how tall will each candle be at 11:00 PM when johnsons put the candles out for the night

Answer:

To find the solutions of the equation x^2+4x+3=0, you can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 4, and c = 3. Plugging these values into the formula gives:

x = (-4 +/- sqrt(16 - 413)) / (2*1)

x = (-4 +/- sqrt(4)) / 2

x = (-4 +/- 2) / 2

This means the two solutions for x are (-4 - 2) / 2 = -3 and (-4 + 2) / 2 = -1.

So the biggest and lowest numbers you can get with the number x^2+4x+3=0 are -3 and -1, respectively.

Answer: The biggest number is  x= -1 and

                   the lowest number is    x= -3 .

Step-by-step explanation: Solution

or, x^2+4x+3=0

or, x^2+ ( 3+1 )x+3=0

or, x^2+3x + x +3=0

or, x (x + 3)+ 1(x + 3)=0

or, (x + 3) (x + 1)=0

Either,

        (x + 3)= 0  ,    (x + 1)= 0

     or, x= -3       ,    x= -1

Therefore, The biggest number is  x= -1 and

                   the lowest number is    x= -3 .

The scale factor of the dilation is one-fifth, two-fifths, five-halves, or 5.

The scale factor of a dilation describes the ratio of the lengths of corresponding sides of the image and the preimage. To calculate the scale factor, we must first identify the lengths of the preimage and the image. Let's say that the preimage has a length of 10 units, and the image has a length of 5 units. To calculate the scale factor, we divide the length of the image by the length of the preimage: 5/10 = 1/2.

This tells us that the scale factor of the dilation is 1/2, or one-half. To determine the scale factor in terms of a fraction with a denominator of five, we can multiply the numerator and denominator of the fraction by five, resulting in a scale factor of 2/5, or two-fifths. To express the scale factor as a fraction with a numerator of five, we can multiply the numerator and denominator of the fraction by two, resulting in a scale factor of 5/2, or five-halves. Finally, to express the scale factor as a decimal, we can divide the numerator by the denominator, resulting in a scale factor of 2.5, or 5.

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Answer: C

Step-by-step explanation: 5/2

There are 166 integers between 1 and 1000 that are divisible by 3 and 5.

1000/3 = 333.3333

1000/5 = 200

333.3333 * 200 = 66,666.66

66,666.66 / 15 = 4444.444

4,444.444 rounded to 4,445

4,445 - 1 = 4,444

4,444 + 1 = 4,445

4,445 integers between 1 and 1000 that are divisible by 3 and 5.

There are 4,445 integers between 1 and 1000 that are divisible by both 3 and 5. The calculation to determine this is 1000 divided by 3, then 1000 divided by 5, then multiplying the two numbers together, then dividing by 15 and rounding the result to the nearest integer, then subtracting and adding 1 to the result.

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The cost price of an article is Rs.600 and the profit of dealer is Rs.200

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given;

An article marked at Rs.800 sold at a discount of 10%.

That means,

selling price = 800 - 10% 0f 800

                 =  800 - (10 x 800 / 100)

                 = 800 - 80

                 = 720

The dealer makes a profit of 20% means is selling the article at 120%.

120%=720

1%=6

Hence, 100% = 600

Thus, the cost price of article = 600

Profit= SP-CP = 800-600 = 200

Therefore, Rs.600 is the cost price and the profit is Rs.200

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The line could pass through any of the following points: (1, 0),(2, 1),(3, 2),(4, 3), and (5, 4).

A line with a positive slope passes through points that are higher and to the right of the starting point. The line could also pass through points with higher y-values and smaller x-values, such as (1, 2) or (0, 5), but it could not pass through points with lower y-values or larger x-values. For example, the line could not pass through the point (-1, 0) because it has a larger x-value than the starting point (0, -1) and a positive slope. Similarly, the line could not pass through the point (1, -2) because it has a lower y-value than the starting point and a positive slope.

Therefore, the line could pass through any of the following points:

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For a line with a positive slope that passes through (0, 1), the points that can't be on the line are:

(-3, 1) and (5, -2)

Now, According to the question:

Given a line with

To find:

The point from the list that is not on the same line

Slope formula is m = (y2 - y1)/(x2 - x1)

Using one given point, we get the slope:

m = (y - 1)/(x - 0)

m = (y - 1)/x and m > 0

Let's verify the answer choices:

Point (12, 3)

m = (3- 1)/12 = 2/12 > 0, yes, on the line

Point (-2,-5)

m = (-5 - 1)/( -2) = 3 > 0, yes, on the line

Point (-3, 1)

m = (1 - 1)/(-3) = 0, no, not on the line

Point (1, 15)

m = (15 - 1)/1 = 14 > 0, yes, on the line

Point (5,-2)​

m = (-2 - 1)/5 = -3/5 < 0, no, not on the line

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The complete question is this:

A line passes through the point (0, –1) and has a positive slope. Which of these points could that line pass through? Check all that apply.

(12, 3)

(–2, –5)

(–3, 1)

(1, 15)

(5, –2)

Answer: a) [tex]4\frac{3}{5}[/tex]

              b) [tex]3\frac{1}{6}[/tex]

Step-by-step explanation: I separately wrote down the steps and explanation please refer to the explanation I wrote down for better understanding.

The roots of a polynomial are the values of x for which the polynomial evaluates to 0.

A complex root is a root for which the real and imaginary parts are not both 0. If a polynomial has a complex root, that means that there is at least one value of x for which the polynomial evaluates to 0.

This can happen in two ways: either the polynomial has a real root and an imaginary root, or it has two complex roots. In either case, the complex roots must be found in order to determine the polynomial's factorization.

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After taking the common, the factor of [tex]x^2+2x^2+9[/tex] is [tex]3(x^2+3)[/tex].

In the given question, we have to find the factors of [tex]x^2+2x^2+9[/tex]

(1) Find the expression's numbers' greatest common factor before analyzing each variable or expression separately to identify the GCF. Factor out the least power that arises if the variable or expression appears in every term.

(2) Write the GCF outside the parentheses and divide each term by the GCF inside the parentheses to factor out a GCF.

The given expression is [tex]x^2+2x^2+9[/tex].

In the given term first and second term have the same power of term. So we add them.

[tex]x^2+2x^2+9[/tex] = [tex]3x^2+9[/tex]

Now we take 3 common in both term

[tex]x^2+2x^2+9[/tex] = [tex]3(x^2+3)[/tex]

Hence, the factor of [tex]x^2+2x^2+9[/tex] is [tex]3(x^2+3)[/tex].

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The complete question is:

What are the factors of [tex]x^2+2x^2+9[/tex]?

Answer:

The answer is 195mile

Step by step explanation:

We've

to solve this we need to draw a triangle

then we need to find the distance traveled by each after 3 hours

S(1) = t × V(1) = 3 × 52 = 156 mile

S(2) = t × V(2)= 3× 39 = 117 mile

the distance between them is our z

S(1) = x

S(2) = y

using the Pythagorean Theorem

z = √x^2 + y^2 = √(156)^2 + (117)^2 = √ 13689+24336 = √38025 = 195 mile

Answer:

like fraction

unlike fraction

proper fraction

improper fraction

Step-by-step explanation:

The expression of 7 is subtracted from the square of a number will be :

x² - 7 .

Given,

7 is subtracted from the square of a number .

Here,

Firstly ,

Let a number be x .

Square of a number will be x² .

Now we have to subtract 7 from the x² .

So,

The expression will be :

x² - 7.

Thus its is the required expression .

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Answer: 2nd option

Step-by-step explanation:

If m stands for miles, we know it must be $0.85m. Since there is a $0.75 and $0.10 charge, we add those together to get $0.85. Then, we must add the tourist charge of $2.50. So, the equation. 0.85m+ 2.50

Answer:

0.85m + 2.50

Step-by-step explanation:

mileage charge is equal to 0.75 dollars each mile

city gas tax is equal to 0.10 dollars each mile

mileage charge plus city gas tax is equal to 0.85

plus the tourist charge , so the answer is

0.85m + 2.50

Answer: Carrots cost(s) the most per pound

Step-by-step explanation:

Answer:

To put this equation in standard form, you need to complete the square for both the x's and the y's.

First, complete the square for the x's by adding and subtracting (16/2)^2 = 16^2/2^2 = 32/2 = 16.

4x² - 16x + 16 - 16 - 5y² - 30y - 9 = 0

4x² - 16x + 16 - 5y² - 30y - 9 = 0

Now, complete the square for the y's by adding and subtracting (30/2)^2 = 30^2/2^2 = 900/2 = 450.

4x² - 16x + 16 - 5y² - 30y + 450 - 450 - 9 = 0

4x² - 16x + 16 - 5(y² - 15y + 225) - 9 = 0

Now, you can simplify the expression inside the parentheses by completing the square for y.

4x² - 16x + 16 - 5(y - 15)^2 + 5*225 - 9 = 0

Now, divide everything by -5 to get the equation in standard form:

-4/5x² + 16/5x - 16/5 - (y - 15)^2 = 0

The standard form of the equation is:

(-4/5)x² + (16/5)x - 16/5 - (y - 15)^2 = 0

The distance between the points (-3, 4) and (6, 1) will be 9.49 units.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

The points are given below.

(-3, 4) and (6, 1)

The distance between the points (-3, 4) and (6, 1) will be given as,

D² = (- 3 - 6)² + (4 - 1)²

D² = (-9)² + (3)²

D² = 81 + 9

D² = 90

Take square root on both sides. Then we have

D = √90

D = 9.49 units

The distance between the points (-3, 4) and (6, 1) will be 9.49 units.

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There are 18564 possible juries.

The positive integers that appear as coefficients in the binomial theorem are known as binomial coefficients in mathematics. Typically efficiency is denoted by the display style notation and is indexed by the pair of numbers n k 0. It is the multiplicative formula that may be used to calculate the coefficient of the term in the polynomial expansion of the binomial power (1 + x)n.

There are 18 choose 6 ways to choose a group of 6 people from a group of 18, which is equal to 18564. This means there are 18564 possible juries.

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There are 18564 possible juries.

Now, According to the question:

A trial jury of 6 people will be chosen from among 18 candidates.

This is a combinatoric question. As such, you would have n C r possibilities, where n is equal to the number of distinct objects, in this case 18, and r is equal to the number of things taken at a time, in this case, 6.

When order does not matter (in this case, it doesn’t, since it doesn’t matter who juror 1 and who juror 6 is, as long as there are exactly 6 in the end), it would be:

n C r = n! / r! (n-r)!

[tex]_6C^1^8[/tex] = 18!/ 6! (18 - 6)!

[tex]_6C^1^8[/tex] = 18!/ 6! × 12!

This gives us 18564

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k≤8 is the solution of inequality 16 ≥ 2k

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 16 ≥ 2k

Sixteen greater than or equal to two time of k.

16 ≥ 2k

Divide both sides by 2

8 ≥ k

Eight is greater than or equal to k

k≤8

k is less than or equal to eight

Hence, k≤8 is the solution of inequality 16 ≥ 2k

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The speed of the airplane with no wind is 437.5 miles per hour.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Let x be the maximum speed of the plane and y be the speed of the wind. Speed of the plane with no wind is equal to the maximum speed x.

Total distance travelled = 2100 miles

Time taken to travel the distance against the wind = 6 hours

Time taken to travel the distance with wind = 4 hours

When plane travels against wind, speed of wind becomes negative to get the average speed of both.

x - y = 2100 / 6 = 350 miles/hour

When plane travels with wind, both speeds are added.

x + y = 2100 / 4 = 525 miles/hour

Since x - y = 350 ⇒ y = x - 350

Substituting y = x - 350 in x + y = 525,

x + y = 525

x + (x - 350) = 525

2x - 350 = 525

2x = 875

x = 437.5

Hence the speed of the plane with no wind is 437.5 mph.

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The maximum speed of the plane is 437.5 miles per hour and the speed of the wind is 87.5 miles per hour.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, At maximum speed, an airplane travels 2100 miles against the wind in 6 hours.

Flying with the wind, the plane can travel the same distance in 4 hours.

Let x be the maximum speed of the plane and y be the speed of the wind.

So, the speed of plane with the wind is x+y

The speed of plane against the wind is x-y

Now, x+y =2100/4

x+y=525 --------(I)

x-y =2100/6

x-y=350 --------(II)

Add equation (I) and (II), we get

x+y+x-y=525+350

2x=875

x=875/2

x=437.5 miles per hour

Substitute x=437.5 in equation (I), we get

437.5+y=525

y=525-437.5

y=87.5 miles per hour

Therefore, the maximum speed of the plane is 437.5 miles per hour and the speed of the wind is 87.5 miles per hour.

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The value of m∠3 is 95°.

In general, the alternate internal angles created by a transversal at the intersection of two parallel lines are congruent. The Alternate Interior Angles Theorem is the name of this tenet.

Several pairs of congruent angles are created when two parallel lines intersect a transversal. Corresponding angles are the name given to these pairings of congruent angles.

  Lines l and m are parallel in the given issue and are interrupted by a transversal. This results in the creation of four angles, denoted as m1, m2, m3, and m4. The problem statement states that m1 is 60° and m2 is 125°.

Since lines l and m are parallel, the alternate interior angles formed by the transversal are congruent. This means that m∠1 is congruent to m∠3 and m∠2 is congruent to m∠4. Therefore, m∠3 is congruent to m∠1, which is 60°. Therefore, m∠3 = 60°.

The answer is therefore 95°.

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Answer:

y = 2x - 11

Step-by-step explanation:

In y = 2x - 7, the slope is 2.

A slope parallel to this would also be 2.

y = 2x + b

-1 = 2(5) + b

-1 = 10 + b

b = -11

y = 2x - 11

Properties of Logarithms are as follows: Product Property, Quotient Property, Power Rule, Change of base rule, Reciprocal Rule, Natural logarithmic Properties and Number raised to log property.

The properties of the logarithms are used to expand a single log expression into multiple or compress multiple log expressions into a single one. Seven logarithmic properties are as follows:

Product Rule :    [tex]log_{a}mn = log_{a}m + log_{a}n[/tex]

Quotient Rule :    [tex]log_{a}\frac{m}{n} = log_{a}m - log_{a}n[/tex]

Power Rule :     [tex]log_{a}m^{n} = n* log_{a}m[/tex]

Change of base rule :   [tex]log_{a}m = \frac{log_{n}m}{log_{n}a}[/tex]       Where [tex]m, n, a[/tex] are positive integers and [tex]n\neq 1, a\neq 1[/tex]

Reciprocal Rule :   [tex]log_{a}m = \frac{1}{log_{m}a}[/tex]  where [tex]m,a[/tex] are positive integers other than 1.
Natural logarithmic Properties:    [tex]ln(mn) = ln(m) + ln(n)[/tex]

                                                       [tex]ln\frac{m}{n} = ln(m) - ln(n)[/tex]

                                                        [tex]ln(m^{n}) = n* ln(m)[/tex]

The number raised to log :     [tex]a^{log_{a}m} = m[/tex]

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The monthly payment of loan is $180.26.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Given principal = $4,000

APR = 4%

time = 2 years

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A =[tex]P(1 + r/n)^{nt}[/tex]

A = 4,000.00(1 + 0.04/1)¹ˣ²

A = 4,000.00(1 + 0.04)²

A = $4,326.40

amount for 2 years = $4,326.40

monthly payment  = 4326.40/24

monthly payment  =  $180.26

Hence the monthly payment is $180.26

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The gold, silver, and bronze in a ratio of 2 : 2 : 5 will be 4, gold, 4 silver and 10 bronzes.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this situation, team wins 18 medals at a track meet. The medals are gold, silver, and bronze in a ratio of 2 : 2 : 5.

Gold = 2/9 × 18

= 4 gold's

Silver = 2/9 × 18

= 4 silvers

Bronze = 5/9 × 18

= 10 bronzes.

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When dividing two numbers written in scientific notation, you divide the base numbers and subtract the exponents of the powers of ten.

