Gabriel's father has a garden in the back yard. The dimensions of the garden are shown here.

A green rectangle is shown. The width is labeled as 2 and two-thirds feet. The length is labeled as 7 and three-fourths feet.

Part A

Calculate the area of the garden. Show at least one step before you show your solution.

Part B

You found the area of the garden in Part A. Explain briefly, without doing any calculations, how you would find

5/6 of this area.

The right angles would be named as:

3. ∠PNL 4. ∠PNO

Right angles can be named in a few different ways, depending on the context in which they are being used. One common way is:

Using three points: use the names of the three points that form the angle, with the vertex of the angle in the middle. For example, if the right angle is formed by the line segments AB and BC, you could name it angle ABC.

The sign "∠" means angle, therefore, it can be named also as ∠ABC.

Thus, the right angles in the given diagram can be named accordingly as:

∠PNL and ∠PNO

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Answer:

[tex]\textsf{1.} \quad \left(f \cdot g \right)(x)=x^6+2x^5 -6x^4+3x^2+6x -18[/tex]

[tex]\textsf{2.} \quad\left(f -g \right)(x)=- x^4+x^2+2x-9[/tex]

Step-by-step explanation:

To calculate (f ⋅ g)(x), multiply function f(x) by function g(x) by distributing the parentheses:

[tex]\begin{aligned}\left(f \cdot g \right)(x)&=(x^2+2x-6)(x^4+3)\\&=x^2 \cdot x^4 +x^2 \cdot 3+2x \cdot x^4+2x \cdot 3 -6 \cdot x^4 -6 \cdot 3\\&=x^6+3x^2+2x^5+6x -6x^4 -18\\&=x^6+2x^5 -6x^4+3x^2+6x -18\\\end{aligned}[/tex]

To calculate (f - g)(x), subtract function g(x) from function f(x) by applying the distributive law -(a + b) = -a - b:

[tex]\begin{aligned}\left(f -g \right)(x)&=(x^2+2x-6) - (x^4+3)\\&=x^2+2x-6 - x^4-3\\&=- x^4+x^2+2x-6 -3\\&=- x^4+x^2+2x-9\end{aligned}[/tex]

Note:  The standard form of a polynomial is expressed by writing the term with the highest degree first, followed by the other terms in order of decreasing powers.

The exponential function [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex] determines the amοunt of substance after 36 years to be 0.2 grams.

The fοrmula for an exponential functiοn is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The amοunt of a radioactive substance left after a certain number of half-lives can be calculated using the expοnential equation formula -

[tex]A = A_0 \times \frac{1}{2}^{\frac{t}{T}}[/tex]

where -

A0 is the initial amοunt of the substance

A is the amοunt of the substance remaining after t years

T is the half-life οf the substance

In this case, the half-life is 8 years, sο T = 8.

We want tο know how much of the original 3.2 grams of the substance wοuld be left after 36 years, so t = 36.

We can plug these values intο the formula to get -

[tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex]

A ≈ 0.2 grams

Therefοre, after 36 years, only about 0.2 grams of the original 3.2 grams of the substance wοuld be left.

The equation that best mοdels this situation is -

[tex]A = 3.3 \times \frac{1}{2}^{\frac{t}{8}}[/tex]

where A represents the amοunt of the substance remaining after t years, in grams.

Therefοre, the equation is [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex].

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The decay of Element X can be modeled by the equation:

N = N0 * (1/2)^(t/t1/2)

where N is the amount of Element X remaining after time t, N0 is the initial amount of Element X, t1/2 is the half-life of Element X, and ^(t/t1/2) denotes exponentiation with base 1/2.

We know that the initial amount of Element X is 470 grams, the half-life is 8 minutes, and we want to find the time it takes for Element X to decay to 10 grams. Let t be the time in minutes.

Then, we can set up the following equation:

10 = 470 * (1/2)^(t/8)

Dividing both sides by 470, we get:

(1/47) = (1/2)^(t/8)

Taking the natural logarithm of both sides, we get:

ln(1/47) = (t/8) * ln(1/2)

Solving for t, we get:

t = -8 * ln(47)/ln(2)

t ≈ 59.3

Therefore, it would take about 59.3 minutes, to the nearest tenth of a minute, for Element X to decay to 10 grams.

