Study the steps shown to solve the given equation.
(√30 - 2x)= x - 3
30 - 2x = x2 - 6x + 9
0 = x2 - 4x - 21
0 = (x + 3)(x - 7)
Based on the above work, possible solutions of the equation are
and
Check the answers in the original equation. The extraneous solution
is x=

Answer:

[tex]-145[/tex]

Step-by-step explanation:

Step 1:  Set x to -5

[tex]x^3+125/x+5[/tex]

[tex](-5)^3 + 125/-5 + 5[/tex]

[tex]-125 - 25 + 5[/tex]

[tex]-145[/tex]

Answer:  [tex]-145[/tex]

Answer:8:15

Step-by-step explanation: Because half past 7 means 7:30 and 7:30 + 45 minutes = 8:15.

the sum of (6p^2+3) and (6-5p^3+3p^2) is

[tex](6p^2+3)+(6-5p^3+3p^2)= 6p^2+3+6-5p^3+3p^2=-5p^3+9p^2+9[/tex]

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P.S. Hello from Russia :^)

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Answer:

9 P ^ 2 + 9 - 5 p ^ 3

Step-by-step explanation:

6p^ 2 + 3 + 6 - 5p ^ 3 + 3p ^ 2

Given:

Dante bought a new graduated cylinder for his chemistry class.

Volume of the cylinder = 662.7π milliliters of liquid

Converting to cubic centimeter, we get;

Volume of the cylinder = 662.7π cm³

Radius of the cylinder = 4.7 cm

We need to determine the height of the cylinder.

Height of the cylinder:

The height of the cylinder can be determined using the formula,

[tex]V=\pi r^2 h[/tex]

Substituting the values, we have;

[tex]662.7 \pi=\pi (4.7)^2h[/tex]

[tex]662.7 \pi=\pi (22.09)h[/tex]

Dividing both sides by 22.09π, we get;

[tex]30=h[/tex]

Therefore, the height of the cylinder is 30 cm.

Hence, Option C is the correct answer.

The calculated height of the graduated cylinder is approximately 30 cm, which is option C.

To determine how tall Dante's graduated cylinder is, given it holds 662.7π milliliters (mL) of liquid, we should use the formula for the volume of a cylinder, V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height.

Since 1 milliliter is equivalent to 1 cubic centimeter (cm³), we have V = 662.7π cm³, and the radius 'r' is given as 4.7 cm. Inserting these values into the formula and solving for 'h' gives us:

V = πr²h

662.7π cm³ = π × (4.7 cm)² × h

662.7π cm³ = π × (22.09 cm²) × h

662.7π cm³ = 22.09π × h

h = 662.7 cm³ /22.09

h ≈ 30cm

Therefore, the height of the cylinder is approximately option c. 30 cm.

The above question is incomplete, the complete question is:

Dante bought a new graduated cylinder for his chemistry class. It holds 662.7π milliliters of liquid. If the cylinder has a radius of 4.7 cm, then how tall is the cylinder? (Note: 1 milliliter is equal to 1 cubic centimeter)

A.

141 cm

B.

19,881 cm

C.

30 cm

D.

70.5 cm

Answer:

x=5

Step-by-step explanation:

x+5 = -3x+25

Add 3x to each side

x+3x+5 = -3x+3x+25

4x +5 = 25

Subtract 5 from each side

4x+5-5 = 25-5

4x = 20

Divide each side by 4

4x/4 = 20/4

x =5

Answer: x=5

Step-by-step explanation:

x+5= 3x+25

collect like terms

subtract

4x=20

divide both sides by four

x=5  

Answer:

20!

Step-by-step explanation:

Answer:

2880 or 20!

Step-by-step explanation:

Whenever you have a number with a (!) after it, it means that the number is in factorial. So if you have a equation like 3!, it would be equal to 3·2·1. So in that case—

5! = 1·2·3·4·5

We can multiply this sequence of numbers simply.

