one number is less than 3 times another if their sum is increased by 5 the result is 25 find the number​

[tex]\begin{cases} x = 6 &\implies x -6=0\\ x = -5 &\implies x +5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -6 )( x +5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 4}}{a=4} \\\\\\ 4(x-6)(x+5)=y\implies 4(x^2-x-30)=y\implies \boxed{4x^2-4x-120=y}[/tex]

Answer:

If the roots of a quadratic equation are given as x = -1 ± 2i, then the equation can be written in the form:

(x - (-1 + 2i))(x - (-1 - 2i)) = 0

Simplifying this expression, we get:

(x + 1 - 2i)(x + 1 + 2i) = 0

Expanding the left side of this equation, we get:

x^2 + x(2 - 2i + 2 + 2i) + (1 - 2i)(1 + 2i) = 0

Simplifying this expression, we get:

x^2 + 2x + 5 = 0

Therefore, the quadratic equation with roots of x = -1 ± 2i is:

x^2 + 2x + 5 = 0

the probability that the CDs are in alphabetical order is 1/12528

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain to occur.

Given by the question.

Let's assume that the CDs are labeled as CD1, CD2, CD3, ..., CD9.

If CD1 is placed first, then there is only one way to place the remaining CDs in alphabetical order.

If CD2 is placed first, then there is only one way to place CD1 and CD3-CD9 in alphabetical order.

If CD3 is placed first, then there are two ways to place CD1-CD2 and CD4-CD9 in alphabetical order arrange (CD1-CD2-CD4-CD5-CD6-CD7-CD8-CD9 or CD2-CD1-CD4-CD5-CD6-CD7-CD8-CD9).

Similarly, for CD4-CD9, there are 3, 4, 5, 6, and 7 ways to place the remaining CDs in alphabetical order.

Therefore, the total number of ways to arrange the CDs in alphabetical order is:

[tex]1 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 29[/tex]

Hence, the probability of the CDs ending up in alphabetical order is:

[tex]1/12528[/tex]

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Answer:

Step-by-step explanation:

Assuming you can follow how the equation was solved for y, the 2 comes from the "±" in front of the square root. That means that there is a positive and a negative result when you plug in a number for x. For example, if we were asked to solve

[tex]x^2=4[/tex]

we would take the square root of both sides, giving us

x = ±2

This is because a positive 2 squared gives us a positive 4, and a negative 2 squared also gives us a positive 4. There will ALWAYS be 2 solutions when you take a square root of a number, both the positive (principle) and negative roots.

Answer:

Step-by-step explanation:

To evaluate the function graphically, we need to plot the two lines on graph and see where they intersect.Then find the value of f(x) at that point.Therefore, f(4) = -4, which matches with the graphical evaluation.

A function is a mathematical rule that maps every input from a set (the domain) to a unique output from another set (the range), where each input has only one corresponding output.

The two lines intersect at the point (2,-4). Therefore, the value of f(x) at x=4 is -4.

To find f(4), we can use the equation of line 1, which is:

y - (-8) = (2 - (-8))/(1 - (-5)) × (x - (-5))

Simplifying, we get:

y + 8 = (10/6) × (x + 5)

y + 8 = (5/3) × (x + 5)

y = (5/3) × x - 19/3

Substituting x=4, we get:

y = (5/3) × 4 - 19/3

y = -4

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The value of the equation of the ellipse is (x + 1)² + (y + 1)² = 9, the center of the ellipse is at (-1, -1), thus graph B is correct.

E = c/a, where c is the distance from the ellipse's centre to either focus and an is the distance from the ellipse's centre to either end of the main axis, is the formula for an ellipse's eccentricity.

The distance between the foci is 2a = 6, where an is the separation between any focus and the elliptic centre.

The middle of the ellipse is at the midway of the foci since they are both on the same horizontal line, which is (-1, -1).

The main axis measures 18 inches, or 2b, where b is the distance between the ellipse's center and either end of the major axis.

Inputting the values we are familiar with yields:

b² + (c = 3)² = a²

b² + 9 = 9

b^2 = 0

So b = 0, which means the ellipse is a circle with radius a = 3 centered at (-1, -1). The equation for a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Substituting the values we know, we get:

(x + 1)² + (y + 1)² = 9

Hence, the value of the equation of the ellipse is (x + 1)² + (y + 1)² = 9, the center of the ellipse is at (-1, -1), thus graph B is correct.

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Hence, in response to the provided question, we can say that 2-2 = 0 is not a polynomial expression and S is not a polynomial expression

A polynomial is a mathematical statement made up of parameters and uncertainty that exclusively uses additions, substitutions, multiplications, and nonzero powers of variables. A single uncertain x polynomial is denoted by the expression x2 4x + 7. An formula in mathematics characterized as both a polynomial is constituted of variable (formerly known as different flavored) and coefficients which may be added, deleted, multiplied, and increased to negative integer factors of semi. A polynomial is an algebraic statement having variables and coefficients. Just the operations addition, reduction, multiply, and non-negative integer multipliers are permitted in an expression. These formulas are known as polynomials.

6x³+11x²-5x-12 = (2x-3)(3x+4)(x+1)

3x+4 = 3x+4

2x² + x - 8 = (2x-4)(x+2)

6x +7x³-9x²+13x-12 = 7x³-9x²+(6+13)x-12 = 7x³-9x²+19x-12

3x²-x+3 = 3x²-3x+4x+3 = 3x(x-1)+3(x-1) = (3x+3)(x-1)

2x² + 3x - 4 = (2x-1)(x+4)

2x²+x-3 = (2x-1)(x-3)

2-2 = 0

S = S (not a polynomial expression)

So, the matches are:

6x³+11x²-5x-12 = (2x-3)(3x+4)(x+1)

3x+4 = 3x+4

2x² + x - 8 = (2x-4)(x+2)

6x +7x³-9x²+13x-12 = 7x³-9x²+19x-12

3x²-x+3 = (3x+3)(x-1)

2x² + 3x - 4 = (2x-1)(x+4)

2x²+x-3 = (2x-1)(x-3)

2-2 = 0 is not a polynomial expression

S is not a polynomial expression

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The function value of g[f(-1)] when f(x) = 2x² + 4x and g(x)=-3x-1 is 5.

In mathematics, a function is a rule that assigns each element from a set (called the domain) to a unique element from another set (called the range or codomain). It is a way of describing the relationship between two sets of numbers. The input values of a function are called the independent variable or argument, and the output values are called the dependent variable. The most common way to represent a function is by using an equation.

Here,

To evaluate g[f(-1)], we need to first find f(-1), then use that value as the input to the function g.

We have:

f(x) = 2x² + 4x

So, to find f(-1), we substitute -1 for x:

f(-1) = 2(-1)² + 4(-1)

= 2 - 4

= -2

Now that we have f(-1) = -2, we can evaluate g[f(-1)] by substituting -2 for x in the function g:

g[f(-1)] = g[-2]

= -3(-2) - 1

= 5

Therefore, g[f(-1)] = 5.

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The dimensions of the original piece of cardboard are 15 inches by 23 inches.

Let's start by defining the variables we'll need for this problem:

w = width of the original piece of cardboard (in inches)

l = length of the original piece of cardboard (in inches)

h = height of the box (in inches)

We know that the length of the original piece of cardboard is 8 inches more than the width, so we can write:

l = w + 8

When Lorene cuts out 4-inch squares from each corner of the rectangular sheet, the resulting height of the box will be 4 inches. Therefore, the height of the box is:

h = 4

The base of the box will have dimensions (w - 8) inches by (l - 8) inches, since 4 inches are removed from each side of the width and length. The volume of the box is given as 420 cubic inches, so we can write:

V = (w - 8)(l - 8)(4)

Substituting the expression for l in terms of w, we get:

420 = (w - 8)(w + 8 - 8)(4)

420 = (w - 8)(w)(4)

105 = w(w - 8)

Solving for w using the quadratic formula, we get:

w = 15 or w = -7

Since w must be a positive value, we can discard the solution w = -7. Therefore, the width of the original piece of cardboard is:

w = 15 inches

Using the expression for l in terms of w, we can find the length of the original piece of cardboard:

l = w + 8 = 23 inches

Therefore, the dimensions of the original piece of cardboard are 15 inches by 23 inches.

Answer:

sorry i am very sorry

Step-by-step explanation:

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Answer:

a person randomly grabs candies out of a bag there are 480 candles in the bag the person looked and they pulled out 20% if the candies were yell0ow and 15% of them were green how many more were yellow than green

Step-by-step explanation:

it's B

Answer: 5 more yellow candies than 15 candies, or 5

Step-by-step explanation: Think, if there are 20 yellow candies and 15 of them green;

You need to take away 20 - 15 which will be 5, 5 more yellow candies than 15 candies

Keep up the good work=)

To answer this question, we need to calculate the population of both towns for each year and compare them.

For Town A:

1980 population = 1200

1981 population = 1200 + 300 = 1500

1982 population = 1500 + 300 = 1800

1983 population = 1800 + 300 = 2100

and so on

For Town B:

1980 population = 500

1981 population = 500 + 0.12(500) = 560

1982 population = 560 + 0.12(560) = 627.2

1983 population = 627.2 + 0.12(627.2) = 702.464

and so on

To determine which town will eventually have the greater population, we can calculate the limit of each population as time goes to infinity. For Town A, the population limit is infinity because the population keeps increasing by 300 every year. For Town B, the population limit is also infinity because the population grows exponentially due to the 12% increase each year. However, we can still compare their growth rates.

For Town A, the annual growth rate is constant at 300 people per year, whereas for Town B, the growth rate is decreasing over time due to the compounding effect of the percentage increase.

Therefore, initially, Town A has a smaller population than Town B. However, over time, Town A's growth rate remains constant while Town B's growth rate slows down. Eventually, Town A will surpass Town B in population.

To determine which town had a greater population in 2005, we need to calculate the population of each town in 2005 using the growth rates we calculated above.

For Town A:

1980 population = 1200

2005 population = 1200 + 300(25) = 8700

For Town B:

1980 population = 500

2005 population = 500(1.12)^25 = 4544.73

Therefore, in 2005, Town A had a greater population than Town B.

Ending Balance: $14,450

Cash typically refers to physical currency and coins that are used as a medium of exchange for goods and services. It includes banknotes and coins that are issued by a government or central bank and are accepted as legal tender within a country.

Given by the question.

Certainly, here is an example of a monthly cash budget:

Monthly Cash Budget:

Starting Balance: $10,000

Income:

Expenses:

Notes:

Starting Balance refers to the amount of cash you have at the beginning of the month.

Income includes all sources of cash inflow.

Expenses includes all sources of cash outflow.

Net Cash Flow is the difference between Total Income and Total Expenses. If it is positive, you have a surplus. If it is negative, you have a deficit.

Ending Balance is the amount of cash you have at the end of the month after all income and expenses have been accounted for.

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Part 1 - Circumcenter: The point where all three sides of the triangle meet and intersect, also the center of the circle that passes through all three vertices of the triangle.

Intersect is an operation used in mathematics and computing to determine the common elements of two or more sets. It is usually written as a symbol (∩) and is used to return the set of all elements that are in both sets. For example, if A is the set of all even numbers and B is the set of all prime numbers, then A ∩ B will return the set of all prime even numbers.

- Orthocenter: The point where the three altitudes of the triangle intersect.
- Centroid: The point where the three medians of the triangle intersect.

Part 3: The three centers of the triangle (circumcenter, orthocenter, and centroid) can all be constructed using a straightedge and compass. The circumcenter is located at the intersection of the three sides, the orthocenter is located at the intersection of the three altitudes, and the centroid is located at the intersection of the three medians. From this, we can make the hypothesis that these three centers of a triangle are related in that they are all located at the intersection of two or more lines that form the triangle.

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Answer:

hollow circle at 7, with an arrow extending to the left

Step-by-step explanation:

These expression shows Carly picked 20 mangοes

a. (m+4)/2

b. (2m+2)/3

c. (m+4)/2 - (2m+2)/3 = 3

d. Carly picked 20 mangοes.

An algebraic equatiοn is a mathematical statement that uses variables and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn tο express the equality οf twο algebraic expressiοns.

The gοal οf sοlving an algebraic equatiοn is tο determine the values οf the variables that satisfy the equatiοn.

a) The number οf mangοes in each grοup that Carly shared equally οn Mοnday can be represented by the expressiοn: (m+4)/2

b) The number οf mangοes in each grοup that Carly shared equally οn Tuesday can be represented by the expressiοn: (2m+2)/3

c) If Carly subtracted the number οf mangοes in each grοup οn Tuesday frοm the number οf mangοes in each grοup οn Mοnday and gοt 3 mangοes left, the equatiοn representing this infοrmatiοn is:

(m+4)/2 - (2m+2)/3 = 3

d) Sοlving the equatiοn frοm part c) fοr m, we get:

9m + 6 - 4(2m + 2) = 18

9m + 6 - 8m - 8 = 18

m = 20

Therefοre, Carly picked 20 mangοes.

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The distance between zero and point P is 5 units.

To find the distance between two points on the number line, we must take the difference between the values ​​corresponding to those points.

The value of 0 is trivially 0.

The value of P is between -4 and -6, so we conclude that:

P = -5

Taking the difference between these values ​​we obtain:

distance = 0 - (-5)

distance = 0 + 5 = 5

The distance between those values ​​is 5 units.

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The new carpet will cοst $1,908.00.

The size οf a regiοn οn a surface is measured by its area. While surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject, the area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina.

Area can be interpreted as the quantity οf material with a particular thickness required tο create a mοdel οf the shape οr as the quantity οf paint required tο cοmpletely cοver a surface in a single cοat. It is the twο-dimensiοnal equivalent οf the vοlume οf a sοlid οr the length οf a curve (a οne-dimensiοnal cοncept) (a three-dimensiοnal cοncept).

The area οf the classrοοm is the square οf the length οf its side, which is:

6 yards × 6 yards = 36 square yardsTο find the cοst οf the new carpet, we need tο multiply the area οf the classrοοm by the cοst per square yard:

36 square yards × $53.00/square yard = $1,908.00

Therefοre, the new carpet will cοst $1,908.00.

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The scale applied to the replica model made by the carpenter is 1:12. This means that 1 inch on the replica model is equal to 12 inches on the full-size table.

What is a replica model?

A replica model in mathematics is a type of modelling technique used to analyse the behaviour of complex systems. It is useful for studying dynamic systems, such as those in physics, engineering, economics, and biology, since it allows for a more accurate analysis of how the system may respond to different inputs.

The scale of the replica model made by the carpenter can be determined by using the ratio of the size of the replica model compared to the size of the full-size table. The ratio of the length of the replica model to the full-size table is 3 inches to 37.5 inches. This can be expressed as a scale by dividing the size of the replica model by the size of the full-size table.

In this example, 3 inches divided by 37.5 inches is equal to 0.08. This means that the scale of the replica model is 1:12, meaning 1 inch on the model is equal to 12 inches on the full-size table. This means that the carpenter used a 1:12 scale when making the replica model of the table.

In conclusion, the scale applied to the replica model made by the carpenter is 1:12. This means that 1 inch on the replica model is equal to 12 inches on the full-size table. This ratio can be determined by taking the ratio of the size of the replica model compared to the size of the full-size table.

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Answer:

Kayla is farther along in the book after 4 days, since she is on page 58 while Bilquis is on page 51.

Step-by-step explanation:

Answer: The sales manager, with weekly earnings of $1006.25.

Step-by-step explanation:

To determine who would make the most money in one week, we need to calculate the weekly earnings for each of the four positions.

Let's start with the sales manager, who works 35 hours at a rate of $28.75 per hour:

Weekly earnings for sales manager = 35 hours x $28.75 per hour = $1006.25

Next, let's consider the head mechanic, who works 25 hours. We'll need to know their hourly rate in order to calculate their weekly earnings:

Hourly rate for head mechanic = $35 per hour

Weekly earnings for head mechanic = 25 hours x $35 per hour = $875

Now, let's move on to the assistant mechanic, who works 30 hours:

Hourly rate for assistant mechanic = $20 per hour

Weekly earnings for assistant mechanic = 30 hours x $20 per hour = $600

Finally, let's consider the front desk clerk, who works 40 hours:

Hourly rate for front desk clerk = $15 per hour

Weekly earnings for front desk clerk = 40 hours x $15 per hour = $600

Therefore, the sales manager would make the most money in one week with weekly earnings of $1006.25.

Answer: Sales Manager

Step-by-step explanation:

Let's calculate the total pay for each worker:
Sales manager: $28.75 per hour x 35 hours = $1,006.25

Head mechanic: $32.50 per hour x 25 hours = $812.50
Assistant mechanic: $25.00 per hour x 30 hours = $750.00
Front desk clerk: $20.00 per hour x 40 hours = $800.00

Answer:

Step-by-step explanation:

To solve for x in the equation x^2 - 16 = 0, we can use the difference of squares formula:x^2 - 16 = (x + 4)(x - 4) = 0

Now we can set each factor equal to zero and solve for x:x + 4 = 0 or x - 4 = 0x = -4 or x = 4
Therefore, the solutions to the equation x^2 - 16 = 0 are x = -4 and x = 4.

Answer:

Step-by-step explanation:

To find two points on the line represented by the function r(x) = 4 - 32x, we can arbitrarily choose two values of x and then find the corresponding values of r(x) using the equation.

For example, if we choose x = 0, then r(0) = 4 - 32(0) = 4. So the point (0,4) is on the line.

Similarly, if we choose x = 1, then r(1) = 4 - 32(1) = -28. So the point (1,-28) is on the line.

Therefore, we have two points (0,4) and (1,-28) on the line represented by the function r(x) = 4 - 32x. These two points can be used to graph the function.

An exponential function is a function in which the independent variable x appears as an exponent.

a is the y-intercept.

b is the rate of change.

The function is exponential growth when b > 1.

The function is exponential growth when b < 1.

y-intercept is the initial value of the function when x is equal to 0.

Asymptote is the line that the function approaches but does not cross.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch or cross.

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According to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

Since p:q:r = √3:1:1, we can write:

p = √3x

q = x

r = x

where x is a common factor.

We can see that triangle ABC is a 30-60-90 triangle with angle A = 60 degrees, and that angle BOC is a right angle. Therefore, we can use the ratios of sides in a 30-60-90 triangle to find the values of P, O, and R:

P = AB = p = √3x

O = BC/2 = q/2 = x/2

R = AC = r = x

Therefore, the ratio P:O:R is:

P:O:R = √3x : x/2 : x

We can simplify this ratio by multiplying all terms by 2 to get rid of the fraction:

2√3x : x : 2x

We can further simplify by dividing all terms by x:

2√3 : 1 : 2

Therefore, according to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

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Answer: Since we know that the two variables are independent, we can use the addition rule of probability to find the probability of selecting a student who is either female or a psychology major:

P(female or psychology major) = P(female) + P(psychology major) - P(female and psychology major)

Since the variables are independent, we know that P(female and psychology major) = P(female) x P(psychology major) = 0 x 0.1 = 0.

Therefore:

P(female or psychology major) = 0 + 0.1 - 0 = 0.1

So the probability of randomly selecting a student who is either female or a psychology major is 0.1.

Step-by-step explanation:

Answer:

y = 1/3x +2

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b  

where m is the slope and b is the y intercept.

y = 1/3x +2

Answer:

y = 1/3x + 2

Step-by-step explanation:

The equation for slope intercept form of a line is:

y = mx + c

Here,

m = slope

c = y intercept

Given that,

m = 1/3

c = 2

So, to find equation of the line, replace m and c with the given values.

y = mx + c

y = 1/3x + 2

Answer:

When we raise a power to another power, we multiply the exponents. So:

(6^7)^8 = 6^(7*8) = 6^56

Therefore, (6^7)^8 can be written in the form 6^56, where k=56.

Step-by-step explanation: