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The slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2

The formula for calculating the slope of a line is expressed according to the equations:

Slope = y₂-y₁/x₂-x₁

Using the coordinate points (0, 0) and (6, 3) on the line. On substituting, we will have;

Slope = 3-0/6-0

Slope = 3/6

Simplify

Slope =1/2

Hence the slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2

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Answer:

Yes si true

Step-by-step explanation:

If you analyze the figures you will realize that they are the same, the size differentiates it but they have the same angles.

Step-by-step explanation:

2 × 7 × 7.................

The solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1

The equation is given as

y + 2x = 5

Subtract 2x from both sides of the equation

So, we have

y + 2x - 2x = 5 - 2x

Evaluate the like terms

y = 5 - 2x

Next, we solve the function for the values of x

When x = -2, we have:

y = 5 - 2 * -2

Evaluate

y = 9

When x = 0, we have:

y = 5 - 2 * 0

Evaluate

y = 5

When x = 3, we have:

y = 5 - 2 * 3

Evaluate

y = -1

Hence, the solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1

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The value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.

Given the equation;

y + 2x = 5

Make 'y' the subject of formula

y = 5 - 2x    (1)

When x = -2

Let's substitute the value of x as -2 in equation (1)

y = 5 - 2(-2)

expand the bracket

y = 5 + 4

y = 9

When x = 0

Substitute the value of x = 0

y = 5 -2(0)

y = 5 - 0

y = 5

When x = 3

Substitute the value of x = 3

y = 5 - 2(3)

y = 5 - 6

y = -1

Thus, the value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.

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The reflection of the triangle gives the co-ordinates A'(5, 2) B'(0, -3) C'(-4,-1) .

In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane; this set is also known as plane of reflection or the axis. The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.

When an object is reflected across the x -axis , the image will be at same distance from the x axis as the object or point is on the cartesian plane.

So if a point P has the co-ordinates (x , y) .  When reflected across the x-axis the the reflection has the co-ordinates P'(x , -y ) .

The co-ordinates of the 3 points are A(5,-2) B(0, 3) C(-4,1).

When reflected across the x-axis the co-ordinates become :

A(5,-2) →A'(5,2)

B(0, 3)→B'(0,-3)

C(-4,1)→C'(-4,-1)

Hence the second option is correct, the reflected image of the triangle has the coordinates  A'(5, 2) B'(0, -3) C'(-4,-1) .

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Answer:

  9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

  d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

  d ≈ 9.2

The distance between A and B is about 9.2 units.

Reason:

It is impossible to pass a single vertical line through more than one point on the graph. This relation passes the vertical line test.

The other graphs fail the vertical line test. For instance, in the upper right corner we have a vertical line through x = -1 which passes through more than one point. The input x = -1 leads to multiple outputs y = -1 and y = 3 at the same time.

A function is only possible when each input leads to exactly one output.

The value is 102.

Here the expression is 2x² - 5x.

We have to find the value of the algebraic expression for x = -6.

Expression = 2x² - 5x

Now put the value of x = -6 in the expression, we get

2x² - 5x = 2(-6)² - 5(-6)

             = 2×36 + 30

             = 72 + 30

             = 102

Therefore the value of an algebraic expression is 102.

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Answer: B

Step-by-step explanation:

f(2) = 2, and is defined/exists. Holes (and asymptotes) like the hole at (2, -2) ruins continuity. The limit exists, but is not equal to f(2) which is why continuity is ruined at x=2

Answer: B

Step-by-step explanation:

f(2) = 2 and exists/is defined Holes (and asymptotes) such as the one at (2, -2) destroy continuity. The limit exists, but it is not equal to f(2), hence continuity is broken at x=2.

Answer:

x - 4

Step-by-step explanation:

The quickest way to do this is to Factor and "cancel". (Cancelling is not a mathematical term--it really is dividing)

x^2 - 16 is the difference of two squares. Its super-beneficial to recognize a difference of two squares and its factored form:

(x - 4)(x + 4)

Now you have:

(x - 4 )(x + 4) / x+4

The x+4 term "cancels" and you end up with x-4 as your answer.

You could also do this division problem using long division or synthetic division. You will get the same answer.

Answer:

True statements are 4 and 5

Step-by-step explanation:

This s basically using set theory to evaluate line segments

The union of two(or more) sets is the set of elements that are in either or both sets.

Here is an example
If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6} then
A ∪ B = (1, 2, 3, 4, 5, 6}
Note that there cannot be any duplicates in a set

We have to treat the line segments as sets  to solve this problem.

For easier explanation, I am going to view each segment as having points which I am labeling 1, 2, 3 etc.

The individual independent line segments are JL, LM, MN, and NT, basically each is a set of the points that comprise each segment

You have to visualize each of these line segments as being comprised of these points.

Note that these are distinct sets ie there is  no common point when we consider the above 4 sets

Let set
JL have the points {1, 2, 3} we say JL = {1, 2, 3}

LM = {4, 5}

MN = {6, 7}

NT = {8, 9}

We see that there are no common points between each of the four sets below

1. JL ∪ MN = set of points that lie in JL or MN or both. Since JL and MN are distinct sets, the union of these two sets is s
JL U MN = {1, 2, 3} U {5, 6} = {1, 2, 3, 5, 6} . However, JM contains all the points from J to M which is {1, 2, 3, 4, 5} which is not the same as JL U MN

So Statement 1 is false

2. JL U MN = {1, 2, 3} U {6, 7} = {1, 2, 3, 6, 7} so it contains more points than MN{6, 7} and therefore Statement 2 is false

3. LM U LN
We can see that LN contains all the points in LM and MN = {4, 5, 6, 7}. LM U LN = {4, 5} U { 4, 5, 6, 7} = {4, 5, 6, 7}. But LM is only a subset of LN and has fewer points {4, 5}  so Statement 3 is false

4. LM U LN
LM = {4, 5}, LN = {4, 5, 6, 7} so LM U LN = {4, 5, 6, 7} = LN. Remember sets don't duplicate. So Statement 4 is True

5. NT U JT
NT = {8, 9} and JT = set of all points in the segment from J to T which is all the points. So JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} and NT U JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} which is the set of all points in JT. Therefore Statement 5 is True

The figure below shows a graphical representation of what I wrote above. If you look at LN for instance, it has 4 points {4, 5, 6, 7} and therefore represents all the points in LM and LN (without duplication of points). This is Statement 4, by the way

Answer:

14x+14

Step-by-step explanation:

9x+5+5x+9

=9x+5+5x+9

=(9x+5x)+(5+9)

=14x+14

The point on the graph y = -f(x) is (-2 , -8)

According to the question the coordinates we have been given is (-2 , 8) and it is on the graph y = f(x)

That is we have been given that

                f(-2) = 8            (1)

Now we have to find the point on the graph y = -f(x)

So we will choose the value of x = -2 in f(x)

 Thus, putting the required value we get

                y = - f(-2)

As the value of f(-2) is 8 from equation (1). we will equate the value in the above equation we get

               y = -(8)

               y = -8

Hence the point on the graph is (-2 , -8)

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Answer:

Step-by-step explanation:

Equation f (x) = |x| represent the Absolute Value Functions.

Parent functions are the simplest form of a given family of functions. A family of functions is a group of functions that share the same highest degree and, consequently, the same shape for their graphs.

Absolute Value Functions :

The parent function of absolute value functions is y = |x|. Absolute value functions are expected to return V-shaped graphs.

The vertex of y = |x| is found at the origin as well. Since it extends on both ends of the x-axis, y= |x| has a domain at (-∞, ∞).  Absolute values can never be negative, so the parent function has a range of [0, ∞].

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Because the height are in proportion, a possible value of the height of the tree is 70 m

The complete question is added as an attachment

The given parameters from the question are given as:

In the above expression, we have the following observations:

From the figure, we can see  that the height of the tree is about 5 times the height of the castle tower

This is represented as

Height of the tree = k * Height of the castle tower

Where

Scale factor, k = 5

Substitute the known values in the above equation

So, we have

Height of the tree = 5 * 14 m

Evaluate the products

So, we have

Height of the tree = 70 m

Hence, the possible height of the tree is 70 m

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Answer:

Step-by-step explanation:

Answer:

124.59

Step-by-step explanation:

Answer:

the answer would be 20,313,04

Step-by-step explanation:

last place = 8 rounds up makes the thousandth place 5 which rounds up and makes the hundreth place 0 which doesnt change tyhe 4 giving us our aanswer. PLEASE MARK BRAINLIEST.

Answer: All the answers you need are attached in the file.

Step-by-step explanation: Hope it helps!

The meaning of the point (378,9) is with 9 yards of yarn, Paula can knit 378 knot hats.

Given that:-

The number of hats h she can knit varies directly with the amount of yarn y in yards she has.

Also, the constant of proportionality is 42.

Hence, we can write,

h ∝ y

h = ky

where, k is the constant of proportionality, hence,

h = 42y

We have to interpret the meaning of  (378, 9).

From, the equation, h = 42y

We can observe that,

When y = 9

h = 42*9 = 378.

Hence, we can write that, the meaning of the point (378,9) is with 9 yards of yarn, Paula can knit 378 knot hats.

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a) The work done is 3.3 J

b) The new force would  stretch it  1.9 cm beyond its natural length.

Hooke's law states that, the force of elasticity that tends to stretch a spring is directly proportional to the extension that is caused by the force as long as we do not by any means exceed the elastic limit of the material. This implies that the Hooke's law can only be found to hold when the elastic limit of the material has not been exceeded and the material has not become plastic.

Now;

F = Ke

W =1/2 Fe

F = 2W/e

W = work done

F = force exerted

e = extension

F = 2 * 23 /(44 - 30) * 10^-2

F = 328.6 N

a) To stretch  34 cm to 36 cm;

W = 1/2 *  328.6 N * 2 * 10^-2

W = 3.3 J

The work done is 3.3 J

b) F = Ke

328.6 N/(44 - 30) * 10^-2 = K

K = 2347 N/m

Then;

45 N =  2347 N/m * e

e = 45 N/ 2347 N/m

e = 0.019 m or 1.9 cm

New length = 30 cm + 1.9 cm = 31.9 cm

The new force would stretch it to a distance of 31.9 cm or 1.9 cm beyond its natural length.

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Solving a system of equations, we conclude that 35 tickets for movie a were sold

Let's define the variables:

Here we know that a total of 47 tickets were sold, then:

x + y = 47

And they sold for a total of $200, then:

x*$4 + y*$5 = $200

So we have a system of equations:

x + y = 47

x*$4 + y*$5 = $200

We want to solve this for x, then we need to isolate the variable y in one of the equations, doing that in the first one we get:

y = 47 - x

Now we can replace that in the other equation to get:

x*$4 + (47 - x)*$5 = $200

x*$4 + $235 - x*$5 = $200

$235 - x*$1 = $200

$235 - $200 = x*$1

$35 = x*$1

$35/$1 = x = 35

This means that 35 tickets for the movie a were sold.

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Answer:

0+15 =15

Step-by-step explanation:

it is said that the sum should have a 0

Answer:

0.06(50h)

Step-by-step explanation:

Tax is usually computed by taking a percentage of the cost of a good or service. In the expression, we see that h represents the number of hours worked that are being paid for. Naturally, the cost of a service is the price times the hours worked. Therefore, 50 must represent the number of hours worked, and 50h represents the price Deborah must pay before tax. Knowing all this, we can deduce that the expression 0.06(50h) represents the tax that she must pay as it is a tax rate (6%) being multiplied by the cost before tax.

Applying the triangle proportionality theorem, the value of x and the value of y are:

C. y = 5, x = 10.

Since lines m and n are said to be parallel lines, therefore, according to the triangle proportionality theorem, the ratios below can be created.

4/12 = y/15 [proportional sides]

Cross multiply

(y)(12) = (4)(15)

12y = 60

Divide both sides by 12

12y/12 = 60/12

y = 5

x = 15 - y

Plug in the value of y

x = 15 - 5

x = 10

Thus, applying the triangle proportionality theorem, the value of x and the value of y are:

C. y = 5, x = 10.

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Answer:Cylinder B has the radius r and the height as h. The lateral surface area of cone is. The lateral surface area of cylinder is. 1/2 × lateral surface area of cylinder B, ⇒. ⇒ = lateral surface area of cone A. Hence we can conclude that the lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.

Hope this helped you :)

False, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, Lateral area of cone is given by: πrl

where r is the radius and l is the slant height

Here r = r and l = h

Hence, lateral area of cone A= π × r × h

                                           = πrh

And, Lateral area of cylinder is given by:

= 2πrh

where r is the radius and h is the height

Hence, Lateral area of cylinder B=2πrh

Clearly, both the lateral areas are not equal.

Hence, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.

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The evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3

From the question, we are to evaluate the subtraction operation using the number line

From the number line we can observe that the magnitude of the distance between two successive mark is 1/3

Now, we are subtract

-2/3 - (-1 1/3)

If we count from - 1 1/3 to -2/3, we will observe that there are two marks.

Thus,

1/3 + 1/3 = 2/3

Hence, the evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (5000)(0.025)(1) \implies I = 125[/tex]

Answer:

80 percent

Step-by-step explanation:

4/5 = 80 percent (4/5 = .8, .8*100= 80)