Given m ∥ n m∥n, find the value of x. m n t (x+9)° (2x+6)°

Answer:

It's the red option.

Answer:

y = x + 8

Step-by-step explanation:

Let's build the equation:

There are 8 entries to start

y = 8

Adding 1 entry every day

y = x + 8

Answer:

The odds of rolling a specific number on a 6-sided dice is 1 in 6, which can be written as a percentage by dividing 1 by 6 and then multiplying by 100. This gives us a percentage of 16.666666...%, which can be rounded to 16.67% if needed.

The average speed and average velocity of the car are 40/3 m/s and 4/3 m/s respectively.

Growth rates refer to the percentage change of a specific variable within a specific time period.

Given is that salsa's little brother is learning to talk he has a vocabulary of 30 words each week his vocabulary grows by 6%.

We can write the function to calculate the words learned by him as -

y = 30(6)ˣ

For {x} = 5, we can write -

y = 30(6)⁵

y = 7776 x 30

y = 233280

Therefore, salsa's little brother, at the given rate would learn 233280 words.

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Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

P' is located at (1, 0) after the transformation (x - 2, y + 3).

The transformation that we have to apply is (x - 2, y + 3), so we have to move the point in the x axis as well as y axis direction of the coordinate axes in the plane.

P' = (3 - 2, -3 + 3)

P' = (1, 0) is the outcome of applying the transformation on the point P, which is located at the coordinates (3, -3). Now, the point P', is located at (1, 0) after the transformation of the point P as per the given condition to us.

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Answer:

use a calculator if you don't have one use a google calculator

Step-by-step explanation:

Answer:

  f(x) = (x+2)²(x+4)

Step-by-step explanation:

Given the polynomial f(x) = x³ +8x² +20x +16 and the observations that f(-2) = 0, f(0) = 16, and f(2) = 96, you want the factored form using the box method.

The observation that f(-2) = 0 means (x +2) is a factor. If the other factors are (x+a) and (x+b), then ...

  f(0) = 16 = (0 +2)(0 +a)(0 +b) = 2ab

  ab = 8

And ...

  f(2) = 96 = (2 +2)(2 +a)(2 +b) = 4(4 +2(a+b) +ab)

  24 = 4 +2(a +b) +ab . . . . . . divide by 4

  12 = 2(a +b) . . . . . . . . . substitute ab=8 and subtract 12

  a +b = 6 . . . . . . . . . divide by 2

Then the quadratic factor is ...

  (x +a)(x +b) = x² +(a+b)x +ab = x² +6x +8

Using the box method, we write the first and last terms on the downward diagonal, then look for terms with the product 8x² that have a total of 6x. These get written on the upper diagonal.

  \(\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac{b}{g}}x^2&\textsf{2x}\\\cline{1-2}\vphantom{\dfrac{b}{g}}\textsf{4x}&8\\\cline{1-2}\end{array}\)

This means the quadratic factor can be written as ...

  x² +2x +4x +8 = x(x +2) +4(x +2) = (x +4)(x +2)

The fully factored polynomial is ...

  f(x) = (x +2)(x +4)(x +2)

  f(x) = (x +2)²(x +4)

__

Additional comment

The box method seems irrelevant here, as we know before we get to the box that the factors are (x +a) and (x +b) with ab=8 and (a+b)=6. A listing of the factors of 8 quickly tells us the values of 'a' and 'b', without the box.

  8 = 1·8 = 2·4 . . . . . . factor pairs with sums of 9 and 6   ⇒   a=2, b=4.

The assignment of {2, 4} to {a, b} can be in either order, as the factors come out (x +2) and (x +4) however you do it.

The factors of the polynomial f(x) = x³+8x²+20x+16 are (x+2), (x+2) and (x+4).

The box method is to find the factors of polynomials.

The first phrase should go in the first box, and the last term should go in the last box. The first and last boxes are then multiplied. Find two words that combine to form the middle term and are the product of the first and last boxes. Fill in the remaining boxes using these expressions.

We have the polynomial,

f(x) = x³+8x²+20x+16

And given, f(-2) = 0

That means, x = -2 is the zeros of the polynomial.

(x+2) is one factor.

Now, we know (x+2) is one factor.

