Show the expression ^2−−6 in factored form and explain what the solution would mean for the equation.

Answer:

Step-by-step explanation:

Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:

rate = cost/length = 92 cents/23 inches = 4 cents/inch

Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:

cost = rate * length = 4 cents/inch * 34 inches = 136 cents

So, 34 inches of wire will cost 136 cents.

Step-by-step explanation:

the trick is to find the "norm" rate, which is the rate for one unit.

from there we can get the rate for any number of units just by multiplying.

so,

23 in for 92 cents.

that means the rate is

23/92 = 23/(23×4) = 1/4

so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.

so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)

1/4 × 34/34 = 34/136

that means 34 inches cost 136 cents (= $1.36).

The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.

What is meant by combination?

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.

Given,

Number of engineers in the faculty = 20

Number of engineers required to form a committee = 20

1) Number of ways when either engr. Marzo or engr. William is only present.

   Excluding Marzo and William, we have 18 engineers.

So we can select 6 engineers from these 18 = 18C6 =  [tex]\frac{18!}{6!12!}[/tex] = 18564

Number of ways we can select only one from Marzo and William = 2C1 = 2

So the total number of combinations for forming a committee = 18564 + 2 = 18566

2) Engr. Cara and Eng. Danny are present.

   Engr. Hillary is not considered.

So we have to select 5 members from the rest of the 15 people

Number of combinations are = 15C5 = 3003

3) Engineers Gilliam, Fernando and Ophelia are selected.

    Now we have to select the rest of the 4 members from the remaining 15 people

Number of combinations = 15C4 = 1365

Therefore the number of combinations of different engineers are found to form a 7 member committee.

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The slope for:

1 = 1/2  (Option E)

2 = 2 (Option C)

3 = -1/2 (Option H)

4 = -2 (Option A)

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

The formula for slope (m) is given as:

m = Rise/Run = y2-y1/x2-x1

(x1,y1) = Coordinates of the first point in the line

(x2,y2) = Coordinates of the second point in the line.

1) The points are:

x1= -2

y1 = 2

x2 =2

y2  = 4

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

m = 2 / 4

m = 1/2

Thus, Δy/Δx = 1/2

2) The points are:

x1= -1

y1 = -12

x2 =5

yx  = 0

m = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

m = (0 - (-12)) / (5 - (-1))

m = 12 / 6

m = 2

Thus, Δy/Δx = 2


3) Where the points are:
x1= 2

y1 = -6

x2 = - 4

y2  = -3

Substituting the given values, we get:

m = (-3 - (-6)) / (-4 - 2)

m = 3 / (-6)

m = -1/2

Thus, Δy/Δx = -1/2


4)  Where the points are:
x1= 0

y1 = 3

x2 = 1.5

y2  = 0

Substituting the given values, we get:

m = (0 - 3) / (1.5 - 0)

m = -3 / 1.5

m = -2


Thus, Δy/Δx = -2

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The annual interest rate on the saving account is 5%.

Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.

To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.

Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:

$200 = $1,000 * r * 4

r = $200 / ($1,000 * 4)

r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.

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Answer:

No

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

x + 32 + 4x + 20 + 4x + 20 = 180

9x + 72 = 180  ( subtract 72 from both sides )

9x = 108 ( divide both sides by 9 )

x = 12

then the 3 angles are

x + 32 = 12 + 32 = 44°

4x + 20 = 4(12) + 20 = 48 + 20 = 68°

4x + 20 = 68°

an obtuse angle is greater than 90°

none of the 3 angles in the triangle are obtuse

Answer:

No

Step-by-step explanation:

All angles of a triangle add up to 180°.

4x + 20 + 4x + 20 + x + 32 = 180

1. Simplify

9x + 72 = 180

2. Subtract 72 from both sides.

9x = 108

3. Divide both sides by 9.

x = 12

Replace x by 12 in each angle.

-  12 + 32 = 44°

-  4(12) + 20 = 68°

-  4(12) + 20 = 68°

All of the angles are less than 90°, so they aren't obtuse.

The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = ( -4x² + 36 ) / ( x + 3 )

On simplifying , we get

g ( x ) = -4 ( x² - 9 ) / ( x + 3 )

On further simplification , we get

g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )

g ( x ) = -4 ( x - 3 )

g ( x ) = -4x + 12

Now , the function has a vertical asymptote at ( 0 , 12 )

The function has a horizontal asymptote at ( 3 , 0 )

Hence , the function is solved

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Answer:

at least one x-intercept

at least one y-intercept

domain of x

Step-by-step explanation:

took ed2023

Answer:

C. 2

Step-by-step explanation:

A polynomial function has one or more real numbers as roots or zeros. These roots correspond to the values of x for which the function takes on the value of zero.

In this case, y = (x-2)(x+3)², we can factor the equation to find its zeros. The expression (x-2)(x+3)² can be factored into two terms: (x-2) and (x+3)².

The first term, (x-2), is equal to zero when x = 2, meaning that x = 2 is a root of the function.

The second term, (x+3)², is equal to zero when x = -3, meaning that x = -3 is another root of the function.

