a 12 foot ladder is leaning aginst a building. if the base of the ladder is 5 feet from the base of the house how high up the house will the ladder reach

Answer:

x∈(-∞,-0.854)⋃(5.854,∞) or x<-0.854 or x>5.854

Step-by-step explanation:

depends on what u want

Answer: [tex]x=0, -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}[/tex]

Answer: 3u⋅(9u−9v) = 285

Step-by-step explanation:

We can start by using the distributive property for the dot product:

3u⋅(9u−9v) = 3u⋅9u - 3u⋅9v

We also know that the dot product of two vectors u and v is u⋅v = ∥u∥∥v∥cos(θ), where θ is the angle between vectors u and v. Therefore,

u⋅v = 5 = 107cos(θ)

So we can write:

cos(θ) = 5/(10*7) = 1/14

Then we can use this value to find the dot product of u and v.

3u⋅9u = 3 * (10^2) = 300

3u⋅9v = 3 * (10)(7)(1/14) = 15

So the final answer is:

3u⋅(9u−9v) = 300 - 15 = 285

Explanation: By using the distributive property and the dot product definition, it was possible to find the dot product of 3u⋅9u and 3u⋅9v. By subtracting the latter from the former, we obtained the final answer of 285.

The total number of gallons of oil consumed during the first 14 days of the month is (b) 13.739

From the question, we have the following parameters that can be used in our computation:

F (t) = 0.3 + 0.1t — 0.85 cos(2pi/15 (t+ 5))

The question is asking for the total number of gallons of oil consumed by the furnace during the first 14 days of the month,

This can be found by integrating the function F(t) with respect to t from 0 to 14

Using a graphing calculator, we have the integrated function to be

f(t) =  0.3t + 0.05t^2 - 0.85(2/15)sin(2π/15(t+5))

Also, we have

f(14) - f(0) = 13.739

Hence, the solution is 13.739

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In the given table, y = 6x is the function as 6 = (6)1, 12 = (6)2 and 18 = (6)3. Thus, option D is correct.

A function f from domain X to domain Y is written as f: X Y. A function is described as a map that associates each element in the domain with precisely one element in the codomain. In order to determine the value returned by a function given by an argument x, Euler was the first to use the modern representation f(x) (read "f of x). Assume that the function f converts x to Y and y to Y. Then, we can write it as y = f. (x).

A function transformation in mathematics is a function that converts one function or graph into another, typically related function or graph. For instance, when a quadratic graph is translated, the vertex and axis of symmetry are moved, but the overall shape of the parabola remains the same.

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The area under the standard normal curve to the right of Z (3.15) = 0.0008

The total area under the standard normal curve happens to be 1 which is divided between two parts having an area under the curve = 0.5 on each side.

I.e. from 0 to the right side, the area under the curve = 0.5

Similarly, from 0 to the left side, the area under the curve = 0.5

Now, from the standard normal table,                                  

                                                          {the table is given in the attachment}

The area under the curve for the value of Z (3.15) = 0.4992

                                                                         {This value is the area under the curve from 0 to Z (=3.15)}

Hence, the Area under the curve to the right of Z (3.15) = 0.5 – 0.4992

                                                                                            = 0.0008

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For z = 3.15, the area under the standard normal curve is 0.99918365.

Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data.

The standard normal distribution, represented by the letter Z, is the normal distribution having a mean of 0 and a standard deviation of 1.

If {X} is a random variable from a normal distribution with mean {μ} and standard deviation {σ}, its Z-score may be calculated from X by subtracting μ and dividing by the standard deviation :

[tex]${\displaystyle Z={\frac {X-\mu }{\sigma }}}[/tex]

If {X} is the mean of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the standard error is σ/√n :

[tex]${\displaystyle Z={\frac {{\overline {X}}-\mu }{\sigma /{\sqrt {n}}}}}[/tex]

If [tex]{\textstyle \sum X}[/tex] is the total of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the expected total is nμ and the standard error is σ √n :

[tex]${\displaystyle Z={\frac {\sum {X}-n\mu }{\sigma {\sqrt {n}}}}}[/tex]

Given is the value of z = 3.15.

For z = 3.15, the area under the standard normal curve is 0.99918365.

Therefore, for z = 3.15, the area under the standard normal curve is 0.99918365.

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Answer:

[tex]\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]2 \frac{5}{8} = \frac{21}{8}[/tex]

Divide [tex]\frac{21}{8}[/tex] by [tex]\frac{3}{4}[/tex]

[tex]\frac{21}{8}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{7}{2}[/tex]

Here, two sides of the triangle are equal.

Therefore, perimeter of the triangle

= p - 5 + p - 5 + 2p + 8

= 4p - 2

= 2(2p - 1)

Answer:

2(2p - 1)

Hope it helps.

Answer: 4p - 2

Step-by-step explanation:

Sum of all sides is the perimeter.

According to the figure, the two sides are equal.

therefore, perimeter = p - 5 + p - 5 + 2p + 8

= 4p - 2

Answer: y = x/4 -7

Step-by-step explanation: hope this is right i was always good at math

Answer: 103

Step-by-step explanation: 309/3 = 103

The average cost of your item, based on a gross margin of 3%, is $108.20.

The average cost is the cost per unit.

It can be computed as the quotient of the total cost and the number of units.

The gross margin is the percentage difference between the cost of goods sold and the sales revenue.

The gross margin percentage is expressed as a quotient of the sales revenue multiplied by 100.

Selling price = $111.55

Gross margin = 3%

Selling price = 100%

Cost of goods sold = 97% (100 - 3)

Average cost (cost per unit) = Selling Price x Percentage Cost/Selling Price Percentage

$108.20 ($111.55 x 97/100)

Thus, the average cost of the product is $108.20.

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Answer:

$5.91

Step-by-step explanation:

The amount of simple interest gained from a sum of money can be represented as:

[tex]\textrm{Interest} = P\cdot r\cdot t[/tex]

where [tex]P[/tex] is the principal amount (original sum of money), [tex]r[/tex] is the rate of simple interest per time period, and [tex]t[/tex] is the period of time in relation to a year.

To solve this problem, we simply have to plug the given values into the above formula and round the result to the hundredths place (cents).

[tex]P = \$525[/tex],  [tex]r = \dfrac{4.5\%}{\textrm{month}}[/tex],  [tex]t = 3 \textrm{ months} = \dfrac{1}{4} \text{ year}[/tex]

[tex]\textrm{Interest} = \$525 \cdot 4.5\% \cdot \dfrac{1}{4}[/tex]

[tex]\boxed{\textrm{Interest} \approx \$5.91}[/tex]

Answer:

$5.91 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I=Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

As the value of t has been given in months, we need to convert it to years before inputting it into the formula.

[tex]\sf \implies 3\; months=\dfrac{3}{12}\;year=\dfrac{1}{4}\; year[/tex]

Therefore, the values to input into the formula are:

Substitute the values into the formula and solve for I:

[tex]\implies I=525 \cdot 0.045 \cdot \dfrac{1}{4}[/tex]

[tex]\implies I=23.625 \cdot \dfrac{1}{4}[/tex]

[tex]\implies I=5.90625[/tex]

Therefore, the amount of interest you would receive on a deposit of $525 for three months at a rate of 4.5% is $5.91 (nearest cent).

Answer:I don’t know

Step-by-step explanation:

The critical points of the function f are x = 1 or x = - 2

The critical point of a function is the value at which the function changes direction.

It is also the value at which the first derivative of the function equals zero.

To find the critical points of the function f, since we have the derivative of the function F'(x) = (x - 1)(x + 2).

At the critical point, the derivative of the function F'(x) equals zero.

So, we have that F'(x) = 0.

So, equating the function F'(x) to zero, we have that

F'(x) = 0

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

x - 1 = 0 or x + 2 = 0

x = 1 or x = - 2

So, the critical points are x = 1 or x = - 2

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The equation of the line passing through the point (0, 2) and (2, 12) is y = 5x + 2

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let us assume the line passes through the point (0, 2) and (2, 12), hence:

y - 2 = [(12 - 2)/(2 - 0)](x - 0)

y = 5x + 2

The equation of the line is y = 5x + 2

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the  parallelogram JKLM is a square.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

JM = -5² = 25

KL =  -5² = 25

JK = -4²=16

LM =-4²=16

So, the parallelogram JKLM is a square.

