5. A deck should have a perimeter of 90 feet and a minimum area
of 450 square feet. Write and solve an inequality to find the
possible width of the deck.​

Answer:

[tex]\displaystyle 24x^{2} - 41x + 12 = 24\left(x - \frac{3}{8}\right) \cdot \left(x - \frac{4}{3}\right) = (8x-3)\cdot (3x - 4)[/tex].

Step-by-step explanation:

Apply the quadratic formula to find all factors. For a quadratic equation in the form

[tex]a\cdot x^{2} + b\cdot x + c = 0[/tex],

where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants, the two roots will be

[tex]\displaystyle x_1 = \frac{-b + \sqrt{b^{2} - 4\cdot a \cdot c}}{2a}[/tex], and

[tex]\displaystyle x_2 = \frac{-b - \sqrt{b^{2} - 4\cdot a \cdot c}}{2a}[/tex].

For this quadratic polynomial,

Apply the quadratic formula to find any [tex]x[/tex] value or values that will set this polynomial to zero:

[tex]\displaystyle x_1 = \frac{-(-41) + \sqrt{(-41)^{2} - 4\times 24 \times 12}}{2\times 24} = \frac{3}{8}[/tex].

[tex]\displaystyle x_2 = \frac{-(-41) - \sqrt{(-41)^{2} - 4\times 24 \times 12}}{2\times 24} = \frac{4}{3}[/tex].

Apply the factor theorem to find the two factors of this polynomial:

Keep in mind that simply multiplying the two factors will not reproduce the original polynomial. Doing so assumes that the leading coefficient of [tex]x[/tex] in the original polynomial is one, which isn't the case for this question.

Multiply the product of the two factors by the leading coefficient of [tex]x[/tex] in the original polynomial.

[tex]\displaystyle 24\left(x - \frac{3}{8}\right) \cdot \left(x - \frac{4}{3}\right) = (8x-3)\cdot (3x - 4)[/tex].

Expand to make sure that the factored form is equivalent to the original polynomial:

[tex](8x-3)\cdot (3x - 4)\\ = (8\times 3)x^{2} + ((-3)\times 3 + (-4)\times 8)\cdot x + ((-3)\times (-4))\\ = 24x^{2} - 41x + 12[/tex].

Answer:

Third option. I am sure it!

Step-by-step explanation:

Mark other guy brainliest. He's a great answer and he helped me before

Answer:

The third option choice

Step-by-step explanation:

Here you have the term (n^-6)(p^3)

(n^-6)(p^3) = (n^-6)(p^3)/1

[And whole number can be written over 1. For example, 4 = 4/1.]

You can see that n has a negative exponent, -6.

My teacher taught it to me like this:

If this is our expression;

(n^-6)(p^3)

---------------  <------ [and thats a fraction bar]

       1

Think of the fraction bar as a bunk bed. Since the (n^-6) isn't happy being "on top of the bunk bed," [since its a negative exponent] move it to the bottom bunk.

So your new expression would be:

 (p^3)

--------------  <-------- [fraction bar]

 (n^6)

Moving n^6 to the bottom changes it into a positive exponent.

So, the third option choice would be correct.

That's the best way I can explain it! I hope this helps!!! :)

Answer:

3.7

Step-by-step explanation:

To write 34/9 as a decimal you have to divide numerator by the denominator of the fraction.  

We divide now 34 by 9 what we write down as 34/9 and we get 3.7777777777778  

And finally we have:  

34/9 as a decimal equals 3.7777777777778

Please mark brainliest and have a great day!

Answer:3.8

Step-by-step explanation:

34/9

9 into 34 is 3 remainder 7

:. 34/9

= (9 x 3 + 7)/9

=3.777778

=3.8

Answer:

A

Step-by-step explanation:

Hihi. So, this is a nice application of interest rates as well as properties of exponentials/logarithms. As you know, the basic equation for interest rates is A= Pe^(rt) where A is your final amount, P is your initial, r is your rate of interest, and t is the time the money was accumulating interest. After cleaning up, you get in a situation due to you having e still lying around. Luckily, if you take the natural log of e, all you have left behind is the previous exponent. Thus, you can take the natural log of both sides, divide by 4, and then simplify to see that your final interest rate is ~6%

Answer:

A. 6%

Step-by-step explanation:

Since, the given amount formula is,

[tex]A=Pe^{rt}[/tex]

Where, P is the initial amount,

r is the periodic rate of interest,

t is the number of periods,

Here, P = $ 2000,

t = 4 years,

A = $ 2543,

By substituting the values,

[tex]2543=2000e^{4r}[/tex]

[tex]1.2715=e^{4r}[/tex]

Taking ln on both sides,

[tex]ln(1.2715)=4r[/tex]

[tex]\implies r = 0.06004932647\approx 0.06 = 6\%[/tex]

Hence, the rate of interest is 6 %.

Option 'A' is correct.

Answer:

Answer 1:4 or 1/4

Step-by-step explanation:

30/120 reduced is 1/4 which would equal 1:4.

I'm learning this right now too well relearning and i hope i have helped you!

Answer:

1/4

Step-by-step explanation:

Answer:

8s + 4(4s - 3) = 4(6s + 4) - 4

8s + 16s - 12 = 24s + 16 - 4

24s - 12 = 24s + 12

This equation has no solution.

Answer: 36 units

Step-by-step explanation:

once you plot out the points, it shows a polygon. cut the polygon into a square and a triangle, and count the units to get the lengths, widths, and heights.

you find that the height of the square is 6, and the width is 5. multiply those to get the area of the square: 30.

the width of the triangle is 2 units, and the height is 6. multiply those to get 12, then divide it in half to get the area: 6.

then you add the area of the square to the area of the triangle to get the total area of 36 units squared.

hope this is an understandable explanation!!

Answer:

The answer is A and B.

Step-by-step explanation:

The equivalent exponential form of the equation log2n=4 is 2⁴ = n, which simplifies to n = 16.

The equation log2n=4 can be rewritten using the definition of a logarithm. To convert from logarithmic to exponential form, we use the fact that a logarithm answers 'to power must the base be raised to produce the given number'. So, log2n = 4 is equivalent to 24 = n, because 2 is the base in this logarithm, and 4 is the power to which this base must be raised. Therefore, n is equal to 16, as 2 raised to the fourth power is 16 (24 = 16).

Answer:

36

Step-by-step explanation:

The only number that is a perfect square is 36

6*6 = 36

Answer:

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\\\sqrt5-not\ rational\\\\\sqrt8-not\ rational\\\\\sqrt{36}=6-rational\qquad(\sqrt{36}=6\ because\ 6^2=36)\\\\\sqrt{44}-not\ rational[/tex]

Answer:  B) Circle

Step-by-step explanation:

First, complete the square:

x² + 2x +  1    + y² - 8y +  16   = 13 +  1   +  16  

       ↓       ↑             ↓         ↑

   (2/2) = (1)²          (-8/2) = (-4)²

       (x + 1)²    +             (y - 4)²   =  30

The result is a circle whose center is (-1, 4) and radius is √30

conic section of the equation  B .Circle.

A conic section (or simply conic, sometimes named a quadratic curve) exists as a curve acquired as the intersection of the surface of a cone with a plane.

The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be uniquely identified or standardized.

Canonical equation for circle is (x — x0)2 + (3, yo)2 = R2 ,

hence (x + 1)2 + (y — 3)2 = 4 describes a circle.

conic section of the equation  B .Circle.

Standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

Often, it is one which provides the simplest representation of an object and which allows it to be identified in a unique way.

To learn more about  conic section, refer

https://brainly.com/question/1941177

#SPJ2

Answer:

Option B 3,-3,-6 is correct.

Step-by-step explanation:

We need to find real zeroes of [tex]x^3+6x^2-9x-54[/tex]

Solving

[tex]x^3+6x^2-9x-54\\=(x^3+6x^2)+(-9x-54)[/tex]

Taking x^2 common from first 2 terms and -9 from last two terms we get

[tex]=(x^3+6x^2)+(-9x-54)\\=x^2(x+6)-9(x+6)\\[/tex]

Taking (x+6) common

[tex](x+6)(x^2-9)\\[/tex]

x^2-9 can be solved using formula a^2-b^2 = (a+b)(a-b)

[tex]=(x+6)((x)^2-(3)^2)\\=(x+6)(x+3)(x-3)[/tex]

Putting it equal to zero,

[tex](x+6)(x+3)(x-3) =0\\x+6 =0, x+3=0\,\, and\,\, x-3=0\\x=-6, x=-3\,\, and\,\,  x=3[/tex]

So, Option B 3,-3,-6 is correct.

