Brenda has a planter box in her backyard that measures 3 2/3 feet by 4 1/8 that measures 3 2/3 feet by 4 1/8 by 2 1/2 feet. What is the volume of brenda's planter box?

9514 1404 393

Answer:

Step-by-step explanation:

1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.

The linear factorization is ...

  f(x) = (x +1)(x -2)(x -i)(x +i)

The roots are -1, 2, -i, +i.

__

2. The graph (blue) shows the zeros are 1, 3, 4.

You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as

  (x -3)(x -4) . . . zeros of 3 and 4

__

I have attached a spreadsheet that does synthetic division. There are web sites that will do this, too. The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1). When you fill in the zero and coefficients, the built-in formulas do the rest.

9514 1404 393

Answer:

real: -1, 2; complex: +i, -i

1, 3, 4

Step-by-step explanation:

1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.

The linear factorization is ...

 f(x) = (x +1)(x -2)(x -i)(x +i)

The roots are -1, 2, -i, +i.

__

2. The graph (blue) shows the zeros are 1, 3, 4.

You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as

 (x -3)(x -4) . . . zeros of 3 and 4

__ The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1).

Answer:

∠F ≈ 53°

General Formulas and Concepts:

Trigonometry

Step-by-step explanation:

Step 1: Define

Looking at ∠F

opposite leg of ∠F = ED = 8

hypotenuse = FE = 10

Step 2: Find m∠F

9514 1404 393

Answer:

Step-by-step explanation:

The area of the rectangle is given by ...

  A = LW

  A = (20 m)(14 m) = 280 m²

__

The area of the semicircle is ...

  A = (1/2)πr²

  A = (1/2)π(7 m)² = 24.5π m² ≈ 77 m²

__

Then the total area is ...

  280 m² +77 m² = 357 m²

_____

The width of the rectangle is the diameter of the circle, which is twice its radius. The area of a semicircle is 1/2 the area of a circle.

Answer:

-3,-2,-1,0,1,2,3

Step-by-step explanation:

Answer:

11 widgets

Step-by-step explanation:

544.50/4.5 = 121

square root 121 = 11

Answer:

The answer is "0.45385".

Step-by-step explanation:

The time is taken to reach the coast [tex]= \frac{\sqrt{(2^2 + x^2)}}{4}[/tex]

The  time is taken to reach Q after reaching the coast [tex]= \frac{\sqrt{(1 + (3-x)^2)}}{4}[/tex]

Total time, [tex]T= \frac{\sqrt{(1 + (3-x)^2)}}{4}+ \frac{\sqrt{(1 + (3-x)^2)}}{4}[/tex]

This has to be minimum,

[tex]\to \frac{dt}{dx} = 0[/tex]

[tex]\to \frac{\sqrt{(2^2 + x^2)}}{2} + \frac{\sqrt{1 + (3-x)^2}}{3}\\\\ \frac{x}{4}\sqrt{(4+x^2)} + \frac{(x-3)}{(4\sqrt{(x^2-6x+10)}} = 0\\\\\frac{x^2}{16} \times (4+x^2) = \frac{(x-3)^2}{16 \times (x^2-6x+10)}\\\\x^2(4+x^2) = \frac{(x-3)^2}{(x^2-6x+10)}\\\\4x^2+x^4 = \frac{ x^2+9-6x}{(x^2-6x+10)}\\\\ 4x^2+x^4(x^2-6x+10) = x^2+9-6x\\\\4x^4-24x^3+40x^2+x^6-6x^5+10x^4= x^2+9-6x\\\\x^6-6x^5+ 14x^4-24x^3+39x^2+6x-9=0\\\\[/tex]

x=0.45385

Answer: 1a. 0.538

1b. 0.231

Step-by-step explanation:

For Section A.

Given data:

Numbers to be drawn = 1 to 13

Odd numbers = 7

Even numbers = 6

1a. Probability of drawing an odd number

= 7/13

= 0.538

1b. Probability of drawing a number less than 4.

= 3/13

= 0.231

Section B.

You need to provide me with the table containing the data, for me to be able to assist you with it.

Answer:

[tex]x=5[/tex] is the required digit that can be used to correctly complete the equation.

Step-by-step explanation:

Given the equation

_____ × 1/10 = 1/2

Let 'x' be the required digit

If we put x=5 the L.H.S will be equal to R.H.S.

i.e.

5 × 1/10 = 5/10 = 1/2

so the equation becomes

Therefore, [tex]x=5[/tex] is the required digit that can be used to correctly complete the equation.

The quadratic model for the data set is  y = 1.2246x² - 5.0511x + 24.288

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, quadratic, cubic etc.

The standard form of polynomial (of degree 2) is:

y = ax² + bx + c

The quadratic model for the data set is  y = 1.2246x² - 5.0511x + 24.288

Find out more on polynomial at: brainly.com/question/2833285

Answer:

-1/2

Step-by-step explanation:

slope = m = (y2 - y1)/(x2 - x1) = (-2 - (-5))/(11 - 17) = 3/(-6) = -1/2

Answer:

Slope= [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

When you are looking for slope you should use this [tex]slope=m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] then just plug in what you already know.

