced

y: Cost of producing

y is a function of x that in this problem is called C(x) so y = C(x).

No we are told that C(x) is a linear function. All linear functions follow the rule:

C(x) = mx+b

where m is the slope of the line and b is the intercept in the y - axis or the value of the function when x=0 .  To find a formula for C(x) we can use the information given because these are two points of the line where

Point 1

x1= 300  and  y1 = 30.43

Point 2

x2= 500 and y2 = 49.83

With these two points we can find the slope with the formula

m= y2-y1/x2-x1 = (49.83-30.43)/(500-300) = 19.42/200 = 0.097

so we have that;

C(x) = mx+b = 0.097x+b.

Now we have to know b the intercept in y.For this problem this is equivalent to the cost that we would have to pay if we did not produced any cup so b is our fixed initial cost. Because we have a point, we can replace it in the equation and solve for b. It doesnt matter which point we use.

C(x) = 0.097x + b

b = C(x)  - 0.097x

With Point 2 =  x = 500 and C(x) = 49.83

b = C(x)  - 0.097x

b = 49.83  - (0.097 * 500) = 49.83 -48.5 = 1.33

So the final  formula for C(x) is

C(x) = 0.097x + 1.33

b) As I said before, the initial cost or fixed cost is the cost incurred if we would not produce anything or mathematically when x = 0

C(x) = 0.097x + 1.33

C(0) = 0.097*0 + 1.33 = 0+1.33 = 1.33

The fixed cost is $ 1.33 that is the same as b parameter.

c) Now that we have an equation for C(x) we only need to replace for the point x = 1200

C(x) = 0.097x + 1.33

C(1200) = (0.097*1200) + 1.33 = 116.4 +1.33 =  $ 117.73

The formula for the cost function C(x) is C(x) = $0.097x + $1.33, where $1.33 represents the fixed cost. Using this formula, the total cost of producing 1200 cups of coffee is $117.73.

Find the Cost Function C(x)

To find the cost function C(x), we need two points to determine a linear function: (300, $30.43) and (500, $49.83). First, find the slope (m) of the cost function using the formula m = (y2 - y1) / (x2 - x1), which in our case is m = ($49.83 - $30.43) / (500 - 300), so m = $19.40 / 200 = $0.097 per cup. The slope represents the variable cost per cup of coffee.

With the slope, we can use one of the points to find the y-intercept (b), the fixed or initial cost. Plug in the values into y = mx + b, so $30.43 = $0.097*300 + b, which gives us b = $30.43 - $29.10 = $1.33. Therefore, the formula for C(x) is C(x) = $0.097x + $1.33.

To find the total cost of producing 1200 cups, plug x = 1200 into the cost function: C(1200) = $0.097*1200 + $1.33, which calculates to C(1200) = $116.40 + $1.33 = $117.73.

Hence, the total cost of producing 1200 cups of coffee is $117.73

Answer:

The X, should be 4

Step-by-step explanation:

7/2x - 5/2 = 23/2

7/2x = 23/2 + 5/2

7/2 = 14

x = 14 . 2/7

x= 4

The solution to the equation [tex]\frac{7}{2}x - \frac{5}{2} = \frac{23}{2}[/tex] is x = 4. By substituting x = 4 back into the equation, we confirm that it satisfies the original equation, proving that the solution is correct.

Let’s solve the equation [tex]\frac{7}{2}x - \frac{5}{2} = \frac{23}{2}[/tex] step-by-step as shown below-

Let's isolate the x-term by adding [tex]\frac{5}{2}[/tex] to both sides of the equation

This simplifies to:

Next, simplify the right-hand side:

Now, multiply both sides by [tex]\frac{7}{2}[/tex] to solve for x:

And the final solution is:

To check the solution, substitute x = 4 back into the original equation:

This becomes:

The left side simplifies to:

Which confirms:

Thus, the solution x = 4 is correct.

The algebra tile configuration described represents the polynomial 2x^2 - 4x - 6.

The algebra tile configuration you have described is representing the polynomial 2x2 - 4x - 6. This is deciphered as follows:

In conclusion, the three parts together give us the polynomial: 2x2 - 4x - 6.

