the drop down menus choices are: two imaginary solutionstwo real solutionsone real solution

The equation to illustrate the cost of a pen is two and half times the cost of a pencil is C = 2.5p.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the cost of a pen is two and half times the cost of a pencil.

Let the pencil be represented as p.

Let the cost be represented as c.

The cost will be:

C = 2.5 × p

C = 2.5p

This illustrates the equation.

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Answer:

R = 75

O = 75

F = 30

Step-by-step explanation:

15x + 15x + 6x = 180

add like terms

36x = 180

divide

x = 5

The measure of angle P is 30°, angle R is 75° and angle O is 75° in triangle POR.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

From the given triangle POR, ∠R=15x, ∠O=15x and ∠P=6x.

By using angle sum property, we get

∠P+∠O+∠R=180°

6x+15x+15x=180

36x=180

x=180/36

x=5

So, ∠R=15x=75°, ∠O=15x=75° and ∠P=6x=30°

Therefore, the measure of angle P is 30°, angle R is 75° and angle O is 75° in triangle POR.

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Unknown, the correct equation is:

- 4,863 + 81.1m = - 3,645 + 76.9m

And to solve for m, you use the standard form:

Like terms:

81.1m - 76.9m = -3,645 + 4,863

4.2m = 1,218

Answer:Nuts

Step-by-step explanation:

green on green

If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x

The cost of flower vase = $15

The cost of each flower = $2

Consider the number of flowers as x

Then the linear equation that represents the cost of buying flowers = The cost of flower vase + The cost of each flower × x

Substitute the values in the equation

The equation that represents the cost of buying flowers = 15+2x

Hence, If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x

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Answer:

Explanation:

Given:

y=4x-5

3x+4y=7

We can check if the lines are parallel, intersect, or coincide by graphing. To graph, we plug in any values for x to determine the y values.

The graph of the lines is shown below:

So based on the graph, the lines intersect at a point.

Therefore, the lines intersect.

20/6 = p/12

cross-multiply

p x 6 = 20 x 12

6p = 240

divide both-side of the equation by 6

p = 240/6

p = 40

The elements that are in  ( A ∪ B ) = { 2, 4, 5, 7, 8, 9, 10 , 11, 12, 14, 15, 17, 18, 19, 20}

The elements of the set that are in ( A ∩ B ) = {9, 12, 15, 17, 18 }

This is the term that is used to refer to all of the elements that are contained in a two or more sets which are a subset of the Universal set.

In this case, the union of the set is given as the elements in both A and B written together as { 2, 4, 5, 7, 8, 9, 10 , 11, 12, 14, 15, 17, 18, 19, 20}. All of these values are in A and B.

This is the term that is used to refer to all of the values that would appear in the two sets that are in the subset of the universal set.

Here we have the value of A ∩ B = {9, 12, 15, 17, 18 }

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The distributive property of multiplication states the following:

So, for the given expression, we have:

We have two points known to be ( S ) and ( T ). A line connects two points.

The minimum number of points that are required to form a straight line in a cartesian coordinate system are ( two ).

The minimum number of points that are required to form a plane in a cartesian coordinate system are ( three ) which will form two vectors i.e it requires two lines formed with a common point.

Two planes always intersect at exactly one point with direction normal to the two plane normal vectors.

Hence, the only possible postulate that relates two points is the formation of a line between two points; hence, the correct postulate for the given statement is:

Okay, here we have this:

Considering that the range of a function is the complete set of all possible resulting values of the dependent variable (y), we can see in the graph of the function that:

The values of the variable "y" go from -1 to plus infinity, this mean that the range is:

-1≤y<∞

Finally we obtain that the correct option is the first option.

The coordinates are;

Given,

Quadrilateral DEFG with vertices;

We have to find the coordinates of E', F', G'.

A figure is translated when it is moved to the left, right, up, or down.

The original figure's points are all translated (moved) by the same amount and in the same direction.

Here,

Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.

D = (-1, 2)

D' = (-2, -2)

The x-coordinate has be translated 1 unit to the left.

The y-coordinate has been translated 4 units down.

Then,

The mapping rule is:

(x, y) → (x-1, y-4)

To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:

⇒ E' = (-2-1, 0-4) = (-3, -4)

⇒ F' = (-1-1, -1-4) = (-2, -5)

⇒ G' = (1-1, 3-4) = (0, -1)

That is,

The coordinates are;

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The answer is option(b) i.e,the given statements are not equivalent.

What is Truth table?

A truth table is a breakdown of a logic function by listing all possible values the function can attain. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.

Let's proof it by using truth table :

p     q   (~q → ~p)   (~p → ~q)

F      F     T                 T

F      T     T                 F

T      F      F                 T

T      T     T                 T

As you've seen in truth table (~q → ~p)  ≠ (~p → ~q)

Therefore, the answer is option(b) i.e,the given statements are not equivalent.

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Find the quotient given below:

When managing complex numbers, we must recall:

Multiply and divide the expression by the conjugate of the denominator:

Multiply the expressions in the numerator and in the denominator. We can apply the special product formula in the denominator:

Operating:

Operate and simplify:

Applying the property mentioned above:

Simplifying:

Answer:

Explanation:

The Two Tangent Theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.

To be able to find AB we have to 1st of all find the value of x by equating both lengths together since both AB and AD are equal as shown below;

S

ANSWER

EXPLANATION

Nancy has $100.

The charges are:

=> $5 admission per person. She has x cousins and herself to pay for, this means that she pays $5 for (x + 1) persons.

The admission charge is therefore:

$5 * (x + 1) = $5(x + 1)

=> $3 per ticket for rides. The number of rides she can pay for is y. So the charge for rides is:

$3 * y = $3y

Since she only has $100, everything she pays for can only be less than $100 or equal to $100.

