Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One- half of the comission goes to the broker, and one- half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.

The intersection of these lines is the answer to the given system of equations. → (-1, -2)

Given the system of equations,

y = x - 1

y = 3x + 1

Now, equating both the given equations,

x - 1 = 3x + 1

3x - x = -2

2x = -2

x = -1

From, y = x - 1

          y = -1 - 1

          y = -2

The answer to the given system of equations is located at the intersection of these lines.

⇒ (-1, -2)

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Functions of the form  f(x)=kx represents direct variation.

The table of values that appears a constant proportion between two variables speaks to a direct variation function. In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion.  the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. Typically since direct proportion is spoken to by the direct variation formula that's given by. Functions of the form, there may be a constant, are the as it were functions that can speak to a direct variety. Typically since coordinate proportion is spoken to by the coordinate variation formula that's given by y=kx.

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The minimum possible volume of this rectangular prism is 176.78 ft³.

The maximum possible volume of this rectangular prism is 131.11 ft³.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

In order to determine the minimum possible volume of this rectangular prism, we would add the greatest possible error to each measurement and then multiply as follows:

Vmin = (3.5 + 0.25) × (8.4 + 0.25) × (5.2 + 0.25)

Vmin = 3.75 × 8.65 × 5.45

Minimum possible volume, Vmin = 176.78 ft³.

In order to determine the maximum possible volume of this rectangular prism, we would subtract the greatest possible error from each measurement and then multiply as follows:

Vmax = (3.5 - 0.25) × (8.4 - 0.25) × (5.2 - 0.25)

Vmax = 3.25 × 8.15 × 4.95

Maximum possible volume, Vmax = 131.11 ft³.

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The property that defines the number sentence 6 + 0 = 6 is Additive Identity Property.

Given,

6 + 0 = 6

We have to find the property that defines the number sentence;

Additive Identity Property;

Additive identity property says that if zero is added to any real number, the resultant would be the same real number.

Here,

6 + 0 = 6

In this instance, we have added 0 to a real number (6) and have received back the same real number (6).

That is,

Additive Identity Property is the property that defines the number sentence 6 + 0 = 6

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The value y is -36.

Proportionality is the property of two variables being in a multiplicative relation to a constant.

Given that, y varies jointly with x and z and y=-60 when x=-5 and z=4,

y ∝ xz

Let k be the Proportionality constant,

y = kxz

-60 = k*4*-5

k = 3

When x = 4 and z = -3

y = 3*4*-3

y = -36

Hence, The value y is -36.

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The volume of the rectangular prism with length of 5 units, width of 4 units and height of 3 units is 60 unit³

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Volume is the amount of space occupied by a three dimensional side or object.

Let us assume that the rectangle prism have length of 5 units, width of 4 units and height of 3 units. Hence:

Volume of prism = length * width * height

Volume = 5 units * 4 units * 3 units = 60 unit³

The volume is 60 unit³

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The area of the paperboard remaining after a semicircle is cut out of it is 235.52 in².

The area is the amount of space within the perimeter of a 2D shape.

To calculate the area of the rectangular board that remain, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the paperbaord left is 235.52 in².

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Answer:11x

Step-by-step explanation:

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.

There are three additional names for a rhombus:

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The length of 1 on AC is 54.6 cm.

Given:

Let x be the length

we know that,

AC dimensions = 54.6 * 175.7 * 85.6 cm

It is the volume = l * b * h

Volume :

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Length :

Length is defined as the measurement or extent of something from end to end.

Breadth :

The breadth of something is the distance between its two sides.

On comparing both

Length l = 54.6 cm

Breadth b = 175.7 cm

Height h = 85.6 cm

Therefore the length of 1 on AC is 54.6 cm.

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The equation that could represent the relationship between [d] and [t] is d = 60t.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken.

We can write the equation that could represent the relationship between [d] and [t] with the help of the equation of a straight line.

y = mx + c

for c = 0

y = mx

m = 120/2

m = 60

So -

y = 60t

or

d = 60t

Therefore, the equation that could represent the relationship between [d] and [t] is d = 60t.

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Answer: 2.6

Step-by-step explanation:

Use long division:

16.64 over 6.4

First multiply the numerator by 10 to get 166.4 over 64

Then divide 166.4 by 64 (using long division)

At the end you'll get 2.6

To rewrite equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

We know that,

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

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The answer to this question is after solving definite integration 0,1,-4,-10

What is Definite integration?