1·2·3·4·5=120

Now, since we have the first factorial, we move on to the second.

4!=1·2·3·4

Again, we can multiply this sequence simply.

1·2·3·4=24

Now we move on to the final step. We have factoriazed the numbers, so we can substitute those in the equation.

120·24

Now we can finally multiply these 2 numbers to get your answer.

120·24=2880

That is the evaluation.

If you want to simplify the expression, multiply the numbers.

4!·5!=20!

2y = -2x + 8

3y = 9

y = 3

3 = 2x + 1

2x = 2

x = 1

Answer

x = 1

y = 3

Hope this helps :)

Answer:

1/5

Step-by-step explanation:

When changing a decimal to a fraction, think of the decimal "out of 1." In mathematical terms, "out of" generally means division.

For example on this question, think of 0.2 as 0.2 out of 1, which would be shown as 0.2/1

To more easily simplify this, multiply both the top and bottom by 10

0.2/1 x 10/10

You are able to do this because 10/10 is equal to 1 and multiplying by a number and  1  results in the same number.

Then you get  2 /10 . Both  2  and  10  are divisible by  2

2 /2  = 1 and  10 /2  = 5

So the final answer is 1/5

Answer:

Step-by-step explanation:

y + 20 = 3(x + 4)

y + 20 = 3x + 12

y = 3x - 8

answer is b

Answer:

-22

Step-by-step explanation:

f(x) = -x2 + 4x - 9

g(x) = x - 8,

g(f(-1))

First find f(-1)

f(-1) = - (-1)^2 + 4(-1) - 9 = -1 -4-9 = -14

The find g(-14)

g(-14) = -14-8 = -22

Answer:

The mean may not be a fair representation of the date

Step-by-step explanation:

because the average is easily influenced by outliers (very small or large values in the data set that are not typical). The median is another way to measure the center of a numerical data set. ... Thus, the median is truly the middle of the data set.

Answer: Top row: -8. 2nd row: 1, -9. 3rd row: -5, 6, -15. 4th row: 3,-8, 14, -29.

Step-by-step explanation: Work from the bottom up.

The numbers that add up to -15 (to the left of -29) can be found by subtracting 15 from 29. 29-15=14. -29+14=-15.

The numbers that add up to -5 (to the left of -8) can be found by subtracting 5 from 8. 8-5=3. -8+3=-5.

The numbers that add up to 1 (next to -5) can be found by adding 1 and 5. 1+5=6. -5+6=1.

To find the number next to 1, add -15 and the number we just found between -5 and -15 (6). -15+6=-9.

To find the top number, add -9 and 1. -9+1=-8.

This explanation doesn't make the most sense, but it's how I found them.

Its B please brainleiest

Answer:

Let g = length of green ribbon.

So 1.5g + 6.5 = length of blue ribbon.

g + 1.5g + 6.5 = 50.25

2.5g = 43.75

g = 17.5 meters of green ribbon

1.5(17.5) + 6.5 = 32.25 meters of blue ribbon

Step-by-step explanation: Its D.

Circumference equals 2 * pi * radius. Your radius is 37 feet. So 2*2.14*37

and that equals 232.36

Final answer:

The circumference of a circular playground with a radius of 37 feet, using 3.14 for pi, is approximately 232.36 feet. The correct answer is option D.

Explanation:

To calculate the circumference of a circular playground, we can use the formula C = 2πr, where π (pi) is approximately 3.14 and r is the radius of the playground. In this case, the radius is given as 37 feet.

Substituting the values, we get:

C = 2 × 3.14 × 37

C = 2 × 3.14 × 37

C = 6.28 × 37

C ≈ 232.36 feet

Therefore, the approximate circumference of the playground is 232.36 feet.

Answer:

There is two dots above 2 if this stays correct then 2 dots above 4 is incorrect.

Step-by-step explanation:

As there is only  1 ( 2 dot ) there should not be two dots above 2.

