2x squared minus 1 equals 21​

Answer:

180.55 in².

Step-by-step explanation:

Data obtained from the question include the following:

Height (h) = 9 in.

Diameter (d) = 5 in

Pi (π) = 3.14

Area of the label =..?

Next, we shall determine the radius.

Diameter (d) = 5 in

Radius (r) =.. ?

Radius (r) = Diameter (d) /2

r = d/2

r = 5/2

r = 2.5 in.

Next, we shall determine the area of the label that needs to be printed to go around the new container by calculating the surface area of the cylinder.

This is illustrated below:

Height (h) = 9 in.

Pi (π) = 3.14

Radius (r) = 2.5 in.

Surface Area (SA) =.?

SA = 2πrh + 2πr²

SA = (2×3.14×2.5×9) + (2×3.14×2.5²)

SA = 141.3 + 39.25

SA = 180.55 in²

The surface area of the cylinder is 180.55 in².

Therefore, the area of the label that needs to be printed to go around the new container is 180.55 in².

Answer:

Step-by-step explanation:

i dont have the work but the answer is 182.6

Answer:

200 ft^2

Step-by-step explanation:

The surface area of the pyramid is the sum of the area of the base and the areas of the 4 congruent triangular sides.

SA = LW + 4 * bh/2

SA = 10 ft * 10 ft + 4 * (10 ft)(5 ft)/2

SA = 100 ft^2 + 2(50 ft^2)

SA = 200 ft^2

(P.S. It's impossible to make a pyramid with these dimensions.)

Answer:

[tex]\boxed{\sf 200 \ feet^2}[/tex]

Step-by-step explanation:

The 3D shape is a square-based pyramid.

The surface area of a square-based pyramid is given as:

[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]

Plug in the values.

[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]

[tex]\sf SA=100 + 100[/tex]

[tex]\sf SA=200[/tex]

Answer:

240 mL.

Step-by-step explanation:

The following data were obtained from the question:

Ratio of Flour = 5

Ratio of brown sugar = 3

Ratio of chocolate = 4

Total volume = 720 mL

Next, we shall determine the total ratio. This can be obtained as follow:

Total ratio = ratio of flour + ratio of brown sugar + ratio of chocolate

Total ratio = 5 + 3 + 4

Total ratio = 12

Finally, we shall determine the volume of the chocolate chips in the mixture as shown below:

Volume of chocolate chips = ratio of chocolate /total ratio x total volume

Ratio of chocolate = 4

Total ratio = 12

Total volume = 720 mL

Volume of chocolate chips =..?

Volume of chocolate chips = ratio of chocolate /total ratio x total volume

Volume of chocolate chip = 4/12 x 720

Volume of chocolate chip = 240 mL

Therefore, the volume of the chocolate chips in the mixture is 240 mL.

Answer:

son2: 5

son1: 10

Step-by-step explanation:

2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59

3x = 15

x = 5

The age of each boy at present will be 2 years and 3 years.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Let the age of the sons will be x and y.

A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be

x = 2y

In 3 years, the sum of all their ages will be 59 years. Then the equation will be

x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59

Simplify the equation, we have

3x + 3y + 41 = 59

      6y + 3y = 59 – 41

              9y = 18

                y = 2

Then the value of x will be

x = 2y

x = 2(2)

x = 4

Thus, the age of each boy at present will be 2 years and 3 years.

More about the linear system link is given below.

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Answer:

24 square units

Step-by-step explanation:

Use the formula for area of a parallelogram to solve.  The base is 6 units, and the height is 4 units.

A = bh

A = (6)(4)

A = 24 square units

The area of the parallelogram is 24 square units.

Answer:

The answer to this question can be defined as follows:

In option A, the answer is "- 357.14 miles per hour".  

In option B, the answer is "-0.98".

Step-by-step explanation:

Given:

[tex]\frac{dx}{dt} =- 300 \text{ miles per hour}[/tex]

[tex]\frac{dy}{dt} =- 400 \text{ miles per hour}[/tex]

find:

[tex]\frac{ds}{dt} =?[/tex] when

[tex]x= 150 \\y= 200\\s=x+y\\\\[/tex]

  [tex]= 150+200 \\\\=350[/tex]

[tex]\to s^2=x^2+y^2\\[/tex]

differentiate the above value:

[tex]\to 2s\frac{ds}{dt}= 2x \frac{dx}{dt}+2y \frac{dy}{dt}[/tex]

