Compare and contrast expanding and simplifying algebraic expressions with simplifying numeric expressions. for example, compare simplifying 3(x – 2) (x – 1) with 3(5 – 2) (5 – 1).

The dot product associated to sides AB and BC is 0.

In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:

Side BA

BA = (5, 3) - (0, 0)

BA = (5, 3)

Side BC

BC = (- 3, 5) - (0, 0)

BC = (- 3, 5)

By definition of dot product, the result associated to the two sides of the triangle is:

BA • BC = (5, 3) • (- 3, 5)

BA • BC = (5) · (- 3) + (3) · (5)

BA • BC = - 15 + 15

BA • BC = 0

The dot product associated to sides AB and BC is 0.

The statement is poorly formatted, the correct form is shown below:

If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:

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[tex] \rm log_{5}(125) \\ \rm log_{5}( {5}^{3} ) \\ \rm1 \cdot3 \\ 3 \\ \therefore \tt log_{5}(125) = 3[/tex]

24 is the answer! Its all about isolation, i tried to show it a little better in the image attached. Hope this helps!!

The car will be worth $20467 in 2017

The given parameters are:

Initial value, a = 38000

Depreciation rate, r = 6%

The value of the car after x years is represented by the following exponential equation

V(x)= a(1 - r)^x

Substitute the known values in the above equation

V(x) = 38000 * (1 - 6%)^x

2017 is 10 years from 2007

This means that x = 10

So, we have:

V(x) = 38000 * (1 - 6%)^10

Evaluate

V(x) = 20467

Hence, the car will be worth $20467 in 2017

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The solutions for the quadratic equation are given as follows:

x = -1, x = 7/5

A quadratic function is given according to the following rule:

y = ax^2 + bx + c

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

For this problem, the equation is:

5x² - 2x - 7 = 0.

Hence the coefficients are a = 5, b = -2 and c = -7, and then the solutions are found as follows:

The solutions are:

x = -1, x = 7/5

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Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.

Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.

An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.

The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.

In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.

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The equation represents a population of 370 animals that increases at an annual rate of 11% is .

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1.

Given that,

A population of 370 animals that increases at an annual rate of 11%

a = 370, r = 11%

[tex]p=a(1+r)^{t}[/tex]

  = [tex]370(1+0.11)^{t}[/tex]

p  =  [tex]370(1.11)^{t}[/tex]

Hence, The equation represents a population of 370 animals that increases at an annual rate of 11% is .

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Answer:

4

Step-by-step explanation:

1. Convert from mixed number to fraction

[tex]5\frac{1}{2} =\frac{5(2)+1}{2} =\frac{11}{2}[/tex]

[tex]1\frac{3}{8}=\frac{(1)(8)+3}{8} =\frac{11}{8}[/tex]

2. Divide fractions

[tex]\frac{\frac{11}{2} }{\frac{11}{8} } =\frac{(11)(8)}{(11)(2)} =\frac{8}{2} =4[/tex]

Hope this helps

The amount of cloth needed to make 1 headband is 10 meters.

Cloth needed to make 1 headband = Number of headbands Anne made / Total clothes used

= 6 ÷ 3/5

= 6 × 5/3

= (6 × 5) / 3

= 30/3

= 10 meters

Therefore, the amount of cloth needed to make 1 headband is 10 meters.

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Distance hour hand travel in 5 hours is 20.94 inches.

To find the distance hour hand travel in 5 hours:

Therefore, the distance hour hand travel in 5 hours is 20.94 inches.

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Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10

The given parameters are:

f(x) = 3x^2 + kx - 7

Divisor = x - 4

Remainder = 81

To solve for k, we use the remainder theorem

Set the divisor to 0

x -4 = 0

Add 4 to both sides of the above equation

x - 4 + 4 = 0 + 4

This gives

x = 4

Substitute x = 4 in the function f(x) = 3x^2 + kx - 7

f(4) = 3(4)^2 + k * 4 - 7

Evaluate the exponents

f(4) = 3 * 16 + k * 4 - 7

Evaluate the products

f(4) = 48 + 4k - 7

So, we have:

f(4) = 41 + 4k

The remainder is 81.

So, we have

41 + 4k = 81

Subtract 41 from both sides

4k = 40

Divide both sides of the above equation by 4

4k/4 = 40/4

Evaluate the division

k = 10

Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem

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Answer:

300 points

Step-by-step explanation:

Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:

[tex]\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300[/tex]

In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.

Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:

Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)

Slope (m) = 2/1

Slope (m) = 2

To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b

3 = 1(2) + b

3 = 2 + b

Subtract 2 from both sides

3 - 2 = 2 + b - 2

1 = b

b = 1

Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

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Hi :)

Let's use some Algebra skills to find w ^•^

First off, let's subtract both sides by 6

[tex]\longrightarrow\darkblue\sf{-9-6 > 5w}[/tex]

[tex]\longrightarrow\darkblue\sf{-15 < 5w}[/tex]

Divide both sides by 5

[tex]\longrightarrow\sf{-3 < w}[/tex]

Or

[tex]\longrightarrow\sf{w > -3}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

Answer:

Since the graph looks like this, I would say solid line

Answer:

To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction.

The answer is Figure A.

Given: "If it is an triangle, then it has three vertices.

To find which diagram represents the given statement.

From the first diagram

Triangles have three vertices because they are formed by the intersection of three triangles.

using the second diagram

Three vertices make up the triangle's intersection zone.

Therefore, we cannot infer from the second diagram that a triangle has three vertices.

As a result, figure A represents the stated assertion.

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The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.

According to the statement

We have given that the there is a algorithm which is used to data cleanup problem of removing 0 values from a data set, and scans a list from left to right and copies every legitimate value into a new list.

and we have to explain about that algorithm.

So,

Here we given that the algorithm copies and paste the values in the new files then

the algorithm is called the copy over algorithm.

So, The copy over algorithm is a a single specimen of something that occurs in a multiple edition, such as a book, article, etc. a matter to be reproduced in print or an imitation or reproduction of an original.

So, The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.

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The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

According to the statement

we have given that the radius of the clock face is 10 inches and the face of a clock is divided into 12 equal parts.

And we have to choose the three statements which are correct from the given options.

So,

Check the all given options to find the correct options.

So, OPTION A :

360/12=30 degrees between each number

3-1 = 2 2*30 = 60 degrees so A is FALSE

Now, OPTION B:

C=2 x π x r

r=10

using 3.14 for PI = 10*3.14 =31.4 x 2 = 62.8 so B is TRUE

Now OPTION C:

30 x 4 = 120 degrees = TRUE

Now, OPTION D:

10-3 = 7

7/12 x 62.8 = 0.5833*62.8 = 36.63 inches = FALSE

Now, OPTION E:

1/12=0.0833 x 62.8 = 5.23 rounded to 5.2 = TRUE

So, The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Disclaimer: This question was incomplete. Please find the full content below.

Questions:

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.

Which statements about the clock are accurate? Check all that apply.

A. The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.

B. The circumference of the clock is approximately 62.8 inches.

C.The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

D. The length of the major arc between 3 and 10 is approximately 31.4 inches.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

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The general solution of the given system of odes is

m=1 ; m=4    (real roots)

In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.

the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.

It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.

dx/dt = 2x+2y =   x^1 = 2x+2y     1

dy/dt = x+3y =    y^1 = x+ 3y        2

differentiating 1 with respect to 't'

x^11 = 2x^1+ 2y^1

y^1 = x+3y

x^11 = 2x^1= 2(x+3y)

x^11 = 2x^1+ 2x+ 6y

x^11 = 2x^1+ 2x+ 6(x^1-2x/2)

x^11 = 2x^1+ 2x+ 3x^1- 6x

x^11 = 5x^1 - 4x

x^11 -5x^1 - 4x

x^11 - 5x^1 -4x =0

Auxillary equation is m^5- 5m+4=0

m^2 - m - 4m + 4 = 0

m(m-1) -4 (m-1) =0

(m-1) (m-4) = 0

m=1 ; m=4    (real roots)

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The ratio of white to black horses is 2:5.

Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers with each other. It shows the frequency that one value is contained within other value(s).

The ratio of white to black horses = number of white horses : number of black horses

The ratio of white to black horses = 6 : 15

6 : 15 is not expressed in its simplest form yet. To convert the ratio to its simplest form, divide the numbers by a common factor of 6 and 15. A common factor is a number that divides two or more numbers perfectly with leaving any remainder. A common factor of both numbers is 3

(6/3) : (15/3) =  2 : 5

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Answer:

Step-by-step explanation:

x+3y=1

The probability that at least $15$ cents worth of coins come up heads is

P(H)=1/16

This is further explained below.

