Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?

Answer:

x^2 +3

Step-by-step explanation:

f(x) = 2x^2 + 2

g(x) = x2 – 1,

find (f – g)(X).

f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)

Distribute the minus sign

             = 2x^2 +2 -x^2 +1

             = x^2 +3

Answer: Speed = 5.6 mph

              Oxygen consumption = 71.6 mL/lb/min

Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:

f(x) = g(x)

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10[/tex]

Resolving:

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0[/tex]

[tex]\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0[/tex]

[tex]\frac{5}{3}x^{2} - \frac{28x}{3}=0[/tex]

[tex]\frac{x}{3}(5x - 28)=0[/tex]

[tex]\frac{x}{3} = 0[/tex]

x=0

5x - 28 = 0

[tex]x = \frac{28}{5}[/tex]

x = 5.6

The speed when the oxygen consuption is the same is 5.6 mph.

For the level of oxygen consumption:

f(5.6) = g(5.6)

g(5.6) = 11*5.6 + 10

g(5.6) = 71.6

The level of oxygen consumption is 71.6 mL/lb/min

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption is 71.6 milliliter per pound per minute

The oxygen consumption for a person walking at x mph is given by,

             [tex]f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10[/tex]

The oxygen consumption for a runner at x mph is approximated given by the function,

             [tex]g(x)=11x+10[/tex]

To be oxygen consumption same for both walker and runner, both function must be equal.

             [tex]f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph[/tex]

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption at that speed is,

             [tex]g(5.6)=11(5.6)+10=71.6[/tex]

Learn more:

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Answer:

[tex]\boxed{\sf A. \ 0.34}[/tex]

Step-by-step explanation:

The first triangle is a right triangle and it has one acute angle of 70 degrees.

We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.

The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.

The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.

[tex]\sf \frac{3.4}{10} =0.34[/tex]

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

Answer:

13

Step-by-step explanation:

We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is [tex]13^{3}[/tex]. This will go inside of your cube root. You now have [tex]\sqrt[3]{13^{3} }[/tex]. Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.

Answer:

[tex]\boxed{13}[/tex]

Step-by-step explanation:

=> [tex]\sqrt[3]{2197}[/tex]

Factorizing 2197 gives 13 * 13 * 13

=> [tex]\sqrt[3]{13*13*13}[/tex]

=> [tex]\sqrt[3]{13^3}[/tex]

We know that [tex]\sqrt[3]{} = ^{1/3}[/tex]

=> [tex]13^{3 * 1/3}[/tex]

=> [tex]13^1[/tex]

=> 13

Answer:

52 dimes and 54 nickels

Step-by-step explanation: 52 dimes is $5.20 and 54 nickels is $2.70

Total coins 106 total $7.90

Answer: 1unit.

Step-by-step explanation:

Area of the rectangle

A = length × width

Since the area = 20 and the width is x and the length is x + 1.

We now substitute for the values in the above formula and solve for x

20 = x × x + 1

20 = x( x + 1 ), we now open

20 = x² + x , then re arrange.

x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means

Here, I am going to solve using factorization by grouping

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x( x + 5 ) - 4( x + 5 ) = 0

( x + 5 )( x - 4 ). = 0

Therefore, the solution for x will be

x = -5 or 4, but x can not be -5 ( negative), so x = 4.

Now the difference between width and the length can easily be calculated from the above,

Width = 4 (x) , and length = 5 (4 + 1),

Now difference will be

5 - 4 = 1unit.

Answer:

viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.

"cooling the fluid raises its viscosity"

a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.

plural noun: viscosities

"silicone oils can be obtained with different viscosities"

Step-by-step explanation:

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)

Answer:

O An oil's resistance to flow at different temperatures

Step-by-step explanation:

Internal friction of a moving fluid .

Answer:

$153

Step-by-step explanation:

Since she claimed two exemptions, Grace Kelly income's tax will only be $153, and $1847 being the yearly take home.

Effective tax rate is set at 7.65%

Answer:

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Step-by-step explanation:

Using the fundamental theorem of calculus

Taking the derivative of the integral gives back the function

Since the lower limit is a constant when we take the derivative it is zero

d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]

g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))

Replacing t with x

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Answer:

63%

225 buyers

Step-by-step explanation:

To find the percent take the number that liked it over the total

376/600

Change to decimal form

.62666666

Change to percent by multiplying by 100

62.66666666%

The nearest percent is 63%

37.5 % would but it then multiply by the number of shoppers

37.5 % ( 600)

Change to decimal form

.375 * 600

225

Answer:

( 2A - kn) /k = m

Step-by-step explanation:

A = k/2(m+n)

Multiply each side by 2/k

2/k *A =2/k * k/2(m+n)

2A /k = m+n

Subtract n from each side

2A /k - n = m+n -n

2A /k - n = m

Getting a common denominator

2A/k - kn/k = m

( 2A - kn) /k = m

Answer:

Step-by-step explanation:

[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]

Answer:

(2y + 22) years

Step-by-step explanation:

kamau is now 2 years older than Jane if Janes age is y now what will be the total age in 10 years​.

Answer: If Jane is y years old now and Kamau is 2 years older than Jane, therefore the age of Kamau now would be 2 + y years.

In ten years time Jane age would be y + 10 years while the age of Kamau would be y + 2 + 10 = y + 12 years.

To get their total age we just have to add their individual age. Therefore the total age in 10 years​  = Age of Kamau in ten years + age of Jane in ten years = (y + 12) + (y + 10) = y + 12 + y + 10 = y + y + 12 + 10 = 2y + 22 years

Answer:

18.03 inches

Step-by-step explanation:

The cardboard is cut as shown below.

The line c cuts the rectangle into 2 right angled triangles.

To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:

[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]

=> c = 18.03" = 18.03 inches

The length of c, the diagonal, is 18.03 inches.

Answer:

[tex]y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]  ,  [tex]y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right][/tex]

Step-by-step explanation:

[tex]x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]    and [tex]x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right][/tex]

Using Gram-Schmidt process to produce an orthogonal basis for W

[tex]y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]

Now we know X₁ , X₂ and Y₁

Lets solve for Y₂

[tex]y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1[/tex]

see attached for the solution of Y₂

Answer:

-7/3x + 3

Step-by-step explanation:

Answer:

(9x-7)/3x or (3-7/3x)

Step-by-step explanation:

Divide each term of numerator by denominator.

-28x^5/12x^6 +36x^6/12x^6

-7/3x +3

Answer:

x=5

Step-by-step explanation:

2 − x = −3

Subtract 2 from each side

2-2 − x = −3-2

-x = -5

Multiply by -1

x = 5

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

Answer:

vol = 96

Step-by-step explanation:

Area of a triangle = 1/2 * b * h

b = 4

h = 6

A = 0.5 * 4 * 6

A = 12

length = 8

vol = Area * length

vol = 12 * 8

vol = 96

Answer:

(104 + 16 sqrt 13)

Step-by-step explanation:

i did this on my school, it was correct

Answer:

A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Step-by-step explanation:

As we know that

The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation

In mathematically

[tex]\sigma = \sqrt{variance}[/tex]

And,

[tex]variance = \sigma^2[/tex]

Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive

Hence, the correct option is a.

Answer:

B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Answer:

x=60

Step-by-step explanation:

This is an equilateral triangle which means all the sides are equal.

If all the sides are equal then all the angles are equal

180/3 = 60

x=60

Answer:

x= 60°

Step-by-step explanation:

We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°

Answer:

the amount of money Ian invested is P =  £2,500

Step-by-step explanation:

The standard formula for compound interest is given as;

[tex]A = P(1+r/n)^{nt} \\P = \frac{A}{(1+r/n)^{nt}} ...........1\\[/tex]

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case, Given that;

A = £2652.25

t = 2 years

n = 1 (semiannually)

r = 3% = 0.03

substituting the given values into equation 1;

[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]

P =  £2,500

the amount of money Ian invested is P =  £2,500

Answer:

Step-by-step explanation:

From the given question, it can be concluded that Jessica and Kayla's planes took off an hour earlier than that of Lauren and at least two hours earlier than that of Maria. This implies that Maria's plane took off last among them.

Since each person's flight last 8 hours and Maria's plane lands at 4:45 pm, then Jessica and Kayla's planes land simultaneously at least at 2:45 pm. And that of Lauren lands exactly at 3:45 pm.

Answer:

1.9375.

Step-by-step explanation:

To solve this, we must use PEMDAS.

The first things we take care of are parentheses and exponents.

Since there are no parentheses, we do exponents.

4^-1+8^-1÷1/2/3^3​

= [tex]\frac{1}{4} +\frac{1}{8} / 1/ 2/ 27[/tex]

= 1/4 + (1/8) / 1 * (27 / 2)

= 1/4 + (27 / 8) / 2

= 1/4 + (27 / 8) * (1 / 2)

= 1/4 + (27 / 16)

= 4 / 16 + 27 / 16

= 31 / 16

= 1.9375.

Hope this helps!

The correct answer is 24.5 m. You're given four different values but if you notice closely, not all the units match. Before you can add the values together, you need to get the same units. Because cm (centimeters) is the only one that's out of place, it will be easier to change it to m (meters). I think of centimeters as a century (same prefix) which equals 100. Therefore, to convert 300 cm to m, we will divide 300 by 100 to get 3. After that, add all the values together (6m+3m+3.5m+12m) to get a grand total of 24.5 m. I hope this helps!

The tape required to apply on the edge of the tape is 21.8m.

Perimeter is the sum of the length of the outer edges of a two-dimensional object.

A quadrilateral is a two-dimensional shape that is a polygon of four sides, one of the opposite sides of a quadrilateral is parallel.

Dan needs to apply tape on the edges of the stage, the tape required will be calculated by determining the perimeter of the stage.

The stage is in the shape of a quadrilateral.

The sides of the quadrilateral are as follows:

Side 1 = 6m

Side 2 = 300cm

Side 3 = 3.5m

Side 4 = 12m

300 cm will be converted into m

100 cm = 1m

300 cm = 0.3 m

The perimeter = Side 1 + Side 2 + Side 3+ Side 4

Perimeter = 6 + 0.3 +3.5 + 12

Perimeter = 21.8 m

The perimeter of the stage is 21.8m.

To know more about Perimeter

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Answer:

15 J

Step-by-step explanation:

There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.

1. Set up the equation

80 + x + 5 = 100

2. Simplify

x + 85 = 100

3. Solve for x by subtracting 85 from both sides

x = 15

Answer:

The correct answer is 15J which is B.

Answer:

11[tex]\sqrt{x6/4[/tex]

Given:

The triangle on the left ( triangle 1) has a 60º, a 90º, and a side that equals 11.

So we know the triangle on the right (triangle 2) has a 45º and a 90º angle.

Triangle 2

Since triangle angles always have a sum of 180º, we can solve for the third angle of triangle 2. 180 - (45 + 90) = 45. So the third angle of triangle 2 is 45º.

This is a special type of right triangle called a 45-45-90. An image of the leg/hypotenuse is uploaded below. Meaning, if we solve for the leg that joins the two triangles, we can solve for the hypotenuse.

Triangle 1

To solve for the middle leg, we work with the information we have. So first, find the third angle. 190 - (60 + 90) = 30. This brings us to a second type of special right triangle. An image of the leg/hypotenuse is uploaded below.

Given that we have a side angle of 11, we know that is 2x due to orientation. So 2x=11 simplifies to x=5.5. We then plug that back in to find the leg that we want: 5.5[tex]\sqrt{3}[/tex] .

Triangle 2

Now that we have a side length for the second triangle we can solve. x for this triangle is 5.5[tex]\sqrt{3}[/tex] so to find the hypotenuse we plug into x[tex]\sqrt{2}[/tex]. This turns into (5.5[tex]\sqrt{3}[/tex][tex]\sqrt{2}[/tex]) which simplifies into 5.5[tex]\sqrt{6}[/tex] = 13.47

Answers

The answers are not in the correct form. By going through and finding the decimal form of each, you find out that 11[tex]\sqrt{6/4}[/tex] is equivalent to 13.47, therefore your answer.

Answer:

[tex]1x=\frac{1\sqrt{129} }{8}[/tex]

Step-by-step explanation:

In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±

hope this helps!