This means that, if we add all the charges, they must be either less than or equal to $100.

That is:

That is Option C.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

Let the rate of change of  the edge length x, y, and z of a closed rectangular box are:

dx/dt= 1m/s

dy/dt= -2 m/s

dz/dt= 0.5 m/s

a) The volume of the box

From the formula of the volume,

V=xyz

Then,

differentiate w.r.t t

[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]

[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]

put the value of x, y, z , then we get

[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]

[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]

[tex]\frac{dV}{dt} = 8m^3/s[/tex]

The rate of change of the volume of the box is 8m³/s.

b) surface area of the box

surface area of the rectangular box is

s = 2xy + 2yz + 2zx

differentiate w.r.t t

[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]

[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]

[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]

[tex]\frac{ds}{dt} = -19m^2/s[/tex]

The rate of change of the surface area of the box is -19m²/s.

c) diagonal of the box

lengths of  the boxes for the diagonal is

s = 2x² + y² + z²

differentiate equation w.r.t t

[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]

[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]

[tex]\frac{ds}{dt} =1m/s[/tex]

The rate of change of the diagonal of the box is 1m/s.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

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Let us break the shape into two triangles and solve for the unknowns.

The first triangle is shown below:

We will use the Pythagorean Theorem defined to be:

Therefore, we can relate the sides of the triangles as shown below:

Solving, we have:

Hence, we can have the second triangle to be:

Applying the Pythagorean Theorem, we have:

Solving, we have:

The values of the unknowns are:

The value of k when one angle measures 140°, and another angle measures (5k + 85)° and if the angles are vertical angles is 11.

Vertical angles are angles opposite each other where two lines cross.

Note: Vertical angles are equal.

To calculate the value of k, we use the principle of vertical angle

From the question,

Solve for k

Divide both side by the coefficient of k (5)

Hence, the value of k is 11.

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The distance between points N and A is 7, and we can take that as the base of the tringle (up side down)

The distance between the base (NA) and the point P is 6, and we can take that as the height of the triangle

Area of a triangle = (Base x Height)/2

Area = (7 x 6)/2 = 42/2 = 21

Answer:

Area = 21

In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:

Comparing with the given equation, we have a = -5, b = -270 and c = -520.

Now, let's calculate the x-coordinate of the vertex using the formula below:

Using this value of x in the equation, we can find the y-coordinate of the vertex:

Therefore the vertex is located at (-27, 3125).

Explanation

Step 1

when you have a coordinate (x,y) and you want to get the image after a dilationi, make

then

let

coordinate=(-5,1)

dilation scale=5

now, replace

I hope this helps you

The fraction for the amount of honey each jar holds is 2/3.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, Daniel fills 24 equal sized jars with honey and he brings a total of 16 cups of honey to sell at the farmers' market.

The amount of honey will be:

= Number of cups / Number of jars

= 16 / 24

= 2/3

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Answer:

0.135% or 0.00135

Explanation:

• The population mean height = 68 inches

• The population standard deviation = 4 inches

• Sample Size, n = 36

First, find the sample standard deviation:

Next, for X=70, find the z-score:

Since we are looking for the probability that their average height is more than 70 inches, we need to find:

• P(X>70)=P(z>3)

Using the z-score table:

The probability that their average height is more than 70 inches is 0.135%.

The slope formula is

we can use this formula by introducing the values of the given points. In our case

Hence, we have

It yields,

hence, the answer is

Our equation

is a quadratic equation. In simple words, it's a parabola, whose graph (red curve) is the following:

The axis of symmetry of a parabola is just the line dividing the parabola into its two arms. In the graph, the axis of symmetry is the blue vertical line. It's usually represented algebraically by

The axis of symmetry of our quadratic equation is

Answer:

To solve the system of two linear inequalities graphically,

For step 1,

Draw a line 4x+6y=24

Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.

Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,

Similarly for the inequality,

It covers the region right side of the line x=2,

we get the siolution region as the intersecting region of both inequality which defined in the graph as,

Dark blue shaded region is the required solution set for the given inequalities.

The first compound indequality is:

We can view this in the real line:

There is no number that can be both greater AND less than 7, which makes the correct answer "No solution".

The second is:

Now, we are not looking for intercetion, we are looking for the union of both. The firts inequality takes all number less than 7 and the second all that are greater than 7, so the only one that is not a solution is 7, which means the correct answer is "all real numbers except 7"

The third is:

This is the same as the first one, but now the 7 is included in both:

So, there is only 7 that can be in both indequalitys, thus the correct answer is "one solution, 7".

The fourth is

This is similar to the second, but now 7 is included, which means it is also a solution, thus the answer is "all real numbers".

For a line to be parallel to another line, the slope will be the same

1st equation:

Since the slope of the first line = 2/5, the slope of the second line will also be 2/5

We would insert the slope and the given point into equation of line to get y-intercept of the second line:

The equation for the line that passes through (-7, 6) and parallel to line 2x - 5y - 8 = 0:

The most appropriate choice for equation of line in slope intercept form will be given by

x + 2y = -16 is the required equation of line

What is equation of line in slope intercept form?

Equation of line in slope intercept form is given by y = mx + c

Where, m is the slope of the line and c is the y intercept of the line

The distance from the origin to the point where the line cuts the x axis is called x intercept

The distance from the origin to the point where the line cuts the y axis is called y intercept

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

[tex]m=tan\theta[/tex]

If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

The line passes through (0, -8) and (-2, -7)

Slope =

[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]

The line passes through (0, -8)

Equation of line

[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]

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