Four times the difference of some number and 3 amounts to the quotient of 144 and 12.
Written as an equation

The dimensions of the fenced-in area is

either length = 35 yards and width = 80 yards ,  

or length = 40 yards and width = 70 yards .

In the question ,

it is given that

the total length of the fence = 150 yards

let L be the length of the area to be fenced

let B be the width of the house

Given that one side of the area is fenced using the back side of the house

So, the perimeter of the area to be fenced is 2L+B

equating both the perimeter we get

2L+B=150

B=150-2L       ....(i)

Given the area fenced-in portion = 2800 yards

also the fenced-in portion area = L×B

hence

L*B=2800

Substituting the values of B from equation(i) , we get

L*(150-2L)=2800

150L - 2L² = 2800

2L² - 150L + 2800 = 0

simplifying further , we get

L² - 75L + 1400 = 0

L² -40L -35L +1400 = 0

L(L-40) -35(L-40) = 0

(L-35)(L-40) = 0

So , L = 35 yards or L = 40 yards

Using L = 35 yards , we get B = 150-2(35) = 80 yards

and using L =40 yards , we get B = 150-2(40) = 70 yards .

Therefore , The dimensions of the fenced-in area is

either length = 35 yards and width = 80 yards   ,

or length = 40 yards and width = 70 yards   .

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The most appropriapriate choice for factorization will be given by-

[tex](x^2+12+4x)(x^2+12-4x)[/tex] is the required factorization.

What is factorization?

The process of breaking an algebraic expression into product of different factors is called factorization.

Here,

The factorization of [tex]x^4+8x^2+144[/tex] has been shown below-

[tex]x^4+8x^2+144[/tex]

[tex](x^{2} )^2 + 24x^2 +144 -16x^2\\(x^{2} )^2 + 2\times x^2\times 12+ 12^2-16x^2\\(x^2+12)^2 - (4x)^2\\(x^2 + 12+4x)(x^2+12-4x)[/tex]

This is the required factorization

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Answer:

20% off

Step-by-step explanation:

22-17.60=4.4

(5)4.4=22

The total number of dots tells us the total number of observations of the values. the dot plot of the information are attached below.

A Dot Plot is a graphical display of quantitative data consisting of dots plotted on a simple scale.  Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line.

If a value occurs more than once, then the dots are placed one above the other thus, that the height of the column of dots represents the frequency for that value.

Given data set:

{0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12}

First we need to Label the increments on the given line to include the range of data.

Then Label them order -2 to 16 increasing in 1 unit.

Now Label the dot plot with a suitable describing the dot plot.

Then Count the number of data points for each discrete category.

The dot plot of the information are attached below.

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The equation for the linear function f(x) is f(x) = 2 / 7 x - 10 / 7

The linear function is f(x)

f(-2) = - 2 and f(5) = 0

Therefore, let's find the equation for the linear function f(x):

A linear function is a function that represents a straight line on the coordinate plane.

Therefore, linear function is represented as follows:

y = mx + b

where

Hence,

-2 = m(-2) + b

0 = 5m + b

b = -5m

Therefore,

m(-2) + - 5m = -2

-2m - 5m = -2

-7m = -2

m = 2 / 7

Therefore,

b = - 5 (2 / 7)

b = - 10 / 7

Hence,

f(x) = 2 / 7 x - 10 / 7

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The slope of the line is [tex]\frac{2}{3}[/tex]

The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout.

Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

The slope of the line is [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]

⇒ [tex]\frac{-7-(-5)}{9-6}[/tex]

⇒ [tex]\frac{-7 + 5}{ 3} = \frac{2 }{3}[/tex]

Thus m = 2/3

Similarly in second case : [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]

⇒ [tex]\frac{-15 - (-11)}{ 21 - 15}[/tex]

⇒ [tex]\frac{4}{6}[/tex]

= 2/3

Thus the slope of the given table is 2/3

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Written in Slope Intercept Form:

[tex]y=-\frac{5}{4} x-14[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

Given that P is a point on the perpendicular bisector, l, of MN, we have proved that PM = PN because By the definition of reflection, point P is the image of itself and point N is the image of N.

We are given :

P is a point on the perpendicular bisector, l, of MN.

Now, we want to prove that PM = PN

A Reflection is a transformation in which the figure is the mirror image of the other. Every point is a mirror reflection of itself .

By the definition of reflection, we can deduce that point P is the image of itself , and point N is the image of M .

The line l acts as a Line of symmetry or axis of reflection.

Now, in transformations, we know that reflections preserve length and as a result, PM = PN.

Therefore, we will conclude that point N is the image of M .

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Answer: Point M

Step-by-step explanation:edge 2023

Two triangles cannot be proven to be congruent using the method: A. Prove all sets of corresponding angles are congruent.

Two triangles are congruent to each other if they have the same shape and the same size, that is, all three sets of corresponding sides and all three sets of corresponding angles of the two triangles are congruent to each other.

Also, the following condition or criteria can be used to determine if two triangles are congruent to each other:

Thus, the method that cannot be used is: A. Prove all sets of corresponding angles are congruent.

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The equation of the line passing through points (-2, 5) can be written as follows

Equation of a straight line is an equation of the form y = mx + c, where

The slope is the gradient which is the ratio of the difference in the y direction to the difference in x direction.

given that the equation of the line is x + 3y = 7

rewriting the equation gives

y = -x/3 + 7/3

hence the slope is -1/3, and this is equated with the formula for slope

[tex]\frac{y-y_{1} }{x-x_{1} }=-\frac{1}{3}[/tex]

substituting the values for points  (-2,5)  and cross multiplying gives

3 (y - 5) = - ( x - -2)

y - 5 = - (x + 2 ) /3

y - 5 = -x/3 - 2/3

y = -x/3 - 2/3 + 5

y = -x/3 + 13/3

Rewriting the equation of the line in standard form is done as follows

y = -x/3 + 13/3

3y = -x + 13

x + 3y = 13

The equations are gotten from substitution the values to the formula for slope and substituting. Rearranging the equation gives the equation in slope intercept form and in standard form.

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The correct option for Negative abscissa, positive ordinate is -

• Quadrant 2

For the given question;

The other names for x and y axis are;

x -axis - abscissa

y- axis - ordinate

Thus, Negative abscissa means negative x axis.

And, positive ordinate means positive y axis.

This, lines in second quadrant.

Thus, Negative abscissa, positive ordinate will give the point is second quadrant.

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After simplifying the expression we get: 12√6

Given, √864

Take the LCM of the given number:

864 = 2×2×2×2×2×3×3×3

Minimize the terms:

= √4×4×2×9×3

Reduce the terms:

= √16×9×2×3

multiply the terms:

= √144×2×3

= 12√6

Hence after simplifying we get the answer as 12√6

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A. The absolute maximum of the function f(x) is : f(-8) = 4.

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The relation which is a function among the answer choices is; A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.

A function is a relation in which each element of the domain is associated with exactly one element of the codomain.

A relation can be tagged a function if it describes that there should be only one output (y - value) for each input ( x - value). Put simply, a function is a kind of relation (defined by a set of ordered pairs) in which case, it ensures that every x-value is associated with only one y-value.

On this note, since the relation described in the first answer choice is such that every x-value is associated with only one y-value as it is a parabola (quadratic function), it is termed a function.

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The number of ways that 5 players can be selected from the 11 eligible players is; 462 ways

The number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth is; 120 Ways

We are given that In a soccer match;

A tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the penalty mark.

Each kick must be taken by a different player

Now, to find the number of ways that 5 players can be selected from the 11 eligible players, we will use combination to get;

11C5 = 11!/(5! * (11 - 5)!)

= 11!/(5! * 6!)

= 462 ways

Now, if we care about order or position, we will use permutation to get the number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth;

5P5 = 5!/(5 - 5)

= 120 Ways

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Answer:

A

Step-by-step explanation:

below is the parent function graphed and according to the chart we move the graph down 2 units and reflect it over the x axis and a is the only option

y = -1/5x +1/2 linear function has the same slope .

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

First solve for the slope

m =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=[tex]\frac{0-\frac{3}{5} }{\frac{1}{2} -\frac{1}{5} }[/tex]

m = [tex]\frac{-1}{5}[/tex]

Look for the linear equation with the same value of m after determining the slope (parallel equation).

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Answer:

bottom right

Step-by-step explanation:

bottom right

The answer to the expression [2−||−23−2(−15)||]÷(−13) is 5/13.

In the question ,

the expression is given as

=[2−||−23−2(−15)||]÷(−13)

Solving the terms inside [ ] , we have

2*(-15) = -30

Substituting the value of 2*(-15) in the expression , we get

=[2-||-23-(-30)||]÷(−13)

=[2−||−23+30||]÷(−13)   ....as -(-30) = 30

Solving the terms inside the modulus ||  || , we get

=[2−||+7||]÷(−13)      ...as ||-23+30|| represents the modulus(norm) value ..

So ,Simplifying further , we get

=[2−7]÷(−13)                ....as 2-7 = -5

=[-5]÷(−13)       ...as a÷b can be written as a/b

= -5/-13

writing the answer in the simplified form .

= 5/13

Therefore , the answer to the expression [2−||−23−2(−15)||]÷(−13) is 5/13.