Generally, We are doing a simultaneous toss of four coins. How likely is it that every coin will land with the head side facing up?

It has been established by everyone who has participated so far that the solution is 116, which can be written as

(1/2)4=1/16.

On the other hand, a person who is just starting out can benefit from another method to see things.

I'm going to go ahead and make the assumption that each coin is balanced and that each side has an equal chance of facing up.

Each coin has the potential to exist in either of two states (heads or tails). Therefore, there are

2^4 = 16 different permutations (states) that the four coins may be in together as a group.

Only one of these possible permutations results in all heads. This results in the correct value of 1/16.

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Answer: [tex]-8x^2 -40x-50[/tex]

Step-by-step explanation:

[tex]h(g(f(x))\\\\=h(g(2x+5))\\\\=h((2x+5)^2)\\\\=h(4x^2 +20x+25)\\\\=-2(4x^2 +20x+25)\\\\=-8x^2 -40x-50[/tex]

The value of the composite function h(g(f(x))) = -8x² - 40x - 50.

We have,

To find the composition h(g(f(x))), we need to substitute the function g(f(x)) into h(x) and simplify.

Given:

f(x) = 2x + 5

g(x) = x²

h(x) = -2x

First, we find g(f(x)) by substituting f(x) into g(x):

g(f(x)) = g(2x + 5) = (2x + 5)² = (2x + 5)(2x + 5) = 4x² + 20x + 25

Now, we substitute g(f(x)) into h(x):

h(g(f(x))) = h(4x² + 20x + 25) = -2(4x² + 20x + 25) = -8x² - 40x - 50

Therefore,

The value of the composite function h(g(f(x))) = -8x² - 40x - 50.

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It looks like the integral is

[tex]\displaystyle 6 \int yz\cos(x) \, ds[/tex]

With [tex]x=t[/tex], [tex]y=\cos(t)[/tex], and [tex]z=\sin(t)[/tex], the line element is

[tex]ds = \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt}\right)^2 + \left(\dfrac{dz}{dt}\right)^2} \, dt = \sqrt2 \, dt[/tex]

and so

[tex]\displaystyle 6 \int yz\cos(x) \, ds = 6\sqrt2 \int_0^\pi \cos^2(t) \sin(t) \, dt[/tex]

Substitute [tex]u = \cos(t)[/tex] and [tex]du=-\sin(t)\,dt[/tex], then

[tex]\displaystyle 6 \int yz\cos(x) \, ds = -6\sqrt2 \int_1^{-1} u^2 \, du = 12\sqrt2 \int_0^1 u^2 \, du = \boxed{4\sqrt2}[/tex]

where in the second-to-last equality, we have

[tex]\displaystyle -\int_1^{-1} = \int_{-1}^1[/tex]

and

[tex]\displaystyle \int_{-1}^1 u^2 \, du = 2 \int_0^1 u^2\,du[/tex]

by symmetry.

The polynomial that should be subtracted from the dividend first is; x³ + 2x²

The long division we are given is;

        __________

x + 2 ) x³ + 3x² + x

Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².

Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;

(x + 2) * (x²) = x³ + 2x²

Thus, the polynomial to be subtracted is x³ + 2x²

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a. x=5

b. y=x

c. y=0

d. y=x-7

The name of the polygon is (B) hexagon.

To find the name of the polygon:

Therefore, the name of the polygon is (B) hexagon.

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The complete question is given below:

A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?

A) Octagon

B) Hexagon

C) Heptagon

D) Quadrilateral

The minimum number of pounds of mozzarella cheese is necessary to say that your medium pizza ranked in the top 3% of all medium pizzas in terms of cheese content.

P(z < 0.2) = 0.5793

Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."

In conclusion, To begin, we calculate the z score to determine the crucial value. If

[tex]z =\frac{ (x - u)}{ s}[/tex]

x = critical value = 0.5

u = mean = 0.495

Hence

[tex]z =\frac{ (x - u)}{ s}[/tex]

z= 0.2

Therefore, by making use of a table or some other kind of technology, the left-tailed area of this is

P(z < 0.2) = 0.5793

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Complete Question

A pizza shop advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. In addition, it is discovered that the quantity of cheese put on the population of all medium pizzas has a Normal distribution with a mean of 0.495 and standard deviation 0.025. The probability that a randomly selected pizza has less than the advertised amount of mozzarella cheese is:

a) 0.2000

b) 0.5793

c) 0.4207

d) 0.800