Find the exact solution to the equation 42 equals 3 x squared, leaving your answer in square root form. Show your work.
State if your solution is rational or irrational. Explain.
Find the closest integer approximation to your solution and explain how you found it.

Answer:

Step-by-step explanation:

To solve the equation of 7/3x+1/3x=1+5/3x, isolate the term of x from one side of the equation.

First, you subtract by 5/3x from both sides.

[tex]\rightarrow \sf{\dfrac{7}{3}x+\dfrac{1}{3}x-\dfrac{5}{3}x=1+\dfrac{5}{3}x-\dfrac{5}{3}x}[/tex]

Solve.

[tex]\rightarrow \boxed{\sf{x=1}}[/tex]

Therefore, the solution is x=1, which is our answer.

I hope this helps, let me know if you have any questions.

David takes a car to get to the airport in time for his trip. 210 miles distance is the airport from his house in miles.

Given that,

David takes a car to get to the airport in time for his trip. He travels 35 miles in the first hour but understands that if he keeps going at this rate, he will be one hour late. For the final 15 miles to the airport, he speeds up by 15 mph and gets there 30 minutes early.

We have to find how far is the airport from his house in miles.

Distance traveled after 1 hour

Let us take the distance traveled after first 1 hour as y

Distance/speed = time

After 1 hour his speed = (35 + 15) = 50 mph

Total time count of 1 hour and 30 mins is 1.5 hr

y/50 + 1.5 = y/35

Multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Therefore, the distance between David's home and the airport is 210 miles.

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Answer:

Step 3

Step-by-step explanation:

The mistake was made in Step 3.

Center of circle = (-3, 6)

Diameter = 6

General equation of circle: x² + y² = r²

our answer will be in the form:

(x+a)² + (y+b)² = r²

Substitute center values and radius:

a = 3 (x was -3 but we don't trust it! It should be positive instead of negative)

b = -6 (same rules apply. Don't trust the value in the center. Its the opposite.)

r = 6/2 which is 3

answer: (x+3)² + (y-6)² = 3²

Recall the definition of the cosecant function in terms of the sine function:

Draw the angle -210º in the unit circle to find a reference triangle for that angle:

Notice that a 30-60-90 triangle is formed:

Since the side opposite to the 30º angle has a length of 1/2, then:

On the other hand, notice that since the angle of -210º lies in the second quadrant, then the value of sin(-210º) is positive:

Use the definition of the cosecant function to find csc(-210º):

Therefore, the value of csc(-210º) is equal to 2.

Answer:

Step-by-step explanation:

The formula is :

(y - y1) = m(x - x1)

the given values are x1 = 19, y1 = -12 and m = slope = -3

putting values

(y + 12)= -3(x-19)

y + 12 = -3x +57

y+ 3x - 35 = 0

This is the required equation.

The value of the coordinates of the median AM is (0.5, -1.5)

Given: A(0,1), B(1, -4), C(5,2)

Consider the image attached:

The distance AM is the midpoint of the distance AB. So we can use the midpoint formula:

Xm = (Xa + Xb) /2 and Ym = Ya + Yb/2

Where Xm and Ym are the x and y coordinates of the midpoint M

SInce A(0,1): Xa = 0, Ya = 1

Also B(1, -4);  Xb = 1, Yb = -4

Xm = 0 + 1/2 = 1/2 = 0.5

Ym = 1 + (- 4)/2  = -3/2 = -1.5

Therefore, the coordinates of the median AM is (0.5, -1.5)

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Answer:

y=2x+5, y=4x, y=-3+9/2x

Step-by-step explanation:

8x+4y=20 turns into:

y=2x+5

3y-12x=0 turns into:

y=4x

9x-2y=6 turns into:

y=-3+9/2x

W+(9+3) is the equivalent expression of  (w+9)+3 by using associate property

An expression is combination of variables, numbers and operators.

The given expression is (w+9)+3

The operator in given expression is plus and variable is W.

The associative property of addition states that Changing the grouping of addends does not change the sum.

(x+y)+z=x+(y+z)

Similarly (W+9)+3=W+(9+3)

W+(9+3) is the equivalent expression of  (w+9)+3 by using associate property

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Answer: Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles. They are seen everywhere, for example, in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines.

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

both sides are 14 and the other triangle is 7 so 14/7=2 and 18/2=9

All the rational numbers are;

2. - √25

4. 100

5. √0.36

6. √0.0144

7. √36

8. √ 49

What is Rational number?

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Given that;

All the numbers are,

1. √75

2. - √25

3. 2√7

4. 100

5. √0.36

6. √0.0144

7. √36

8. √ 49

Now,

1. √75 = 8.660250

Clearly, It cannot be written as the form of p / q.

So, It is not a rational number.

2.  - √25 = - 5

It can be written as;

- √25 = - 5 / 1

So, It is a rational number.

3. 2√7

Since,  √7 is an irrational number.

So, 2√7 is not a rational number.

4. 100

It can be written as;

100 / 1

So, It is a rational number.

5. √0.36 = 0.6

              = 6 / 10

              = 3 / 5

Thus, It is a rational number.

6. √0.0144 = 0.12

                 = 12 / 100

                 = 3 / 25

So, It is a rational number.

7. √36 = 6

          = 6 / 1

So, It is a rational number.

8. √ 49 = 7      

            = 7 / 1

So, It is a rational number.

Therefore, All the rational numbers are;

2. - √25

4. 100

5. √0.36

6. √0.0144

7. √36

8. √ 49

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The order of the outcomes is irrelevant when calculating the total outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations.

15 different 2-member committees are possible.

C(6,2) = 6!/(4!2!) = 15.

15 different 2-member committees are possible.

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EXPLANATION

Since the vertex is at (-1, -3), the only appropriate option is to translate the function one unit to the left, and again translating 3 units down, with the following form:

g(x) = |x+1| - 3

Therefore, the solution is the last option.

Answer:

18

Step-by-step explanation:

The range is the biggest number minus the smallest number.

The biggest number is 12.

The smallest number is -6 .

Range = 12-(-6) = 18

test of 250 questions

40% of the fist 125 are ok, this means that 125(0.4) = 50 questions of the first 125 are ok

If jassi needs 60% of the 250 ok, that is 250(0.6) = 150

If of the first half she already has 50 questions ok, and needs 150, she needs to have 100 questions our of the second 125

If she needs 100 out of 125, this percent is 100/125 = 0.8, this means 80%

Answer:

Jassi needs 80% of the second 125 questions to be ok

Answer:[tex]\left(x^2+1\right)\left(5x^6-5x^4+5x^2-6\right)[/tex]

Step-by-step explanation:

Answer:

b = 18

The mortar is 17 times ( 3 / 8 ) tall.

The brick height is equal to 18 times ( 2 + ( 1 / 4 ) ).

I don't know the options, so you have to use those values.

Step-by-step explanation:

The question uses imperial units which are generally bad.

12 inches = 1 feet;

The height of the wall should be written in inches for convenience.

4 feet = 4 * 12 inches;

4 feet = 48 inches;

The wall is short 1 + ( 1 / 8 ) inches short of 4 feet.

48 inches - ( 1 + ( 1 / 8 ) inches ) = 46 + ( 7 / 8 ) inches;

Now that the wall is done let's do the bricks. The height of the bricks is 2 + ( 1 / 4 ) inches and the mortar is ( 3 / 8 ) inches tall. The amount of mortar is the number of bricks - 1 because nobody puts extra mortar on the top of the wall.

let b;

46 + ( 7 / 8 ) = b( 2 + ( 1 / 4 ) ) + ( b - 1 )( 3 / 8 );

375 / 8 = b( 9 / 4 ) + ( 3 / 8 )b - ( 3 / 8 );

375 / 8 = ( ( 9 / 4 ) + ( 3 / 8 ) )b - ( 3 / 8 );

375 / 8 = ( ( 18 / 8 ) + ( 3 / 8 ) )b - ( 3 / 8 );

375 / 8 = ( 21 / 8 )b - ( 3 / 8 );

Multiply both sides by 8 to get rid of those annoying fractions.

375 = 21b - 3;

Add 3 to both sides.

378 = 21b;

Divide both sides by 21.

18 = b;

The probability that the sample mean would differ from the true mean by more than $2.5 is 0.0062

Mean cost of the five pound shrimp bag = $40

Variance of the five pound shrimp bag = $36

The number of the shrimp bag = 43

The given mean value = $2.5

The z-score = $2.5

The probability of the sample mean differ by $2.5 from the true mean can be calculated by

  P(z > 2.5) = 1 - P(z < 2.5)

From the z table , we can get the value of  z < 2.5 which is 0.9938

    P(z > 2.5) = 1 - 0.9938

   P(z > 2.5) = 0.0062

Therefore , the probability of sample mean from the true mean by 2.5 is 0.0062

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Answer: W=−1/10

Step-by-step explanation:

Move all terms not containing

W

to the right side of the equation.

Exact Form:

W=−1/10

Decimal Form:

W=−0.1

The addition symbol (+) can be used in between the two parentheses to show that you will be using the distributive property.

Distributive property:

The distributive property states that multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

It can be written as,

a x (b + c) = (a x b) + (a x c)

Where a, b and c are the values of the variables.

Given,

Here we have the expression:

8 x 57 = (8 x 50) _____(8x7)

Here we need to find the symbol that can be used in between the two parentheses to show that it will be using the distributive property.

Based on the definition of the distributive property we have know that the symbol (+) can be used to make this one as distributive property used equation.

Therefore, the expression is written as,

8 x 57 = (8 x 50) + (8x7)

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Answer:

x = ?

Step-by-step explanation:

Since there are two congruent angles, their respective sides are also congruent (an angle's respective side is the side opposing it, the side that it does not touch). Meaning, the 3x-7 side is congruent to the 2x side.

So just set them equal to each other to find x.

3x - 7 = 2x

x = ? (You can do this. Solve for x algebraically.)

The 4x-10 doesn't really matter here since you just need to find x.

Answer: 26.25%  basketball practice

Step-by-step explanation: At basketball practice I made 21 out of 80 shots.

Therefore the percentage of shots I made is = 21/80×100%

                                                                          =26.25%

Its a bill question , and percentages

20% of $90.00 .

then 10% of $90 is 9 dollars

so then 2x10% = 20% of $90 is 2x9= 18 dollars

Now add then original pay to tip Pay ,

then

Pay original + Tip = $90 + 18 = $108 dollars

For all the given reactions there is a type name for it they are,

1. A + B → AB

2. AB → A + B

3. Hydrocarbon + O₂ → CO₂ + H₂O

4. AB + CD → AD + CB

All the above-mentioned chemical reactions are of the following types

1 → Synthesis

2 → Decomposition

3 → Combustion

4 → Replacement

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As a first step we are going to isolate y in both equations:

(1) y=7x-2

(2) -2y=-14x+3

y=7x-3/2

Since they have the same slope 7, that mean these lines are parallel

By definition, a Right triangle is a triangle that has an angle whose measure is 90 degrees (which is also called "Right angle").

You can identify that the triangle STU is a Right triangle, because:

The following is one of the Trigonometric ratios. It's called "Secant":

In this case you can identify that:

Then, substituting values, you get that the answer is:

Answer:

Domain: [0,∞)

Range: (-∞,4]

Step-by-step explanation:

The domain is the numbers along the x-axis, and the range is the numbers along the y-axis. This graph includes a domain from zero to infinity and a range from negative infinity to four. The parentheses () mean that these numbers aren't included, and since infinity isn't an actual number, it gets a parenthesis. The brackets [ ] are used to include a number exactly. Since four and zero are real numbers and are included in this graph they get brackets. We also know that four and zero are included because the dot at point (0,4) is solid and not hollow, which means those numbers are to be included in the domain and the range. Also something to note: you always write the domain and range going from the smallest number to the largest number, this is why the range is written as (-∞, 4] and not [4, -∞).

The area of the rectangle is, 128 square inches.

What is perimeter, area?

The area of a shape or figure is the area it occupies, whereas the perimeter of a shape is the distance it encircles on all sides. 

The square unit or unit2 is used as the unit of area, and the unit is also used for the perimeter.

Given: A rectangle has a length that is twice the size of its width. The perimeter of the rectangle is 48 inches.

Suppose the width of the rectangle is x.

So, the length is 2x.

As perimeter is 48 inches.

So, x + x + 2x + 2x = 48

6x = 48

x = 8 inch.

The width of the rectangle is 8 inches.

Therefore, the length of the rectangle is 2x = 2(8) = 16 inches.

Now to find area of the rectangle,

Since,

Area of rectangle =  length x width

                             =  16 x 8

Area of rectangle = 128 inch^2.

Therefore, the area of the rectangle is 128 square inches.

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