To determine this :

When performing mathematical operations with numbers written in scientific notation, it is important to remember that the base number and the exponent of the power of ten are treated separately. For example, consider the following problem:

(3.2 x 10³) / (2.4 x 10²)

To solve this problem, you would divide the base numbers 3.2 and 2.4 as you would with any other division problem:

3.2 / 2.4 = 1.3333...

Then, you would subtract the exponents of the powers of ten:

3 - 2 = 1

The result of the division problem is then written as 1.3333... x 10¹.

So, to summarize, when dividing two numbers written in scientific notation, you divide the base numbers and subtract the exponents of the powers of ten.

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The percentage increase in his hourly wage between year 1 and year 2 is 5.88 %

Percentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.

What is a percentage increase?

The percentage increase is the ratio of value increased to the original value and multiplied by 100.

It is expressed in percentage.

If there is an increase in the value of anything, then there is an increase in percentage.

We have,

Wage in the first year per hour = $8.65

Wage in the second year per hour = $10

The percentage increase in hourly wage:

= [ (13.5 - 12.75) / 8.65 ] x 100

= ( 0.75 / 12.75 ) x 100

= 5.88 %

Thus the percentage increase in his hourly wage between year 1 and year 2 is 5.88 %

Option C is the correct answer.

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If Malcom got a raise in his wage from $12.75 an hour to $13.50 an hour in one year, the percent increase in his hourly wage between year 1 and year 2 is 5.88%.

Therefore the answer is c) 5.88%

Malcolm's wage in his first year was $12.75 an hour and in year 2, it was raised to $13.50 an hour. Percentage increase in his hourly wage between year 1 and year 2 can be calculated by

% = ((wage in year 2) - (wage in year 1))/ (wage in year 1) × 100, that is

[tex]% = \frac{(wage\ in\ year\ 2)\ -\ (wage\ in\ year\ 1)}{wage\ in\ year\ 1}[/tex][tex]\% =\ \frac{(wage\ in\ year\ 2)\ -\ (wage\ in\ year\ 1)}{wage\ in\ year\ 1} \ 100[/tex]

% = (13.50 - 12.75)/ 12.75 × 100, that is

[tex]\% =\ \frac{13.50\ -\ 12.75}{12.75} \ 100[/tex]

% = 0.75/ 12.75 × 100

% ≈ 5.88

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Using the same-side exterior angles theorem, the value of y is: 92°.

The same-side exterior angles theorem states that if two lines are cut by a transversal, and the alternate interior angles are congruent (equal in measure), then the same-side exterior angles are supplementary (add up to 180 degrees).

The image shows two angles that are same-side interior angles, which are (x + 1) and (x - 3) degrees. Therefore, their sum would be equal to 180 degrees. This means that:

(x + 1) + (x - 3) = 180 [based on the same-side exterior angles theorem]

x + 1 + x - 3 = 180

2x - 2 = 180

2x = 180 + 2

2x = 182

2x/2 = 182/2

x = 91

Thus, based on the alternate interior angles, we also have:

x + 1 = y

Plug in the value of x:

91 + 1 = y

92 = y

y = 92°

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The slope of the line is 7/3 the y-intercept is -3 and the function is y = 7/3x - 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -3 - 4 ) / ( 0 - 3 )

Slope = -7 / -3 = 7 / 3

The y-intercept will be,

y = mx + c

y = 7 / 3x + c

-3 = 0 + c

c = -3

The equation of the line will be,

y = mx + c

y = 7/3x - 3

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The cost of the 12 units sold is, $224 - $144 = $80

Using the FIFO periodic inventory method, the cost of the 12 units that are sold is $120. This is because the first 12 units sold were the ones that were purchased on February 3 for $12 each. The total cost of these units is 12 units * $12/unit = $12*12=144. The remaining 8 units in the inventory were purchased on February 1 for $10 each, for a total cost of 8 units * $10/unit = $8*10=80. The total cost of the inventory is therefore $144 + $80 = $224. The cost of the 12 units sold is, therefore, $224 - $144 =$80.

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