How to solve for x/ extraneous solutions

Answer:

3.)

Step-by-step explanation:

Answer:

96 in²

Step-by-step explanation:

The surface area of the square pyramid is the area of the square base plus the area of the four triangular faces.  The slant length is the height of each triangle.

A = s² + 4 (½ sL)

A = s² + 2sL

Given s = 6 and L = 5:

A = (6)² + 2(6)(5)

A = 36 + 60

A = 96

The area that needs to be painted is 96 in².

Answer:

3.71 miles farther.

Step-by-step explanation:

To answer this, subtract 3  5/8 miles from 7  1/3 miles:

22/3 - 29/8 (miles)

Here the LCD is 24.  Thus, we have:

176      87                       89

------ - ------  (miles), or -------  (miles)

24       24                       24

Arun has to walk another 89/24 miles, or 3.71 miles.

Check:  do 3  5/8 miles and 3.71 miles add up to 7  1/3 miles?  Yes, approximately.

Arun has 89/24 miles left to walk to reach his friend's house.

Arun decided to walk 7 1/3 miles to his friend's house. After walking 3 5/8 miles, he stopped to rest. To calculate how much farther Arun has to walk to reach his friend's house, we subtract the distance he has already walked from the total distance he needs to walk.

The total distance to his friend's house: 7 1/3 miles = 7 + 1/3 = (7 × 3 + 1)/3 = 22/3 miles.

Distance already walked: 3 5/8 miles = 3 + 5/8 = (3 × 8 + 5)/8 = 29/8 miles.

To find the remaining distance, we subtract 29/8 miles from 22/3 miles:

First, find a common denominator for the fractions, which is 24. Convert both fractions: 22/3 × 8/8 = 176/24 and 29/8 × 3/3 = 87/24.

Now subtract the distances: 176/24 - 87/24 = 89/24 miles.

Therefore, Arun has 89/24 miles left to walk to reach his friend's house.

Answer:

Can't really show a graph but I'll explain how to:

Step-by-step explanation:

Plot the point (0,-2) since -2 is the y=intercept. After, just count-down 1 unit and count 5 units to the right. I hoped this helped!

Answer:

a.) 14:6

b.) 6:8

Hope this helped!

Step-by-step explanation:

Answer:

see rexplanation

Step-by-step explanation:

A

There are a total of 14 marbles of which 8 are red and 6 are blue

ratio of all : blue = 14 : 6 = 7 : 3 ← in simplest form

B

ratio of blue : red = 6 : 8 = 3 : 4 ← in simplest form

Answer:

The population of 75 hours from now would be 40,000.

Step-by-step explanation:

The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.

The population of a bacterial colony that doubles every 25 hours will increase exponentially. In this case, starting from a population of 10,000 bacteria, after 75 hours, we will have 80,000 bacteria. This demonstrates the concept of exponential growth commonly seen in bacteria.

The population of a bacterial colony that doubles every 25 hours follows an exponential growth model. This process is where the increasing rate is proportional to the current scope, leading to continued growth. If we start with a colony of 10,000, after 25 hours, we will have 20,000 bacteria. After another 25 hours, this will double again to 40,000. And after a final 25 hours, we double the number again to 80,000.

Here are the calculations:

This demonstrates the concept of exponential growth commonly seen in the bacteria populations. The growth rate increases over time due to the characteristic of bacteria to divide and reproduce, leading to a rapid increase in their numbers.

https://brainly.com/question/12490064

#SPJ3

Answer:

2205

3570

LCM = 74970

1100

1576

GCF = 4

1100

1576

LCM = 433400

456

4680

GCF = 24

456

4680

LCM = 88920

Step-by-step explanation:

18837429928373829193

Answer:

The width of the drawer is [tex]15\ in[/tex]

Step-by-step explanation:

we know that

The volume of the drawer is equal to

[tex]V=LWH[/tex]

we have

[tex]L=15\ in[/tex]

[tex]H=5\ in[/tex] -----> the deep of the drawer

[tex]V=1,125\ in^{3}[/tex]

substitute the given values in the formula and solve for W

[tex]1,125=(15)(W)(5)[/tex]

[tex]1,125=(75)(W)[/tex]

[tex]W=1,125/(75)[/tex]

[tex]W=15\ in[/tex]

Answer:

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Step-by-step explanation:

Answer: $25

Step-by-step explanation: 2/3 of $300 is $200. 1/4 of $300 is $75. The total money she used is $275. $300-$275= $25.

Answer:

$75

Step-by-step explanation:

2/3 of 300 is 200 which means $100 bucks is left and 1/4 on food is $25 so what is left over is $75

Answer:

True

Step-by-step explanation:

Each time a spinner is spun, there is an equal chance that each result will occur, thus each of these spins are independent.

The answer is true

Hope this helped

The linear equation -3y=x-6 can be graphed using the slope-intercept form y = -1/3x + 2. By choosing different values for x and solving for y, we can find three points that solve the equation. Plotting these points on a graph and connecting them with a line represents the linear equation.

The linear equation -3y=x-6 can be rewritten in slope-intercept form as y = -1/3x + 2. This form allows us to easily determine the slope and y-intercept of the equation. The slope is -1/3, which means for every increase of 1 in x, y decreases by 1/3. The y-intercept is 2, which indicates that the line crosses the y-axis at the point (0, 2).

To find three points that solve the equation, we can choose different values for x and substitute them into the equation to solve for y. Let's choose x = 0, x = 3, and x = -3. Plugging these values into the equation, we get y = 2, y = 1, and y = 3, respectively.

Therefore, the three points that solve the equation are (0, 2), (3, 1), and (-3, 3). When we plot these points on a graph, we can then connect them with a straight line to represent the linear equation.

Answer:

Snowboard can be purchased for the lowest price from Store C offering 40% discount.

Step-by-step explanation:

We need to compare discounts of 3 stores and find the store selling snowboard lowest of them.

Store A: Sale of 30% off and a successive discount of 10% off.

The formula used for successive discount is = (x+y - xy /100)%

here x= 30 and y =10 so total discount is:

Total discount = ( 30 +10 - (30*10)/100)%

                       = (40 - 300/100) %

                       = (40 -3) % = 37%

Original price = $189.59

Discount offered = 37% of $189.59

                            = 37/100 * 189.59 = $70.15

Selling Price = Original price - Discount offered

                     = $189.59 - $70.15

                     = $ 119.44

Store B: Sale of 20% off and a successive discount of 20% off.

The formula used for successive discount is = (x+y - xy /100)%

here x= 20 and y =20 so total discount is:

Total discount = ( 20 +20 - (20*20)/100)%

                       = (40 - 400/100) %

                       = (40 -4) % = 36%

Original price = $189.59

Discount offered = 36% of $189.59

                            = 36/100 * 189.59 = $68.25

Selling Price = Original price - Discount offered

                     = $189.59 - $68.25

                    = $ 121.34

Store C: Sale of 40% off.

Original price = $189.59

Discount offered = 40% of $189.59

                            = 40/100 * 189.59 = $75.84

Selling Price = Original price - Discount offered

                     = $189.59 - $75.84

                    = $ 113.75

So, Store A Sale price is: $ 119.44

Store B Sale price is: $ 121.34

and Store C Sale price is: $ 113.75

So, Comparing them we found that snowboard can be purchased for the lowest price from Store C offering 40% discount.

Answer:

store c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Solving the inequality

[tex]\frac{1}{2}[/tex] x - 2 > 0 ( add 2 to both sides )

[tex]\frac{1}{2}[/tex] x > 2 ( multiply both sides by 2 )

x > 4

Since greater than 4 we want a number line with an open circle at 4, indicating x is not equal to 4 and arrow pointing to the right.

Hence C

Answer:

8

Step-by-step explanation:

If you cut one apple pie in half, then you have two halves. Do the same with the other 3 pies and you will have 8 halves of the pie to give to neighbors.

Answer:

95 miles more.

Step-by-step explanation:

There are 365 days in the normal year.