Answer: A, x= -9

I have a site that I will tell you about if you want

Answer:

a

Step-by-step explanation:

The correct interpretation is that the slope of the line is indeed 15, indicating that the cost of one admission ticket is $15, and point (1, 15) represents the unit rate.

The correct answer is option B.

The given graph illustrates the relationship between the number of people in a group and the cost of admission tickets. The statement correctly identifies that the slope of the line on this graph represents the unit rate of admission tickets.

The slope of a line on a graph signifies the rate of change between the two variables involved. In this context, the horizontal axis (x-axis) represents the number of people in a group, while the vertical axis (y-axis) represents the cost of admission tickets.

To compute the slope, you select two points on the line. The statement correctly utilizes the points (0, 0) and (1, 15) for this purpose. The slope formula, which is the change in y divided by the change in x, is applied as follows:

Slope = (y2 - y1) / (x2 - x1)

In this instance, x1 = 0, y1 = 0, x2 = 1, and y2 = 15. Substituting these values into the formula yields:

Slope = (15 - 0) / (1 - 0) = 15 / 1 = 15

This signifies that for each additional person in the group, the cost of admission tickets increases by $15. Consequently, $15 represents the cost of one admission ticket, and the point (1, 15) represents the unit rate.

Therefore, the conclusion that option B is the answer is accurate.

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The question probable may be:

The graph below shows the relationship between the number of people in a group and the total cost of admission tickets for a circus

Answer:

[tex]\frac{9}{22}[/tex]

Step-by-step explanation:

add all qestions together 10+3+9=22

and put the number of free responces on top of the total number of qestions

[tex]\frac{9}{22\\}[/tex]

and you cant simplify it so its in its simplist form

The probability that the first question is a free response is 9/22.

Probability is used to determine how likely it is that an event would occur.  The chances that an event would happen 0 and 1. A value of 0 is attached to an event that does not occur and 1 if the event happens.

For example, if the probability that a football team plays a game. The probability that the team would win is 1 and the probability that the team would lose is 0.

The probability that the first question is a free response is the ratio of the number of free response to the total number of questions.

The probability that the first question is a free response = number of free responses / total number of questions

Number of free responses = 9

Total number of questions = 9 + 10 + 3 = 22

=9/22

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Answer: 7/3

Step-by-step explanation:

2 1/3 is in simplest form and is a mixed number. We can make this an improper fraction.

2 * 3 + 1 = 7

7/3

Answer:

7/3

Step-by-step explanation:

first you multiply the denominator by the whole number(2)

2x3=6

Then you add 1

2+1=7

Finally 7 goes up to the numerator and the denominator does not change so it stays 3

Answer:

Height, 24, 80, and cubic feet

Step-by-step explanation:

I just did this on edge-unity and it gave me that.

Area of the regular hexagon base is 24√3 square feet and the volume of the same is 80√3 cube feet.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given that,

The base of a right pyramid is regular hexagon.

Edge length of regular hexagon = 4 feet

Area of equilateral triangle with sides 4 feet = 4√3 square feet

A regular hexagon can be divided in to 6 equilateral triangles.

Area of the base of the pyramid = 6 × area of an equilateral triangle

                                                     = 6 × 4√3

                                                     = 24√3 square feet

The volume of a hexagonal pyramid = [tex]\frac{\sqrt{3} }{2}[/tex] b² h

where h is the height and b is the edge length of the base.

Height of the pyramid = 10 feet and b = 4 feet

Volume = [tex]\frac{\sqrt{3} }{2}[/tex] 4² × 10 = 80√3 cube feet

Hence the area of the base is 24√3 square feet and volume is 80√3 cube feet.

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When you decrease £262 by 39% using the multiplier method, you get £159.82 as the result.

To decrease £262 by 39% using the multiplier method, follow these steps:

Convert the percentage decrease to a decimal:

39% = 0.39

Calculate the multiplier (the factor by which you'll multiply the original amount to decrease it):

Multiplier = 1 - Percentage Decrease (as a decimal)

Multiplier = 1 - 0.39

Multiplier = 0.61

Multiply the original amount by the multiplier to find the decreased amount:

Decreased Amount = Original Amount × Multiplier

Decreased Amount = £262 × 0.61

Now, calculate the decreased amount:

Decreased Amount = £159.82

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Answer:

Step-by-step explanation:

The wind speed can be found using the Law of Cosines. It will be the unknown side of a triangle with sides 6 and 5 and included angle 30°.

  s^2 = 6^2 +5^2 -2·6·5·cos(30°) ≈ 9.038476

  s ≈ √9.038476 ≈ 3.0064 . . . . m/s

The direction of the wind can be found from the Law of Sines, which tells us the relationship of the internal angle A to velocity vector a is ...

  sin(A)/a = sin(30°)/3.0064

  A = arcsin(5/3.0064·sin(30°) ≈ 56.26°

To find the desired angle, we must add 180° to this value.

The wind is blowing 3.0 m/s in direction 236.3°.

Answer:

11

Step-by-step explanation:

Let his age be x then the opposite of his age is - x, then

- x + 38 = 27 ( subtract 38 from both sides )

- x = - 11 ( multiply both sides by - 1 )

x = 11

Thus he is 11 years old

Answer:

Step-by-step explanation:

hello :

y = 6x - 10 (*)

2x + 3y = 10...(**)

by (*) put this value of y into (**) : 2x+3(6x-10)=10

2x+18x-30 = 10

20x=40  so :  x= 2  but  y = 6x - 10        y = 6(2)-10 =2

one solutions (2,2)

Answer:

147/20 = 7,35

Step-by-step explanation:

6/5 × 7/4 × 7/2 = 3/5 × 7/4 × 7 = 147/20 = 7,35

Final answer:

To estimate the square root of 27, find the two nearest perfect squares which are 25 (5 squared) and 36 (6 squared). Since 27 is closer to 25, the square root of 27 is estimated to be 5.

Explanation:

To estimate the square root of 27 to the nearest whole number, we should look for two consecutive perfect squares between which 27 lies. The perfect squares closest to 27 are 25 (which is 5 squared) and 36 (which is 6 squared). The square root of 25 is 5 and the square root of 36 is 6. Since 27 is closer to 25 than to 36, we estimate that the square root of 27 is closer to 5. But, because 27 is more than 25, we know it must be slightly greater than 5, so the nearest whole number would be 5.

Answer:

1/15 of their time is free time.

Step-by-step explanation:

To find the answer to this 2-step problem, we have to add all the fractions up, then find how much of that time is not part of the fraction.

So to add all the fractions, you have the equation:

1/4 + 3/5 + 1/12

The first thing we have to do is to find a common denominator.

4, 5, and 12 are each able to multiply into 60.

So we can make the equation now with a common denominator.

15/60+36/60+5/60=56/60.

We now can simplfy this.

56/60=14/15

Now that we know how long it is to do all the other activities, it tells us that the rest of the time is free time. To find the rest of the time, we have to do:

1-14/15=1/15

So 1/15 of their time is free time.

The total time spent is 14/15 and the free time is 1/15 if students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1'12 studying.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

At boarding school, students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1/12 studying

Add all the fractions:

= 1/4 + 3/5 + 1/12

= 14/15

Free time = 1 - 14/15

= 1/15

Thus, the total time spent is 14/15 and the free time is 1/15 if students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1'12 studying.

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Answer:

D (option 4)

Step-by-step explanation:

Difference of medians:

110 - 80 = 30

Ranges:

Johnston: 140 - 80 = 60

30 = ½(60)

Martinville: 120 - 40 = 80

30 = ⅜(80)

Answer:

Divide both sides by "R".

V = IR

V/R = I

Step-by-step explanation: