Find the slope of the line that passes through each of the following sets of points (0, 0) and (1, 4)

Answer:"There are 24 ​pennies, 21 ​dimes, and 29 quarters", so there are 25+21+29 = 75 coins so far. This is the amount of coins that aren't nickels. The rest are nickels, which is some amount n. This adds to the 75 to get 75+n. Set this equal to 92 because there are 92 coins in all. That's how we end up with 75+n = 92.

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Extra info

The equation 75+n = 92 is the same as n+75 = 92. Subtract 75 from both sides to isolate n. You should get n = 17 after doing so.

Step-by-step explanation:

For us to be able to determine the new coordinates of the triangle after being dilated with a scale factor of 2 centered from the origin, multiply each x and y coordinate value by the scale factor of 2 to find the new coordinates.

We get,

A (2, 3) → A' (4, 6)

B (-5, 4) → B' (-10, 8)

C (0, -12) → C' (0, -24)

Let's now plot it in a graph,

So, we know BC is parallel to EF and 1 is congruent to 3.

Angles between parallel lines have special relationships. The relationships between 2 and 3 is that they are Same-side Interior Angles. This means that angles on the same line, formed by parallel lines intersecting that line (and the angles are on the same side of their respective line) are congruent. So, 2 and 3 are congruent... But by the transitive property, if 1 = 3 and 3 = 2... 1 = 2! And if 1 = 2, they are also Same-side interior angles and thus, the lines they lie on are parallel! So, since 1 and 2 are congruent, AB is parallel to DE.

Answer:

See below.

Step-by-step explanation:

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2} BC \parallel EF & \phantom{\dfrac11}\sf Given\\\\\angle 2=\angle 3 & \textsf{Corresponding Angles Postulate}\\\\\angle 1=\angle 3 & \sf Given\\\\\angle 1=\angle 2 & \textsf{Transitive property of equality}\\&(\angle 2=\angle 3 \; \textsf{and} \; \angle 1=\angle 3)\\\\AB \parallel DE & \textsf{Corresponding Angles Postulate}\\& \textsf{as} \;\angle 1=\angle 2\end{array}[/tex]

As DE intersects the two parallel lines BC and EF, ∠2 is congruent to ∠3 (corresponding angles postulate).

As ∠1 = ∠3 and ∠2 = ∠3, then ∠1 = ∠2 (transitive property of equality).

Therefore, as ∠1 and ∠2 are congruent, AB and DE must be parallel (BC is the transversal).

Answer:

4.3

Step-by-step explanation:

The value of [tex]m^{8} m^{-6}[/tex]  after simplification is [tex]m^{2}[/tex].

According to the question,

We have the following expression:

[tex]m^{8} m^{-6}[/tex]

Now, please note that there are some rules for simplifying expressions with powers. For example, powers are added if the base of the terms in the multiplication are the same. And if the base of the terms are same but they are in division then the powers are subtracted.  

In this case, the base is same (m) and the terms are in multiplication.

So, we are supposed to add their powers.

Now, we have the following expression:

[tex]m^{(8-6)}[/tex]

[tex]m^{2}[/tex]

Hence, the value after solving the given expression is [tex]m^{2}[/tex].

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Through the knowledge and trigonometry, we have :

1. Since a circle's circumference is 360 degrees or two pi radians, a radian is equivalent to 180 degrees. Since radians require knowledge of higher mathematics and contain tangents, sines, and cosines, which are taught in college, they are not as frequently employed in measuring circles and angles as degrees.

2. The measurement of the lowest, positive, acute angle t created by the angle's terminal side is known as the reference angle, t the horizontal axis, too. As a result, positive reference angles can be used as models for angles in other quadrants because their terminal sides are in the first quadrant.

In the 1st Quadrant, All the trigonometric functions are positive,

[tex]t^{'} =t[/tex]

In the 2nd Quadrant. Only Sin is positive,

[tex]t^{'} = 180-t[/tex]

So, [tex]cost^{'} = Cos(180-t) = -Sint[/tex]

3. Secant is the Inverse of Cos and Cosecant is the Inverse of Sine, Hence they are :

[tex]Secant \alpha = \frac{hypotenuse}{base}\\ Cosecant \alpha = \frac{hypotenuse}{perpendicular}[/tex]

4. The x-coordinate is the central angle's adjacent side, while the y-coordinate is its opposite side.

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Answer:

17.245

Step-by-step explanation:

34.49 divided by 0.2 is 17.245

See explanation below

Explanation:

We are told the centres of the two towns are 6miles apart.

This means the distance between Sunnyvale and Gloomington = 6 miles.

We will draw a line with a distance of 6cm to indicate their distance apart.

The two end points of the line will indicate the location of Sunnyvale and Gloomington respectively.

For the developers to locate the mall not more than 3 miles from the center of Sunnyvale, we will draw a circle which has radius of 3cm. This way the mall doesn't exceed 3 miles from Sunnyvale.

For the developers to locate the mall not more than 5 miles from the center of Gloomington, we will draw a circle which has radius of 5cm. This way the mall doesn't exceed 5 miles from Gloomington.

The scale of the drawing will be 1cm represent 1 mile

You can use a compass(drawing tool) to draw the circles. adjusting the legs to suit the measurement of each radius.

The area under the each of the circles are all the possible locations of the map. The location of the new mall cannot go beyond the area under circles but can be within it.

Answer:

  C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.

Step-by-step explanation:

You want to know what transformations are needed to form g(x) = –(x – 6)² + 3 from f(x) = x².

The function transformations we are typically concerned with are ...

Each of these has a recognizable influence on the function.

Translation by 'h' units to the right and 'k' units up transforms the function to ...

  g(x) = f(x -h) +k

Expanding a graph horizontally by a factor of p and vertically by a factor of q transforms the function to ...

  g(x) = q·f(x/p)

Reflecting a graph horizontally across the y-axis replaces x with -x.

Reflecting a graph vertically across the x-axis replaces f(x) with -f(x).

Comparing g(x) = -(x -6)² +3 to the original f(x) = x², we see that ...

This means the graph was shifted right 6 units and up 3 units. The graph was reflected across the x-axis, so the curve opens downward.

Option c, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units. is the correct answer.

What is graph?

In the field of mathematics, a graph is a representation (visual) or diagram that shows the facts or values in an ordered and systematic way.

The relationships between two or more items are frequently represented by the points on a graph.

As given in the question,

[tex]f(x)=x^2[/tex] and [tex]g(x)= -(x-6)^2 + 3[/tex]

Since, [tex]f(x) = x^2[/tex]  we are applying the following three rigid transformations on f(x) to obtain g(x):

Therefore, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.

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Answer:

[tex](0,-\frac{11}{3} ),(1,-\frac{4}{3} ),(2,1)[/tex]

Step-by-step explanation:

Given Equation:

Required:

Steps:

Subtract 7x from both sides of the equation.

-3y = 11 - 7x

Divide each term in -3y = 11 - 7x by -3 and simplify.

-3y/-3 = 11/-3 + -7x/-3

Simplify the left side.

Cancel the common factor of -3.

-3y/-3 (canceled) = 11/-3 + -7x/-3

Divide y by 1.

y = 11/-3 + -7x/-3

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

y = -11/3 + -7x/-3

Dividing two negative values results in a positive value.

y = -11/3 + 7x/3

Choose any value for x that is in the domain to plug in to the equation.

Choose 0 to substitute in for x to find the ordered pair.

Remove parentheses.

y = -11/3 + 7(0)/3

Simplify  -11/3 + 7(0)/3.

⇒ Combine the numerators over the common denominator.

y = -11/3 + 7(0) / 3

Simplify the expression.

y = -11 + 0/3

y = -11/3

y = -11/3

Use the x and y values to form the ordered pair.

(0, -11/3)

Choose 1 to substitute in for x to find the ordered pair.

Remove parentheses.

y = -11/3 + 7(1)/3

Simplify -11/3 + 7(1)/3.

Combine the numerators over the common denominator.

y =  -11/3 + 7(1)/3

Simplify the expression.

Multiply 7 by 1.

y = -11 + 7/3

Add -11 and 7.

y = -4/3

Move the negative in front of the fraction.

y = -4/3

Use the x and y values to form the ordered pair.

(1, -4/3)

Choose 2 to substitute in for the x in the ordered pair.

Remove parentheses.

y = -11/3 + 7(2)/3

Simplify -11/3 + 7(2)/3.

Combine the numerators over the common denominator.

y =  -11/3 + 7(2)/3

Simplify the expression.

Multiply 7 by 2.

y = -11 + 14/3

Add -11 and 14.

y = 3/3

Divide 3 by 3,

y = 1

Use the x and y values to form the ordered pair.

(2, 1)

These are three possible solutions to the equation.

(0, -11/3), (1, -4/3), and (2,1)

Thanks,
Eddie

Answer:

$3375

Step-by-step explanation:

3 3/4 ÷ 1/2

=15/4 × 2/1

=7 1/2

7 1/2 multiply by carpet cost

7 1/2 × 450

= $3375

(your 3rd and 4th option in the multiple choice are the same btw)

Step 1

From the image;

Hence;

The triangles also share similar angles therefore the answer will be;

depending on the question but it's most likely 103

Step-by-step explanation:

Answer:

y = -3x + 13

Step-by-step explanation:

We can use the the point slope form of an equation for this:

y - y1 = m (x - x1)

Replace the y1, x1, and m variables with what we were given:

y - (-2) = -3 (x - 5)

Distribute

y + 2 = -3x + 15

Combine like terms

y =  -3x + 13

Answer: (x-9) and (x+2)

Step-by-step explanation:

You would first have to break the trinomial down into 2 factors.

Since there are two minuses in the trinomial, start off like this : (x- __) (x+__)

Now, what two numbers add to -7, and multiply to -18?

9 and 2, with one term being negative.

Since the 2nd term in the trinomial is a negative, there must be a number added that has a greater negative term than the other positive term, therefore, making 9 the negative term, since 2-9 is -7.

And -9 times 2 is -18.

Now fill in the blanks : (x-9)(x+2)

Since (x-9) and (x+2) are multiplied by each other, they are the dimensions of the desk, being L x W.

Now let's double check the factors:

(x-9)(x+2)

Distribute the terms.

x^2 +2x -9x -18

x^2-7x-18

There, hoped that helped :D

The equation given is,

The y-intercept is determined when x coordinate is zero.

Substitute x equals to 0 in the equation,

Thus, the ordered pair of y-intercpet is,

The correct option is c.

Answer:

A''(3, 2), B''(-1, 4), C''(2, 0)

Step-by-step explanation:

For the first step, negate the y coordinate.

For the second step, add 4 to the x coordinate and 5 to the y coordinate.

[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]

Given:

We're a given figure ABCD

∠ADB = x - 30

∠DBC = -9 - 6x

To find:

The value of x for which ABCD must be a parallelogram.

Step-by-step solution:

For ABCD to be a parallelogram, Its Alternate angles (Z - angles) must be equal.

Thus,

∠ADB = ∠DBC

x - 30 = -9 - 6x

7x = 21

x = 3

Final answer:

For ABCD to be a parallelogram, The value of x should be equal to 3.

Given the data below.

The median of the data above is the middle number

The first quartile is:

The third quartile is:

The box and whisker plot for the data is:

The second option is correct.

(Number 5)

The given equation is:

This function represents the product of x and 2^x, therefore, to find the derivative, we will use the product rule.

When y = UV, dy/dx is given as:

In the equation y = x (2^x):

Substituting the U, V, dU/dx, and dV/dx into the given formula for dy/dx:

Here, we want to calculate the area of the given triangle

Mathematically, the product of the height and base of a triangle divided by 2 gives its area

Now, as we can see the shape, while IJ represents the base, KJ represents the height

We need to calculate the distance between these points before we can get the area of the triangle

To get the distances between the points, we have to use the distance formula

We can proceed with this as follows;

Thus, we have the area of the triangle as follows;

Answer:

It is possible for Gabriella and Lisbet to make a profit

Explanation:

Let's call x the number of bracelets that they will make and y the number of earrings that they will make.