Walking 3 miles daily for a year thus comes to (3 miles/day)(365 days) =

1095 miles total per year.  This is Answer A:  95 miles more than 1000 miles.

Answer:

95 miles

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

= 7 - 1- 6

= 6 - 6

=0

To evaluate the expression 1/3m - 1 - 1/2n with m=21 and n=12, you perform a series of arithmetic operations, resulting in an evaluated expression of 0.

To evaluate the expression 1/3m - 1 - 1/2n when m=21 and n=12, we substitute the given values of m and n into the expression.

Answer

0

Solution

6x+6x=12-12

12x=0

X=0

Answer:

No diagram and no explanation what 9 is.

However, if it is an octagon with each side equal to 9 then

area = (# of sides * side^2) / (4 * tan (180 # of sides))

area = 8 * 9 * 9 / (4* tan (180 / 8)

area = 648 / 4 * 0.41421

area = 391.1059607446

answer is C

Step-by-step explanation:

The area of the considered octagon which has distance from its center to the vertex of 9 m is given by: Option b). 229.1 m²

If the regular octagon has sides of 'a' units, then its area is:

[tex]A = 2(1+\sqrt{2})a^2 \: \rm unit^2[/tex]

Consider the attached figure below (second figure too).

If we find the value of 'a', then we can use the above formula.

Since there are 8 equal sides in a regular octagon, the angle from center to each of the side is full angle / 8 = 360/8 = 45 degrees.

Since the angle OA is perpendicular on BC, due to symmetry, we have the angle BOC divided into 2 parts.

Thus, we get:

m∠AOB = 45/2 degrees = 22.5°

Using the sine ratio from the perspective of angle AOB, we get:

[tex]\sin(m\angle AOB) = \dfrac{|AB|}{|OB|}\\\\\sin(22.5^\circ) = \dfrac{a/2}{9}\\\\a \approx 2 \times 9 \times 0.38268 \approx 6.888[/tex] meters

(since length of AB is half of length of BC, which is 'a' units).

Thus, we get:

[tex]A = 2(1+\sqrt{2})a^2 \approx 2(1+\sqrt{2})(6.888)^2 \approx 229.1\: \rm m^2[/tex]

Thus, the area of the considered octagon which has distance from its center to the vertex of 9 m is given by: Option b). 229.1 m²

Learn more about area of a regular octagon here:

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Answer:

6*2/3 = 12/3 = 4

Step-by-step explanation:

For this case we have a total of 6 cups of berries and per serving of salad we use [tex]\frac {2} {3}[/tex]of cups.

Let "x" be the variable that represents the portions of fruit salad that can be made, then, to find it we divide the number of cups of berries among the amount that is used for a portion:

[tex]x = \frac {6} {\frac {2} {3}} = \frac {6 * 3} {2 * 1} = \frac {18} {2} = 9[/tex]

Thus, 9 portions of salad can be prepared.

Answer:

9 portions

Answer:

y=4x+13  or y-5=4(x+2)

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

In this problem we have

m=4

(x1,y1)=(-2,5)

substitute

y-5=4(x+2) ----> equation of the line into point slope form

Convert to slope intercept form

y-5=4x+8

y=4x+8+5

y=4x+13 ----> equation of the line into slope intercept form

The correct answer is B. 4/5. Hope this helps! : )

Answer:

1/5

Step-by-step explanation:

it said so in usa testprep and i hope this helps you! ^-^

Answer: 192

Step-by-step explanation: 6 inches times 2 is a foot. 12 times 2 is 24 tiles across the top times 8 rows. 24 times 8 is 192

16

Because 8x12=96 and 96/6= 16

Answer:

$3

Step-by-step explanation:

4 / 12 = 3

Answer:

3

Step-by-step explanation:

You Divide $12.00 / 4 And Get You Answer As 3 :)

Answer:

   1

---------

  x^3

Step-by-step explanation:

The proper way to write this is with parentheses:  x^(-3).

If you wish to eliminate the negative exponent, rewrite this x^(-3) as

   1

---------

  x^3

190.18 is the average balance

Answer:

The answer is $190.18

Step-by-step explanation:

When we calculate the average daily balance, we total the balance from each day in the billing cycle and divide the total by the number of days in the cycle. Here the billing cycle is given for July that has 31 days.

