Ellen renovates the foyer of an old farmhouse. The foyer is 15 feet long and 8 feetwide. Calculate the area of the foyer.foyer60 square feet46 square feet120 square feet23 square feet240 square feet

The number of pencils he paid for is 15.

He bought some pencils for N60.00.

If he had paid N1 less for each pencil, he could have bought 5 more pencils.

Let

x = cost of each pencil that amount to N60.00

y = number of pencil

Therefore,

xy = 60

y = 60 / x

(y + 5)(x - 1) = 60

(60 / x + 5)(x - 1) = 60

60 - 60 / x + 5x - 5 = 60

- 60 / x + 5x  + 55 = 60

- 60 / x + 5x = 60 - 55

- 60 / x + 5x = 5

- 60 + 5x² / x = 5

5x = -60 + 5x²

5x² - 5x  - 60 = 0

x² - x - 12 = 0

x² + 3x - 4x - 12 = 0

x(x + 3) - 4(x + 3) = 0

(x - 4)(x + 3)

Hence,

x = 4 and x = -3

We can only use positive value.

xy = 60

y = 60 / 4

y = 15

Therefore, he paid for 15 pencils.

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Answer:

2x=128⁰ x=64⁰

Step-by-step explanation:

since they are corresponding angles, the other side (2x) will also be 128⁰. This means that x=64⁰

and 2x=128⁰

Answer:

x = 16

Step-by-step explanation:

the derivitvte of 2x^2(cotx) is −4cot2xcsc^2(2x)

Blaise Pascal and Pierre de Fermat, two eminent mathematicians, exchanged correspondence in the middle of the 17th century that provided the groundwork for probability and altered how scientists and mathematicians regarded uncertainty and risk.

The issue with the Duke of Tuscany (1560)

The Duke of Tuscany was a constant competitor. He had noticed that number 10 frequently occurred over number 9 in a game where three dice are tossed and the points are added. De Duke, however, asserts that there are six different ways to generate both figures.

Pyramidal dice (four-sided), which date back to Summer in the third millennium bce, are just as old as cubical dice. These dice were discovered alongside the so-called Royal Game of Ur, one of the oldest complete board games ever uncovered.

In his book A Pocket Guide to Dice & Dice Games, Keith Souter develops the Sir Farkle theory and fixes Iceland as the setting and the year as 1492.

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Answer:

Step-by-step explanation:

it 10

Jacinda get 12% of commission

How to find percentage :

The cost of shoe that customer purchased is $259.50

The amount that Jacinda get commission is $31.14

To calculate the percentage of commission divide 31.14 by 259.50 and multiply by 100.

That is percentage of commission = 31.14/259.50 * 100

                                                         = 12%

Jacinda get 12% of commission.

What is percentage ?

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Answer:what photo

Step-by-step explanation:

where

Answer:

y = ( 6 / 5 )x - 5;

Step-by-step explanation:

y = - ( 1 / m )x + c;

Convert dual intercept to standard form.

5x + 6y = 18;

Subtract 5x from both sides.

6y = - 5x + 18;

Divide both sides by 6.

y = ( - 5x + 18 ) / 6;

y = ( - 5x / 6 ) + ( 18 / 6 );

y = ( - 5 / 6 )x  + 3;

Get the perpendicular line.

y = ( 6 / 5 )x + c;

Substitute the point.

7 = ( 6 / 5 )( 10 ) + c;

7 = 12 + c;

Subtract 12 from both sides.

- 5 = c;

c = - 5;

y = ( 6 / 5 )x - 5;

Answer:-1a+2

Step-by-step explanation:

add like terms

Hey there!

(2a - 5) - (3a + 5)

= 2a - 5 - 3a + 5

COMBINE the LIKE TERMS

= (2a - 3a) + (-5 + 3)

= 2a - 3a + (-5) + 3

= -1a - 2

Therefore, your answer should be:

-1a - 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The cost function of the box is C(x) = 2. x² + 160/x and the dimension that lead to the minimum cost is length = ∛40 ft., width = ∛40 ft., height = ∛5 ft.

Let:

x = the bottom's side length

h = the height of the box

Then, the surface area of top and bottom:

A1 = 2. x²

The surface area of vertical sides:

A2 = 4 x. h

The cost function is:

C(x)  = 2. x² . 1 + 4 x. h . 2

C(x) =  2. x² + 8 x. h

The volume of the box is:

V = x² . h

20 = x² . h

h = 20 / x²

Substitute h = 20 / x² into the cost function:

C(x) =  2. x² + 8 x. h

C(x) =  2. x² + 8 x. 20 / x²

C(x) = 2. x² + 160/x

At the minimum point, the derivative of a function is equal to zero. Hence,

C'(x) = 4x -160 / x² = 0

x³ = 40

x = ∛40

Substitute x = ∛40 to find the height:

h = 20 / x²

   = 2 . 10 / (∛4² . ∛10²)

   = ∛10 / ∛2 = ∛5

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(a) The probability that the next page you read contain zero is 0.8187.

(b) The probability that the next page you read contains  or more typographical errors is 0.0175.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes

The probability that the next page you read contains zero. The expected number of typographical errors on a page of a certain magazine is  

That is, y = 0.2

Let  is a random variable representing the number of typos per page.

Since, we have a large number of letters per page, and the number of errors in one page will be small, we use Poisson distribution. The probability function of the Poisson distribution is defined as,

[tex]P(x = i) = e^-^y\frac{y^i}{i!},..... i = 0, 1, 2, ...[/tex]          ...(1)

Here, y is a parameter.

Find the probability that the next page you read contains zero.

That is, find P(y = 0)

plug y = 0 in equation (1), we get

P(x = 0) = 0.8187

The probability that the next page you read contain zero is 0.8187

Given the question that the probability that the next page you read contains  more typographical errors. The expected number of typographical errors on a page of a certain magazine is 0.2

That is y = 0.2

Let is a random variable representing the number of typos per page.

Find the probability that the next page you read contains more typographical errors.

That is find P(x ≥ 2)

P(x ≥ 2) = 1 - P(x ≤ 1)

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

= 1 - 0.982477

= 0.0175

The probability that the next page you read contains  or more typographical errors is 0.0175.

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(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.

(b) The random variable may assume the values in the interval (0, ∞).

(c) The random variable "X" is continuous in nature.

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Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:

2x² + 5x + 1.

In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:

8, 26, 19 and 3.

The divisor is found as follows:

4x + 3 = 0

4x = -3

x = -3/4

x = -0.75.

The resulting coefficients of the quotient are given as follows:

8, 20, 4 and remainder of 0.

Hence the quotient is:

8x² + 20x + 4.

Which can be simplified as:

2x² + 5x + 1.

The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.

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For first, ∠J=55°, ∠L=55°, ∠K=70°. For second, ∠T=34°, ∠S=34°, ∠R=112°,

For third, AB=5, BC=10, AC=10. For fourth, XY=29, XZ=48, YZ=29

An isosceles triangle definition states it as a polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.

For 1,

in ΔKJL,

KJ=KL

So,

∠J=∠L

∠J=180-125

∠J=55°

∠L=55°

∠K=180-(55+55)

∠K=70°

For 2,

in ΔRST,

RS=RT

So,

∠T=∠S=3x-2

3x-2+3x-2+9x+4=180°

15x=180°

x=12

∠T=3x-2=34°

∠S=3x-2=34°

∠R=9x+4=112°

For 3,

in ΔABC,

AC=BC

So,

3x+4=10

3x=6

x=2

AB=x+3=5

BC=10

AC=3x+4=10

For 4,

in ΔXYZ,

XY=YZ

So,

4x+1=29

4x=28

x=7

XY=4x+1=29

XZ=7x-1=48

YZ=29

For first, ∠J=55°, ∠L=55°, ∠K=70°.

For second, ∠T=34°, ∠S=34°, ∠R=112°,

For third, AB=5, BC=10, AC=10.

For fourth, XY=29, XZ=48, YZ=29

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Answer:

D

Step-by-step explanation:

22.5÷3 is 7.5 and 52.5÷3 is 7.5 as well

Money is y axis (x,y) and candles is x axis (x,y)

Answer:

Step-by-step explanation:

yes it does

x² -16=0

1) Since we have two roots and any quadratic equation can be rewritten as once we have the roots:

So let's find one equation whose roots are 4 and -4, with coefficient a=1

(x-4)(x+4)=0

x² -16=0

2) So the equation x² -16= 0 has roots x_1=4 and x_2= -4 S={-4,4}

Answer:

Angles gh, fh,  and jh are perpendicular :)

Step-by-step explanation:

perpendicular is when line touch and they make a 90* angle and the three angles that i have listed all touch and make 90*

The corresponding element in the range when 6 is an element in the domain is f(6) = -4.

Given function f(x) = 8–2x.

6 is an element in the domain of this function.

To find the corresponding element in the range of the function,

Substitute x = 6 in the given function f(x).

So,

f(6) = 8 - 2(6)

f(6) = 8 -12

f(6) = -4

Hence, the corresponding element in the range when 6 is an element in the domain is -4.

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Using a graphing calculator, the features of the function are given as follows:

In a graph, the domain and the range of the function are given as follows:

This function is defined for all real values and also assumes all real values, hence both the domain and the range are (-∞,∞).

From the graph, the function is classified as decreasing or increasing as follows:

Hence the intervals are given as follows:

The relative minimum is when the function changes from decreasing to increasing, hence it is at this following point:

(1.184, -1.089).

The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:

(2.816, 1.089).

The end behavior of the function is given by the limits of the function when x go to infinity, hence:

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The amount of time it would take Element X to decay to a mass of 230 grams is 9.5 minutes.

Mathematically, the mass of a radioactive element that is remaining after time (t-hours) is given by this exponential function:

A(t) = A₀·e^{t/τ}

Where:

Next, we would determine the time constant by using this mathematical expression:

Time constant, τ = t/ln2

Time constant, τ = 5/0.6932

Time constant, τ = 7.2130 minutes.

Now, we can determine the amount of time to decay by making half-life (t) the subject of formula as follows:

A(t) = A₀·e^{t/τ}

Half-life, t = -τ·ln(A(t)/A₀)

Substituting the parameters into the formula, we have;

Half-life, t = -7.2130·ln(230/860)

Half-life, t = -7.2130 × ln(0.2674)

Half-life, t = -7.2130 × -1.3190

Half-life, t = 9.51 ≈ 9.5 minutes.

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a) We know that in the northern Hemisphere we have 4 seasons: Summer where is more sun, Spring, and autumn that the sun is like 50/50 and winter that is the season with less sun. So we can made a graph with this so:

b) In this case if we have a simple interest is going to be a streight light that is going to increase. So the graph will be:

c) An item that increase it's price by 50% is going to be increasing each time more, so this case will be an exponential so the graph will be:

d) The high of a triangle and the base of the triangle are going to to have a constant rate. so the graph will be a horizontal line so:

Step-by-step explanation:

Hope it helps you ..

MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER

The solution to the inequalities given are graphed in the diagram attached below.

When graphing an inequality, a full circle is used when the sign involved is "≤ or ≥", while an empty circle is used to indicate the point on the graph when the inequality sign is "< or >".

The inequalities would be solved as shown below:

15. ¾x + 5 > 11

Subtract 5 from both sides

¾x > 11 - 5

¾x > 6

3x > 24

Divide both sides by 3

3x/3 > 24/3

x > 8

16. -5/6x - 1 ≥ 14

Add 1 to both sides

-5/6x ≥ 14 + 1

-5/6x ≥ 15

-5x ≥ 90

Divide both sides by -5

x ≤ -18

17. 5x - 2 ≤ -7

Add 2 to both sides

5x ≤ -7 + 2

5x ≤ -5

x ≤ -1

18. 6 - x ≤ 14

Subtract 6 from both sides

-x ≤ 14 - 6

-x ≤ -8

x ≥ 8

19. 4 - 1/3x > 11

Subtract 4 from both sides

-1/3x > 11 - 4

-1/3x > 7

-x > 21

x < -21

20. (x + 11)/-2 < -2

x + 11 < 4

Subtract both sides by 11

x < 4 - 11

x < -7

See the image below for the graph of the solution to each inequality given.

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Let

x -----> number of rides

y ----> the total cost

so

The linear equation that represents both situations are

y=40 -----> equation A

y=x+15 ----> equation B

equate both equations

40=x+15

solve for x

x=40-15

x=25

therefore

The cost of the total bill for the friends is $154.665.

This implies a levy that's paid to the government by individuals and firms.

From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.

The total bill will be:

= Cost of food + Tax + Tip

= $122.75 + (8% × $122.75) + (18% × $122.75)

= $122.75 + $9.82 + $22.095

= $154.665

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The amount of honey each jar holds is 1/2 cup by jar

To solve this exercise we have to perform a mathematical operation of division with fractions:

Information about the problem:

To find the amount of honey each jar holds we state the following equation:

Amount of honey by jar = Cups brought / Jars filled

Amount of honey by jar = 14 cups /28 jar

Simplifying to its minimum expression, we have:

Amount of honey by jar = 7 cups / 14 jar

Amount of honey by jar = 1 cup / 2 jar

Amount of honey by jar = 1/2 cup by jar

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

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A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function.

The set of ordered pairs is a function exists {(1, 5), (1, 6), (2,7), (3, 8)}.

A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function. A function is defined by an equation that generates a set of ordered pairs. Each x value in a relation must have a unique value for the y value for it to be a function. if there are multiple y-values associated with an x-value.

Because no two ordered pairs have the same first coordinates with the same second coordinates, the initial set of ordered pairs is a function.

A relationship and a function vary in that a relationship can have multiple outputs for a single input, whereas a function only needs one input to produce one outcome. This is the fundamental criterion used to distinguish between relation and function. These model concepts are created through the usage of relations.

Therefore, the correct answer is option C. {(1, 5), (1, 6), (2,7), (3, 8)}.

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