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The polynomial represented by the algebra tiles is [tex]\(2x^2 - 4x - 6\).[/tex]Therefore, the correct option is [tex]\(2x^2 - 4x - 6\).[/tex]

To determine which polynomial is represented by the given algebra tile configuration, we need to understand the values assigned to each type of tile.

Step 1:

Interpret the tiles.

The largest tiles represent [tex]\(x^2\),[/tex] the tiles labeled negative x represent [tex]\(-x\),[/tex] and the tiles labeled minus represent [tex]\(-1\).[/tex]

Step 2:

Assign values to the tiles.

Each largest tile represents [tex]\(x^2\),[/tex] so we have [tex]\(2x^2\).[/tex]

There are 4 tiles labeled negative x, each representing [tex]\(-x\),[/tex] so we have [tex]\(-4x\).[/tex]

There are 6 tiles labeled "minus," each representing [tex]\(-1\),[/tex] so we have [tex]\(-6\).[/tex]

Step 3:

Combine the terms.

Combining the terms, we get [tex]\(2x^2 - 4x - 6\).[/tex]

So, the polynomial represented by the algebra tiles is [tex]\(2x^2 - 4x - 6\).[/tex]Therefore, the correct option is[tex]\(2x^2 - 4x - 6\).[/tex]

Answer:

  C.  4,100

Step-by-step explanation:

"60% more" is represented by a multiplier of 1 + 0.60 = 1.60.

"60% fewer" is represented by a multiplier of 1 - 0.60 = 0.40.

__

Let b represent the number of booklets distributed by Team B. Then the number distributed by Team A is ...

  1.60 × (0.40b) . . . . 60% more boxes, each with 60% fewer booklets

  = 0.64b

Then the total distributed by both teams is ...

  b + 0.64b = 1.64b = (164/100)b = (41/25)b

The only answer choice that is a multiple of 41 is ...

  4,100 . . . choice C

__

For 4100 to be the number of booklets distributed by both teams, Team B will have distributed 2500 booklets, and Team A will have distributed 1600 booklets. Team A might have distributed 160 boxes of 100 booklets, while Team B might have distributed 100 boxes of 250 booklets.

Answer:

Step-by-step explanation:

1 ) k²-8k = 0

k(k-8)=0

k = 0 or k=8

2) a²+5a=0

a(a+5) = 0

a=0 or a  = - 5

3 ) 6n²+5n-25=0

delta = b²-4ac      b =5 and a = 6   and   c= - 25

delta = 5²-4(6)(-25) = 625 = 25²

n 1 = (-5+25)/12 = 20/12 = 5/3

n 2 = (-5-25)/12 = -  30/12  = -5/2

same method for 4) and 5)

Answer:

327692

Step-by-step explanation:

[tex]65536 = (-4)^{8} \\ \\ 65536 \times 5 = 327680 \\ \\ 327680 - 3(-4) = 327680 + 12 = 327692[/tex]

According to the Order of Operations [GEMS(A)\BOMDAS\PEMDAS etc.], in this case, you evaluate the exponent BEFORE multiplying. This is a common mistake people make.

I am joyous to assist you anytime.

Answer:

A. (-2,-1,0,1) .......

Answer:

Impossible to know. Numbers provided on the statement are for June, though question is made for september. If, by any chance, question is not correctly stated, answer will be True

Step-by-step explanation:

According to the problem, there were 214 births. Seven of those 214 births were via C-section. Then: 100%*(7/214)=3.3%

It does not matter which births were natural, or C sectioned, as they are considered in the same group.

Answer:

The answer to your question is:  4 x 10 ⁶ = population of Oregon

Step-by-step explanation:

Data

Population of the USA = 3.2 x 10⁸

Population of the USA = 80 population of Oregon

Process

                           3.2 x 10⁸  = 80 population of Oregon

                           3.2 x 10⁸ / 80 = population of Oregon

                          4 000 000 = population of Oregon

                           4 x 10 ⁶ = population of Oregon

The population of Oregon will be 4 x 10⁶.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The population of the United States = 3.2 x 10⁸

And, The population of the United States is about 80 times the population of Oregon.

Let population of Oregon = x

Then, We can formulate;

3.2 x 10⁸ = 80 × x

Solve for x as;

3.2 x 10⁸ = 80 × x

x = 3.2 x 10⁸ / 80

x = 0.04 x 10⁸

x = 4 x 10⁻² x 10⁸

x = 4 x 10⁶

Thus, The population of Oregon will be 4 x 10⁶.

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Answer:

  37 1/2 C

Step-by-step explanation:

25 × 1 1/2 C = 37 1/2 C

The temperature would have dropped 37 1/2 C.

_____

The ground temperature is irrelevant to the question.

Answer:

Yes, SDS > SDT

Step-by-step explanation:

List S

25, 30, 40, 50, XS

Average list S = 40

So, we could write,

Average list S = 40 = (25 + 30 + 40 + 50 + XS) / 5

Solving for XS

XS = 40 x 5 – 25 – 30 – 40 – 50 = 200 – 145 = 55  

SDs = SD (25, 30, 40, 50, 55) = 12.74

List T

30, 40, 45, 50, XT

Average list T = 40

So, we could write,

Average list T = 40 = (30 + 40 + 45 + 50 + XT) / 5

Solving for XT

XT = 40 x 5 – 30 – 40 – 45 – 50 = 200 – 165 = 35  

SDT = SD (30, 35, 40, 45, 50) = 7.1

Even at first sight SDS > SDT  because 25 is out of the range 30-50, while 45 is within that range.

List S is more spread than list T.

A lower or higher number than the mean in a list can increase the standard deviation. In this case, the standard deviation of list S is greater than list T due to the presence of 25, which is farther from the mean of 40 than the numbers in list T.

The question asked relates to the standard deviation of two sets of positive integers, list S and list T. For each list, we calculate the standard deviation, which is a measure of how spread out the numbers are around the mean value. Based on the information provided:

The presence of a number lower or higher than the mean in list S or T respectively, will increase the standard deviation because the deviation or difference from the mean is greater. Remember, standard deviation measures the variation or dispersion from the average. Hence, if the integer 25 is in List S and the integer 45 is in list T, the standard deviation will be greater for list, S, considering these numbers are farther from the mean of 40 compared to the numbers in List T.

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Alisa's conjecture is true because the numbers in set A differ by two magnitudes, making the comparison easier. Alisa could have compared the leading digits in the ten thousand place to determine that the numbers in set B are relatively close in magnitude.

In order to construct an argument justifying whether Alisa's conjecture is true, we can compare the magnitude of the numbers in each set. Looking at set A, we have 45,000 and 1,025,680. The first number has four digits, while the second number has six digits, indicating a difference of two magnitudes.

Now let's look at set B, which consists of 492,111 and 409,867. Both numbers in set B have six digits, so they are of the same magnitude.

Based on this analysis, we can conclude that Alisa's conjecture is true. It is indeed easier to compare the numbers in set A because their magnitudes differ by two, making the comparison more straightforward.

When comparing set B using the ten thousand place, Alisa could have used the strategy of looking at the leading digit in the ten thousand place. In this case, the leading digits are 4 and 4, indicating that the numbers in set B are relatively close in magnitude.

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Answer: He jogs 12 miles per hour

Step-by-step explanation: Every 15 minutes he jogs 3 miles, there are 60 minutes in an hour, 60/15 = 4, 4 x 3 = 12

Answer:

The correlation between sales and advertising is positive.

Step-by-step explanation:

For every $35 spent on advertising, sales increase by $1

Is FALSE, since y = 500 + 35 x $35, sales increase more than $1

Even if no money is spent on advertising, the company realizes $35 of sales

Is FALSE, if no money is spent, the sales amount to $ 500 (when X = 0)

The coefficient of correlation between sales and advertising is 0.81

Is FALSE, since R² = 0.9. The coefficient of correlation = R = 0.94, not 0.81

Answer:

10 months

Step-by-step explanation:

Let X represent the number of months

The cost equation for the first plan = $20 + 10x

The cost equation for the second plan =$ 40+8x

The number of months at which the cost for the two plans will be equal can be worked out by equating the costs for the two plans and then calculate the value of x.