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Dragon needs 2.16 seconds to eat 90 kilograms of human beings.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that,

If a dragon can eat an entire cow weighing 500 kilograms in 12 seconds,

500 kilograms = 12 seconds

By unitary method

1 kilogram = 12 / 500

1 kilogram = 0.024 second

For 90 kilograms

90 kilogram=90 × 0.024 second

90 kilogram = 2.16 second

Thus, a dragon needs 2.16 seconds to eat 90 kilograms of human beings.

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Answer:

Equation = 1/4 x + 25 = 70

Solution = $180

Explanation:

Let the original amount she had before she went shopping be x

If she spent one-fourth on sloth, then the amount spent on cloth will be;

1/4 x

If she receives another $25 a week later totalling her money $70, then the equation that represents the situation will be;

1/4 x + 25 = 70

Find the solution

1/4 x + 25 = 70

1/4 x = 70 - 25

1/4 x = 45

x = 45 * 4

x = 180

Hence the amount she had before going for shoppind was $180

Answer:

This video provides an example of how to determine the original price of an item given the discounted price and the percent mark

Step-by-step explanation:

Answer:

32% or 31.82%

Step-by-step explanation:

so total = 11 billion and export + ethanol = about 3.5 billion so the probability is 3.5/11 or 35/110 which, as a percent, can be written as 32% or more accurate, 31.82% so this is answer

Answer:

the ratio is 6.5 : 1.5

Step-by-step explanation:

it asks "what is the ratio of time spent studying in math to studying for English?"

ratio uses the ":" mark. also you put the parts like this:

first part : second part

the parts can be found by looking for the "to" as indicated bold in the question

the first part of the ratio it asks is the "time spent studying in math" in hours which is 6.5

the second part of the ratio it asks is the "time spent studying in English" in hours which is 1.5

so the answer is:

6.5 : 1.5

Answer:

Ratio of time spent studying in math to studying for English

[tex]\large \text{$=\dfrac{13}{3}$ }[/tex]

Step-by-step explanation:

What is a ratio?
We use ratios to compare two numeric quantities or quantities with the same units

Basically a ratio of one quantity x to another quantity y can be expressed in the following ways, all read as the ratio of x to y

x/ y

x to y

x : y

The most useful way of representing a ratio is by using the fractional form because it can be used in determining other quantities

In this problem you spend 6.5 hours/week  studying for math and 1.5 hours/week studying for English

Since both units are the same (hours/week) we can compute the ratio as

[tex]{\dfrac{\text{Number of hours studying math}}{\text{Number of hours studying English}}\\\\= \dfrac{6.5}{1.5}\\\\[/tex]

We can simply this fraction as follows

Multiply both numerator and denominator by 10

[tex]= \dfrac{65}{15}\\\\[/tex]

Divide both sides by 5

[tex]\dfrac{65 \div 5}{15 \div 5}\\\\= \boxed{\bold{\dfrac{13}{3}\\\\}}[/tex]

This is the same as 13:3 or 13 to 3

(Be careful what is the numerator and what is the denominator.
If the question had asked for the ratio of hours studying English to hours studying Math then the ratio would be 1.5/65 = 15/65 = 3/13)

To fence in a portion of Amitie Park for an inclusive play space for children total fencing required of the section with diameter 90 feet is 282.6 feet.

As given in the question,

To fence in a portion of Amitie Park for an inclusive play space for children

Diameter of the section = 90 feet

Let r be the radius

r = diameter/2

⇒ r = 90 / 2

⇒r = 45 feet

Total fencing required to fence a play space

= 2πr

= 2 × 3.14 × 45

= 282.6 feet

Therefore, to fence in a portion of Amitie Park for an inclusive play space for children total fencing required of the section with diameter 90 feet is 282.6 feet.

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Dilate figure A with center o and scale factor 2

What is transformation?
The transformation, or f: X → X, is the name given to a function, f, that maps to itself. The pre-image X becomes the picture X following the transformation. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
Example: A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.

We know that re-sizing an item uses a transition called dilation.
In the figure the dimensions of the figures differ by a factor of 2.
Thus, dilation of figure A by a factor of 2 shows figure A is similar to Figure B

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Part a: Cost of downloading album B = 13.3 euros

Part b: Cost of downloading album B = 12.6 euros

Number of tracks in album A = 11 tracks

The total cost of downloading album A = 10.45 euro

Cost of each track on album A = Total cost of album/Number of tracks in the album

= 10.45/11

= 0.95 euro

Part a:

Number of tracks in album B = 14 tracks

Cost of album B = Number of tracks in album B * Cost of each track

= 0.95*14

= 13.3 euros

Part b:

The cost of 5 tracks on album B is 5p less therefore, the cost of 5 tracks will be 0.90*5 = 3.60 euros

The cost of 9 tracks on album B is 5p more therefore, the cost of 9 tracks will be = 1*9 = 9 euros

The total cost of downloading album B = 9+3.6 = 12.6 euros

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