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The constant interest rate of the Jordan's investment is 3.8%

The amount in 2017 is calculated to be $578.86

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,   f(x) = a(b)ˣ

the starting, a = 370

the base = ?

the exponents = year periods

the base is calculated below

form 2012 to 2005 is 7 years hence x = 7

amount inn 2012 = amount in 2005 (b)ˣ

480 = 370 * b⁷

48/27 = b⁷

b = 1.038

this is same as 3.8% increment

The amount in 2017

from 2017 to 2005 is 12

= 370 * 1.038¹²

= 578.86

The amount in 2017 is $578.86

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Step-by-step explanation:

The amount of heat released in the given situation would be as follows:

-66.2 KJ−66.2KJ

Given that,

Weight of H2OH2O = 27g=27g

The Temperature of the Liquid = 314 k=314k

The Temperature of the Solid = 263 K=263K

Melting point of H2O = 273 KH2O=273K

To find,

The amount of heat released = [Q[Q × C_{p}lC

p

l ×(T_{final} - T_{Initial} ) +(T

final

−T

Initial

)+ Δ Hfusion + [mHfusion+[m × C_{p}sC

p

s × T_{final} - T_{Initial} ]T

final

−T

Initial

]

By putting the values in the above formula,

∵ Heat released = -66.2 KJ−66.2KJ

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The equation to solve the missing the side length is x² + 10² = 26²

What is right-angled triangle ?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

Lets take the missing side be x

The equation be

x² + 10² = 26²

x² = 26² - 10²

x² = (26 + 10)(26 - 10)

x² = 36*16

x² = 576

x = √576

  = 24

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a) In a week in which Landon made $1,500 in sales, his weekly earnings would be $625.

b) In a week in which Landon made x in sales, his weekly earnings would be $400 + 0.15x.

The weekly earnings are the sum of Landon's guaranteed or base salary per week and the sales commission he earns.

The sales commission is based on the sales Landon achieves per week and the commission rate of 15%.

The above situation implies that a percentage of the sales is paid out to Landon as a commission.  Generally, sales commissions are paid to encourage increased sales.

Guaranteed salary per week = $400

Sales commission on total weekly sales = 15%

Total weekly sales = $1,500

Landon's total earnings for the week = $625 [$400 + $1,500(0.15)]

Landon's total earnings in a week he made xx dollars in sales = $400 + 0.15x

Thus, we can conclude that Landon gets 15 cents (15%) from each dollar in sales in addition to his weekly base salary of $400.

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Answer:

To determine which cream cheese is a better buy, we need to compare the price per unit of volume for each brand.

For Brand Y cream cheese:

Price per unit = 44 AED / 220 ml = 0.2 AED/ml

For Brand Z cream cheese:

Price per unit = 100 AED / 470 ml = 0.2127 AED/ml

Since the price per unit of volume for Brand Y cream cheese is 0.2 AED/ml and the price per unit of volume for Brand Z cream cheese is 0.2127 AED/ml, Brand Y cream cheese is cheaper per unit of volume. Therefore, Brand Y cream cheese is a better buy.

Answer:

amazon

Step-by-step explanation:

let's find the price per pack to solve

best buy:

7 packs = 28 dollars

divide both sides by 7 to get 1 pack = something

1 pack = 4 dollars

amazon:

12 packs = 38 dollars

divide both sides by 12 to get 1 pack = something

1 pack = 38/12 dollars = 3.16666666667 dollars which is less than 4 dollars, so amazon is cheaper in terms of price per pack

Answer: 1000%

Step-by-step explanation:

Suppose the newborn mass is 100%. 4000 is 10 times that, which is 1000%.

Answer: %1000

What is a percentage?

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If we know that the newborn cat's weight is equivalent to 400g, and when it is fully grown it is equal to 4000 grams, we need to know how many times more is the full-grown cats' mass is compared to the newborn.

400 × 10 = 4000

We now know that the adult cat is 10 times larger than the newborn cat, meaning that it is %1000 of the newborn cat's size.

Answer:

Not rounded:

1.62 increased by 8% of the value = 1.7496

The actual change:

1.7496 - 1.62 = 0.1296

Rounded off to max. 2 decimal places:

1.62 increased by 8% of the value ≈ 1.75

The actual change:

1.75 - 1.62 ≈ 0.13

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

8% = 8 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100

8% = 8/100 = 8 ÷ 100 = 0.08

100% = 100/100 = 100 ÷ 100 = 1

The value of the percentage increase = 8% × 1.62

The new value = 1.62 + The value of the percentage increase

The new value =

1.62 + The value of the percentage increase =

1.62 + (8% × 1.62) =

1.62 + 8% × 1.62 =

(1 + 8%) × 1.62 =

(100% + 8%) × 1.62 =

108% × 1.62 =

108 ÷ 100 × 1.62 =

108 × 1.62 ÷ 100 =

174.96 ÷ 100 =

1.7496 ≈

1.75

The actual change =

The new value - 1.62 =

1.7496 - 1.62 =

0.1296 ≈

0.13

The value of the percentage increase =

8% × 1.62 =

8 ÷ 100 × 1.62 =

8 × 1.62 ÷ 100 =

12.96 ÷ 100 =

0.1296 ≈

0.13

The equation for Khloe's distance from her car in miles, y, as a function of the time in hours, x, is y = -3x + 11.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.

We have the two points of x and y.

After 1 hour, Khloe is 8 miles from her car.

When x = 1, y = 8

After 3 hours, Khloe is 2 miles from the car.

When x = 3, y = 2

Points of the linear function are (1, 8) and (3, 2)

Slope of the line = (2 - 8) / (3 - 1) = -6/2 = -3

Take a point (1, 8).

Equation of the linear function in point slope form can be written as,

y - 8 = -3(x - 1)

y - 8 = -3x + 3

y = -3x + 3 + 8

y = -3x + 11

Hence the linear function representing the situation is y = -3x + 11.

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y = 1/2x + 1 is the line's equation in slope-intercept form.

The equation of a line in slope intercept form is expressed as y = mx + b where:

m is the slope

b is the y-intercept

Given the following coordinate points (4, 3) and (0, 1), the slope is calculated as:

Slope = 1-3/0-4
Slope = -2/-4
Slope = 1/2

For the y-intercept, it is the point where the x-coordinate is zero, hence the y-intercept if (0, 1)

Determine the required equation
y = mx + b

y = 1/2x + 1

Hence the equation of the line in slope-intercept form is y = 1/2x +1

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Answer: The unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.

Step-by-step explanation:

To find the unit cost for a pound of sugar, we need to divide the total cost of the 4 lb bag of sugar by the weight of the bag.

Unit cost = Total cost / Weight

Total cost = $2.99

Weight = 4 lbs

Unit cost = $2.99 / 4 lbs = $0.75 per pound

So, the unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.

It's worth noting that this calculation gives us the unit price of the sugar, which is the price per pound of sugar, and not the unit cost which is the total cost of production divided by the total number of units produced.

It's also worth noting that some sellers may use different units of measurement, and you should always check that you are comparing the same units when comparing prices.

Answer:

The unit cost for a pound of sugar would be $0.75.

To find the unit cost, divide the total cost by the number of pounds: $2.99 / 4 lbs = $0.75/lb.

Step-by-step explanation:

Anderson's mistake in solving the rational expression, is he cancelled out variable and numbers without taking them in common.

A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.

Given that, Anderson multiplies two rational expressions with the following results.

The given expression is  [tex]\frac{x^{2} -16}{x^{2} -8x+16} . \frac{x+1}{x^{2} +2x+1} = \frac{-1}{-8x(x^{2} +2)}[/tex]

His error is, he cancelled out the variables and numbers without taking them common, we can not cancel variables and numbers if they are in addition or subtraction with other variables and numbers.

Hence, the correct solution is;

[tex]\frac{x^{2} -16}{x^{2} -8x+16} . \frac{x+1}{x^{2} +2x+1}\\\\= \frac{(x+4)(x-4)}{x^{2} -4x-4x+16} . \frac{x+1}{x^{2} +x+x+1} \\= \frac{(x+4)(x-4)}{(x-4)(x-4)} .\frac{x+1}{(x+1)(x+1)} \\=\frac{x+4}{(x-4)(x+1)}[/tex]

Hence, the correct solution is [tex]=\frac{x+4}{(x-4)(x+1)}[/tex]

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The cost for a consumption of 15 cubic meters of water is 23.85 dollars

The cost for a consumption of 30 cubic meters of water is 67.8 dollars

The cost for a consumption of 50 cubic meters of water is 113 dollars

The cost for a consumption of 70 cubic meters of water is 404.6 dollars

A piecewise-defined function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

We have the  piece-wise cost function for different number of "X" cubic meters of water consumed:

          { 1.59x ,si 0< x ≤ 20

C(x) =  { 2.26x ,si 20 < x ≤ 50

          {5.78x ,si            50< x

The cost in dollars, for a consumption of 15 cubic meters of water:

Use C(x) = 1.59x and x = 15

C(15) = 1.59 × 15 = 23.85 dollars

The cost in dollars, for a consumption of 30 cubic meters of water:

Use C(x) = 2.26x and x = 30

C(30) = 2.26 × 30 = 67.8 dollars

The cost in dollars, for a consumption of 50 cubic meters of water:

Use C(x) = 2.26x and x = 50

C(50) = 2.26 × 50 = 113 dollars

The cost in dollars, for a consumption of 70 cubic meters of water.

Use C(x) = 5.78x and x = 70

C(70) = 5.78 × 70 = 404.6 dollars

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