So, the function y = (x-2)(x+3)² has two roots, or zeros, at x = 2 and x = -3.

To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.

Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.

Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:

ad^2 + cd^2 = ac^2

We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:

bd^2 + cd^2 = ac^2

We also know that c lies on ab, so we can write:

ac = ab - bc

Substituting this into our equation, we get:

bd^2 + cd^2 = ab^2 - 2abbc + bc^2

Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:

bd^2 + y^2 = (x + y)^2 - 2xy + x^2

Simplifying, we get:

bd^2 - x^2 = 2xy - y^2

Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.

To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.

Since angle adb = angle bad, we can write:

2 angle adb + angle acd = 180 degrees

Substituting in the values of our angles, we get:

2 angle adb + 90 degrees = 180 degrees

Solving for angle adb, we get:

angle adb = 45 degrees

Now, we can use the fact that triangle adb is isosceles to write:

angle bad = (180 - 45)/2 = 67.5 degrees

Finally, we can use the law of sines to relate bd and x:

bd/sin(67.5) = x/sin(45)

Simplifying, we get:

bd = x

Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.

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Answer:

The correct answer is D. inventory; number of employees on payroll. An accountant records on hand to note a company's inventory, which is the stock of goods available for sale or use in the production process. The number of employees on payroll refers to the human resources aspect of a company, which is separate from the inventory.

The total weight of the bottles the truck carries is 6020 ounces.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

Example:

2 + 1x + 4y = 7 is an expression.

3 + 3x + 3 = 7 is an expression.

We have,

Number of bottles the truck carries = 430

One bottle weight = 14 ounces

Now,

The total weight of the bottles.

= Number of bottles x Weight of one bottle

= 430 x 14

= 6020 ounces

Thus,

The total weight of the bottles the truck carries is 6020 ounces.

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The echelon form of the given augmented matrix with 1's on the diagonal is:

1 -1 0 1000

0 1 0 1100

0 0 1 300

To find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:

Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:

1 -1 2 400

0 1 -2 500

0 -2 5 -700

Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:

1 -1 2 400

0 1 -2 500

0 0 1 300

Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:

1 -1 0 1000

0 1 0 1100

0 0 1 300

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Answer:

7 degrees C

Step-by-step explanation:

To solve this question, we can start by ordering the temperatures from least to greatest:

4, 1, 0, -2, -1, -3, 1, -2, 3, -1  --> -3, -2, -2, -1, -1, 0, 1, 1, 3, 4

the lowest temperature would be -3 in this list, and the highest temperature in this list would be 4. We can find the difference in temperature using subtraction:

4-(-3) = 4+3=7

The difference is 7 degrees C.

since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.

[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]

The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.

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Answer:

(-3,-1)

Step-by-step explanation:

The two lines intersect at that point. -3 is in the x axis and -1 is in the y axis.

Answer:

Step-by-step explanation:

I believe that you put the right answer in.

Answer:

$10576.38

Step-by-step explanation:

To calculate the investment amount required to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you can use the formula for compound interest:

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

where:

A is the amount of money you have after "t" years,

P is the initial investment amount (what you want to find),

r is the interest rate as a decimal,

n is the number of times the interest is compounded per year,

t is the number of years the investment will be compounded for.

In this case,

r = 0.036

n = 12 (because the interest is compounded monthly)

t = 15

So, we can plug in the values into the formula and solve for P:

A = P * (1 + 0.036/12)^(12 * 15)

$23711 = P * (1.003)^(180)

$23711 = P * 2.2375

Dividing both sides by 2.2375:

P = $23711 / 2.2375

P = $10576.38

So, to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you would need to invest $10576.38. Rounded to the nearest dollar, this amount is $10576.

Answer:

Step-by-step explanation:

To determine the percentage increase between 2017 and 2018, we need to calculate the difference between the two years and then divide by the 2017 value and multiply by 100. So, the calculation would be:

(9960,000 - 9640,000) / 9640,000 * 100 = 3.125%

So, the number of households increased by 3.125% from 2017 to 2018.

To find the number of households in 2019, we need to find the increase from 2018 to 2019. We can do this by multiplying the number of households in 2018 by the percentage increase, and then add that to the 2018 value. So, the calculation would be:

9960,000 * (3.125 / 100) + 9960,000 = 10,298,800

Therefore, there would be approximately 10,298,800 households in 2019, rounded to the nearest ten thousand.

Answer:

Marianna will have $19,700 in her annuity after 6 years.

Step-by-step explanation:

To find the amount of money in the annuity after 6 years, we need to calculate the compound interest earned over that time period.

First, let's find the interest rate per quarter: 8% annual interest divided by 4 quarters per year = 2% interest per quarter.

Next, we'll calculate the number of quarters that the money is invested: 6 years x 4 quarters per year = 24 quarters.

Now we can use the formula for compound interest to find the total amount of money in the annuity after 6 years:

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

Where:

A = final amount

P = initial investment ($10,000 in this case)

r = interest rate per quarter (2% or 0.02)

n = number of times the interest is compounded in a year (4)

t = number of years invested (6)

Plugging in the values:

A = $10,000 * (1 + 0.02)^(24)

A = $10,000 * 1.96634438

A = $19,663.44

Rounding to the nearest hundred dollars: $19,700

So, Marianna will have $19,700 in her annuity after 6 years.

Answer:

I have graphed it and attached an image in the explanation part.

Step-by-step explanation:

Using division operation, the number of containers that Linden would get from his supply of milk is 79 containers.

Division operation involves the dividend divided by the divisor to obtain a result called the quotient.

Division operation is one of the four basic mathematical operations, including multiplication, addition, and subtraction.

Total liters of milk = 237

The content of the liter containers = 3 liters

The number of containers = 79 (237 ÷ 3)

Thus, based on division operation, Linden, who is sharing 237 liters of milk in containers will need 79 3-liter containers.

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The value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

We carry out specific operations in mathematics, such as addition, subtraction, multiplication, etc. Generally speaking, these operators accept two or more operands and output a result dependent on the operation carried out. Similar to this, in set theory, several operations are typically done on two or more sets to obtain a new set of elements depending on the operation. The number of elements supplied by the operation and processing the result of a collective set is represented by the union and overlap of sets. All of the components are taken into account in the outcome when there is a union, but only the ones that are shared when there is an intersection.

The union of the two sets depict all the terms present in both the sets.

Thus, the value of (A ∪ B) is:

(A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}

The intersection of the sets depict all the common terms present in the two sets thus the value of (A ∩ B) is:

(A ∩ B) = {7}

Hence, the value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

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Answer:  -151

Step-by-step explanation:  

First Plug everything in

-7(5)^(2)+2(5)+2(7)

Then use order of operations and first deal with the exponent

-7(25)+2(5)+2(7)

then multiply left to right

-175+10+14

combine

so the answer is -151

Answer: -3, 0

Step-by-step explanation:

If a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, an endpoint of this rotated segment is (-3, 0) and (-7, 0).

In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of this line segment with endpoints (0,−3) and (0,−7), the coordinate of its image;

(x, y)                            →            (y, -x)

Point (0,−3)          →     Point (-3, 0)

Point (0, -7)          →     Point (-7, 0)

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a) The table represents an exponential growth function.

b) The number of people that will have visited the website after 47 days online is given as follows: 17,716 people.

An exponential function is modeled as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Considering that the reference day is the day 42, the function is defined as follows:

y = 11000(1.1)^(x - 42).

Hence, after day 47, the number of visitors is given as follows:

y = 11000 x (1.1)^5.

y = 17,716.

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The number of widgets that Justin can make in 36 minutes is given as follows:

y = 36k.

In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

The constant is obtained as follows:

k = y/x.

For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:

y = 36k.

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Answer:

(a)

smaller value = 125 ft

larger value = 250 ft

(b)

31250 ft²

Step-by-step explanation:

(a)

In total, the farmer used 875ft worth of fencing.

In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x

This means 7x=875ft. Dividing both sides by 7, we find x=125ft

The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".

(b)

Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:

125ft * 250ft = 31250 ft²

Answer:

(a)

smaller value =125 ft

larger value = 250 ft

(b)

31250 ft?

In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.

In right triangle ABC,

BC is the base.

Midpoint of AB is D.

CD bisects ACB.

Measure of ∠ACD = Measure of ∠BCD

AC = 4

BC = 7.5

AD = 3

BD = x

CD bisects angle ACB and intersect at midpoint of AB at point D.

This implies

BD / AD = BC / AC

⇒x / 3 = 7.5 / 4

⇒ x = ( 7.5 × 3 ) / 4

⇒ x = 22.5 / 4

⇒ x = 5.625

Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.

The above question is incomplete , the complete question is :

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.

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The statements are (a) False, (b) True and (c) False

Right angles are angles whose measure is 90 degrees.

In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.

(a) ∠AHB and ∠AHG are vertical angles.

Vertical angles are angles which are formed on the opposite sides of two intersecting lines.

∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.

So the statement is false.

(b) ∠EHF and ∠DHE are adjacent angles.

∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.

So the statement is true.

(c) The measure of ∠FHG is equal to the measure ∠DHF.

We know that DG is a straight line.

∠FHG and ∠DHF are linear pair of angles.

So, ∠FHG + ∠DHF = 180°

Given that ∠FHG is right angle.

90° + ∠DHF = 180°

∠DHF = 180° - 90°

∠DHF = 90°

So the statement is true.

Hence the statements (a), (b) and (c) are false, true and true respectively.

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Your question is incomplete. The complete question with the figure is given below.

1. the number ( of people without college degree ) = 125 - (24 +38)= 63

2. number of people without experience ) = 125- ( 41+38) = 46

3. number ( of applicants with college degree but no experience) = 24

4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

number of people that have previous work experience only) = 79-38 = 41

number ( of persons that have college degree only) = 62- 38 = 24

1. the n( of people without college degree ) = 125 - (24 +38)= 63

2. n( of people without experience ) = 125- ( 41+38) = 46

3. n( of applicants with college degree but no experience) = 24

4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103

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