Answer:

B. 3,-3,-6

Step-by-step explanation:

Answer:

Domain is {10,-16,18,19,5}

Range is {12,-10,-12,19,-9,22}

This is not a function because 18 is in the domain twice

The Domain is {10,-16,18,19,5}

The Range is {12,-10,-12,19,-9,22}

And, This is not a function because 18 is in the domain twice.

Here,

In the table is shown in figure.

We have to find the domain, range and determine if it is a function.

What is Function?

A function is a relation between inputs and outputs where each input is related to exactly one output.

Now,

Domain is the inputs (values of x) on the table.

Hence, The Domain is {10,-16,18,19,5}

And, Range is the outputs (values of y) on the table.

Hence, The Range is {12,-10,-12,19,-9,22}.

Since, In the table 18 is twice in the domain.

So, It is not a function.

Therefore,

The Domain is {10,-16,18,19,5}

The Range is {12,-10,-12,19,-9,22}

And, This is not a function because 18 is in the domain twice.

Learn more about the function visit:

https://brainly.com/question/15602982

#SPJ2

Answer:

Step-by-step explanation:

yes. polynomials only have rational numbers

The answer is C

Step-by-step explanation:

The pair of given triangles which satisfied the HL theorem of congruency is given by option C. Both right triangles with hypotenuse and one corresponding leg congruent.

HL theorem also named as Hypothenuse Leg theorem,

It states hypotenuse and any one leg of one right angled triangle is congruent to hypotenuse and corresponding leg of another right angled triangle.

This implies both the triangles are congruent using HL theorem.

To check which pair of triangles are congruent using HL theorem are as follow,

a. In the first pair of right angled triangles only hypotenuse is marked as congruent side of two different triangles.

So it is not true.

b. In the second pair of triangles,

Both the triangles are obtuse angled triangle.

It does not satisfied HL theorem.

So , it is also not true.

c. In the third pair of the right angled triangle,

Hypotenuse of both the triangle are marked congruent.

One of the corresponding leg is also congruent.

It satisfied the HL theorem.

And both the triangles are congruent to each other using HL theorem.

Option C. is true.

d. IN fourth pair of triangles,

Triangles are not right angled triangle.

It satisfied the SSS (Side -Side- Side) congruency theorem.

It is not a correct option for HL theorem.

Therefore, pair of triangles which satisfied the HL theorem of congruency is option C. Both right triangles.

Learn more about triangles here

brainly.com/question/27506927

#SPJ2

The formula for slope is [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

In this case:

[tex]y_{2} = 1\\ y_{1} }= -3\\x_{2} = -4\\x_{1} = 0[/tex]

so...

[tex]\frac{1 - (-3)}{-4 - 0}[/tex]

[tex]\frac{4}{-4}[/tex]

-1 <<<The slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

m = -1

Step-by-step explanation:

The slope is also called the gradient, m.

m=(y2-y1)/(x2-x1)

x1 = 0

y1 = 3

x2 = -4

y2 = 1

we therefore substitute for the values in the formula

m = (1-⁻3)/(⁻4-0)

m = -1

Shown below

The first system of inequality is the following:

[tex]\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y<2x+\frac{1}{3}\end{array}\right.[/tex]

To find the solution here, let's take one point, say, [tex](0,0)[/tex] and let's taste this point into both inequalities, so:

First inequality:

[tex]y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False![/tex]

The region is not the one where the point [tex](0,0)[/tex] lies

Second inequality:

[tex]y<2x+\frac{1}{3} \\ \\ 0<2(0)+\frac{1}{3} \\ \\ 0<\frac{1}{3} \ True![/tex]

The region is the one where the point [tex](0,0)[/tex] lies

So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there

First inequality:

[tex]y<2x+\frac{2}{3} \\ \\ 0<2(0)+\frac{2}{3} \\ \\ 0<\frac{2}{3} \ True![/tex]

The region is the one where the point [tex](0,0)[/tex] lies

Second inequality:

[tex]y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True![/tex]

The region is not the one where the point [tex](0,0)[/tex] lies

So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.

CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.

Answer:

[-5,39]

Step-by-step explanation:

The vertex is at (-6,-5)

The interval is from -10 to 5 (inclusive of both endpoints...

Absolute function is open up because 4 is positive

I will plug in both endpoints now:

f(-10)=4|-10+6|-5                               f(5)=4|5+6|-5

f(-10)=4(4)-5                                      f(5)=4(11)-5

f(-10)=11                                             f(5)=39

So the highest reached by f(5) which is 39 so our range will go up to 39 (inclusive)

11 is not the lowest reached, -5 is because our vertex was included within the domain

So the range is [-5,39]

The answer would be 5, - 8

Answer:5,-8

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

slope formula: (y2-y1)/(x2-x1)

(-8-9)/(x-(-3))=-17/10

-17/x+3=10

-17/7+3=10

-17/10=10

To find the missing value so that the two points have a slope of -17/10, we can use the slope formula. Substituting the coordinates into the formula, we get an equation -17/(x + 3) = -17/10. Solving for x, we find x = 7.

To find the missing value so that the two points have a slope of −17/10, we can use the slope formula. The slope formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the first point is (-3, 9) and the second point is (x, -8).

Substituting the coordinates into the slope formula,

we have (-8 - 9) / (x - (-3)) = -17/10.

Simplifying this equation,

we get -17 / (x + 3) = -17/10.

Cross multiplying, we find x + 3 = 10.

Solving for x, we subtract 3 from both sides, giving x = 7.

Therefore, the missing value is 7.

https://brainly.com/question/34207674

#SPJ3

The distance between the pair of points A(-1,8) and B(-8,4)​ is 15.

In geometry, the distance formula is:

√(x2-x1)2+(y2-y1)2

Now we can just plug in the x and y values:

√(-1-8)2+(8-(-4)2

√(-1-8)2+(8+4)2

√(-9)2+(12)2

√(81+144)

√(225)

15

So our distance is 15 units.

Learn more about the pair of points at

https://brainly.com/question/23848540

#SPJ2

Final answer:

The distance between points A(-1,8) and B(-8,4) is calculated using the distance formula derived from the Pythagorean Theorem and is approximately 8.06 units.

Explanation:

To find the distance between two points on the Cartesian plane, you can use the distance formula, which is derived from the Pythagorean Theorem. In this case, the points are A(-1,8) and B(-8,4). The formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

Here's how it's done step-by-step:

Subtract the x-coordinates of the two points: -8 - (-1) = -7.

Subtract the y-coordinates of the two points: 4 - 8 = -4.

Square both differences: (-7)² = 49 and (-4)² = 16.

Add the squares of the differences: 49 + 16 = 65.

Take the square root of the sum:
√65 approx 8.06.

Therefore, the distance between points A and B is approximately 8.06 units.

Answer:8 ,-8

Step-by-step explanation:the absolute value of a number is how far it is from 0 so 8 and -8 are both 8 spots from 0. Hope this helps!

Answer:

0 and -5/2

Step-by-step explanation:

g is the first function we consider because that is the function we are first plugging in values into since the order is f o g and not g o f.

g has domain all real numbers meaning you can plug in any number into g and get a number back

So now let's look at plugging in g(x) into f(x)

that is f(g(x))=f(2x^2+5x)=5/(2x^2+5x)

Here you are dividing by a variable

You have to watch out dividing by 0

The variable, 2x^2+5x, is 0 when....

2x^2+5x=0

x(2x+5)=0

x=0 or x=-5/2

So The domain is all real numbers except x=0 or x=-5/2

[tex](f \circ g)(x)=\dfrac{5}{2x^2+5x}\\\\2x^2+5x\not =0\\x(2x+5)\not=0\\x\not =0 \wedge x\not =-\dfrac{5}{2}[/tex]

Answer:

y > 2x + 2 and y < 2x-1 .

Step-by-step explanation:

The line which the blue shaded area represent has y intercept 2 and slope [tex]\frac{2}{1} =2[/tex]

Hence equation of the line is y=2x+2.

To check the inequality for the shaded region we take any  point (-3,0) in the shaded region .Plugging the values in the given equation :

0 > 2(-3)+2  or 0 >-4.

The inequality equation represented by the blue shaded part is y > 2x+2.

The line for the red shaded region has y intercept -1 and slope 2.

Hence equation of the line is y= 2x-1 .

Taking a point (2,0) in the shaded part and substituting the values in the equation of line we have :

0< 2(2)-1 or 0< 3 .

Hence the inequality representing the red shaded region is y<2x-1 .

y > 2x + 2 and y < 2x - 1

In this problem, we will compose the system of linear inequalities is represented by the graph. Firstly, let us state each line on the graph in terms of the equation of the line.

A shortcut to form a linear equation through the intercepts of the axes at (0, a) and (b, 0) is [tex]\boxed{\boxed{ \ ax + by = ab \ }}[/tex].

Part-1: a dashed line that intersects the axes at points (0, 2) and (-1, 0).

Step-1: make a linear function  

[tex]\boxed{ \ ax + by = ab \ } \rightarrow \boxed{ \ 2x + (-1)y = 2 \times (-1) \ }[/tex]

2x - y = -2

Add by 2 and y on both sides.

Hence, the equation of line is [tex]\boxed{y = 2x + 2 \ }[/tex]  

Step-2: make a linear inequality  

Since the test point (0, 0) is not in the blue shaded area, which means the test results must be false (or 0 > 2), then linear inequality is arranged as follows:

[tex]\boxed{\boxed{ \ y > 2x + 2 \ }}[/tex]

Part-2: a dashed line that intersects the axes at points (¹/₂, 0) and (0, -1)..

Step-1: make a linear function  

[tex]\boxed{ \ ax + by = ab \ } \rightarrow \boxed{ \ (-1)x + \frac{1}{2}y = -1 \times \frac{1}{2} \ }[/tex]

[tex]\boxed{ \ -x + \frac{1}{2}y = -\frac{1}{2} \ }[/tex]

Multiply by 2 on both sides.

-2x + y = -1

Add by 2x on both sides.

Hence, the equation of line is [tex]\boxed{y = 2x - 1 \ }[/tex]  

Step-2: make a linear inequality  

Since the test point (0, 0) is not in the red shaded area, which means the test results must be false (or 0 < -1), then linear inequality is arranged as follows:

[tex]\boxed{\boxed{ \ y < 2x - 1 \ }}[/tex]

Thus the system of linear inequalities is represented by the  graph is y > 2x + 2 and y < 2x - 1.

nothing can further be done with this?

The solution to the system of equations given by the ordered pairs (7x+3y,2x+3y) and (24, 0) is x= -4.8 and y=3.2.

To solve for x and y, you need to equate each component of the ordered pairs and solve the resulting equations. In this case, you have:

Solving the second equation for x: x = -1.5y

Substitute x into the first equation: 7(-1.5y) + 3y = 24, which becomes -10.5y + 3y = 24, then -7.5y = 24

Solving for y, you get: y = -24 / -7.5 which equals y = 3.2.

Substituting y into the second equation 2x + 3(3.2) = 0, we get 2x = -9.6, so x = -9.6 / 2, so x = -4.8.

So, the values of x and y are -4.8 and 3.2 respectively.

https://brainly.com/question/29050831

#SPJ3

Answer:

C

Step-by-step explanation:

The area (A) of a regular decagon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

perimeter = 10 × 8 = 80 in, thus

A = 0.5 × 80 × 12.3 = 492 in² → D

Answer:

see below

Step-by-step explanation:

Let L = lisa's age

seven years younger than Lisa

L-7

Answer:

The z-score for this kernel is -2.3

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The popping-times of the kernels in a certain brand of microwave

  popcorn are  normally distributed

- The mean is 150 seconds

- The standard deviation is 10 seconds

- The first kernel pops is 127 seconds

- We want to find the z-score for this kernel

∵ z-score = (x - μ)/σ

∵ x = 127

∵ μ = 150

∵ σ = 10

∴ z-score = (127 - 150)/10 = -23/10 = -2.3

* The z-score for this kernel is -2.3

Answer:

-2.3

Step-by-step explanation:

Answer:

[tex]V=5,676.16cm^3[/tex]

Step-by-step explanation:

The volume of a triangular prism is defined by the formula:

[tex]V=(area-of-base)*(length)[/tex]

In this case the base is triangular and the area of a triangle is: [tex]A=\frac{1}{2}(base)*(height)[/tex]

Then the volume is:

[tex]V=\frac{1}{2}(base*height*length)[/tex]

Now we have to replace with the given values:

[tex]V=\frac{1}{2}(22.4cm*18.1cm*28cm)\\\\V=\frac{1}{2}(11,352.32cm^3)\\\\V=5,676.16cm^3[/tex]

Then the correct answer is the third option.

[tex]V=5,676.16cm^3[/tex]

Answer:

5,676.16 is your answer 2021 Edge

I got it right

Step-by-step explanation: