Multiply, if possible. Then simplify.

√8 . √32

===========================================

Explanation:

x = amount (in inches) the spring is stretched

y = force applied (in pounds)

y = kx for some constant k, since x and y vary directly

---------------

Plug in the given info that x = 5 and y = 150 pair up together

Solve for k

150 = k*5

150/5 = k

k = 30

The equation goes from y = kx to y = 30x. Whatever the stretching distance (x) is, you multiply by 30 to get the force needed (y) to pull the spring.

---------------

Plug in y = 180 to solve for x

y = 30x

180 = 30x

30x = 180

x = 180/30

x = 6

The spring will be stretched 6 inches if you apply a force of 180 pounds.

Answer:

x = 36

∠M = 36

∠P = 71

∠N = 73

Step-by-step explanation:

Answer:

144m^3

Step-by-step explanation:

Answer: The value of R is 6.

Explanation: I recommend you go to these two links for an easier understanding:

https://www.wikihow.com/Find-the-Y-Intercept

https://www.wikihow.com/Find-the-X-Intercept

Answer:

=169x

Step-by-step explanation:

I hope this helps you

Answer:

\( y = -65x + 420 \)

Step-by-step explanation:

Slope-intercept form equation is given as \( y = mx + b \)

Where,

y = distance remaining

x = hours driven

m = slope/constant rate. In this case, the value of m would be -65. This means the distance will reduce at a constant rate of 65 miles per hour.

b = y-intercept, which is the initial value or the distance between the cities = 420

Plug in the values into the slope-intercept equation, to represent the distance y in miles remaining after driving x hours. You would have:

\( y = -65x + 420 \)

The equation in slope intercept form is \(y =-65x + 420\)

A linear function is a function whose value changes at a constant rate.

The given parameters are:

A linear function is represented as:

\(y = mx + c\)

Where

So, the function becomes

\(y =-65x + 420\)

Hence, the equation in slope intercept form is \(y =-65x + 420\)

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Answer:

Step-by-step explanation:

9.2  to  9.3    the top right one

For h(x), to find out the maximum, you would need to use this formula: \(c-(\frac{b^{2} }{4a} )\)

We are given the equation: \(h(x)=-x^{2}+4x-2\).

So, a = -1, b = 4, and c = -2. Then, substitute the numbers into the formula:

h(x)'s maximum = \(c-(\frac{b^{2} }{4a} )\)

                          = \((-2)-(\frac{(4)^{2} }{4(-1)} )\)

                          = \((-2)-(\frac{16 }{-4} )\)

                          = \((-2)-(-4)\)

                          = \(2\)

For g(x), to find out the maximum, just look at the highest point of y on the graph of the function, which is 2.

Thus, the answer you have chosen is the correct answer, which is choice 3: functions g and h have the same maximum of 2. Hope this helps :)

The if  they will have exactly the same length to donate. The long will their hair be is 8.5

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given ,

Two friends, Jeanette and Zoe, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer.

Jeanette's hair is already 29 centimeters long and grows at a constant rate of 1 centimeter per month.

29+n = 12+2n

2n-n = 29-12

n = 17/2

n = 8.5

Hence, The if  they will have exactly the same length to donate. The long will their hair be is 8.5

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The total fees for the month are $71.50.

To calculate the total fees for the month, we need to determine the charges for each transaction and then add them up.

Let's start by breaking down the fees for each transaction:

- Basic charge: Let's assume the basic charge is $10.

- Bill payments: Let's assume each bill payment incurs a $1 fee, so 7 bill payments would be $7.

- International wire transfer: Let's assume the fee for an international wire transfer is $25.

- ATM transactions: Let's assume the fee for a regional network ATM transaction is $1.50 and the fee for a national network ATM transaction is $2.50, so 4 regional network transactions would be $6 and 4 national network transactions would be $10.

- Cash advance: Let's assume the fee for a cash advance is 3% of the amount, so $450 cash advance would be $13.50.

Now we can add up all the fees:

$10 (basic charge) + $7 (bill payments) + $25 (wire transfer) + $6 (regional ATM transactions) + $10 (national ATM transactions) + $13.50 (cash advance fee) = $71.50

Therefore, the total fees for the month are $71.50.

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Answer: $1040

Step-by-step explanation:

There are 52 weeks in a year so they will get 26 haircuts in the year at every 2 weeks.

26x$40 =$1040

For a simple random sample with size 22 and mean of 129, the computed value the standard error of the mean is equals to the 0.6396.

The standard error is a statistical term that measures the accuracy for which a sample distribution represents a population by using standard deviation. The deviation of sample mean from population mean is called the standard error of mean. SEM is calculated by the standard deviation divided by the square root of the sample size, \(SEM = \frac{ \sigma}{\sqrt{n}}\)

We have a simple random sample from a population that has a normal distribution. Also, Mean of sample = 129

Sample size, n = 22

Standard deviations of sample, σ = 3

Using the formula of standard error of mean is, SEM \(= \frac{ 3}{\sqrt{22}}\)

= 0.63960

Hence, required value is 0.6396.

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Answer:

the answer is 589.4

Step-by-step explanation:

In doing this equation you do the order of operations:

(2.1 x 104)= 218.4

(3.5 x 106)= 371

you then add the answers together to get:

218.4 + 371 = 589.4

Answer:

Na dimio reso

Ta pidi yo

Era olvida yo contigo

Step-by-step explanation:

there's no explanation

Answer:

x = \(\frac{1}{2}\)

Step-by-step explanation:

Given that z is inversely proportional to x then the equation relating them is

z = \(\frac{k}{x}\) ← k is the constant of proportion

To find k use the condition z = 5 when x = 7 , then

5 = \(\frac{k}{7}\) ( multiply both sides by 7 )

35 = k

z = \(\frac{35}{x}\) ← equation of proportion

When z = 70 , then

70 = \(\frac{35}{x}\) ( multiply both sides by x )

70x = 35 ( divide both sides by 70 )

x = \(\frac{35}{70}\) = \(\frac{1}{2}\)

The equation y = x^2 - 10x + 3 is in standard form

Megan should replace the a in y = (x + a)^2 + 3 + b with -5

The function is given as:

y = x^2 - 10x + 3

Rewrite as:

y = (x^2 - 10x) + 3

Take the coefficient (k) of x

k = -10

Divide by 2

k/2 = -5

Square both sides

(k/2)^2 = 25

So, we have:

y = (x^2 - 10x + 25 - 25) + 3

Rewrite as:

y = (x^2 - 10x + 25) - 25 + 3

Express as a perfect square

y = (x - 5)^2 - 25 + 3

From the question, we have:

y = (x + a)^2 + 3 + b

By comparing both equations, we have:

a = -5

Hence, Megan should replace the a in y = (x + a)^2 + 3 + b with -5

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Answer:

21x² + 22x - 8

Step-by-step explanation:

(3x+4)(7x-2)​ = 21x² - 6x + 28x - 8 = 21x² + 22x - 8

Answer:

B.

Step-by-step explanation:

Let's use the FOIL (First, Outside, Inner, Last) method.

We need to multiply the first terms in each pair of parentheses, which are

3x and 7x.

Multiplying, we get \(21x^2\).

We multiply the outside terms in each pair, which are 3x and -2.

Multiplying, we get \(-6x\). Remember that since -2 is negative, then the whole product is negative.

We need to multiply the inner terms now. They are 4 and 7x.

Multiplying, we get \(28x\).

Finally, we multiply the last terms in each pair of parentheses. they are 4 and -2.

Multiplying, we get \(-8\).

Now, we put the terms together.

\(21x^2-6x+28x-8\)

We can combine -6x, and 28x. Doing this, we get

\(21x^2+22x-8\). Which gives us B.

I hope this helped.

Answer:

B= 12.14

14 multiplied by B= 170

170/14 = 12.14

Step-by-step explanation:

Answer: 0.06, 6/100, 3/50

Step-by-step explanation:

The gradient of the normal to the curve of h at x =3 is 1/20.

The provided is that h(x) = f(g(x))

Also provided,

g(3) = 7

g'(3) = 4

And f'(7) = -5

Taking,

h(x) = f(g(x))

Differentiating with respect to x,

h'(x) = f('g(x)).g'(x)

h'(x) is the gradient of the curve at x,

Now, putting the value of x = 3,

h'(x) = f('g(3)).g'(3)

We know, g(3) = 7 and g'(x) = 4,

h'(x) = f'(7).4

We know, f'(x) = -5

h'(x) = -5(4)

h'(x) = -20

The slope to the curve at x = 3 is -20.

We know the slope of the normal M1 and the slope at the curve M2 at the same point has their product value as -1,

So,

M1.M2 = -1

M1(-20) = -1

M1 = 1/20

So, the slope of the normal at the curve at x = 3 is 1/20.

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0.60792 liters x 1000 = 607.92 mL

Multiplying the volume in liters by 1000 converts it to milliliters.

Answer:

Other root of equation, \(\frac{8}{3}\)

Value of (\(b\)), \(-17\)

Step-by-step explanation:

The given quadratic equation is in standard form. Standard form is the basic format of representing a quadratic equation, a quadratic equation in standard form would use the following format,

\(y=ax^2+bx+c\)

To solve this problem, one could use Vieta's theorems. Vieta's theorems state the following, let (\(x_1\)) and (\(x_2\)) represent the roots of the equation,

\((x_1)+(x_2)=-\frac{b}{a}\)

\((x_1)(x_2)=\frac{c}{a}\)

Substitute the given values into the equation,

\(3+(x_2)=-\frac{b}{3}\)

\((3)(x_2)=\frac{24}{3}\)

Simplify,

\((3)+(x_2)=-\frac{b}{3}\)

\((3)(x_2)=8\)

Inverse operations,

\((3)+(x_2)=-\frac{b}{3}\)

\(x_2=\frac{8}{3}\)

Substitute in the value of (\(x_2\)),

\((3)+(\frac{8}{3})=-\frac{b}{3}\)

Simplify, convert to improper fractions and combine like terms,

\(\frac{9}{3}+\frac{8}{3}=-\frac{b}{3}\)

\(\frac{17}{3}=-\frac{b}{3}\)

Multiply both sides of the equation by (\(3\)) to remove the denominator,

\(17=-b\)

Answer:

y= -40

Step-by-step explanation:

We then applied the formula for factoring perfect square trinomials to obtain the fully factored form, which is 4(2x - 3)2.

To factor 16x2 - 48x + 36 completely, we can first factor out the greatest common factor of 4:

16x2 - 48x + 36 = 4(4x2 - 12x + 9)

Now,

we can see that the expression inside the parentheses is a perfect square trinomial, which can be factored as:

4x2 - 12x + 9 = (2x - 3)2

Therefore, putting the pieces together, we have:

16x2 - 48x + 36 = 4(4x2 - 12x + 9) = 4(2x - 3)2

Hence, the fully factored form of the given expression is 4(2x - 3)2, which is option D).

The reason why we can recognize 4x2 - 12x + 9 as a perfect square trinomial is because it has the form a2 - 2ab + b2, where a = 2x and b = 3. This form can always be factored as (a - b)2, which in this case gives (2x - 3)2. The factor of 4 in the final answer comes from the fact that we initially factored out a 4 from the given expression.

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The calculated solution for the ratio given as a : b : c is 1/3 : 1/4 : 1/5

From the question, we have the following parameters that can be used in our computation:

1/a : 1/b : 1/c = 3 : 4 : 5

Take the inverse of both sides

So, we have

a : b : c = 1/3 : 1/4 : 1/5

The above means that the solution for a : b : c is 1/3 : 1/4 : 1/5

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Answer:

y = -x +2

Step-by-step explanation:

4x + 4y = 8 to its slope-intercept form, y = mx + b:

Subtract 4x from both sides of the equation:

4x + 4y - 4x = 8 - 4x

4y = -4x + 8

Divide both sides of the equation by 4 to isolate y:

\(\frac{4y}{4} = \frac{-4x}{4} + \frac{8}{4}\)

y = -x + 2

Answer:

The formula to find the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.

Given that the radius of the cylinder is 2 inches and the height is 4 inches, we can substitute these values into the formula to find the volume:

V = πr²h

V = 3.14 x 2² x 4

V = 3.14 x 4 x 4

V = 50.24

Rounding this value to the nearest whole number, the volume of the cylinder is 50 in³.

If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m,  height be 6 m then the surface area of composite figure be 444 \(m^{2}\).

Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.

Surface area is basically sum of area of all the sides of a figure.

Surface area of composite figure =  area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.

=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)

=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]

=2(80+20+64)-80+2*50+2(48)

=2(164)-80+100+96

=328-80+196

=248+196

=444\(m^{2}\)

Hence the surface area of composite figure having a cuboid and pyramid on top is 444\(m^{2}\).

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Answer:

\( \frac{3x + 4}{y} = \frac{3(6) + 4}{(2)} \\ = \frac{18 + 4}{2} = \frac{22}{2} \\ = 11\)

The equation of a circle with its center at the origin and passes through the point (5,0):   x2+y2=25

the equation of a circle of with the center (2,3) and containing the point (3,2): x2+y2=2

Origin is referred to as the first point or the starting point from which we begin our calculations or measurements in mathematics, particularly in the subject of coordinate geometry. The 0 on a ruler is the point at which we begin taking measurements; as a result, it is referred regarded as the scale's origin.

(x-h)^2+(y-k)^2=r2

                          is the equation for a circle with center (h,k) and radius (r).

This yields the more well-known equation

x2+y2=r2

             for a circle centered at the origin.

Since we are aware that the circle's center is at its origin, i.e.

This fact, together with the circle's intersection point (5,0), can be used to determine the radius. The distance formula is used for this.

r=√(x2−x1)^2+(y2−y1)^2

In light of (0,0) and (5,0):

r=√(5−0)^2+(0−0)^2

=√25+0

√25=5

⇒ r=5

Therefore, x^2+y^2=(5)^2

                   x2+y2=25 is the equation for the circle.

(x-h)^2+(y-k)^2=r2 is the equation for a circle with center (h,k) and radius (r).

This yields the more well-known equation x2+y2=r2 for a circle centered at the (2,3).

Since we are aware that the circle's center is at (2,3), i.e.

This fact, together with the circle's intersection point (3,2), can be used to determine the radius. The distance formula is used for this.

r=√(x^2−x1)^2+(y2−y1)^2

In light of (2,3) and (3,2):

r=√(3−2)^2+(2−3)^2

r = √(1)^2+(-1)^2

= √1+1

=√2

⇒ r=√2

Therefore, x2+y2=(√2)^2

                   x2+y2=2 is the equation for the circle.

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