What is the equation of the line that passes through the point (6, -8) and has a
slope of -2/3?

The slop-intercept form of 2x + y = -2 is y = -2x - 2.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To convert the equation 2x + y = -2 into slope-intercept form, we can follow these steps:

1. Isolate y on one side of the equation. We can do this by subtracting 2x from both sides: y = -2x - 2

2. Now we have y = -2x - 2, which is in slope-intercept form.

So, the slope-intercept form of 2x + y = -2 is y = -2x - 2. The slope of the line is -2 and the y-intercept is (-2,0).

Therefore, the slope-intercept form of the equation 2x + y = -2 is y = -2x - 2.

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There are 2 pounds of apples Hannah buy for the cost for her purchase to be the same from both stores.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.

And, At Shop & Save, the apples are $1.05 per pound and a box of

cereal is $3.37.

Now,

Let number of pounds of apples can Hannah buy for the cost for her purchase to be the same from both stores = x

So, We can formulate;

For, At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.

The total cost is,

⇒ $2.89 + $1.29x

And, For Shop & Save, the apples are $1.05 per pound and a box of

cereal is $3.37.

Total cost is,

⇒ $3.37 + $1.05x

Now, We can equate both the equation to find the number of pounds of apple to buy.

⇒ $3.37 + $1.05x = $2.89 + $1.29x

⇒ 3.37 + 1.05x = 2.89 + 1.29x

⇒ 3.37 - 2.89 = 1.29x - 1.05x

⇒ 0.48 = 0.24x

⇒ x = 0.48 / 0.24

⇒ x = 2

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1 ) P be Pepperoni, Q be Quail, R be Ricotta cheese, S be Sausage.

To translate Geoff's order using Discrete Math,

2 ) Geoff is a truth-teller. Based on his last statement, where ricotta (R) is implied from pepperoni (P) or quail (Q) , we would have no way of knowing if R is true/false if (P or Q) was false- so, R must be true if (P or Q) is false because of the whole “innocent until proven guilty” thing. therefore, since a lie in P or Q would lead to truth, Geoff must be a truth-teller because he can’t tell all lies.

Using this information, that Geoff always tells the truth.

For the third statement, if Geoff is lying then the truth is "I must have pepperoni or quail and I cannot have ricotta cheese."

~[(P ∨ Q) → R] = [(P v Q) ∧ ~R)]

Or in more general terms, ~(a → b) = (a ∧ ~b)

Which, gives us (a → b) = (~a ∨ b)

Anyhow, even if Geoff tells all lies, there is a valid statement that can be made: Pepperoni and sausage, no quail, no ricotta.

Also, if Geoff tells the truth, there's nothing that says he can't have quail with pepperoni: pepperoni, quail, and ricotta is also valid.

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Answer:

x = 1

Step-by-step explanation:

Since all the fractions have a common denominator of 3, you can multiply both sides by 3 to get rid of the denominator. (Make sure you distribute)

[tex]\frac{7}{3}x+\frac{1}{3}x=1+\frac{5}{3}x[/tex]

[tex]3(\frac{7}{3}x+\frac{1}{3}x)=3(1+\frac{5}{3}x )[/tex]

7x + x = 3 + 5x

8x = 3 + 5x

8x - 5x = 3 + 5x - 5x

3x = 3

x = 3/3

x = 1

Answer: 67 peeps

Step-by-step explanation:

Answer:

r< -0.9

Step-by-step explanation:

Just subtract 0.2 from both sides...

The graph of the equation, x = 3, would be a vertical line that intersects the x axis at x = 3.

The slope of the graph would be undefined.

Vertical lines have an undefined slope because slopes are based on the change in the horizontal climb of a line. Seeing as vertical lines have no horizontal change, it means that the slope in undefined.

The line, x = 3 is a vertical line because the x - axis is the horizontal line. A line that would intersect it at x = 3 would therefore have to be a vertical line which is straight or it would not remain at x = 3 in perpetuity.

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The Height of the plant is (8-x) inches

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

A plant measured x inches tall last week, and 8 inches tall this week.

So, to find the exact growth of plant from x inches to 8 inches then we have to find the difference between these two heights.

Then, the height of tree per week

= height of plant this week - height if plant previous week.

= 8- x

Hence, the expression is 8-x.

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They made more than 1,000 sales per week for 26 weeks.

A sale is a transaction that involves exchanging products or services for a certain sum of money. To put it another way, a sale is any action that includes giving the buyer possession of a thing or commodity in return for payment.

The first sale is 15 units.

Sales are rising at a weekly rate of 18%.

1000 are the final sales.

The next week is when sales reach 1,000 or more:

[tex]1000=15 \times\left(1+\frac{18}{100}\right)^t \\\frac{1000}{15}=\left(\frac{118}{100}\right)^t \\\frac{200}{3}=(1.18)^t[/tex]

Solving further we get,

[tex](\left.\log\frac{200}{3}\right)=t \log 1.18[/tex]

Thus we get,

t=25.37

In the twenty-fifth week, the company makes 1000 in sales.

As a result, the company's revenues exceeded 1000 in the 26th week.

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The compound interest would be Rs. 35835.51.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

To calculate the total amount to be paid after 1.5 years at 15% p.a. compounded half-yearly, the formula is:

A = P(1 + r/n)^(nt)

Where:

A = total amount

P = principal amount (Rs 128000)

r = interest rate (15%)

n = number of times the interest is compounded per year (2 times per year)

t = number of years (1.5 years)

So, the total amount to be paid after 1.5 years would be:

A = 128000 * (1 + 0.15/2)^(2*1.5) = Rs 163835.51

The compound interest can be calculated by subtracting the principal amount from the total amount:

CI = A - P = 163835.51 - 128000 = Rs 35835.51

Hence, the compound interest would be Rs. 35835.51.

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Answer:

85

Step-by-step explanation:

It would take a car 5 hours to cover 200 km at a speed of 40 km/h.

The car moves at a constant speed of 40 km/hr.

The car has to travel a total distance of 200 km.

As we know the formula of speed is distance/time,

Hence, s = d/t km/hr

So t = d/s hr

Let speed, distance and time be s, d, t respectively.

So by putting the values,

time t = 200/40 = 5 hours

Hence it can be said that the car would cover 200 km at the speed of 40 km/hr in 5 hours.

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Answer:

g = 59⁰

h = 9

(by using opposite sides and angles of a parallelogram are equal.)

The standard form of linear equation is written as ax + by = c, where a, b, and c are real numbers and a and b are not both zero.

In this form, the coefficients a and b are the slopes of the line and c is the y-intercept.

In the equation x = -5, the coefficient of x is 1 and the constant is -5. This equation can be written as 1x + 0y = -5, which is the standard form of the equation.

To solve this equation, we can first subtract 5 from both sides:

1x + 0y - 5 = -5 - 5

1x + 0y = 0

This is the simplest form of the equation and can be used to find the x-intercept of the line. By setting y = 0 and solving for x, we get x = 0. This means that the x-intercept of the line is (0, -5). We can also use this equation to find the slope of the line. The slope of the line is equal to the coefficient of x, which is 1. This means that the slope of the line is 1.

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Answer:

0.038cm

Step-by-step explanation:

50 cards
1.9cm thick

1.9/50=0.038cm

Within a yard, there are 36 inches (yd). In both the US customary and imperial systems of measurement, length is expressed in both inches and yards.since there are 313 by 36 inches in a yard.

Within a yard, there are 36 inches (yd). In both the US customary and imperial systems of measurement, length is expressed in both inches and yards.In the United States, the United Kingdom, and its territories, these units are primarily used.

A man's belt or girdle, as it was referred as, measured a yard in length originally.King Henry I of England established the yard in the 12th century as being equal to the distance between his thumb and nose on his extended arm.

There are 36 inches today.

So, 313 yards = 11,268 inches.

There are 36 inches in one yard

You need to multiply 313 yards by 36 inches to get your answer,

which is 31336 = 11,268.

so 313 yards equal 11,268 inches

So, 313 yards = 11,268 inches.

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The number of ants after 1 year=464 and the table will follow no-linear function as the equation will be a exponential equation for the growth of ants.

What is a exponential equation?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 6^2y - 7 = 121 etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.

Now,

The exponential equation that will be followed by given ant's growth will be

y=29(2)^t/3

where 29=initial population

t=Number of months

and It will represent a non-linear function as a exponential function is a no-linear function.

Population after 1 year

                                   y=29(2)^12/3

                                     =29*16

                                      =464

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You can use the Pythagorean Theorem to write an equation that describes how the side lengths are related as 20² + 15² = 25².

The Pythagorean theorem can be defined as a mathematical expression in Euclidean geometry that can be used to solve for any of the three (3) side lengths of a right triangle.

Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

20² + 15² = 25².

400 + 225 = 625

625 = 625 (proof).

In conclusion, you would know that the geometric proof of the Pythagorean Theorem can be applied to all right triangles because the square of the hypotenuse is always equal to the sum of the square of the opposite side and the adjacent side of a right triangle.

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The current age of Sam is 30 years and Harry is 10 years.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

Let Sam's age be y years and Harry's age be x years.

Sam is currently three times harry's age.

The equation formed: y = 3x

Sam's age is also 10 more than twice harry's age.

The equation formed: y = 2x + 10

Substitute the value of y from first equation in second equation:

3x = 2x + 10

x = 10

Put the value of x in first equation:

y = 3x = 3*10 = 30

Thus, the current age of Sam is 30 years and Harry is 10 years.

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Answer:

This equation is Linear.

Step-by-step explanation:

We can set up a system of equations to represent the information given:

What does the term "system of equations" mean?

simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

x + y = 10 (the total number of bananas and peaches is 10)

0.5x + 1.5y = 9 (the total cost of the bananas and peaches is $9)

To graphically solve this system, we can plot the two equations on the same coordinate plane. The first equation, x + y = 10, represents a line with a slope of -1 and a y-intercept of 10. The second equation, 0.5x + 1.5y = 9, represents a line with a slope of -3 and a y-intercept of 9.

When the two lines intersect, we have the solution to the system of equations. The point of intersection represents the values of x and y that satisfy both equations. We can see that the solution is x=4, y=6. This means that Houa bought 4 bananas and 6 peaches.

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He coined a term from the two ancient Greek terms logos, meaning proportion, and Arithmos, meaning number; compounding them to produce the word “logarithm.

An exponential equation is an equation in which the variable appears in an exponent.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.

Divide each term in

log(2)x=2

by log(2).

log(2) x log(2)=2log(2)

Simplify the left side.

Cancel the common factor of

log(2).

x=2log(2)

The result can be shown in multiple forms.

Exact Form:

x=2log(2)

Decimal Form:

x=6.6438561

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Answer:

The geometric sequence is 15, 9, 27/5, 81/25, 243/125

Step-by-step explanation:

The truth also called as  property of sentences , assertions and beliefs.

What is Declaration of truth and false in the mathematics?

Declaration of truth and false in mathematics are 1 and 0 respectively.

Questions on fact and falsity saturate our lifestyles as humans. while we may not continually understand what's actual, we've intuitive thoughts of what it might mean for some thing to be actual and work very difficult to get “nearer” to it. We often make claims approximately what's authentic apparently with little to no problem. but we find ourselves in a consistent conflict with falsehoods. Our paintings, our love lives, or even our most loved leisure times are laden with discovering fact over falsehood. Is that concept real.

Hence, The truth is property of sentences , assertions and beliefs.

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The measure of reference angles to problems are,

7. Ф = 41.81°.

8. Ф = 64.23°.

10. Ф = 51.31°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

7. With respect to the reference angle opposite and the hypotenuse is given,

sin = opposite/hypotenuse.

sinФ = 4/6.

Ф = sin⁻¹(4/6).

Ф = 41.81°.

8. With respect to the reference angle opposite and adjacent is given,

tan = opposite/adjacent.

tanФ = 29/14.

Ф = tan⁻¹ (29/14).

Ф = 64.23°.

9. With respect to the reference angle opposite and the hypotenuse is given, Similar to problem 7.

10. With respect to the reference angle hypotenuse and adjacent is given,

cos = adjacent/hypotenuse.

cosФ = 25/40.

Ф = cos⁻¹(25/40).

Ф = 51.31°.

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An estimate of the total number of televisions that would need repairing in Clover City is A. Between 546,000 and 972,000 televisions.

Thanks to the research by the local television repair shop, we know that on average, 2.53 ± 0.71 per family will need to be fixed.

The lower bound of this mean range would be:

= ( Mean - error ) x Number of households

= ( 2. 53 - 0. 71 ) x 300, 000

= 546, 000 televisions

The upper bound of the mean range is:

= ( 2. 53 + 0. 71 ) x 300, 000

= 972, 000 televisions

The estimate for televisions to be repaired is therefore between 546,000 and 972,000 televisions.

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The coefficient of $x^2$ when $-5x^3 - 5x^2 - 7x 1$ is multiplied by $-x^2 - 6x + 1$ and the like terms are combined is 36.

Let the first term be [tex]-5x^3 - 5x^2 - 7x + 1[/tex]

The second term be  [tex]-x^2 - 6x + 1[/tex]

When they are multiplied,

=[tex](-5x^3 - 5x^2 - 7x + 1)[/tex]  [tex](-x^2 - 6x + 1)[/tex]

= [tex]5x^5 + 30x^4 - 5x^3+5x^4+30x^3-5x^2+7x^3+42x^2-7x-x^2-6x+1[/tex]

= [tex]5x^5+35x^4+32x^3+36x^2-13x+1[/tex]

Therefore coefficient pf x² is +36.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

Like terms in mathematics are summands in a sum that differ only by a little number. Regrouping similar concepts is possible by adding their coefficients. Like terms in a polynomial equation are those that, possibly with different coefficients, contain the same variables raised to the same powers.

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The solution of the equation in the interval [0, 2π] is π or 180.

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given the equation;

Sinx = cosx + 1

Then Square both sides of the equation;

Sin²x = (cos x + 1)²

Sin²x = cos²x + 2cos x + 1

Since Sin²x = 1 - cos²x

1 - cos²x = cos²x + 2cos x + 1

Collect like terms;

1-1-cos²x-cos²x-2cos x  = 0

-2cos²x-2cos x = 0

-2cos²x = 2cos x

-cosx = 1

cos x = -1

x = 180 degrees

Hence, the value of x = π

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The given expression in standard form is 8a-28b+15c.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 4(2a)+7(-4b)+(3×c×5)

Now, 8a-28b+15c

Therefore, the given expression in standard form is 8a-28b+15c.

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"Your question is incomplete, probably the complete question/missing part is:"

Write the expression in standard form: 4(2a)+7(-4b)+(3×c×5).

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