Solve the system by substitution.
-7x + 5y = -27
y = 2x

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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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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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:

80 percent

Step-by-step explanation:

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

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.

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:

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.

Answer:

14x+14

Step-by-step explanation:

9x+5+5x+9

=9x+5+5x+9

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

=14x+14

Answer:

[tex]77, 385[/tex]

Step-by-step explanation:

Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.

One number is one-fifth of the other number:

[tex]x=\frac{1}{5}y[/tex]

The difference between the two numbers is 308:

[tex]y-x=308[/tex]

This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.

Now we have a system of equations:

[tex]\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.[/tex]

I will rewrite the first equation for simplicity:

[tex]5x=y[/tex]

Now, I will substitute y from the first equation for y in the second equation:

[tex]5x-x=308[/tex]

Simplify:

[tex]4x=308\\x=77[/tex]

Now, use x to find y using the second equation:

[tex]y-77=308\\y=385[/tex]

Now, I can check the solutions by plugging them into the first equation!

[tex]x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77[/tex]

The solution is correct!

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 slope of the lined graph is 5 / 3

The formula for determining the slope of a line is expressed as;

Slope = y2 - y1/ x2 - x1

From the graph shown;

Now, let's substitute the values

Slope, m = 4 - (-1) / 3 - 0

Find the differences

Slope, m = 4 + 1/ 3

Slope, m = 5 / 3

Thus, the slope of the lined graph is 5 / 3

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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:

0+15 =15

Step-by-step explanation:

it is said that the sum should have a 0

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

Step-by-step explanation: Hope it helps!

Step-by-step explanation:

2 × 7 × 7.................

[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:

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

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: 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.

Zendaya will travel $ 1 and 17/21  of a mile per hour on her roller skates.

Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. We can simply write this statement in mathematical form as,

Total distance covered by Zendaya in 3 hours on her roller skates = $( 5 + ( 3/7 )  of a mile

Total distance covered by Zendaya in 3 hours on her roller skates = $ ( ( 35 + 3)/7 ) of a mile

Total distance covered by Zendaya in 3 hours on her roller skates = $ ( 38/7 )

Total distance covered by Zendaya in 1 hours on her roller skates = $ (( 38/7 )/3 ) = $ (38/21) of a mile

or we can write also write  ( 38 /21 ) miles per hour as ( 1 and 17/21 ) miles per hour.

So, Zendaya will travel $ 1 and 17/21  of a mile per hour on her roller skates.

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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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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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The function that is positive for the entire interval [-3,-2] is given by:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).

We have to look at the graph of the function relative to the x-axis, as follows:

The graphs for this function are given at the end of the answer, and the only function for which it is positive, that is, above the x-axis, in the entire interval [-3,-2] is the second, hence the correct option is:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).

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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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