Thus,

$20+10x = $40 +8x

        10x -8x =$40-$20  

            2x = $ 20

              x= 20/2

                 x= 10

Substituting X in each equation,

  $20 +$10(10) = $40 + $8(10)

   $ 20 +$100 =$40 +$80

       $120 =$120

Thus, the amount after ten months = $120

Answer:

1. No

2.Yes

3.Yes

4.Yes

5.No

Step-by-step explanation:

Plug in the numbers

1. 3+3 = 9+9  /  6 = 18  /  NO

2. 20-0 = 20+0  /  20 = 20  /  Yes

3. 3+0/3-0  /  3/3 = 1  /  Yes

4. 4+3 = 16-9  /  7 = 7  / Yes

5. 0+1 = 1-0/0  /  1 = 1/0 / No

Rate as Brainliest plz

Answer: No Yes Yes Yes No

Step-by-step explanation: brain power

Answer:

$58.26.

Step-by-step explanation:

Total cost without sales tax and tip =  3 * 6.25 + 3 * 7.50 + 6 *1.25

= $48.75

Plus Sales tax and tip:

= 48.75 + 0.045*48.74 + 0.15*48.75

= $58.26.

Answer:

58.25

Step-by-step explanation:

Answer:

  see the attachment

Step-by-step explanation:

(a) Clockwise rotation moves a point from (x, y) to (y, -x).

__

(b) Reflection across x=1 moves a point from (x, y) to (2-x, y).

Answer:

d. c = 1 and d = -4

Step-by-step explanation:

If a function is even, then f(-x) = f(x).  Graphically, this means it's symmetrical about the y-axis.

f(-a) = f(a)

3c + 1 = 6 − 2c

5c = 5

c = 1

f(-b) = f(b)

2d − 5 = 4d + 3

-2d = 8

d = -4

Therefore, c = 1 and d = -4.

Answer:

Joseph is not correct

Each digit from the leftmost digit is ten times the digit before it  

Step-by-step explanation:

* Lets explain how to solve the problem

- Any number formed from some digits, each digit has a place value

- Ex: 2,345 this number formed from 4 digits

 The place value of 5 is ones ⇒ 5

 The place value of 4 is tens ⇒ 40

 The place value of 3 is hundreds ⇒ 300

 The place value of 2 is thousands ⇒ 2,000

 2,345 = 2,000 + 300 + 40 + 5

* Lets check our problem

∵ The number is 9,999,999

- The number formed from 7 digits, the digits have different places value

∴ They couldn't have the same value

∴ Joseph is not correct

∵ The number formed from 7 digits

- The place value of the leftmost digit is millions

- The place value of the digit before the million is hundred thousands

- The place value of the digit before the hundred thousands is

 ten thousands

- The place value of the digit ten thousands is thousands

- The place value of the digit before thousands is hundreds

- The place value of the digit before hundreds is tens

- The place value of the digit before tens is ones

∴ 9,999,999 = 9,000,000 + 900,000 + 90,000 + 9,000 + 900

   + 90 + 9

∴ Each digit from the leftmost digit is ten times the digit before it  

Answer

 B) x + 20 ≥ 50

Step-by-step explanation:

Answer:

B) x + 20 ≥ 50

Step-by-step explanation:

Given,

The hours she already has for social studies = 20,

After getting x more hours,

The total hours she has now = x + 20,

According to the question,

Total hours ≥ 50

[tex]\implies x + 20\geq 50[/tex]

Which is the required inequality to model give situation,

Hence, OPTION B is correct.

Answer:

y = - 7.5

Step-by-step explanation:

Given

- 140 = 18 + 4(5y - 2) ← distribute and simolify right side

- 140 = 18 + 20y - 8

- 140 = 10 + 20y ( subtract 10 from both sides )

- 150 = 20y ( divide both sides by 20 )

- 7.5 = y