Solving Systems by Substitution


y=-4
y=-2x-20

So, y = (1/2)(x + 8) is the equation of the linear function.

To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

This is the equation of the linear function.

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y - y1 = m(x - x1)

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

[tex] \frac{ - 8}{19} + \frac{ - 2}{57} \\ \\ [/tex]

LCM of 19 and 57 is 57

so,

[tex] \frac{ - 8 \times 3}{19 \times 3} \\ + \\ \frac{ - 2 \times 1}{57 \times 1} [/tex]

[tex] \frac{ - 24}{57} + \frac{ - 2}{57} \\ [/tex]

as negative negative cancel out each other.

[tex] \frac{24}{57} + \frac{2}{57} \\ [/tex]

now simply add this

[tex] \frac{24 + 2}{57} = \\ \frac{26}{57} [/tex]

Now the answer is :: 26/57

Answer: FOIL method

1. (a + b)(a + b) =

= a² + ab + b² + ab

= a² + 2ab + b²

2. (3a-2b) (3a - 2b) =

= 9a² - 6ab - 6ab + 4b²

= 9a² -12ab + 4b²

3. (x - 4y)(-3x - 2y) =

= -3x² -2xy +12xy +8y²

= -3x² + 10xy + 8y²

4.(-y-2z)(y-2z) =

= -y² + 2yz -2yz + 4z²

= -y² + 4z²

Step-by-step explanation:

The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].

What is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

What is perpendicular ?

The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.

Let y = 3x + 1 is perpendicular ,

differentiate respect of x

[tex]\frac{dy}{dx} = 3[/tex] , m = 3

Thus , [tex]-\frac{1}{m}[/tex]

then [tex]-\frac{1}{3}[/tex]

The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].

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A graph of the distance and time data for distance traveled by this train is shown in the image attached below.

In Mathematics, a scatter plot is sometimes referred to as scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting data points showing any association or correlation between the data set.

In this scenario, the time (in hours) would be plotted on the vertical axis (x-axis) of the scatter plot while the distance (in kilometers) would be plotted on the horizontal axis (y-axis) of the scatter plot by using an Excel worksheet.

From the scatter plot (see attachment) which models the relationship between the distance (in kilometers) and time (in hours), a linear equation for the line of best fit or trend line is y = 99.43x + 11.43.

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ans is 4 I don't really know how to explain it

The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g

what is mass of molecule ?

Watch your pronunciation. pronounced "muh-LEH-kyoo-ler mas" the total atomic mass of every atom in a molecule, calculated using a scale with hydrogen, carbon, nitrogen, and oxygen having atomic masses of 1, 12, 14, and 16, respectively.

solution:

The mass of one methane molecule should be "2.7 × 10⁻²³ gram" instead of "27 × 10⁻³ grams".

Mass of 60,000 molecules of methane

= (2.7 × 10⁻²³ g) × 60,000

= 1.62 × 10⁻¹⁸ g

Therefore,The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g

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Factor (x+1) is the binomial factor for x³ - 6x²+ 3x + 10 using the rational roots test.

If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.

p = ±1,  ±10, ±2, ±5

q = ±1

Find every combination of ± p/q . These are the possible roots of the polynomial function.

±1, ±10, ±2, ±5

Substitute −1 and simplify the expression. In this case, the expression is equal to 0 so −1 is a root of the polynomial.

Substitute: −1 into the polynomial.

(−1)3−6(−1)2+3⋅(−1)+10

Raise −1 to the power of 3.−1−6(−1)2+3⋅−1+10

Raise −1 to the power of 2.−1 −6⋅1 + 3⋅−1+ 10

Multiply −6 by 1.−1−6+3⋅−1+10

Subtract 6 from −1.−7+3⋅−1+10

Multiply 3 by −1.−7−310

Subtract 3 from −7.−10+10

Add −10 and 10.0Since −1 is a known root, divide the polynomial by x+1 to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

x³− 6x²+ 3x+ 10x+ 1

Divide

x³−6x²+ 3x+ 10 by x + 1.

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In mathematics, a discontinuity is a point or set of points at which a function or curve is not defined, or is not "well-behaved," meaning it exhibits some kind of sudden or unexpected change in behavior.

Discontinuities can occur in functions or curves of all types, including functions of one variable, functions of several variables, and geometric curves.

There are several types of discontinuities that can occur in a function. For example, a function may have a jump discontinuity, which occurs when the function has a finite limit from one side but a different finite limit from the other side at a given point.

In all, the presence of discontinuities in a function can make it more difficult to analyze or work with, as the behavior of the function may not be predictable at these points.

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The roots of the quadratic equation 2x2 4x 7 will be two complex conjugate roots.

To determine the nature of roots of a quadratic equation, we can use the formula of the discriminant. The discriminant of a quadratic equation ax2 + bx + c = 0 is given by D = b2 - 4ac.

For the equation 2x2 4x 7, the discriminant is D = (-4)2 - 4(2)(7) = 16 - 56 = -40.

Since the discriminant is negative, the roots will be two complex conjugate roots.

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7 is a constant value and it is a polynomial of degree 0.

7 is a polynomial.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

7

This can be assumed as 0x³ + 0x² + 0x + 7.

This is a polynomial.

Thus,

7 is a polynomial.

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If 800g:1kg is equal to 1:n then the value of n is 1/8.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

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Answer:

Step-by-step explanation:

Given 64 feet of fencing that can be used for three sides of a rectangular enclosure next to a barn wall, you want a function for area in terms of enclosure width, the width that maximizes area, and the maximum area.

If we define the width (x) as the dimension parallel to the barn wall, then the fence available for the "height" (out from the barn wall) is (64-x) in length. Half that is used on either end of the enclosure, so the area is ...

  A = WH

  A(x) = x(64 -x)/2

We notice this function describes a parabola that opens downward, with zeros at x=0 and x=64. The vertex (maximum) is on the line of symmetry, halfway between the zeros:

  x = (0 +64)/2 = 32

The width that maximizes area is x = 32 ft.

Using x=32 in the area formula, we find the maximum area to be ...

  A(32) = 32(64 -32)/2 = 1024/2 = 512 . . . . square feet

The maximum area is 512 square feet.

__

Additional comment

Perhaps you can see that the best width is half the length of the available fence. The other half of the fence is used for the ends of the enclosure. This is the generic solution to this kind of problem.

Answer:

7.62

Step-by-step explanation:

Simplify the following:

7 + 6/10 + 2/100

Express 6/10 in its lowest form by cancelling out gcd(6, 10) = 2 from the numerator and denominator. 6/10 = (2×3)/(2×5) = 3/5:

7 + 3/5 + 2/100

Express 2/100 in its lowest form by cancelling out gcd(2, 100) = 2 from the numerator and denominator. 2/100 = (2×1)/(2×50) = 1/50:

7 + 3/5 + 1/50

Put 7 + 3/5 + 1/50 over the common denominator 50. 7 + 3/5 + 1/50 = (50×7)/50 + (10×3)/50 + 1/50:

(50×7)/50 + (10×3)/50 + 1/50

50×7 = 350:

350/50 + (10×3)/50 + 1/50

10×3 = 30:

350/50 + 30/50 + 1/50

350/50 + 30/50 + 1/50 = (350 + 30 + 1)/50:

(350 + 30 + 1)/50

| 3 | 5 | 0

| | 3 | 0

+ | | | 1

| 3 | 8 | 1:

Answer: |

| 381/50

Binomial theorem is used to calculate the roots of the equations with highest degree in advance mathematical calculation in any subject.

Binomial theorem is represented by :

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Therefore, the binomial theorem help us to calculate the roots of the equations with highest degree in advance mathematical calculations in many subjects.

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Linear graph equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

How do one express the standard form of a linear equation?

A linear equation has the following standard form: ax + by + c = 0.

Here, variables x and y and constants a, b, and c are used.

Also, a ≠ 0, and b ≠ 0.

For linear equations, the slope-intercept formula is: y=mx+b

Where m stands for the line's slope and b represents the y-intercept.

The three types of linear equations are point-slope, slope-intercept, and standard form.

When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.

Steps of drawing linear graphs are described below:

Step 1: Using the provided linear equation, determine the value of y with respect to x.

Step 2: Arrange these data in a table format.

Step 3: Create a graph using the points from the database.

Step 4: Connect the points to form a straight line.

So, ax + by + c = 0 is a linear graph formula.

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In order to prove that KFDE and KGHI are congruent by ASA, you need to know that KFDE and KGHI have two congruent angles (angle F and angle H) and a congruent side (side DE and side HI).

In order to prove that KFDE and KGHI are congruent by AAS, you need to know that KFDE and KGHI have three congruent angles (angle F, angle G, and angle H). This means that the angles in the triangle are equal, which implies that the sides in the triangle are also equal. Thus, for AAS, KFDE and KGHI must have two congruent sides (side DE and side HI).

Therefore, in order to prove that KFDE and KGHI are congruent by ASA or AAS, you must know that both triangles have two congruent angles and a congruent side (for ASA) or three congruent angles and two congruent sides (for AAS).

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Answer:

x=4.6 answer is at most 4 people can go

Step-by-step explanation:

32.50x+10.50=160.00

- 10.50 -10.50

149.50

32.50x = 149.50

Divide 32.50 and 149.50 to find x.

x = 4.6 round down because you cant have a fraction of a person. so 4 people can go.

answer : slope is -2/3

line should look like

y = mx + b

slope is m or the number next to x

slope refers to the rate or speed of something

make 2x + 3y = 12 look like y = mx + b

2x + 3y = 12

3y = -2x + 12

y = (-2x + 12)/3

y = -2/3x + 12/3

y = -2/3x + 4

slope is -2/3

b is called the y intercept

b is +4 which is where the line passes thru in the y axis at (0,4)

when x is 0 but y is not then that means the graph is not proportional

We can identify quadrilateral because a regular polygon must have four equal sides in order to be called a quadrilateral.

Describe the quadrilateral.

Having four sides, four vertices, and four angles, a closed quadrilateral is a type of polygon. It consists of four connected non-collinear points. Quadrilaterals' internal angles always add up to 360 degrees.

According to the given question:

In a quadrilateral -

In order to be considered a quadrilateral, it must have four sides, four angles.

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Answer:

the answer it's-7a^5+10m

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

According to the SSS rule, two triangles are considered to be congruent if the corresponding three sides of each triangle are equal to each other.

The triangles are congruent if all three sets of comparable sides are present.

The side-side-side shortcut is a congruence technique (SSS).

Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.

Therefore, according to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

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750 cubic feet is the volume of the prism and Therefore, the volume of Jake's box is 8 times larger than Havana's box.

A right right triangle hypotenuse is its longest side, its "across" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe both sides of right triangles, we utilize specific terminology. The side opposing its right angle is always the tangent of a right triangle.

Dimensions of the Right Triangular Base

Base = 20 feet

Height= 120 inches = 10 feet

Base Area of the Prism

1/2 * 20 * 10

= 150 sq.feet

Height of the Prism = 5 feet

Volume of the Prism = Base Area X Height

= 150 X 5

=750 cubic feet

Jake's Box

Length: 12 inches

Width: 4 inches

Height: 8 inches

Volume = 12 X 4 X 8 =384 cubic inches

Havana's box

Jake's shipment crate is comparable to the one in Havana, except it is only half as long overall.

Therefore:

Length: 12/2=6 inches

Width: 4/2=2 inches

Height: 8/2=4 inches

Volume = 6 X 2 X 4 =48 cubic inches

Now:

384/48=8

Therefore, Jake's box has an 8-times higher volume than Havana's box.

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Based on the calculation, we get that the cost of the watch is Rs 22.50.

Cost is the amount of resources, time, money, or effort that must be expended to achieve a goal or achieve something. It can refer to the financial or monetary expense of something, but it can also refer to other types of resources or effort that must be invested.

Let C be the cost of the watch.

The profit that Sakhi made on the watch was 15% of C. We can express this as:

Profit = (15/100) * C

If Sakhi had bought the watch at 10% less than the price at which he sold it and sold it for Rs. 28 le, he would have gained 20% on the sale. We can express this as:

Profit = (20/100) * (C - (10/100) * C)

We can set these two expressions for profit equal to each other and solve for C:

(15/100) * C = (20/100) * (C - (10/100) * C)

This simplifies to:

15/100 = 20/100 - (10/100)^2

Which simplifies to:

15 = 20 - (10/100)

Solving for C, we find that the cost of the watch is:

C = Rs. 22.50

Therefore, the cost of the watch is Rs. 22.50.

The missing part in the question is shown below.

Sakhi sold a watch at a profit of 15%. Had he bought it at 10% le and sold for Rs. 28 le, he would have gained 20%. Find the cost of the watch

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There are totally 4 terms in the given polynomial

We have a polynomial given by -x³+4x² +7x − 2

Algebraic expressions with coefficients and variables make up polynomials. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Since there are 4 terms with either an addition or a subtraction performed between them, the total number of terms is given by 4.

Those 4 terms are -x³ ,4x²,7x,−2

Therefore, there are totally 4 terms in the given polynomial.

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Yes, rigid motion is congruent?

A stiff motion occurs when an object is transported from one place to another while maintaining its original size and shape.

If and only if there is a stiff motion that establishes a correspondence of one figure as the likeness of the other, then two figures are said to be congruent. Interior angles are unchanged, as well as side lengths.

An object is rigidly moved from its initial place to the exact same location in a motion known as an identity motion. It appears as though the thing hasn't changed at all.

According to the Common Core, the "principle of superposition" states that two figures are congruent if there is a rigid motion projecting one onto the other.

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The total surface area of the cone is calculated to be

Information given in the problem

the total surface area of the cone in the figure. (Use π = 3.14.)

A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.

The formula of the total surface are of a cone is given by

T = πr(r + l) square units.

calculating for l

l = √(12² + 5²) = 13

= 3.14 * 5 (5 + 13)

= 3.14 * 5 *(18)

= 282.6 cm^2

282.6 cm^2 is the  total surface area of the cone

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The formula to determine the consecutive odd numbers of a specific value "x" is:

x + 2n

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.

If we want to know the consecutive numbers immediately we add +1, +2 and so on.

But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:

If we generalize an equation we have

x + 2n

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The correct sentence is C, "-3 > -8."

Here's how you can determine which sentence is correct:

In sentence A, -3 is not greater than 2, so sentence A is incorrect.

In sentence B, -3 is not less than -6, so sentence B is incorrect.

In sentence C, -3 is indeed greater than -8, so sentence C is correct.

In sentence D, -3 is not greater than -2, so sentence D is incorrect.

Remember that when comparing two negative numbers, the one with the smaller absolute value is the larger negative number. For example, -8 is a larger negative number than -3 because -8 is closer to 0 (which is the smallest possible number). Similarly, -2 is a larger negative number than -3 because -2 is closer to 0.

Hence, The correct sentence is C, "-3 > -8."

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Answer:

11:18.

Step-by-step explanation:

22:36

We divide each number by their Greatest Common Factor.

The GCF of 22 and 36 is 2.

So, in simplest terms

22:36 = 11:18.