So,

f(x) = x³+8x²+20x+16

f(x) = x²(x+2) + 6x(x+2) + 8(x+2)

f(x) = (x+2)  (x²+ 6x+ 8)

We have x²+ 6x+ 8 is a quadratic function.

To find the factors of a quadratic function:

In box method,

In the box, we have 2 columns and 2 rows.

Terms are attached in the box as shown in the image.

The first phrase should go in the first box, and the last term should go in the last box. The first and last boxes are then multiplied. Find two words that combine to form the middle term and are the product of the first and last boxes. Fill in the remaining boxes using these expressions.

That means,

x²+ 6x+ 8

=  x²+ 2x+ 4x + 8

= (x+2)(x+4)

Therefore, the factors are (x+2), (x+2) and (x+4).

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Answer:

1067/10000

Step-by-step explanation:

simple

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Answer:

A and 1/3

Step-by-step explanation:

Answer:

C. Y=2x

Step-by-step explanation:

I hope this help you

New born = 2.6 × 10¹⁰ cells.

Adult         = 4.94 × 10¹³ cells.

How many times more = adult cells ÷ newborn cells

                                      = 4.94 × 10¹³ cells ÷ 2.6 × 10¹⁰ cells

                                      =  1.9 × 10³ cells

Answer:

14cm

Step-by-step explanation:

formula of a rectangular container is LBH and we were given that LBH is 2*11*20 which is equal to 440cm.

Now when the water is transferred into a hollow cylindrical container.the formula for that is 2pierh.440=2*22/7*5*h

440*7=220h

3080=220h

h=14cm

Answer:The volume of a rectangular container is

V = L X B X H, while the volume of the Cylindrical container is

V = pie( r^2)h where ( pie = 3.142 )

Volume of the rectangle = 2 x 11 x 20

= 440cm^3

Now to find the height of the cylinder we now equate the volume of the rectangle with that of the cylinder and make h the subject of the formula

440 = pie(r^2)h

= 3.142 x 5^2 x h

= 3.142 x 25 X h

=78.55h

440 = 78.55h

h. = 440/78.55

= 5.6cm

Step-by-step explanation:

The recursive definition for the amount of the blood pressure medicine in Hareem's bloodstream after n hours can be defined as :

a. a1=25, an= 0.40an-1 + 25

Base Case:

The initial amount of medicine in Hareem's bloodstream after 0 hours is 25 mg.

Recursive Step:

The amount of medicine in Hareem's bloodstream after n hours can be calculated by taking 60% of the amount of medicine in his bloodstream after (n-1) hours, and then adding 25 mg.

To write this recursive definition in mathematical notation:

M(n) = 25 mg, if n = 1

M(n) = 40 mg, if n = 6

M(n) = M(n-1) + (60% * M(n-1)), if n > 6

This recursive definition represents the amount of the blood pressure medicine in Hareem's bloodstream after n hours. The base case sets the initial amount of medicine, and the recursive step calculates the amount of medicine at each hour by taking 60% of the previous amount and adding 25 mg.

The correct option is a. a1=25, an= 0.40an-1 + 25

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Answer:

Step-by-step explanation:

First calculate 55% of 150:

= 150 x 55/100

= 82.5 ans

Now decrease it from 150:

= 150-82.5

= 67.5 ans Hope it helps!!

The magnetic field B at a distance of 2 cm, 10 cm, and 20 cm away from the axis of a solid wire of radius 10 cm carrying a current of 5.0 A uniformly distributed over its cross-section is 0.01 T, 1.0 x 10^-5 T, and 2.5 x 10^-6 T respectively, and a graph of B versus x for 0 < x < 20 cm shows a peak value of 0.01 T at x = 0 and a rapid decrease to approach zero as x approaches the radius of the wire.

To find the magnetic field B at a point at a distance r from the axis of the wire, we can use the formula:

B = μ₀I/(2πr)

where B is the magnetic field, I is the current, r is the distance from the axis, and μ₀ is the permeability of free space (4π x 10^-7 T m/A).

(a) At a distance of 2 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.02 m)

= 0.01 T

(b) At a distance of 10 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.10 m)

= 1.0 x 10^-5 T

(c) At a distance of 20 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.20 m)

= 2.5 x 10^-6 T

To sketch a graph of B versus x for 0 < x < 20 cm, we can use the formula for B and plot it for different values of x. Since the current is distributed uniformly over the cross-section of the wire, the magnetic field will also be symmetric around the axis of the wire. Therefore, the graph will have a maximum at x=0 and will decrease as x increases.

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Answer:

Step-by-step explanation:

2x+32=8

2x=-24

x=-12

Answer:

12 × 12 =144

Step-by-step explanation:

144 :)

The correct answer according to the graph is translation 6 units down and 2 units to the left. This can be observed by looking at the graph and seeing that the shape has moved 6 units down and 2 units to the left.

Graphs are usually used to plot the values of a function or to display the statistical relationship between two or more variables. Graphs can be used to make predictions and to analyze trends. Graphs can help to visualize complex problems and can be used to make decisions in a variety of fields.

In this example, the shape has been shifted 6 units down and 2 units to the left. This can be seen by looking at the graph and seeing that the shape has moved from the point (4,4) to the point (2, -2). This is the result of shifting the shape 6 units down and 2 units to the left.

Reflection over the line y=x+4, reflection over the x-axis and rotation 180° clockwise about the point (4,0) are all incorrect answers to this question. Reflection over the line y=x+4 would result in the shape being mirrored over the line y=x+4, while reflection over the x-axis would result in the shape being mirrored over the x-axis. Rotation 180° clockwise about the point (4,0) would rotate the shape 180° clockwise around the point (4,0). Neither of these transformations would result in the shape being shifted 6 units down and 2 units to the left, as seen in the graph.

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Answer:

i dont understand

Step-by-step explanation:

(a) There are 40 french mathematics books then non-french books not about mathematics are 210. (b) There are 60 french nonmathematics books then non-french books not about mathematics are 150.

(a) If there are 40 French mathematics books, then the number of French books not about mathematics is 70 - 40 = 30.

Thus, the number of non-French books about mathematics is 100 - 40 = 60.

We can then find the number of non-French books not about mathematics by subtracting the number of French non-mathematics books from the total number of non-mathematics books, which is 300 - 60 - 30 = 210.

(b) If there are 60 French non-mathematics books, then the number of French books about mathematics is 70 - 60 = 10. Thus, the number of non-French books about mathematics is 100 - 10 = 90.

We can then find the number of non-French books not about mathematics by subtracting the number of French non-mathematics books from the total number of non-mathematics books, which is 300 - 60 - 90 = 150.

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Siti has folded 43 paper planes. We were able to find this value by using algebraic equations to relate the number of paper planes each friend has folded, and solving for Siti's total.

To find the number of paper planes Siti has folded, we need to first find the number of paper planes Emma has folded. We can do this by subtracting 22 from Siti's total, since Siti has 22 more than Emma.

Next, we need to find the total number of paper planes Julie's folded. We know this is 5 times the sum of Emma and Siti's paper planes, so we can set up the equation:

Julie's paper planes = 5(Emma's paper planes + Siti's paper planes)

Substituting in the value we found for Emma's paper planes, we get:

Julie's paper planes = 5(Siti's paper planes + Emma's paper planes) = 5(Siti's paper planes + (Siti's paper planes - 22))

Simplifying this equation, we get:

Julie's paper planes = 10Siti's paper planes - 110

Finally, we know that Julie's paper planes equals 320, so we can set up the equation:

320 = 10Siti's paper planes - 110

Solving for Siti's paper planes, we get:

Siti's paper planes = 43

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Step-by-step explanation:

for your account the equation will be

y= 50 + 10x

for your friend acc the equation will be

y = 25 + 10x

b) no it will never have the same amount of money

The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer:

327 children and 318 adults

Step-by-step explanation:

The x be the amount of children and y be the amount of adults that were at the swimming pool. We can use this to set up a system of equations:

x+y=645

1.75x+2.50y=1367.25

Move y to the other side in the first equation to isolate x and solve the system using substitution:

x=645-y

  1.75(645-y)+2.50y=1367.25

Distribute

1128.75-1.75y+2.50y=1367.25

         1128.75+0.75y=1367.25

Subtract 1128.75 from both sides

                        0.75y=238.5

Divide both sides by 0.75

                                y=318

x=645-y

x=645-318

x=327

327 children and 318 adults swam at the pool that day