Q3
Work out the volume of each of these items:
a) a bag of sugar of mass 1000 g and density 1.6 g/cm
b) a packet of margarine with density 2.8 g/cm and mass 250 g

Answer:

[tex]y =5(3)^x[/tex]

Step-by-step explanation:

Given

The attached table

Required

Determine the equation of the table

The table represents an exponential function. So, we make use of

[tex]y = ab^x[/tex]

When x = 0, y= 5.

So:

[tex]y = ab^x[/tex] becomes

[tex]5 = ab^0[/tex]

[tex]5 = a*1[/tex]

[tex]5 = a[/tex]

[tex]a = 5[/tex]

When x = 1; y = 15

So;

[tex]y = ab^x[/tex] becomes

[tex]15 = a * b^1[/tex]

[tex]15 = a * b[/tex]

Substitute 5 for a

[tex]15 = 5 * b[/tex]

Divide both sides by 5

[tex]\frac{15}{5} = \frac{5 * b}{5}[/tex]

[tex]3 = b[/tex]

[tex]b = 3[/tex]

Substitute values for a and b in: [tex]y = ab^x[/tex]

[tex]y =5(3)^x[/tex]

Answer:

l=13 ft

w=6.5 ft

Step-by-step explanation:

a rectangular garden would have 4 sides

two of the sides are x feet long

and the other two sides are 2x feet long

therefore

x+x+2x+2x=39

which is the same as saying

6x=39

divide both sides by 6 to get

x=6.5

so the width is 6.5 feet and the length is twice that or 13 feet

Answer:

seventeen degrees(17⁰)

Answer:

134=2x

X= 67

hope it helps

Answer:

810 is 100 times the size of 0.81

Answer:

m(arc CD) = 14.1 cm

Step-by-step explanation:

Measure of an arc of the circle = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Here 'r' = radius of the circle

θ = Angle subtended by the arc at the center of the circle

From triangle OED,

sin(∠EOD) = [tex]\frac{ED}{OD}[/tex]

sin(∠EOD) = [tex]\frac{\frac{12.7}{2}}{9.06}[/tex]

                 = [tex]\frac{6.35}{9.06}[/tex]

                 = 0.7

m∠EOD = 44.498

              ≈ 44.5°

Angle subtended by the arc CD at the center = m∠COD

                                                                            = 2(44.5)

                                                                            = 89°

m(arc CD) = [tex]\frac{89}{360}(2\pi)(9.06)[/tex]

                 = 14.07

                 ≈ 14.1 cm

Answer:3.294. Hope this helps!

Step-by-step explanation:

Answer:

im sooooo confused

Step-by-step explanation:

Answer:

(x-4)(x-3)

Step-by-step explanation:

x^2 - 7x + 12

Find what will multiply to make 12 and add to -7

(x - 4)(x - 3)

Answer:

Step-by-step explanation:

x is the third side

x² + 32² = 68²

x² = 68² - 32² = 3600

x = √3600 = 60

Answer:

44 inches and 24 inches

Step-by-step explanation:

Let [tex]l,b[/tex] denotes length and breadth of a rectangle.

[tex]lb=1056[/tex]

A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides.

New length [tex]=l-6[/tex] inches

New breadth [tex]=b-6[/tex] inches

Height of box [tex]=3[/tex] inches

Volume of box = length × breadth × height

[tex](l-6)(b-6)3=2052[/tex]

[tex]lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l[/tex]

Put [tex]b=68-l[/tex] in [tex]lb=1056[/tex]

[tex]l(68-l)=1056\\l^2-68l+1056=0\\l^2-44l-24l+1056=0\\l(l-44)-24(l-44)=0\\(l-24)(l-44)=0\\l=24,44[/tex]

At [tex]l=24,b=\frac{1056}{24}=44[/tex] inches

At [tex]l=44,b=\frac{1056}{44}=24[/tex] inches

Answer:

2 1/4 or 9/4

Step-by-step explanation:

9/10÷4/10= 9/10*10/4

now simplify the 10

9/1 * 1/4= 9/4

now turn it into a mixed number

2 1/4

Answer:

2.25, 9/4 or 2 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Height = √(90^2-63^2) = √4131 ≈ 64 ft

Answer:

The margin of error is 5. 00 

true

oops, i read it wrong LOL, it's true. .65 is less than .75

Answer:

-4

Step-by-step explanation:

Divide each side by '-1'.

p = -4

Simplifying

p = -4

Answer:

8

Step-by-step explanation:

20 ÷ 5 × 2 = 8

_________________

( 20 ÷ 5 = 4 × 2 = 8 )

full equation ^^

Answer:

no, 71.106 is greater

Step-by-step explanation:

71.08= 71 and 8/100

71.106= 71 and 10/100

71.106's fraction is larger

Answer:

Y = x+3

Step-by-step explanation:

You want to start by figuring out how to get Y alone.

So to get it alone so you add +3 on both sides

Y - 3 = x

+3. +3

Positive 3 and Negative 3 cancel out making it zero.

Visual: 3 - 3 = 0

Since you cant take or add anything from x you leave it as + 3 so the answer should be.

Y = x + 3

I hope I could help :)

Answer:

A

Step-by-step explanation:

This graph represents the inequality x < 2. you may be confused as to why the answer is not x ≤ 2, but the circle at the start of the line is not shaded in. This tells us that an answer to this inequality cannot be x

Answer:

D) 31

Step-by-step explanation:

2x-7+2x+63=180

4x+56=180

4x=180-56

4x=124

x=124/4

x=31

Answer:

(d) x = 31

Step-by-step explanation:

(2x)° + (2x - 7)° + 63° = 180°

4x - 7 + 63 = 180

4x = 180 - 56

4x = 124

x = 31

Answer:

Step-by-step explanation:

2. -x+4+3x+2=2x+6

3. -x-2-4x-3=-5x-5

4.-36-24=-60

5.  9+10-6-6=7

Step-by-step explanation:

x+2x+6x=180

9x=180

x=20°

m<A = 20°

Compute the rightmost product:

[tex]\begin{bmatrix}1&2&0\\2&0&4\\0&4&-1\end{bmatrix}\begin{bmatrix}2\\2\\k\end{bmatrix}=\begin{bmatrix}1\times2+2\times2+0\times k\\2\times2+0\times2+4\times k\\0\times 2+4\times2+(-1)\times k\end{bmatrix}=\begin{bmatrix}6\\4k+4\\8-k\end{bmatrix}[/tex]

Then

[tex]\begin{bmatrix}2&2&k\end{bmatrix}\begin{bmatrix}6\\4k+4\\8-k\end{bmatrix}=2\times6+2\times(4k+4)+k\times(8-k)=-k^2+16k+20[/tex]

Use whatever methods you like to solve the remaining quadratic equation:

-k ² + 16k + 20 = 0   →   k = 8 ± 2√21

[tex]x - \frac{3}{4} \geqslant - \frac{1}{8} [/tex]

[tex]x \geqslant - \frac{1}{8} + \frac{3}{4} [/tex]

Make both fractions to have same denominators by multiply 2 in 3/4 for both numerator and denominator.

[tex]x \geqslant - \frac{1}{8} + \frac{3 \times 2}{4 \times 2} \\ x \geqslant - \frac{ 1}{8} + \frac{6}{8} \\ x \geqslant \frac{5}{8} [/tex]

Hence, the solution is, "x is greater or equal to 5/8."

[tex] \large \boxed{x \geqslant \frac{5}{8} }[/tex]