How do you know if a graph has two solutions?

Answer:

Step-by-step explanation:

You want the equations of the lines parallel and perpendicular to y=-4x+4 through the points (-6, -4) and (-6, 4), respectively.

The equation of the given line is in slope-intercept form. This means its slope is the coefficient of x: -4.

Parallel lines have the same slope, so the parallel line will have slope -4.

Perpendicular lines have opposite reciprocal slopes, so the perpendicular line will have slope -1/(-4) = 1/4.

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

This problem gives you a point on each line, and we know the required slope, so this form of the equation for a line is just what we need.

  m = -4, (h, k) = (-6, -4)

  y +4 = -4(x +6)

  m = 1/4, (h, k) = (-6, 4)

  y -4 = 1/4(x +6)

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:

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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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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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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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 five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().

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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 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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Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Given that,

We have to find what are the 2 characteristics of a regular polygon.

We know that,

Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Regular triangles and quadrilaterals are given unique names, such as squares and equilateral triangles.

Therefore, Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

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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 cone is 91.05[tex]m^{3}[/tex]

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex. We can also define the cone as a pyramid which has a circular cross-section, unlike pyramid which has a triangular cross-section.

circumference of the base of a cone is same as circumference of a circle which is 2[tex]\pi[/tex]r

15.8 = 2[tex]\pi[/tex]r

make r subject of equation

r = [tex]\frac{15.8}{2\pi }[/tex]

r = 2.51m

Volume of a cone = 1/3 x [tex]\pi[/tex][tex]r^{2}h[/tex], but h =13.8m

volume = 1/3 x 3.142 x [tex](2.51)^{2}[/tex] x 13.8 which is 91.05[tex]m^{3}[/tex]

In conclusion the volume of the cone is 91.05[tex]m^{3}[/tex]

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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 function of the graph is g(x) = [x]+2

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of terms

y = output variable

x = input variable

m = slope

c = y intercept

The c from the graph is +2

m for points (1, 3) and (-3, -1)

= (-1 - 3) / (-3 - 1)

= -4/-4

= 1

substituting to the equation  y = mx + c

y = x + 2

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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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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 volume of the pyramid will be 995,328 cubic meters.

Let h be the height of the pyramid, l be the slant height and A be the base area of the pyramid.

Then the volume of the pyramid will be

Volume = (1/3) × A × h

The slant height is given as.

l² = (half of the side)² + h²

A stone pyramid in Egypt has a square base that actions 144 m on each side. The level is 96 m.

Then the volume of the pyramid will be given as,

V = 1/3 x (144 x 144) x 96

V = 48 x 144 x 96

V = 995,328 cubic meters

The volume of the pyramid will be 995,328 cubic meters.

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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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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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The value of side b is 6.15

The value of side c is 6.84

The value of angle A is 26°

From the question, we are to determine the length of side b and c and the measure of angle A.

From the given information,

m ∠B = 64°

and

Angle C is a right angle.

We can write that

m ∠A + m ∠B + m ∠C = 180° (Sum of angles in a triangle)

m ∠A + 64° + 90° = 180°

m ∠A = 180° - 90° - 64°

m ∠A = 26°

From SOH CAH TOA, we can write that

tan B = b/a

tan 64° = b/3

b = 3 × tan 64°

b = 6.15

Also,

cos B = a/c

cos 64° = 3/c

c = 3/cos 64°

c = 6.84

Hence, the value of c is 6.84

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The binary number (100[tex])_2[/tex] in decimal system is written as [tex]4_{10}[/tex].

Given:

Binary number = [tex](100)_2[/tex]

Converting Binary to decimal system:

Binary:

In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one).

Decimal:

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

[tex]100_2 = 1*2^2 + 0*2^1+0*2^0[/tex]

we know that,

[tex]2^0 = 1[/tex]

[tex]2^1 = 2\\2^2 =4[/tex]

substitute these values

[tex]100_2 = 1*4 + 0*2 + 0*1[/tex]

= 4 + 0 + 0

= 4 + 0

= [tex]4_{10}[/tex]

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Answer:

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

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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 higher power of the polynomial equation is its degree when there is one variable. However, if a polynomial comprises numerous variables, the degree of the polynomial can be calculated by adding the powers of the multiple (more than one variable) variables in any terms in the polynomial expression.

Polynomial: A Polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Examples:

•Constants. Example: 1, 2, 3, etc.

•Variables. Example: g, h, x, y, etc.

•Exponents: Example: 5 in x5 etc.

Degree of one variable polynomial:

Example: 4x^4+6x^2-2

The degree of the polynomial is 4 as the highest power of variable is 4.

Degree of more than two variables polynomial:

Example: 6x^2yz^3+2x^2y+zx

The degree of the polynomial is 6 as the addition of powers of variables is 6.

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Answer:

Step-by-step explanation:

V = 16755.1608 m3

The equivalent rational expression of the given expression, 9/5u² - 40u - 45, is 9/(5u + 5)(u - 9)

The equivalent rational expression of the given expression, 2u/5u² + 30u + 25 , is 2u/(5u + 5)(u + 5)

From the question, we are to rewrite the given expressions as equivalent rational expressions.

The given expressions are:

9/5u² - 40u - 45 and 2u/5u² + 30u + 25

Writing an equivalent expression for 9/5u² - 40u - 45

Factorize the denominator

5u² - 40u - 45

5u² - 45u + 5u - 45

5u(u - 9) + 5(u - 9)

(5u + 5)(u - 9)

Thus,

The equivalent expression is 9/(5u + 5)(u - 9)

Writing an equivalent expression for 2u/5u² +30u + 25

Factorize the denominator

5u² +30u + 25

5u² +25u + 5u + 25

5u(u + 5) + 5(u + 5)

(5u + 5)(u + 5)

Thus,

The equivalent expression is 2u/(5u + 5)(u + 5)

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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 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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Answer: It basically it all depends on the type of equations you have.

Step-by-step explanation: For example:  1/2 x 2/5 = ?. We can use a modal to solve this problem.   here is the modal that represents this equation. (Oh and I checked the answer, it was right)

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