Lets calculate each days amount.

Opening balance from 1st July to 7th July = $209.53

So, it is a total of 7 days; amount is [tex]209.53\times7=1466.71[/tex]

On 8th July a payment of $50 is made making the amount

[tex]209.53-50=159.53[/tex]

So, from 8th July to 15th July (8 days), the balance was $159.53 making a total of [tex]159.53\times8=1276.24[/tex] dollars

On 16th July a charge of $20 was added, so from 16th July to 23 July (8 days), the amount became = [tex](159.53+20)\times8=1436.24[/tex] dollars

On 24th July additional charge of $35 was added and the period it remained same was till 31st July, making it 8 days.

So, amount is = [tex]214.53\times8=1716.24[/tex] dollars

Now adding all the charges we get;

[tex]1466.71+1276.24+1436.24+1716.24= 5895.43[/tex] dollars

Now we will divide this by 31 days to get the average daily balance.

[tex]\frac{5895.43}{31}=190.175[/tex]  ≈ $190.18

Answer:

Step-by-step explanation:

If it's parallel, that means it has the same slope: -1/5.

Use point-slope form to write the equation:

y - 4 = -1/5 (x - 7)

If you wish to write in point-intercept form:

y - 4 = -1/5 x + 7/5

y = -1/5 x + 27/5

If two lines are parallel, it means that they will have the same gradient:

And remember, the equation of a line is y = mx +c

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

So we know that the equation of the parallel line is:

y = - [tex]\frac{1}{5}[/tex]x + c        through point (7, 4)

All we need to do now is to work out what c is

Note: at point (7, 4)  x = 7 , and y = 4.

So to work out c, we substitute in the values of x and y, and solve:

y = - [tex]\frac{1}{5}[/tex]x + c

4 = - [tex]\frac{1}{5}[/tex] * 7 + c

4 = -1.4 + c

5.4 = c

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

Finally, we just put the value of c back into the original equation

y = - [tex]\frac{1}{5}[/tex]x + 5.4

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

Answer:

The equation of the a line parallel to y = - [tex]\frac{1}{5}[/tex]x + 3    through point (7,4)

is: y = - [tex]\frac{1}{5}[/tex]x + 5.4

Answer:

It should be  B I me

Step-by-step explanation:

To determine which percentage is higher, we need to calculate the percentage of boys who prefer green and the percentage of girls who prefer red.

Percentage of boys who prefer green:

Total number of boys = 2 + 4 + 4 + 5 = 15

Number of boys who prefer green = 5

Percentage of boys who prefer green = (5/15) x 100% = 33.33% (rounded to the nearest whole number, this is 33%)

Percentage of girls who prefer red:

Total number of girls = 4 + 3 + 1 + 3 = 11

Number of girls who prefer red = 4

Percentage of girls who prefer red = (4/11) x 100% = 36.36% (rounded to the nearest whole number, this is 36%)

Therefore, the percentage of girls who prefer red (36%) is higher than the percentage of boys who prefer green (33%).

The answer is B. At 36%, the percentage of girls who prefer red is higher.

18² is the same as saying 18 * 18, which is 324

Answer:

A

Step-by-step explanation:

1. Line l is cut by line a (let it be named a, because the figure doesn't show its name). Angles 1 and 6 are vertical, so they are congruent.

2.  Line m is cut by line a. Angles 3 and 8 are vertical, so they are congruent.

3. Parallel lines l and m are cut by transversal a. Angles 6 and 3 are congruent as alternate interior angles.

Hence,

[tex]3x+25=4x-17,\\ \\3x-4x=-17-25,\\ \\-x=-42,\\ \\x=42^{\circ}.[/tex]

4. The measure of angle 6 is

[tex]3x+25=3\cdot 42+25=126+25=151^{\circ}.[/tex]

5. Angles 6 and 2 are supplementary angles, so they add up to 180°:

∠2=180°-∠6=180°-151°=29°