It is just basically Simple Integration with limits. In other words it is completely same as area under curve

Solution:

We will proceed by finding area under curve

Here we have to consider the area above x axis as positive and area under x axis as negative area

In First part +ve area and -ve area cancels each other hence answer is 0

In second part after cancellation only 1 square block above x axis remains whose area is 1  hence answer is 1

remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative

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The value of s in the formula

[tex]s = ut + \frac{1}{2}at^2[/tex] is [tex]\frac{19}{4}[/tex]

What is subject of a formula?

At first, it is important to know about formula

Formula is an equation which consists of variables and numbers and they are connected by mathematical operations.

In a formula, there are many variables present.

Subject of a formula is that variable which can be expressed in terms of other variables present in the formula.

Here, s is the subject of the formula

[tex]s = ut + \frac{1}{2}at^2[/tex]

u = 10, a = -2, t = [tex]\frac{1}{2}[/tex]

s = [tex]10 \times \frac{1}{2} + \frac{1}{2}\times (-2) \times (-\frac{1}{2})^2\\[/tex]

s = [tex]5 - \frac{1}{4}[/tex]

s = [tex]\frac{20 - 1}{4}\\[/tex]

s = [tex]\frac{19}{4}[/tex]

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The difference in pressure between the main line and the second floor is 91,100 Pa.

Bernoulli's theorem states that a drop in fluid pressure is connected with an increase in fluid velocity if the fluid flows horizontally so that there is no change in gravitational potential energy.

On the basis of the idea of energy conservation, Bernoulli's principle is explained. According to this law, the total amount of mechanical energy in a fluid travelling along a streamline will be the same at every point along that streamline in a steady flow.

Given ,

The settings provided;

The main line's water speed is 2.0 m/s,

The second floor's water speed is 7.0 m/s,

The water's density is 1.0 x 103 kg/m3.

The following formula can be used to compute the pressure difference between the main line and the second level using Bernoulli's equation:

[tex]p_1+1/2pv2/1+pgh1+ = p2+1/2pv2/2+pgh_2[/tex]

[tex]p1- p2 = 1/2pv2/2 - 1/2pv2/1 + pgh2 - pgh1[/tex]

[tex]p1 - p2 = 1/2p(v2/2 - v 2/1) + pg (h2- h1)[/tex]

p1 - p2 = 1/2(1000)(7² - 2²) + (1000 ×9.8)(5 - (-2))

p1 -  p2  = 91100 pa

Thus, the difference in pressure between the main line and the second floor is 91,100 Pa.

The complete question is : A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103 kg/m 3 . The difference in pressure between the main line and the second floor is _______.

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Answer:

[tex]\textsf{(d)} \quad \sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]

(e)    p ≤ -5

(f)     -m ≥ -9

Step-by-step explanation:

Symbol notation

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

[tex]\textsf{c is between $\dfrac{1}{5}$ and $\dfrac{1}{3}$}.[/tex]

If c is between 1/5 and 1/3, it is greater than 1/5 and less than 1/3 (as 1/5 < 1/3), but not equal to either number:

If p is not greater than -5, then it is less than or equal to -5:

If the negative of m is not less than -9, then it is greater than or equal to -9:

The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Translating the statement, we have the following inequality:

Let the variable x represent the amount of money in pocket.

From $5 to $8 in my pocket = 5 ≤ x ≤ 8.

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The equations of the line are listed according to slope and intercept below:

According to Euclidean geometry, a line can be constructed by knowing the location of two different points set on Cartesian plane. From analytical geometry we find that lines are represented by an equation of the form:

y = m · x + b

Where:

The slope can be found by secant line formula:

m = Δy / Δx

Now we proceed to find the equation of the line for each case:

Case 1 - (x₁, y₁) = (3, 2), (x₂, y₂) = (5, 7)

m = (7 - 2) / (5 - 3)

m = 5 / 2

b = y - m · x

b = 2 - (5 / 2) · 3

b = 2 - 15 / 2

b = - 11 / 2

y = - (5 / 2) · x - 11 / 2

Case 2 - (x, y) = (- 3, 4), m = 2

b = y - m · x

b = 4 - 2 · (- 3)

b = 4 + 6

b = 10

y = 2 · x + 10

Case 3 - m = - 3, b = 5

y = - 3 · x + 5

Case 4 - x-intercept: 3, y-intercept: 0

m · 3 + b = 0

3 · m = - b

m · 0 + b = 0

b = 0

m = 0

y = 0

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Answer:

8 + [8 + (-1*(-3)-4)]÷(-7) = 7/1 = 7

                    Hope this helped answer your question!

Answer:

7

Step by Step Explanation:

Answer:

undefined

Step-by-step explanation:

since all the x are zero it’s undefined and when all y is zero it’s 0

Hopes this helps please mark brainliest

The I quadrant will contain the point (6, 8). The number is in the I quadrant as a result.

What is Quadrant?

A quadrant is any one of the four divisions of the coordinate plane. Additionally, we refer to the sections as they are divided by the coordinate axes when we talk about the sections. The y-axis is situated on this up-down axis, and the x-axis is situated here. As you can see, it divides the coordinate space into four parts.

A point can be mathematically expressed as:

A(x, y )

The intersection of the coordinate axes divides the cartesian plane into four quadrants (x and y-axis).

                        (x, y )

In the first quadrant, the x and y coordinates are both positive.

              (x, y)

Y is positive while x is negative in the second quadrant.

                      (-x, y)

The point will be located in the third quadrant if both x and y are equally negative.

                      (-x, -y)

The point will be located in the fourth quadrant if both x and y are positive.

                       (x, -y)

pointed out; A(6, 8)

The y-coordinate in the highlighted position is positive at (8), while the x-coordinate is negative at (6).

Remember that if the x-coordinate is negative and the y-coordinate is positive, the point is in the I quadrant.

As a result, the provided point (6, 8) is said to be in the I quadrant.

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El espacio que ocupa la casa sería 6/15, el espacio que ocupa el huerto sería 4/15 y el espacio restante del terreno sería 5/15.

Para representar en forma de fracciones el área de los diferentes espacios del terreno de Pedro debemos tener en cuenta que el total tiene 15 metros. Adicionalmente, cuando representamos una fracción estamos informando cuántas unidades de un número x de unidades estamos utilizando. Por ejemplo, en este caso del total (15 metros) del terreno que tiene Pedro, él esta utilizando 6 metros para su casa. Esta fracción se representaría así:

6 / 15

Por otra parte, la fracción para representar el área del huerto de Pedro debe seguir los mismos lineamientos que la anterior, es decir en el numerador (número de la parte de arriba) ponemos el número de unidades que utilizamos y en el denominador (número de la parte de abajo) ponemos el número total de unidades disponibles. Entonces la fracción del huerto sería:

4 / 15

Por ultimo, para saber cuántas unidades quedan disponibles del terreno de Pedro, debemos restarle al total de terreno la cantidad de espacio que usamos:

15 - 4 - 6 = 5

De acuerdo con lo anterior, el espacio disponible serían 5 metros, que expresado en fraccionarios sería:

5 / 15

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The equidistant point of  the triangle is point O , which is shown below.

In the question ,

we have to find the equidistant point in the triangle ,

We know that the equidistant point from the vertices of the triangle is the circumcenter ,

let the circumcenter be point O .

The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .

We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .

So ,we draw OA ,OB and OC .

we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.

that means , OA = OC and OC = OB .

which means OA = OB .

we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.

So, we can say that point O is on the perpendicular bisector of AB .

and

Since OA = OB = OC , the point O is equidistant from A , B and C .

Therefore , the equidistant point of the triangle is the circumcenter (point O) .

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Answer: 11.99 + 0.45t ≤ 16 The most toppings you can have is 8

Step-by-step explanation:

11.99 + 0.45 is a basic cheese pizza plus one topping
11.99 + 0.45t represents a pizza plus an undefined amount of toppings
11.99 + 0.45t ≤ 16 The cost of the pizza has to be 16$ or less
Subtract 11.99 from each side
0.45t ≤ 4.01
Divide both sides by 0.45
t ≤ 8.9111
You can't have a partial number of toppings, and 9 is too much, so we round down to 8.

Answer:

Step-by-step explanation:

V = 16755.1608 m3

No, the centroid and Circumcentre are not same but it is same in equilateral triangle.

The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.

Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.

Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.

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Comparing the box-and-whisker plots for both data of each city, we have:

a. City B had more noon temperatures above 76°F

b. Both had the same interquartile range.

c. City B had a larger median noon temperature

d. City A had the largest noon temperature.

The box-and-whisker plot has the following values it displays about a data distribution:

Interquartile range = Q3 - Q1

Analyzing the box-and-whisker plots given above, we have the following to conclude:

a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.

b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7

Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7

Both had the same interquartile range.

c. Median for City A = 70

Median for City B = 78

City B had a larger median noon temperature

d. City A had the largest noon temperature of 85.

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Answer:

Step-by-step explanation:

27.5 percent of what is 13.75

13.75 : 27.5 * 100 =

(13.75 * 100) : 27.5 =

1375 : 27.5 = 50

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number.

Given,

Equivalent;

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2.

Here,

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

That is,

The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

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