10 3/8. I had this exact question for homework and answered this and got it correct, so I'm pretty sure this is correct :)

Answer: m∠G = 41°

Step-by-step explanation:

      Opposite angles of parallelograms are congruent. This means that m∠G = m∠E, so we can write an equation using the given information.

Given:

      m∠G = m∠E

Substitue:

      5x - 9 = 3x + 11

Add 9 to both sides of the equation:

      5x = 3x + 20

Subtract 3x from both sides of the equation:

      2x = 20

Divide both sides of the equation by 2:

      x = 10

      Then, we will substitute this value of x back into the expression for m∠G.

5x - 9 = 5(10) - 9 = 50 - 9 = 41°

Answer:

eeeeejjbbvvv g gyuuu u grrtyyu

The value of the polynomial equations are

f ( -10 ) = 20201

f ( 2 ) = 17

f ( 3 ) = 142

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , the value of A is

f ( x ) = 2x⁴ + x² - 10x + 1   be equation (1)

Now , when the value of x = -10

f ( -10 ) = 2 ( -10 )⁴ + ( -10 )² - 10 ( -10 ) + 1

On simplifying , we get

f ( -10 ) = 2 ( 10000 ) + 100 + 100 + 1

f ( -10 ) = 20000 + 201

f ( -10 ) = 20201

Now , when the value of x = 2

f ( 2 ) = 2 ( 2 )⁴ + ( 2 )² - 10 ( 2 ) + 1

On simplifying , we get

f ( 2 ) = 2 ( 16 ) + 4 - 20 + 1

f ( 2 ) = 32 - 15

f ( 2 ) = 17

Now , when the value of x = 3 , we get

f ( 3 ) = 2 ( 3 )⁴ + ( 3 )² - 10 ( 3 ) + 1

f ( 3 ) = 2 ( 81 ) + 9 - 30 + 1

f ( 3 ) = 162 - 20

f ( 3 ) = 142

Hence , the polynomial equations are solved

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The trade discount is $15.75.

A trade discount is a regular reduction from a product's regular, established price. The use of trade discounts allows a company to adjust the final price based on the volume or status of each customer.

It is important to note that trade discounts are not the same as early-payment discounts. (Early-payment discounts of 1% or 2% are typically recorded by the seller in an account such as Sales Discounts and by the buyer in an account such as Purchase Discounts using the periodic inventory method.) Neither the seller nor the buyer keeps a separate account for trade discounts.

We must first determine the product's list price in order to determine the trade discount.

List price: $75 plus $3.75 equals $78.75

As the trade discount rate is 20%, the following discount is offered:

Discount = 0.2 times List price = 0.2 times $78.75 = $15.75

The trade discount is therefore $15.75.

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All statements and reasons are shown below.

A triangle is a closed two-dimensional geometric shape that has three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and can be classified according to the length of their sides (scalene, isosceles, or equilateral) or the size of their angles (acute, right, or obtuse). The sum of the angles of a triangle is always 180 degrees, and the Pythagorean theorem can be used to find the length of one side if the other two sides are known in a right triangle.

According to the given figure:

4. In ΔFGH and ΔFJH,

        Statement                                   Reason

5. In ΔTVY and ΔXWY,

        Statement                                   Reason

6. In ΔKML and ΔPMN,

        Statement                                   Reason

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Answer:

4=20

3=?

so 20×3 divide by 4 = 15

Step-by-step explanation:

Answer:25

Step-by-step explanation: 25 25 25

Step-by-step explanation:

1) length of YZ:

[tex]YZ=\sqrt{XZ^2-XY^2} ;= > \ YZ=8.485=8.5;[/tex]

2) angle X:

[tex]m \angle X=arccos(\frac{XY}{XZ});= > \ m \angle X=arccos\frac{1}{3}=70.6 к;[/tex]

3) angle Z:

[tex]m \angle Z=arcsin(\frac{XY}{XZ});= > \ m \angle Z=arcsin\frac{1}{3}=19.4 к;[/tex]

Answer:

Step-by-step explanation:

[tex]16^\frac{1}{n}=2[/tex]     (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])

[tex](2^4)^\frac{1}{n}=2[/tex]

[tex]2^\frac{4}{n}=2[/tex]

[tex]2^\frac{4}{n}=2^1[/tex]

∴[tex]\frac{4}{n} =1[/tex]    (indices must be equal when bases are equal)

∴[tex]n=4[/tex]

Using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.

The height abοve οr belοw a specified reference pοint, mοst frequently a reference geοid, which is a mathematical representatiοn οf the Earth's sea level as an equipοtential gravitatiοnal surface, determines a lοcatiοn's elevatiοn.

A frequently used idea in relatiοn tο height and distance is the angle οf elevatiοn, particularly in trigοnοmetry. It is described as a relatiοnship between an οblique line frοm the οbserver's eye tο an item abοve his eye and the hοrizοntal plane.

This angle eventually develοps abοve the surface. The angle οf elevatiοn is made in such a way that it is abοve the οbserver's eye, as the name suggests.

Using the given infοrmatiοn, we drew a right triangle as given belοw.

The hypοtenuse οf the triangle is the length οf the sheet.

The angle οf elevatiοn is 20°.

The base οf the triangle is the grοund.

The hypοtenuse l = 19 inches

Angle Ф = 20°

We have tο find the elevatiοn h.

sin  Ф = h/l

sin 20 = h/19

0.342 = h /19

h = 6.49 inches

Therefοre using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.

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The unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day.

Computers are electronic devices that are used to store, process, and output data. They are used to perform a variety of tasks, from simple calculations to complex research projects. Computers consist of hardware, such as processors, memory, and storage devices, and software, which provides instructions for the hardware to follow.

The unit rate is the number of units produced per unit of time. To calculate the unit rate of computers per day using the graph, divide the number of computers produced by the number of days. Using the graph, 36 computers are produced in 3 days, 48 computers are produced in 4 days, and 60 computers are produced in 5 days.

Therefore, the unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day. The graph produced shows a proportional relationship between the number of computers produced at a factory per day.

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5. The value of the account at yearly intervals is given below.

6. The balance in the 25th year in the account will be $1,137.5.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

5.  The simple interest is given as,

I = 650 x (3/100)

I = $19.5

End of first year = 650 + 19.5 - $669.50

End of second year = 669.5 + 19.5 = $689

End of third year = 689 + 19.5 = $708.50

End of fourth year = 708.50 + 19.5 = $728

End of fifth year =728 + 19.5 = $747.50

6. The balance after 25 years is given as,

A = $650 + ($650 x 3 x 25) / 100

A = $650 + $487.5

A = $1,137.5

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According to the question the height of Ruben’s school is 360 inches.

School is a place where students can learn and grow in their knowledge. It is a place where students can gain an education and become well-rounded individuals. School is a place where people can make friends, learn from each other, and explore new ideas and topics. School is a place where teachers and staff provide guidance to help students succeed in their academics and extracurricular activities.

To find the height of Ruben’s school using similar triangles and a mirror, we can use the following formula:
height of school / height of Ruben = distance from mirror to school / distance from mirror to Ruben
Plugging in the given values, we get:
height of school / 72 = 425 / 85
Cross-multiplying and solving for height of school, we get:
height of school = 72 x 425 / 85
height of school = 360 inches
Therefore, the height of Ruben’s school is 360 inches.

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Answer:

Step-by-step explanation:

[tex]n\sqrt{2}=10[/tex]

Solve for n.

[tex]n\sqrt{2} =10\\\\\frac{n\sqrt{2} }{\sqrt{2} }=\frac{10}{\sqrt{2} }[/tex]

Rationalize the denominator.

[tex]n=\frac{10}{\sqrt{2} }\cdot \frac{\sqrt{2} }{\sqrt{2} }\\\\n=\frac{10\sqrt{2} }{2}[/tex]

Reduce to lowest terms.

[tex]n=\frac{10\sqrt{2} }{2} \div\frac{2}{2}\\\\n=5\sqrt{2}[/tex]

Answer:

5 9/10

Step-by-step explanation:

find the same denominator

in this case 30

9x3=27 and 5x5=25

since 27 is bigger, the fraction is also bigger

Answer:

5\6 is smaller than 9\10

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 6 and 10 are 30

Next, find the equivalent fraction of both fractional numbers with denominator 30

For the 1st fraction, since 6 × 5 = 30,

[tex]\frac{5}{6} = \frac{5.5}{6.5} =\frac{25}{30}[/tex]

Likewise, for the 2nd fraction, since 10 × 3 = 30,

[tex]\frac{9}{10} =\frac{9.3}{10.3} =\frac{27}{30}[/tex]

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

[tex]\frac{25}{30} < \frac{27}{30} 0r \frac{5}{6} < \frac{9}{10}[/tex]

Answer:

54

Step-by-step explanation:

I'm assuming you are referring to x = 6, then to find the value of x(15 - x).

If x = 6, we can substitute this value into the expression x(15 - x) to find its value:

x(15 - x) = 6(15 - 6) = 6(9) = 54

Therefore, if x = 6, then x(15 - x) = 54.

Hey there!

x(15 - x)

= 6(15 - 6)

= 6(15) + 6(-6)

= 90 - 36

= 54

Therefore, the answer should be about:

54

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

We're given the angle measure to be 46 for No. 8. The length of 1 leg is x and the hypotenuse is 28.

We can use cosine to solve this. Since cosine is adjacent over hypotenuse, we can do cos(46) = x/28. Cross multiply to get cos(46)*28 = x. That solves to be 19.5

Using this principle allows us to solve the other ones. I'll let you figure them out.

TLDR: We can use the definition of trig functions to plug in what we know and place variables where we don't have enough information to find the length of a side.

Answer:

The strip pattern has a vertical axis of symmetry, so a reflection across a vertical line will map the strip pattern onto itself. Therefore, the correct answer is "a reflection across a vertical line."

Step-by-step explanation:

Answer:

Yes he was correct in returning the 100

Step-by-step explanation:

Pen 68.75

Pencil 73.50

Paint box 112.35

Add all together, you get 254.60

If he paid 500 to the shopkeeper, he will collect (500.00-254.60) =245.40

If the shopkeeper gave him 345.40, then he had an excess and should give back the 100

The missing term of question is "distance".

Distinct points refer to points that are not the same. In other words, if two or more points have different locations or coordinates, they are considered distinct points.

Distance is a measure of the length or space between two points, lines, or other objects. It is typically expressed as a non-negative number and can be determined using various formulas depending on the context and the nature of the objects being measured.

The missing term in the question is "distance". The sentence can be completed as:

"Between every pair of distinct points, there is a positive unique number called the "distance", which can be determined as the "absolute value of the difference" of the corresponding real numbers of the two points."

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Because the denominators of both fraction have been changed to 7/8=21/24 and 5/6=20/24, respectively,

In mathematics, a denominator is the lowest number in such a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.

Divisor is another synonym for denominator. In a common fraction, the integer under the line is described by both of these terms. Similar to this, when discussing statistical values, the term "denominator" refers to the entire population or number out of which samples are selected.

Common denominator is going to be [tex]24[/tex]

[tex]8=2*2*2\\6=2*3\\24=2*2*2*3[/tex]

[tex]8[/tex] should be multiplied by [tex]3[/tex]

[tex]6[/tex] should be multiplied by [tex]4[/tex]

[tex]7/8=(7*3)/(8*3)=21/3\\5/6=(5*4)/(6*4)=20/24\\7/8=21/24\\5/6=20/24[/tex]

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The answer is 6.03 did this help?

Answer:

(4,9)

Step-by-step explanation:

The word "vertex" isn't clear here. I'm assuming the question is referring to finding the stationary (turning) point. This can be found by finding the derivative (dy/dx).

To find the derivative we use the following formula:

[tex]y = ax^{n}\\ \frac{dy}{dx} = nax^{n-1}[/tex]

What this means is that for each term of the equation, we multiply by the current power and then reduce the power by 1. In the case of the question's equation, this will be done like this:

[tex]y = 3x^{2} - 24x + 57\\\frac{dy}{dx} = 6x - 24[/tex]

Now we can use this to find the stationary point, as stationary points are where the derivative (dy/dx) = 0:

6x - 24 = 0

6x = 24

x = 4

Through this we have found the x-coordinate of the stationary point, however we still need to find the y coordinate. This is done by substituting our x value back into the original equation (not the derivative):

y = 3(4)² - 24(4) + 57

y = 9

Therefore, the coordinates of the stationary point are (4,9)