[tex]y_{1}=-5\\y_{2}=-2\\x_{1}=17\\x_{2}=11[/tex]

Now we insert it in the formula and solve to get the slope...

[tex]\frac{-2-(-5)}{11-17}=\frac{3}{-6}=-\frac{1}{2}[/tex]

Answer:

a and b

Step-by-step explanation:

Answer:

1.Nonagon-convex, regular

2.Quadrilateral-convex, irregular

3.Hexagon-concave, irregular

Answer:

1.-Nonagon-convex, regular

2.-Quadrilateral-convex, irregular

3.-Hexagon-concave, irregular

Answer:

The simplified term for the given expression is 169.

Step-by-step explanation:

Solving within the parenthesis, given the expression:

13{6^2/(5^2-4^2)+9}

13{36/(25-16)+9}

13{36/9+9}

13(9+4)

13(13)

Therefore, the simplified term in terms of the expression, 13(6^2/5^2-4^2)+9), is 169.

Answer:

169 aidan talk to meee

Step-by-step explanation:

1.1     4 = 22

(4)2 = (22)2 = 24

        (62)      

 13 • (————————— +  9)

       (52 - 24)    

3.1     6 = 2•3

(6)2 = (2•3)2 = 22 • 3    (22•32)    

 13 • (——————— +  9)

          9                 (22•32)

Simplify   ———————

              9    

  4.1      Canceling out  32 as it appears on both sides of the fraction line

13 • (4 +  9) gives you 169

Answer:

There are 3 terms.

Answer:

10.) y=-3x+5

11.) y= -1/2 x+2

Step-by-step explanation:

step by step attchaed below

Answer:

1.44

Step-by-step explanation:

because I am smart

Answer:

40 is the answer

friend me

Answer:

She will not have enough money

Step-by-step explanation:

0.79x85=67.15

67.15+35=105.15

Answer:

3/4 or .75

Step-by-step explanation:

slope = dy/dx

dy = 1 - -2 = 3

dx = 2 - -2 = 4

slope = 3/4

Step-by-step explanation:

(1+2)/(2+2)= 3/4 is the slope

Answer:

The answer is the last line below.

Step-by-step explanation:

g(x) = 4x

h(x) = -3x^2 + 4

(g + h)(x) = 4x - 3x^2 + 4

Answer:

21π/2

Step-by-step explanation:

94.55π is the area of the required surface.

[tex]S=\int\limits^{x_1}_{x_2} {2\pi f(x)\sqrt{1+f'(x)^2} \, dx[/tex]

is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis

Given,

[tex]x=\frac{1}{3}(y^2+2)^{\frac{3}{2}}[/tex]

[tex]\implies (3x)^\frac{2}{3}=y^2+2\\\implies y^2=(3x)^\frac{2}{3}-2[/tex]

[tex]\implies y=\sqrt{(3x)^\frac{2}{3}-2}[/tex]

Let

[tex]y=\sqrt{(3x)^\frac{2}{3}-2}=f(x)[/tex]

Now, the range of y is given 3≤y≤4

hence, the range of x is [tex](\frac{1}{3}(3^2+2)^{\frac{3}{2}}[/tex],[tex]\frac{1}{3}(4^2+2)^{\frac{3}{2}})[/tex]=(12.16,25.46).

So, [tex]S=\int\limits^{25.46}_{12.16} {2\pi f(x)\sqrt{1+f'(x)^2} dx\\\\=[\frac{\pi}{2}(3x)^{\frac{4}{3}}-\pi (3x)^{\frac{2}{3}}]^{25.46}_{12.16}\\=101.63\pi - 6.99 \pi \\= 94.55 \pi[/tex]

is the area of the required surface.

Hence, 94.55π is the area of the required surface.

Learn more about the area of surface- brainly.com/question/24126051

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Answer:

x = 30

y = 2

Step-by-step explanation:

Please note: the value for x is correct only if this triangle is a right triangle.

This can be solved because 2(5y) = 20 and because if a triangle has all congruent angles then its side lengths are also congruent.

Answer:

4 feet/minute

explanation:

The rate of descent = (10 feet)/(2.5 mn) = 4 ft/min

Answer:

[tex](4, -3 )[/tex]

General Formulas and Concepts:

Pre-Algebra I

Algebra I

Step-by-step explanation:

Step 1: Define

R (9, 3)

S (-1, -9)

Step 2: Find midpoint

Answer:

Power

Step-by-step explanation:

An hypothesis is usually formulated at the beginning of research, it is usually in line with the problem statement and gives the possible outcome.

An hypothesis is either accepted or rejected.

Power in hypothesis is the probability of rejecting null hypothesis when it is false. It helps in making a correct decision by rejecting the null hypothesis when it is not true.

power ranges between 0 to 1 when it is close to 1 it is said to be very strong and has the probability of rejecting a null hypothesis when it is not true.

Power helps to avoid a type II error in statistics.

Answer:

the answer is 295 students

Answer:

363-94+26 = 295 students