what is the slope for (3, 8) and (2, 6). ?

The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.

The condition for the maximum will be

f(x)'' < 0

The condition for the minimum will be

f(x)'' > 0

Every summer, Richard plants a garden on a rectangular plot of land.

Last summer, Richard's garden measured 45 feet in length and 18 feet in width.

This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.

The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.

Length = (45 – x)

Width = (18 + 2x)

Then the maximum potential area of this year's resized garden will be

A(x) = (45 – x)(18 + 2x)

A(x) = 810 + 72x – 2x²

A(x) = 2(405 + 36x – x²)

For maximum potential, A'(x) = 0

    A'(x) = 0

36 - 2x = 0

       2x = 36

         x = 18

Then the maximum potential area will be

A(x) = 2(405 + 36 × 18 – 18²)

A(x) = 1458

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The factor computed illustrates that the number of cabins that should be occupied will be 20 cabins.

From the information given, there are 40 children and 30 adults. In this case, the common factors are 1, 2, 3, 5, and 10. The highest common factor is 10.

The question depicts that they will have same cabins. Therefore, the total number of cabins will be:

= 10 × 2

= 20 cabins

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Answer: 3

Step-by-step explanation:

By the intersecting chords theorem,

[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]

The function f(x) is less than 0 at x < -1.8

The missing graph is added as an attachment

The interval where f(x) < 0 are the intervals where the y value of the function is less than 0.

This in other words, represent the negative y-axis

From the attached graph, the function f(x) is less than 0 at x < -1.8.

This extends till x = infinity

Hence, the function f(x) is less than 0 at x < -1.8

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The unit rate of 187pounds of food for 1447.38 is 7.74 per pound

Unit rate = Total cost of food ÷ Quantity of food

= 1447.38 ÷ 187

= 7.74 per pound

Therefore, the unit rate of 187pounds of food for 1447.38 is 7.74 per pound

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Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explaining that one component of math is understanding reasonable answers.

Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable.

Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers.

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el área del pentágono es de 172 centímetros cuadrado.

El área es el espacio ocupado por un objeto bidimensional.

Se calcula en unidades cuadradas.

Se da que , El lado del pentágono mide 10 centímetros

El área del pentágono está dada por

[tex]\rm A = \dfrac{1}{4} \sqrt {5 ( 5 +2\sqrt{5})} \; a^2[/tex]

aquí A es el área

l es la longitud del lado del pentágono

Sustituyendo los valores

[tex]\rm A = \dfrac{1}{4} \sqrt {5 ( 5 +2\sqrt{5})} \; 10^2[/tex]

A = 1.72 * 100

A = 172 centímetro cuadrado

Por lo tanto, el área del pentágono es de 172 centímetros cuadrado.

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Answer:

e) cannot be determined

Step-by-step explanation:

hope this helps!!

Answer:

25

Step-by-step explanation:

We can calculate for a using sine rule.

For angle A,

A + 27° + 82° = 180 ( sum of angles in a triangle).

A + 109 = 180

A = 180 - 109 = 71°

Therefore,

A = 71°

calculating for side a

[tex] \frac{sin \: 27}{12} = \frac{sin71}{a} \\ a = \frac{12 \times sin71}{sin27} \\ a \: = \frac{11.346}{0.454} \\ a = 25[/tex]

Answer:

A. 36

Step-by-step explanation:

Because the two angles at the bottom of both the triangles are congruent, the two triangles are similar. Therefore, the corresponding side lengths of the triangles must be proportional to each other

if the area of a triangle is hb/2,

(with h=length of height, b=length of base)

the height of the first triangle is:

25 = 10h/2

50 = 10h

h=5

you can write ratios representing the proportions of the two triangles:

5/x = 10/12 (with x=height of second triangle)

x=6

then find the area of the second triangle with the height (6) and base (12)

(6*12)/2 = 36

Answer:

Cost of per session the average rate is $45.

Step-by-step explanation:

It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.

It is required to find what is the cost per session.

Step 1 of 1

It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.

To find the cost of per session calculate the average rate.

Now let $f(x)$ be the cost per session use the for the average rate of change, and the input value is the number of personal traings x.

[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$$[/tex]

Now substitute, $125 for [tex]$f\left(x_{2}\right)[/tex], 260 for [tex]$f\left(x_{1}\right), 2$[/tex] for [tex]$x_{1}$[/tex] and 5 for [tex]$x_{2}$[/tex] then,

[tex]$m=\frac{260-125}{5-2}$\$$\begin{aligned}&=\frac{135}{3} \\&=45\end{aligned}$$[/tex]

Cost of per session the average rate is $45.

Answer:

The ANSWER is Option A ( 151° ).

.

.

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Answer:

£ 30 345.

Step-by-step explanation:

15 %  off means that 85% is left

42 000 *  .85   *  .85  =  42 000 (.85)^2 =   30 345

The area of the triangle is 83.14 square centimeters.

If an equilateral triangle is inscribed in a circle of radius R, each side of the triangle measures:

S = R*√3

In this case R = 8cm.

And we know that the area of an equilateral triangle of side length S is:

[tex]A = \frac{\sqrt{3} }{4} *S^2[/tex]

Replacing what we know in the area formula:

[tex]A = \frac{\sqrt{3} }{4} *(\sqrt{3}*8cm)^2 = 83.14 cm^2[/tex]

The area of the triangle is 83.14 square centimeters.

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Answer:

(x + 3)² + (y - 7)² = 81

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

here (h, k ) = (- 3, 7 ) and r = 9 , then

(x - (- 3) )² + (y - 7)² = 9² , that is

(x + 3)² + (y - 7)² = 81

Answer:

[tex]x^2+y^2+6x-14y-23=0[/tex]

Step-by-step explanation:

[tex](x-(-3))^2+(y-7)^2=9^2\\x^2+6x+9+y^2-14y+49=81\\x^2+y^2+6x-14y-23=0[/tex]

Answer:

150 square feet

Step-by-step explanation:

Method 1: The area of a trapezoid is

A = (8 + 17) / 2 x 12 = 150 square feet

Method 2: You can also split it into a rectangle and a triangle.

12 x 8 + 12 x (17 - 8)/2 = 150 square feet

An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A, C, and E.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

To know the expressions that are equivalent to 22c+33d, all the expressions in the options are needed to be simplified.

Let simplify each of the given opion,

A.) (−2c−3d)(−11) = 22c + 33d

B.) 2(11c− 33/2) d = 22c - 33d

C.) (66c+99d)⋅1/3 = 22c + 33d

D.) −1×(−22−33d) = 22 + 33d

E.) 11⋅(2c+3d) = 22c + 33d

Hence, the correct options are A, C, and E.

The complete question is:

Which expressions are equivalent to 22c + 33d?

A. (−2c−3d)(−11)

B. 2(11c− 33/2 d

C. (66c+99d)⋅1/3

D. −1×(−22−33d)

E. 11⋅(2c+3d)

choose 3 answers

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Answer:

x = -1

Step-by-step explanation:

Note: when you send a number across it can change it sign. If it is positive it will turn negative.

5x + 2 = 8x + 5

Send 8x across

5x + 2 - 8x = 5

send 2 across

5x - 8x = 5 - 2

- 3x = 3

Divide both sides by - 3

- 3x/- 3 = 3/- 3

- 3 cancel out - 3

x = 3/ - 3

3 divided by - 3 is - 1

x = -1

The relationship modeled that has the function of  f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times  of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.

For us to know the relationship modeled by the above function, the best way to do it is for one to factor it.

The function is: f(x) = 4x³ - 72x² + 320x

First. we factor it so as to extract the common factor 4x:

Secondly,  we factor the quadratic trinomial.

This is often done by writing it as a product of two binomials where the two constant terms are said to be sum up - 18 and its product is said to be 80.

The above terms are known to be -10 and - 8; so the two factors are said to be (x - 10) and (x - 8).

Therefore The relationship modeled that has the function of  f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times  of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.

Where it has :

x = the desired  length,

4x = 4 times its desired length,

x - 10 = 10 lower than its desired length,

x - 8 = 8 lower than its desired length,

We can therefore say that the volume of the prism is said to be the product of the three factors which are:

V = (4x)(x-10)(x-8)

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Answer:

24

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplification of the given expression can be done as,

[tex]\dfrac{(6x)^2+x-7}{12x^2+14x}\\\\\\=\dfrac{36x^2+x-7}{12x^2+14x}\\\\\\=\dfrac{(6x)^2+x-7}{2(6x^2+7x)}[/tex]

Hence, the simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].

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Answer:

The Area of the Grass is 18 square meters.

Step-by-step explanation:

Find the area of the grass and sand (5*6). The area of the grass and sand is 30.

Next, find the area of just the sand (3*4). The area of the sand is 12.

Subtract the area of the sand (12) from the area of the grass and sand (30).

30-12 = 18

Answer:

99.93 [tex]m^{2}[/tex]

Step-by-step explanation:

1.  The area of a circle is defined by the equation: A = [tex]\pi r^{2}[/tex]

2. We can plug in the radius and solve the equation: A = [tex]\pi *5.64^{2}[/tex]

3. A = π * 31.8096

4. A = 99.932

5. A = 99.93

Answer:

6/17

Step-by-step explanation:

12/18 * 9/17

use 9 to divide 18 u'll be left with

12/2 * 1/17

use 2 to divide 12 u'll be left with

6/1 * 1/17

now u'll multiply leaving you with

6/17 as the final answer or u can also convert to decimal your answer will be

0.352 by approximation.

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The value of 5284 Ib is expressed as 2000 tons 642 lbs

Given the following parameters

2000lb = 1 ton

5284 Ib = 5284lb/2000 = 2.642 tons

2.642 tons = 2000 tons 642 lbs

Hence the value of 5284 Ib is expressed as 2000 tons 642 lbs

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The solution to the division of the given surd is: [tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]

The division of surds follows a systemic approach whereby we divide the whole numbers separately and the root(s) are being divided by each other.

Given that:

[tex]\mathbf{P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }}[/tex]

i.e.

[tex]\mathbf{=\dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )}{ \frac{4x}{(x-1)^{2} }} }[/tex]

Using the fraction rule:

[tex]\mathbf{\dfrac{a}{\dfrac{b}{c}}= \dfrac{a\times c}{b}}[/tex]

[tex]\mathbf{\implies \dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )(x-1)^{2}}{4x}} }[/tex]

By simplification, we have:

[tex]\mathbf{ =\dfrac{\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{2} }{4x} }[/tex]

[tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]

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The t-test for the two means is appropriate in this situation because women and men are independent samples.

Independent samples are those that are chosen at random, ensuring that their results are independent of other observations' values.

The premise that samples are independent underlies many statistical analyses. Others are made to evaluate non-independent sample sets.

The Independent Samples t-Test analyzes the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. A parametric test is the Independent Samples t-Test.

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The possible values of tan^-1(1) are (3π + 4n)/4

The expression is given as:

tan^-1(1)

To determine the possible values, we plot the graphs of

y = tan(x) and y = 1

From the graph, we have the following values

tan^-1(1) = (3π + 4n)/4 when n = ±{0,1,2....}

Hence, the possible values of tan^-1(1) are (3π + 4n)/4

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Answer:

d. 40 feet

Step-by-step explanation:

Perimeter = 140 ft

Width = L + 10

P = 2w + 2L

140 = 2(L + 10) + 2L

140 = 2L + 20 + 2L

120 = 4L

L = 30

w = L + 10

w = 30 + 10

w = 40