[tex]\to 2s\frac{ds}{dt}= 2(x \frac{dx}{dt}+y \frac{dy}{dt})\\\\\to \frac{ds}{dt}= \frac{(x \frac{dx}{dt}+y \frac{dy}{dt})}{s}\\\\[/tex]

        [tex]= \frac{(150 \times -300 +200 \times -400 )}{350}\\\\= \frac{-45000+ (-80000) }{350}\\\\= \frac{- 125000 }{350}\\\\= - 357.14 \ \text{miles per hour}[/tex]

In option B:

[tex]\to d=rt\\\\ \to t= \frac{d}{r}[/tex]

[tex]\to \ \ d= 350 \ \ \ \ \ \ r= -357.14\\[/tex]

[tex]\to t= - \frac{350}{357.14}\\\\\to t= - 0.98[/tex]

That's true. Pi is known to be defined as the ratio of the circumference of a circle to its diameter.

Answer:

100, 101, 102, 103, 104

Step-by-step explanation:

Basically, if the units (or ones, it's the same thing) digit of the first number is 0, the units digit of the second number should be 1, then 2, and so on. Therefore, one possible list of numbers is as follows: 100, 101, 102, 103, 104.

it is [tex]\pi[/tex]

since period of tangent is $\pi$ ,so the period of reciprocal will also be same

The period for the cotangent function is π radians.

The period for function y = A sin(Bx + C) and y = A cos(Bx + C) is 2π/|B| radians. Frequency is described as the wide variety of cycles completed in one 2d. If the duration of a function is denoted via P and f is its frequency, then –f =1/ P.

The tangent function has period π. f(x)=Atan(Bx−C)+D is a tangent with vertical and/or horizontal stretch/compression and shift. The cotangent function has period π and vertical asymptotes at 0,±π,±2π, The range of cotangent is (−∞,∞), and the function is decreasing at each point in its range.

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Answer:

12 inches

Step-by-step explanation:

A=1/2bh

30=1/2b5

(30*2)/5=b

B=12

Answer:

Each team will get 3 eggs

Step-by-step explanation:

First determine the number of eggs

7 * 12 = 84 eggs

Then divide by the number of teams

84/26 =3 with 6 left over

Each team will get 3 eggs

Answer:

[tex]\huge\boxed{Step \ 3}[/tex]

Step-by-step explanation:

In Step # 3, We need to divide rather than to subtract. So, the first mistake is done in step 3.

Answer:

[tex]\Large \boxed{\mathrm{Step \ 4}}[/tex]

Step-by-step explanation:

[tex]20 +20 \div 4-2[/tex]

Division should be performed first, not subtraction.

[tex]20+5-2[/tex]

1. (a) 0 = x² + 4x - 12 (Switch Sides)

x² + 4x - 12 = 0 (Factor Expression)

(x - 2)(x + 6) = 0 (Apply the Zero Factor Principle)

x = 2, and x = - 6

x - intercept : (2, 0) and ( - 6, 0)

(b) y = (0)² + 4(0) - 12 (Simplify)

y = 0 + 4 * 0 - 12 = 0 + 0 - 12 = - 12

y - intercept : (0, - 12)

(c) Our vertex belongs to an upward facing parabola, and hence it will be a minimum, of ( - 2, - 16).

2. Seth's solution is not accurate. He did the calculations accurately, and ended up with x = 3 and x = - 2. However he forgot to substitute those values back into the equations y = x² + 3x - 5 and y = 4x + 1, solving for the y values. Instead of being ( - 2, 0) and (3, 0) it should have been (3, 13), ( - 2, - 7)...

y = (3)² + 3(3) - 5 = 9 + 9 - 5 = 18 - 5 = 13,

y = 4( - 2) + 1 = - 8 + 1 = - 7

Hence we get the solutions (3, 13) and ( - 2, - 7).

Answer:

d. -4

Step-by-step explanation:

Let's plug in g

8 - |2(-3.5) - 5|

8 - |-7-5|

8 - |-12|

The absolute value is always positive of any number,

8 - 12

= -4

Answer:

D. -4

Step-by-step explanation:

We are given this expression:

[tex]8-|2g-5|[/tex]

and asked to evaluate when g= -3.5 Therefore, we must substitute -3.5 in for g.

[tex]8-|2(-3.5)-5|[/tex]

First, multiply 2 and -3.5

2 * -3.5 = -7

[tex]8-|-7-5|[/tex]

Next, subtract 5 from -7.

-7-5= -12

[tex]8-|-12|[/tex]

Next, evaluate the absolute value of -12. The absolute value is how far away a number is from 0, and it is always positive. The absolute value of -12 is 12.

