7. Choose a method to solve the following system of equations. Then write 2-3 sentences
to why the system is set up for that method.
y = -2x + 6
y = 5x - 8
Type your 2-3 sentences in
text box below.

So, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.

A root of an equation is a value that satisfies the equation when it is set equal to zero. In other words, a root of an equation is a solution to the equation of the form x = constant.

The equation x^2 - kx - 5 = 0 is a quadratic equation, which can be factored into (x - r1)(x - r2) = 0 where r1 and r2 are the roots of the equation.

In this case, we can use the fact that 1/2 is a root of the equation x^2 - kx - 5 = 0

We can use the factored form of the equation and substitute x = 1/2

(x-1/2) (x-r2) = 0

Then, we can set each factor equal to zero and solve for r1 and r2:

x - 1/2 = 0 and x - r2 = 0

x = 1/2 and x = r2

We can use the quadratic formula to find the value of r2:

x = (-b ± √(b^2 -4ac) ) / 2a

We can substitute the values in the equation x^2 - kx - 5 = 0

x = (-(-k) ± √((-k)^2 - 41(-5)) ) / 2*1

x = (k ± √(k^2 + 20) ) / 2

x = (k ± √(k^2 + 20) ) / 2

r2 = (k + √(k^2 + 20) ) / 2

Now we have two values of x that satisfies the equation x^2 - kx - 5 = 0

x = 1/2 and x = (k + √(k^2 + 20) ) / 2

We can use the first value x = 1/2 and substitute it back into the original equation:

(1/2)^2 - k(1/2) - 5 = 0

1/4 - k/2 - 5 = 0

k/2 = 6 - 1/4

k = 12 - 1

k = 11

Therefore, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.

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We have expresses 53 Kobo as a decimal of 0.52 Naira.

A number that is not a whole is written using decimals. Between whole numbers are decimal numbers. 12.5, a decimal number that falls between 12 and 13, serves as an illustration of this. It is less than 13, but it is greater than 12. It's crucial to remember that fractions and decimal numbers are equivalent; the only difference is how they are expressed.

In keeping with the previous illustration, the mixed number 12 12 and 12.5 are equivalent numbers. No matter how complex the decimal is, this is true. For instance, 0.75 and 3/4 are equivalent. If you wanted to go even further, you could say that 0.75 is equivalent to 75%.

We know that 1 Kobo = 0.01 naira

Therefore, 52 kobo = 0.01  × 52 naira

                                  = 0.52 naira

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
[tex]R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=[/tex]
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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A polynomial equation can be written in a particular format by using its standard form. A polynomial equation is written in its standard form when the terms are written in descending order of their exponents and the leading coefficient, or the coefficient of the term with the highest exponent, is 1, as in the example above.

   The term with the highest exponent in the equation Y = -5x3 is x3, which has a coefficient of -5. The entire equation must be divided by -5 in order to be written in standard form, which will set the coefficient of the x3 term to 1 and convert the equation to standard form.

  The zero coefficients have been included in the equation when written in this form, however when the equation is read, we only take the term for the non-zero coefficients into account.

  So, the standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

   Therefore ,the answer is  Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

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The standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

The term with the highest exponent in the equation Y = -5x3 is x3, which has a coefficient of -5. The entire equation must be divided by -5 in order to be written in standard form, which will set the coefficient of the x3 term to 1 and convert the equation to standard form.

 The zero coefficients have been included in the equation when written in this form, however when the equation is read, we only take the term for the non-zero coefficients into account.

So, the standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

Therefore ,the answer is  Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

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Answer:

See the image attached.

Step-by-step explanation:

x    y

0    -1

1     -2

The cross product of A & B (A × B) is |A| |B| Sin θ, where θ is the angle between A and B.

The vector product or cross product of two vectors, A and B, is denoted by A × B, and its resultant vector is perpendicular to the vectors A and B.

The cross product is mostly used to determine the vector, which is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the length of the vector.

The cross product of two vectors, say A × B, is equal to another vector at right angles to both, and it happens in the three dimensions.

If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:

|A| |B| Sin θ

--The given question is incorrect; the correct question is

"What is the cross product of A & B?"--

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The scale factor used to produce the second triangle is 5/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size. For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given that, a triangle with base length of 3 units is transformed into a second triangle with a base length of 5 units,

Therefore, the scale factor = 3/5

Therefore, to produce Figure 2 from Figure 1 we will multiply it by 5/3

Hence, the scale factor used to produce the second triangle is 5/3.

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Answer:

If ur options are  one sixth

6

one half

2

then the correct answer is 2

Step-by-step explanation:

I took the quiz and got it right.

The GCD is 30 and the LCM is 13860 for the numbers 420, 630, and 330 .

The highest factor among two or more numbers is the greatest common denominator (GCD).

The lowest common multiple (LCM) is another name for the least common multiple in mathematics. The least common multiple of two or more numbers is the smallest of all the common multiples of the numbers provided.

Take all three numbers and their factors to determine the greatest common divisor.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are the factors for 420.

The factors for 630 are as follows: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630, and 330 are as follows: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.

Of the three, 30 is the common factor with the highest value.

Take all three numbers and their prime factors to determine the lowest common multiple.

The prime factors for 420 = 2 × 2 × 3 × 5 × 7

The prime factors for 630 = 2 × 3 × 3 × 5 × 7

The prime factors for 330 = 2 × 3 × 5 × 11

The LCM of 420,630,330 = 2 × 2 × 3 × 3 × 5 × 7 × 11 = 13860.

Therefore, the GCD and LCM is 30 and 13860 respectively.

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*desmos graphing calculator*

The experimental probability of spinning red and spinning blue is 4 and 2.8.

What is the experimental probability?

Experimental probability is a type of probability that is determined by conducting an experiment and observing the outcomes. It is also known as empirical probability.

It is calculated by counting the number of times an event occurs in a set of trials and then dividing that number by the total number of trials.

The experimental probability of spinning red.

P(red) = 20/5 = 4

The experimental probability of spinning blue

P(red) = 20/7 = 2.8

Hence, The experimental probability of spinning red and spinning blue is 4 and 2.8.

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Answer:

[tex]x\le \cfrac{6}{5}[/tex]

Step-by-step explanation:

[tex]10x+2\le \:14[/tex]

[tex]10x\le \:12[/tex]

[tex]\cfrac{10x}{10}\le \cfrac{12}{10}[/tex]

[tex]x\le \cfrac{6}{5}[/tex]

The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

Let R be a relation from a set A to another set B. Then R is of the form. The inverse relationship of R is denoted by R-1 and its formula is R-1 ={(y, x): y∈B and x∈A}.

The first element of each ordered pair of R = the second element of the corresponding ordered pair of R-1 and

The second element of each ordered pair of R = the first element of the corresponding ordered pair of R-1.

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The side length of square C is given as follows:

5 ft.

The area of a square of side length is given as follows:

A = s².

Hence the side length of A and B are given as follows:

Then the side length of square C is the hypotenuse of a right triangle, and applying the Pythagorean Theorem, it's length is obtained as follows:

C² = 3² + 4²

C² = 25

C = 5 ft.

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Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.

Three equations that can be used to solve for y, the length of the room are:

y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.

750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.

(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.

Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.

The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.

Step-by-step explanation:

A parallelogram is created when two congruent triangles with the same orientation are connected along equal sides.

When two congruent triangles with different orientations are joined along equal sides, they can be used to make a kite or a dart.

Here, ABC and ACD, two triangles that are mirror reflections of one another, combine to make a dart.

Darts and kites both feature two adjacent pairs of equal sides. The sole distinction is that darts are concave whereas kites are convex.

A quadrilateral can be produced if there are more than two congruent triangles. At least two of the sides of such a quadrilateral will be equal if each of its sides is one of the sides of the triangles.

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The rate he would he earn for 9 h will be 83.25

Your pay for each hour of labor is expressed as an hourly rate. You might need to estimate your income for other applications or change your own budget after comparing the hourly and salaried pay rates.

The sum of money charged, received, or earned for each hour of work: Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.

Noah earns 37 for 4 hr of babysitting.

so if you divide 37 by 4 you get the rate per hour

which is 9.25 so if you multiply 9 times 9.25

The rate he would earn for 9 h will be

you would get 83.25.

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The slope of the line is -10, and the y-intercept is 1.

Linear equations can be written in the form y=mx+b, where:y is a y coordinate on the line m is the slope of the line.A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

x is the x coordinate on the line that corresponds with the y coordinate in the equation,b is the y-intercept of the line

So for the equation y=-10x+1:

comparing the above equation with  y=mx+b we get,

m=-10 and b=1 so the slope of the line is -10, and the y-intercept is 1.

Thus, The slope of the line is -10, and the y-intercept is 1.

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The sum of the polynomial is obtained by adding the terms with the same power and variable together.

The steps to determine the sum of the polynomial :

Step 1: Arrange each polynomial with the term with the highest degree first then

in decreasing order of degree.

Step 2: Group the like terms : Like terms are defined as the terms whose variables and exponents are the same. For example 2x² and 3x² are like terms.

Step 3: Simplify by combining like terms.

For example, (2x² + 6x +5) +(-2x + 3x²- 1)

and we have determine sum of polynomial. Follows the above steps :

=> (2x² + 6x +5) + ( 3x²– 2x – 1)

2x² + 3x² + 6x – 2x + 5 -1

= 2x² + 3x² + 6x – 2x + 5 -1

= 5x² + 4x + 4

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Answer: The answer Is 9f

Step-by-step explanation:

The length of the rectangle side x is equal to 35.33 cm approximately to 2 decimal place using the trigonometric ratio of tangent.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the intercept of the diagonal lines in the rectangle with O so that we consider the right triangle ∆AOx, then we solve for the length of Ax and multiply the result by 2 to derive the value of x as follows:

angle 54 and m∠AOD are supplementary so;

m∠AOx = (180 - 54)/2 {m∠AOD/2}

m∠AOx = 63°

tan 63° = (x/2) ÷ 9

tan 63° = x/2 × 1/9 {change division to multiplication}

tan 63° = x/18

x = 18 × tan 63° {cross multiplication}

x = 35.3270

Therefore, 35.33 cm approximately to 2 decimal place is the length of the rectangle side x using the trigonometric ratio of tangent.

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Answer:

36-12s=y

s=3

thats with it all the way simplified

The formula for a circle's arc length is L = r * θ, where L is the arc length, r is the circle's radius, and θ is the arc's central angle, expressed in radians.

We can calculate the radius of the circle by dividing the arc length by the central angle because we know the value of L (7 cm) and that can be calculated from the arc's measure (degrees or radians):

r = L / θ

It is crucial to keep in mind that in order to calculate the radius, you must first know the arc's central angle's measurement in radians.

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Answer:

Obtuse angle

Step-by-step explanation:

Angles greater than 90 degrees are obtuse angles, angles less than 90 degrees are acute angles, and angles at 90 degrees are right angles.

The algebraic expression y = $2x + $10 represent the cost of each ATM transaction for the month where x is the cost of transaction during the month. And $20 is the total cost of 5 ATM transactions with the expression y = $2(5) + $10.

We shall represent the total cost of ATM transaction in a the month with the letter y and the cost of a transaction with the letter x so that we have an algebraic expression as follows:

y = $2x + $10

using the algebraic expression to evaluate for the total cost of 5 ATM transaction, we have;

y = $2(5) + $10

y = $10 + $10

y = $20

Therefore, the algebraic expression y = $2x + $10 can be used to represent the cost of each ATM transaction for the month. And the expression y = $2(5) + $10 with the result $20 represent the total cost of 5 ATM transaction during the month.

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The approximate distance from Town A to Town C is 12.5 miles.

What is the midpoint?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.

The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.

Therefore, Town C is located at (4.5, 3).

To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles

Hence, the approximate distance from Town A to Town C is 12.5 miles.

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Write a logarithmic expression in the form [tex]log_{b}M[/tex] = N.

In an exponential equation, the variable is expressed as an exponent. A logarithmic equation uses the logarithm of an expression including a variable to solve the problem. Check to determine if you can write both sides of an exponential equation as powers of the same number before attempting to solve it. If you can't, use property after taking the common logarithm of both sides of the equation.

Use the properties of logarithms to express the equation in the form  [tex]log_{b}M[/tex] = N, then convert it to exponential form, M = [tex]b^{N}[/tex], to solve an equation requiring logarithms.

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The condition for two lines to be perpendicular lines :

the two lines meet each other at the right angle

We know that the two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°

Since these lines are inclined at 90° to each other, hence they create right angles.

This means, the condition for two lines to be perpendicular lines is that the two lines must meet each other at the right angle

This property of lines is said to be perpendicularity.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

For example, if two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.

The product of slopes of perpendicular lines is always -1.

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The 4 laws of logarithms are product rule, division rule, power rule and change of base rule.

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The equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".

What is algebraic equation ?

An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.

This is an algebraic equation and it represents the mathematical relationship between different values.

The equation is , 7/8 - 1/4 = 5/8

This equation states that if we subtract 1/4 from 7/8 we get 5/8.

It can be verified by solving the equation:

7/8 - 1/4 = (7/8) - (1/4) = (74/84) - (18/48) = 28/32 - 8/32 = 20/32 = 5/8

So, the equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".

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The equation is , 7/8 - 1/4 = 5/8

This equation states that if we subtract 1/4 from 7/8 we get 5/8.

It can be verified by solving the equation:

7/8 - 1/4 = (7/8) - (1/4) = (74/84) - (18/48) = 28/32 - 8/32 = 20/32 = 5/8

So, the equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".