If the bracelets will cost $2 and the earring will cost $3, they will make:

2x + 3y

Then, this quantity should be at least $500, so:

2x + 3y ≥ 500

Additionally, they would like to make less than 50 bracelets, so:

x < 50

So, the system of inequalities is:

2x + 3y ≥ 500

x < 50

Now, to graph the system, we need to identify the lines that separate the regions. So, for x < 50, we get that the line is x = 50, a vertical line that passes through the point (0, 50).

For 2x + 3y ≥ 500, we need to identify two points that belong to the line

2x + 3y = 500 as (250, 0) and (100, 100)

So, the graph of the inequalities is:

Therefore, the solution of the system is the yellow region. Since there is a region in the graph, Gabriella and Lisbet can make a profit.

Answer:

  13.192 seconds

Step-by-step explanation:

You want to know the time to travel 4.500 km at a speed of 341.11 m/s.

The relation between time, speed, and distance is ...

  time = distance/speed

  time = (4500 m)/(341.11 m/s) ≈ 13.192 s

It would take Andy about 13.192 seconds to travel 4.500 km.

__

Additional comment

The distance of 4.500 km is rounded to the nearest meter, so may have an error of 0.5 meters. At 342.11 m/s, it takes about 1.47 ms to travel that distance. This suggests that timing to the nearest millisecond is consistent with the precision of the other numbers in the problem.

One could argue that speed is 5 significant figures, but distance is 4 significant figures. That suggests their ratio, time, is only accurate to 4 significant figures: 13.19 s. Analysis of the worst-case error in the ratio suggests that this reported value throws away some accuracy, so a better result is 13.192 s.

The area A of the circle whose radius is 10 can be calculated by given equation A =pi r^2 is 314.2 cm^2.

What is area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

If we draw a square using a pencil on a sheet of paper. It will have two dimensions. The area of a shape on paper is the area that it occupies and it will be called as area of that square.

For getting the area of the circle we need to put the value of r in the given equation:

r = 10 cm

Putting the value of pi and r in the equation:

A = pi r^2

A = 3.142 (10)^2

A = 3.142 (100)

A = 314.2

Therefor the area of the circle calculated by given equation is 314.2 cm.

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Complete question

A circle of radius r has area A, where A =pir^2, calculate the area of circle whose radius is 10 cm.

[tex]a=\frac{D}{G+3h^{3}}[/tex]

Looking at the equation, we can see that “a” is a part of both terms. Therefore, we can factor it out. Then we divide to get “a” by itself.

See details:

Given: A scale factor of 1/2 and center N of a figure is given.

Required: To dilate the given figure using the given scale factor and center.

Explanation: Dilation is a transformation, used to change the size of the given figure. If the value of dilation>1 then the new figure enlarges. If dilation<1 then the given figure contracts while a dilation=1 means that the new figure is of the same size.

Now here the center is given to be N. And the scaling factor is 1/2.

The coordinates of center N are (3,2). Point M is 2 units left and 4 units down from point N. Hence for dilation of a factor of 1/2, point M' will be 1 unit to the left and 2 units down from point N -

Similarly, point O is 2 units to the right and 6 units down from point N. Hence for dilation of a factor of 1/2, point O' will be 1 unit to the right and 3 units down from point N.

Final Answer: M'=(2,0)

O'=(4,-1)

Answer:

Step-by-step explanation:

Given the following system of equations:

Since on equation 2, x is already isolated, substitute it into equation 1:

Solve for y.

Knowing the value of y, plug it into equation (2) and solve for x:

Since the list price is $39.95

Since the series of discounts 20/10/10

Then we will find the new price by this way

Since the first discount is 20%, then

The new price will be 80% of 39.95

Since the second discount is 10%

Then the new price is 90% of 31.96

Since the third discount is 10%

Then the new price is 90% of 28.764

Since the second option has only a 20/10 discount, then

The new price is 28.764

To find the difference subtract 25.8876 from 28.764

The difference = 28.764 - 25.8876

The difference = 2.8764

The answer is $2.8764

total marbles: 15

brown marbles: 6

Probability : brown marbles / total marbles = 6 /15 (simplify) = 2/5

Answer:

5.49

Step-by-step explanation:

3+ 51= 54                  

54 x 1/10= 5.4    + 9 x 1/100

5.4 + 0.09=

5.49