Nine fewer than half a number is a five more than a four times the number.define a varible, write an equation, and slove to find the number

Eight and one-half years ago the age of Steven was 7 years, then the present age of Steven is 15.5 years.

Mathematical equations with two algebraic symbols on either side of the equal (=) sign are called equation. This connection is illustrated by the left and right expression being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

Assume the current age of Steven is x years.

From the given information in the question,

8.5 years ago from now,

x - 8.5 = 7 years

x = 15.5 years.

So, the current age is 15.5 years.

To know more about Equation:

https://brainly.com/question/10413253

#SPJ3

Step-by-step explanation: Three consecutive odd integers are represents as follows.

X ⇒ first integer

X + 2 ⇒ second integer

X + 4 ⇒ third integer

Since the sum of these is 87, our equation reads X + X + 2 + X + 4 = 87.

Simplifying on the left, we get 3x + 6 = 87.

Subtracting 6 from both sides, 3x = 81.

Now divide both sides by 3 and x = 27.

Since x, our first odd integer is 27, our next consecutive odd integer will be X + 2 or 27 + 2 which is 29 and X + 4 would be 31.

The required algebraic expression for the length of the blade is x = 14 - h.

Given that,

The knife shown below is 14 inches long.
To write an algebraic expression that represents the length of the blade (in inches).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here let the length of the blade of the knife be x,
length of the knife handle be h
Here the total length of the knife is 14 inches
So,
The total length of the knife = length of the blade + length of the handle
14 = x + h
x = 14 - h

Thus, the required algebraic expression for the length of the blade is x = 14 - h.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

The speed of the particle in rpm is 43170.32 rpm.

Given:

The distance of particle (radius) from the axis is [tex]r=6\rm \: cm=0.06\; m[/tex].

The acceleration (centripetal) experienced by the particle is,

[tex]a=125000\rm \; g's\\a=125000\times 9.81 \rm \; m/s^2\\a=1226250\rm \; m/s^2[/tex]

Let ω be the angular velocity of the particle and N be the speed in rpm.

So, ω will be  [tex]\omega=\dfrac{2\pi N}{60}[/tex]

Now, the acceleration of the particle can be written as,

[tex]a=\omega^2r\\a=\left(\dfrac{2\pi N}{60}\right)^2\times 0.06[/tex]

So, the speed of the particle in rpm will be,

[tex]a=\left(\dfrac{2\pi N}{60}\right)^2\times 0.06\\12262550=0.01095N^2\times 0.06\\N=43170.32\rm \; rpm[/tex]

Therefore, the speed of the particle in rpm is 43170.32 rpm.

For more details, refer the link:

https://brainly.com/question/8825608?referrer=searchResults

Answer:

The solution set for the provided inequity is {x | x > 2}.

Step-by-step explanation:

Consider the provided inequity.

[tex]5x+7>17[/tex]

Subtract both the side by 7.

[tex]5x+7-7>17-7[/tex]

[tex]5x>10[/tex]

Now divide both the side by 5.

[tex]\frac{5x}{5}>\frac{10}{5}[/tex]

[tex]x>2[/tex]

Hence, the solution set for the provided inequity is {x | x > 2}.

To convert grams per cubic centimeter to pounds-mass per cubic foot, you can use the conversion factors. By applying the conversion factors of 1 lb = 454 g and 1 ft³ = (30.5 cm)³, you can calculate that 40 grams per cubic centimeter is equal to 500 pounds-mass per cubic foot.

To convert grams per cubic centimeter to pounds-mass per cubic foot, we need to use conversion factors. Firstly, we need to convert grams to pounds by using the conversion factor 1 lb = 454 g. Then, we convert cubic centimeters to cubic feet by using the conversion factor 1 ft³ = (30.5 cm)³. Finally, we combine the two conversion factors to find the desired unit: pounds-mass per cubic foot.

Given:

Conversion factor:

Calculation:

Simplifying the calculation gives:

Therefore, 40 grams per cubic centimeter is equal to 500 pounds-mass per cubic foot.

Answer:

This is FALSE.

Step-by-step explanation:

Writing a check on an account with insufficient funds is never allowed by any bank. This will only lead to check bounce and sometimes can land you up in legal trouble. When a check bounces, you will have to pay your bank the bounce fee also. Hence, we should be careful while writing any check.

Answer:

f⁻¹(x) = (1/2)x +5

Step-by-step explanation:

In y = f(x), swap the variables, then solve for y. The expression you get is f⁻¹(x).

... y = 2x -10

... x = 2y -10 . . . . . . swapped variables

... x +10 = 2y . . . . . add 10

... (1/2)x + 5 = y . . . . divide by 2

... f⁻¹(x) = (1/2)x + 5 . . . . . . rewrite using function notation

Answer:

P=1.2

Step-by-step explanation:

Please mark as brainlest  

Rate and give me thanks

The maximum value of [tex]\(f(x, y)\)[/tex]  is given by:

[tex]\(f\left(\frac{b}{a+b}, \frac{a}{a+b}\right) = \left(\frac{b}{a+b}\right)^a \left(\frac{a}{a+b}\right)^b\)[/tex]

To find the maximum value of the function [tex]\(f(x, y) = x^a y^b\)[/tex] subject to the constraint (x + y = 1, use the method of Lagrange multipliers.

Let's set up the Lagrangian function:

[tex]\(L(x, y, \lambda) = x^a y^b + \lambda(x + y - 1)\)[/tex]

Taking the partial derivatives and setting them to zero:

Equation 1: [tex]\(\frac{\partial L}{\partial x} = a x^{a-1} y^b + \lambda = 0\)[/tex]  

Equation 2: [tex]\(\frac{\partial L}{\partial y} = b x^a y^{b-1} + \lambda = 0\)[/tex]

Equation 3: [tex]\(\frac{\partial L}{\partial \lambda} = x + y - 1 = 0\)[/tex]  

From equations (1) and (2) it can be written as

Equation 4: [tex]\(a x^{a-1} y^b = -\lambda\)[/tex]  ... (4)

Equation 5: [tex]\(b x^a y^{b-1} = -\lambda\)[/tex] ... (5)

Dividing equation (4) by equation (5) gives

[tex]\(\frac{a}{b} \frac{x^{a-1}}{x^a} \frac{y^b}{y^{b-1}} = 1\)[/tex]

[tex]\(\frac{a}{b} \frac{y}{x} = 1\)[/tex]

From equation (3) [tex]\(y = 1 - x\)[/tex].

Substituting [tex]\(y = 1 - x\)[/tex] into the equation [tex]\(\frac{a}{b} \frac{y}{x} = 1\)[/tex]

[tex]\(\frac{a}{b} \frac{1-x}{x} = 1\)[/tex]

[tex]\(a x = b (1-x)\)[/tex]

[tex]\((a + b) x = b\)[/tex]

[tex]\(x = \frac{b}{a+b}\)[/tex]

Substituting [tex]\(x = \frac{b}{a+b}\)[/tex] into the constraint equation (3):

[tex]\(y = 1 - x[/tex]

  [tex]= 1 - \frac{b}{a+b} = \frac{a}{a+b}\)[/tex]

Therefore, the critical point (x, y) that satisfies the constraint equation is:

[tex]\(x = \frac{b}{a+b}\) and \(y = \frac{a}{a+b}\)[/tex]

Therefore, the critical point gives the maximum value of the function [tex]\(f(x, y) = x^a y^b\)[/tex] subject to the constraint x + y = 1.

Learn more about Lagrangian function here:

https://brainly.com/question/33166274

#SPJ4

Answer:

The y-intercept of f(x) is 3 units below the y-intercept of g(x).

Step-by-step explanation:

We are given,

The functions [tex]f(x)=x-1[/tex] and [tex]g(x)=x+2[/tex].

Now, y-intercept is the point where the graph of the function crosses y-axis.

Substituting x= 0 in the functions, we get,

[tex]f(0)=0-1\\f(0)=-1[/tex] and [tex]g(0)=0+2\\g(0)=2[/tex].

Thus, we get that,

The y-intercept of the the function f(x) is -1.

The y-intercept of the function g(x) is at 2.

Thus, the y-intercept of f(x) is 2-(-1)= 3 units below the y-intercept of g(x) as seen below.

The volume of 10 drops of liquid is approximately 0.0001 fluid ounces.

To find the volume of 10 drops of liquid, we can use the given information that the volume of 10000 drops is 10 fluid ounces. Let's set up a proportion to solve for the volume of 10 drops.

Let V be the volume of 10 drops in fluid ounces.

We know that the volume of 10000 drops is 10 fluid ounces, so we can write:

10,000 drops / V = 10 fluid ounces / 10 drops

Now, cross-multiply and solve for V:

10,000 drops * 10 drops = 10 fluid ounces * V

100,000 drops² = 10 fluid ounces * V

Now, divide both sides by 100,000 drops^2 to solve for V:

V = 10 fluid ounces / 100,000 drops^2

V ≈ 0.0001 fluid ounces

Therefore, the volume of 10 drops of liquid is approximately 0.0001 fluid ounces.

Learn about volume here:

brainly.com/question/22886594

#SPJ2

Answer:

option C

[tex]20\°[/tex]

Step-by-step explanation:

we know that

An isosceles triangle has two equal angles and two equal sides. The two equal angles are the base angles and the third angle is the vertex angle

In this problem the base angles are angle B and angle C

so

m∠B=m∠C

substitute

[tex](5x+5)\°=(7x-25)\°[/tex]

[tex](7x-5x)\°=(5+25)\°[/tex]

[tex]2x=30\°[/tex]

[tex]x=15\°[/tex]

m∠B=[tex](5x+5)\°=5*15+5=80\°[/tex]

Remember that the sum of the internal angles of the triangle is equal to [tex]180\°[/tex]

Find m∠A

m∠A=[tex]180\°-2*80\°=20\°[/tex]

The answer is interval or ratio. In interval level of measurement, the distances between have attributes does have a meaning. The best example to be used here is temperature. The distance from 40-50 is like the distance from 70-80. While in ratio level of measurement, there is constantly an absolute zero that is significant. Meaning, that you can build a meaningful fraction (or ratio) with a ratio variable. 

The probability that a Poisson random variable X equals 2, given that its variance is 3, is approximately 0.2240.

The student asks about finding the probability that a Poisson random variable X takes on a value exactly equal to 2, given that the variance of X is 3. We know for a Poisson distribution, the variance is equal to its mean, which is denoted by λ (lambda). Therefore, λ = 3.

Using the formula for the Poisson probability mass function (PMF), P(X = k) = (e^(-λ) * λ^k) / k!, we can calculate P(X = 2). Substituting λ = 3 and k = 2, we have:

P(X = 2) = (e^(-3) * 3^2) / 2! = (0.0497871 * 9) / 2 = 0.224041.

We can round this probability to four decimal places:

P(X = 2) ≈ 0.2240.