[tex]8-12[/tex]

Subtract 12 from 8.

[tex]-4[/tex]

The value of the expression is -4 and D is the correct answer.

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

We can represent each ratio as a fraction, then use the cross products property to find the value of x.

[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]

Hope this helped!

Answer:

60 ships.

Step-by-step explanation:

Let the total number of ships in the naval fleet be represented by x

One-third of the fleet was captured = 1/3x

One-sixth was sunk = 1/6x

Two ships were destroyed by fire = 2

Let surviving ships be represented by y

One-seventh of the surviving ships were lost in a storm after the battle = 1/7y

Finally, the twenty-four remaining ships sailed home

The 24 remaining ships that sailed home =

y - 1/7y = 6/7y of the surviving fleet sailed home.

Hence

24 = 6/7y

24 = 6y/7

24 × 7/ 6

y = 168/6

y = 28

Therefore, total number of ships that survived is 28.

Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4

Total number of ships in the fleet(x) =

x = 1/3x + 1/6x + 2 + 28

Collect like terms

x - (1/3x + 1/6x) = 30

x - (1/2x) = 30

1/2x = 30

x = 30 ÷ 1/2

x = 30 × 2

x = 60

Therefore, ships that were in the fleet before the engagement were 60 ships.

Answer:

1.75 seconds

Step-by-step explanation:

Lets apply the quadratic formula-

- 8 +_ (sqrt of 64 + 19.6)

__________________

-9.8

-8 +_  9.1433

__________________

-9.8

x = 1.74931972 ( since x can only be positive in real life situations like when throwing a ball)

x = 1.75 rounded in seconds

Answer:

Step-by-step explanation:

h(t)= -8±√8^2-4(-4.9)(1)/2(-4.9)

h(t)=-8±√64-19.6/ -9.8

h(t)=-8±√44.4 / -9.8

h(t)=-8±6.6633325/ -9.8

h(t)= 0.14

The height will be 0.14

The time will be 2.02 seconds per meter

Hope that helps.

Answer:

v = -54

Step-by-step explanation:

27= -v/2

Multiply each side by -2

27 *-2= -v/2 *-2

-54 = v

Answer:

-54

Step-by-step explanation:

[tex]27=\frac{-v}{2}[/tex] .... Equation to start with

[tex]27 x 2= \frac{-v}{2} x2[/tex] ..... Cancelling out the denominator and multiplying on the other side

[tex]54 = -v[/tex] .... Multipling

[tex]-54 =v[/tex] ..... Solving for v, not -v, so bring the negative over to the other side

Hope you understood:)

Answer:

( 6,6) is outside

Step-by-step explanation:

(x - 2)^2 + (y - 1)^2 = 25

This is of the form

(x - h)^2 + (y - k)^2 = r^2

where ( h,k) is the center and r is the radius

(x - 2)^2 + (y - 1)^2 = 5^2

The center is at ( 2,1) and the radius is 5

P(0,5), Q(2,2) R(5,-2), and S(6,6)

Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)

( 6,6) is outside the circle

15552|2

7776|2

3888|2

1944|2

972|2

486|2

243|3

81|3

27|3

9|3

3|3

1

[tex]15552=2^6\cdot 3^5=(2^3\cdot3^2)^2\cdot 3[/tex]

[tex](3+1)\cdot(2+1)=4\cdot 3=12[/tex]

It's 12

Answer:

Y*x -2x=40min

Answer:

1. no solution 2. has one solution

Step-by-step explanation:

first you must find the discriminant of each quadratic also remember

if the discriminant is positive  b^{2}-4ac> 0, then the quadratic equation has two solutions.

if the discriminant is equal  b^{2}-4ac= 0, then the quadratic equation has one solution.

if the discriminant is negative  b^{2}-4ac< 0, then the quadratic equation has no solution.

1. the discriminant is [tex]\sqrt{b^2-4ac}[/tex] and when you plug in the numbers you get -55 which is less than 0

2. the discriminant is 0 so there is one solution

Answer:

1. has no real roots, no solutions (unless you can have imaginary solutions)

2. touches the x axis in one point, so one solution

Step-by-step explanation:

500/3 π units

Step-by-step explanation

first state the formula wic is 4/3πr^3 then after u multiply 4 times the radius wic is

4×5^3

=500/3π units

Answer:

0.25%

Step-by-step explanation:

Rate of commission

= (commission*100)/cost of land

=( 20000*100)/8000000

= 2000000/8000000

=2/8

= 0.25%

Answer:

4/5

Step-by-step explanation:

[tex]800 - 160 = 640 \\ \frac{640}{800} = \frac{4}{5} [/tex]

Answer:

Number of 50sen coins  =  13

Step-by-step explanation:

Let the number of 50sen coins be = x

Let the number of 20sen coins be  = y

Total coins  = 20

x + y = 20 ----------------------(i)

Value of 50sen coins = 0.50*x = 0.50x

Value of 20sen coins = 0.20 *y = 0.20y

Total value = RM 6.10

0.5x + 0.2y = 6.10 -------------------(ii)

Multiply (i) by (-0.5) and then add the equations. So, x will be eliminated and we can find the value of y

(i) * (-0.5)      -0.5x - 0.5y = -10

(ii)                  0.5x  + 0.2y = 6.10 { add and now x will be eliminated}

                              - 0.3y = -3.90

Divide both sides by (-0.3)

y = -3.90/-0.3

y = 13

Plug in the value of y in equation (i)

x + 13 = 20

Subtract 13 from both sides

x = 20 -13

x = 7

Number of 50sen coins  =  13

Answer:

the number of 50sen coins:

x = 7

Step-by-step explanation:

Taking the number of 50sen coins as x

50(x)

∴ the number of 20sen coins is 20-x (as total no. of coins are 20)

20(20-x)

total amount = 6.10RM = 610sen

equating:

50x + 20(20-x) = 610

50x + 400-20x = 610

50x - 20x = 610-400

30x = 210

x = 210/30 = 7

Therefore, the number of 50sen coins is 7

20sen coins is 20-7= 13.

verification=

50*7 + 20*13 = 610

310 + 260 = 610

610sen = 610sen

6.10RM = 6.10RM

L.H.S = R.H.S

hence, verified.

Answer:

30.0g

Step-by-step explanation:

In order to determine the amount of each chemical to the nearest tenth of gram prior to computing the sum is shown below:

Like

10.357, 57 > 50, rounded to 10.4

12.062, 62 > 50, rounded to 12.1

7.506, 06 < 50, rounded to 7.5

Now

The Sum is

= 10.4g + 12.1g + 7.5g

= 30.0g

Hence, 30.0g medicine required to make in grams

Answer:

A. 48

Step-by-step explanation:

There is a diameter of the circle through point O. The bottom right angle is an inscribed and that intersects a diameter, so its measure is 90 deg.

a + 90 + 42 = 180

a + 132 = 180

a = 48

The measure of angle 'a' is 48°.

We need to find the measure of 'a'.

Angles are formed by drawing lines from the ends of the diameter of a circle to its circumference from a right angle.

There is a diameter of the circle through point O. The bottom right angle is inscribed and that intersects a diameter, so its measure is 90°.

Now, a + 90°+ 42° = 180°

⇒a + 132°= 180°

⇒a = 48°

Therefore, the measure of angle 'a' is 48°.

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Answer:

1. -y

3. 9a-7

5. 14x-2

7. 7d-6

Step-by-step explanation:

1. 8y-9y=-y

3. 8a-6+a-1

=(8a+a)-(6+1)

=9a-7

5. -x-2+15x

=(-x+15x)-2

=14x-2

7. 8d-4-d-2

=(8d-d)-(4+2)

=7d-6

Answer:

1. -x

3. 9a-7

5. 14x-2

7. 7d-6

Step-by-step explanation:

To do the first one you would just subtract 8 by 9 which is -1 so you would get -x as 1.

To do the third one would would just move the numbers around so you get 8a+a-6-1 and when you simplify you get 9a-7.

To do the fifth one you just have to move the numbers so you get -x+15x-2 and when you simplify you get 14x-2

To do the seventh one you just have to move the numbers so you get 8d-d-4-2 and when you simplify you get 7d-6.

Answer:

a. Please check the explanation for filling of the empty column on the table

b. The mean of the random variable x is 7/11

Step-by-step explanation:

a. Firstly, we are concerned with completing the table.

To do this, we simply need to multiply the values in the column of x by the values in the column of p(x)

Thus, we have the following;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

b. We want to find the mean of the random variable x.

All what we need to do here is add all the values of x•P(x) together, then divide by 11.

Thus, we have

(2/36 + 6/36 + 12/36 + 20/36 + 30/36 + 42/36 + 40/36 + 36/36 + 30/36 + 22/36 + 12/36)/11

Since the denominator is same for all, we simply add all the numerators together;

(252/36) * 11 = 252/396 = 63/99 = 7/11