They have a rectangle ABCD as shown below, where AB = 24cm BC = 10cm and AE = 13cm
A. Calculate the volume of the rectangle ABCD
B. Calculate the circumference of the BCD triangle
C. Calculate the circumference of the BEC triangle
D. Calculate the circumference of the DEC triangle

Answer:

24

Step-by-step explanation:

8 * 3 = 24

12 * 2 = 24

(the star is the multiplication sign)

Hope this helps :)

Answers:

===========================================

Explanation:

The lowest point occurs when y = -2. The highest point occurs when y = 2.

The vertical distance between the highs and lows is 4 units (since 2-(-2) = 2+2 = 4). This cuts in half to get 4/2 = 2.

The amplitude is 2. It measures the vertical distance from the midline to either the peaks or valleys.

-----------------------------

Note that this curve has two lowest points and one highest point shown. What we'll do is shift the graph over to the right so that each of those lowest points snap to a grid point. The lowest point on the left will move to where x = -pi, while the lowest point on the right snaps to x = 3pi/2. We'll keep each point at the same y coordinate.

The horizontal distance from x = -pi to x = 3pi/2 is

(3pi/2) - (-pi) = 3pi/2 + 2pi/2 = 5pi/2

This represents the horizontal distance from the left valley point to the right valley point. This is one full period of the curve. After we arrive at the right valley point, we repeat the process of going up and coming back down in this exact same fashion. The process is repeated forever to generate the cosine curve. The curve repeats itself every 5pi/2 units along the x axis.

Side note: any phase shift of a curve will have the same period as the original curve. This is why we're allowed to shift left or right to help find the period.

Answer:

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]     [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]       [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

Step-by-step explanation:

Represent the volume of the box with V and the dimensions with l, b and h.

The volume (V) is:

[tex]V = l * b * h[/tex]

Make h the subject of the formula

[tex]h = \frac{V}{lb}[/tex]

The surface area (S) of the aquarium is:

[tex]S = lb + 2(lh + bh)[/tex]

Where lb represents the area of the base (i.e. slate):

The cost (C) of the surface area is:

[tex]C = 7 * lb + 1 * 2(lh + bh)[/tex]

[tex]C = 7lb + 2(lh + bh)[/tex]

[tex]C = 7lb + 2h(l + b)[/tex]

Substitute [tex]\frac{V}{lb}[/tex] for h in the above equation

[tex]C = 7lb + 2*\frac{V}{lb}(l + b)[/tex]

[tex]C = 7lb + \frac{2V}{lb}(l + b)[/tex]

[tex]C = 7lb + \frac{2V}{b} + \frac{2V}{l}[/tex]

Differentiate with respect to l and with respect to b

[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex]

[tex]C_b=7l - \frac{2V}{b^2}[/tex] [tex]=0[/tex]

To solve for b and l, we equate both equations and set l to b (to minimize the cost)

[tex]7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}[/tex]

[tex]7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}[/tex]

By comparison:

[tex]l =b[/tex]

[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex] becomes

[tex]7l - \frac{2V}{l^2}=0[/tex]

[tex]7l = \frac{2V}{l^2}[/tex]

Cross Multiply

[tex]7l^3 = 2V[/tex]

Solve for l

[tex]l^3 = \frac{2V}{7}[/tex]

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]

Recall that: [tex]l =b[/tex]

[tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]

Also recall that:

[tex]h = \frac{V}{lb}[/tex]

[tex]h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}[/tex]

[tex]h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}[/tex]

Apply law of indices

[tex]h = \sqrt[3]{\frac{49V^3}{4V^2}}[/tex]

[tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

The dimension that minimizes the cost of material of the aquarium is:

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]     [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]       [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

Answer:

1

Step-by-step explanation:

The answer is actually just positive 1.

Absolute value is the direct opposite of a number with a positive value on a number line. However, the absolute value is always answered in a positive form of the number meaning that no matter what the number is (even if it's a positive number) the answer will always be that same number, but in positive form.

Remember, if a number is in between two of these " | " then the answer will be that same number but in positive form.

Hope this helps and have a nice day.

-R3TR0 Z3R0

Answer:

[tex]\theta=41.18^{\circ}[/tex]

Step-by-step explanation:

Given that,

The height of the tree, h = 14 ft

The height of the shadow, b = 16 ft

We need to find the angle of elevation of the sun from the ground. Let the angle be θ. We can use trigonometry to find it. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{14}{16}\\\\\theta=41.18^{\circ}[/tex]

So, the required angle of elevation of the sun is equal to [tex]41.18^{\circ}[/tex].

Answer:

By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.

Hope this helps(and also if you have a more refined wording please put it in the comments)!

Answer:

By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.

9514 1404 393

Answer:

Step-by-step explanation:

We can express all of the ages in terms of Luna's age. Letting L represent Luna's age, we have ...

The total of their ages is then ...

  L +2L +(2L+6) = 51 . . . . an equation with one variable

  5L = 45

  L = 9

Luna is 9, Camila is 18, and Ava is 24.

Answer A is correct. C is correct.

Step-by-step explanation:

Answer:

it is 222

Step-by-step explanation:

1440 divided by 20 :)

9514 1404 393

Answer:

  x ≈ 0.309906932381 or 4

Step-by-step explanation:

There are no algebraic methods of solving a mixed exponential and polynomial equation. The value of x can be found by guessing, or by other means such as trial and error or graphing.

Attached is a graph showing two solutions. x = 4 is the integer solution (2^4 = 4·4). The irrational solution is approximately x ≈ 0.309906932381. That precision is obtained by Newton's method iteration, easily done by a graphing calculator.

Answer:

11

Step-by-step explanation:

7x2=14

16x1/2=8

14-8=6

6+5=11

The evaluation of the given equation when the a is 0.5 and b = 7 so it should be considered as the 46.

Since the equation is

[tex]b^2 - 16a + 5[/tex]

So,

[tex]= (7)^2 - 16(0.5) + 5[/tex]

= 49 - 8 + 5

= 46

Hence, The evaluation of the given equation when the a is 0.5 and b = 7 so it should be considered as the 46.

Learn more about an equation here: https://brainly.com/question/14170257

You have 2 points with the same x value of 2 and 2 points with the same y value of 4.

You now need 2 points with the same x value of 4 ( you are given 1) and 2 y values of 1 ( you are given 1.

The missing point would need to be (4,1)

The width would be x2-x1 = 4-2 = 2 units

The length would be y2-y1 = 4-1 = 3 units

Area = 3x 2 = 6 square units

Step-by-step explanation:

perp. -1/2

y + 3 = -1/2(x - 4)

y + 3 = -1/2x + 2

y = -1/2x - 1

Answer:

a - Mutual

b - (x+21)+(2x+3)=90

c - 3x +24 =90

3x=90-24

3x=66

X=22

where is the question I dont see it

Answer:

x

∈

R

y

≤

1

Step-by-step explanation:

Answer:

[tex]y\geq -1[/tex]

Step-by-step explanation:

see graph below for reference

Answer:

Never:

Step-by-step explanation:

because its more understandable we know this because it wouldnt be always

Answer:

6 units to the right, 3 units down

Step-by-step explanation:

Answer:

182.82812

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Answer: so here is what you have to do

Step-by-step explanation:Determine Whether a Number

Is a Solution to an Equation

2 Solve Linear Equations

3 Determine Whether an Equation Is a Conditional Equation, Identity, or Contradiction

Preparing for Linear Equations

Before getting started, take this readiness quiz. If you get a problem wrong, go back to the section cited and review the material.

P1. Determine the additive inverse of 5.

P2. Determine the multiplicative inverse of - 3.

P3. Use the Reduction Property to simplify 15 # 5x.

P4. Find the Least Common Denominator of 3 and 5 .

8 12

P5. Use the Distributive Property to remove the parentheses: 61z - 22

P6. What is the coefficient of - 4x?

P7. Simplify by combining like terms: 41y - 22 - y + 5 P8. Evaluate the expression -51x + 32 - 8 when x = -2

P9. Isx = 3inthedomainof 2 ?Isx = -3inthe domain? x + 3

[Section R.3, p. 21] [Section R.3, pp. 23–24]

[Section R.3, pp. 25–26] [Section R.3, pp. 27–28]

[Section R.3, pp. 29–30] [Section R.5, p. 41] [Section R.5, pp. 41–43] [Section R.5, pp. 40–41]

[Section R.5, pp. 43–44]

 In Words

In the equation 2

2 + 5 is the left side of the equation and 0 is the right side. In this equation only the left side contains the variable, y. In the equation 4 +5=-2x+10,theexpression

4 + 5 is the left side of the equation and - 2 + 10 is the right side. In this equation both sides have expressions that contain the variable, x.

1 Determine Whether a Number Is a Solution to an Equation

An equation in one variable is a statement made up of two expressions that are equal, and in the statement, at least one of the expressions contains the variable. The expres- sions are called the sides of the equation. Examples of equations in one variable are

2y + 5 = 0 4x + 5 = -2x + 10 3 = 9 z+2

In this section, we will concentrate on solving linear equations in one variable.

Answer:

$12,375

$12820.50

Step-by-step explanation:

To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49

Hence,

Lower bound = $27.50

Upper bound = $28.49

Therefore. Cost of making 450 chairs ;

27.50 * 450 = $12,375 (lower bound)

28.49 * 450 $12820.50 (upper bound)

-9-(-7)

-9--7

-9+7

7-9

-2

---

hope it helps

Answer:

[tex]-\left(x+7\right)\left(x+8\right)[/tex]

Step-by-step explanation:

[tex]-X^2-15x - 56\\\\\mathrm{Factor\:out\:common\:term\:}-1\\\\=-\left(x^2+15x+56\right)\\\\=-\left(x+7\right)\left(x+8\right)[/tex]

Answer:

[tex]-(x+7) (x+8)[/tex]

Step-by-step explanation:

[tex]-x^{2} - 15x-56[/tex]

Write - 15x as a difference

[tex]-x^{2} -7x-8x-56[/tex]

Factor out - x from the expression

[tex]-x(x+7)-8x-56[/tex]

Factor out - 8 from the expression

[tex]-x (x+7)-8(x+7)[/tex]

Factor out - (x + 7) from the expression

[tex]-(x+7)x(x+8)[/tex]

Answer:

the answer is 11

I hope it helps

have a nice day

#Captainpower

Answer:

Step-by-step explanation:

From the given information:

[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]

A)

[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]

[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]

B)

[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]

[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]

C)

[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]

[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]

D)

[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]

Answer:

Q.1 a²+10a+24

splitting the middle.

a²+6a+4a+24

=a(a+6)+4(a+6)

(a+6)(a+4)

Q.2 x²+9x+18

splitting the middle

x²+6x+3x+18

x(x+6)+3(x+6)

(x+6)(x+3)