TJ’s Cat Food plans to use tins that are the shape of cylinders. The internal measurements of a tin are shown.

(b ) Work out the volume of cat food that the tin contains.

Answer:  -6 only (choice B)

This is because the point (0,-6) is on the blue line. This is the y intercept.

Choice C would be true if you wanted to solve f(x) = 0, instead of f(0) itself.

Answer:

-6

Step-by-step explanation:

f(0) means what is the output when the input is 0

x=0 y= -6

Hello!

a) (t - 2)(t - 2) = (t - 2)² = t² - 4t + 4

b) (3y - 2z)(3y + 2z) = (3y)² - (2z)² = 9y² - 4z²

c) 105 × 98 = 10290

Good luck! :)

Answer:

Step-by-step explanation:

a) Identity : (a- b)² = a²- 2ab +  b²

(t - 2)(t -2) = (t-2)²            {a = t & b =2}

                 = t² -2*t*2 + 2²

                 = t² - 4t + 4

b) (a + b)(a - b) = a² - b²

a = 3y   & y = 2z

(3y - 2z) (3y +2z)  = (3y)² - (2z)²

                             = 3²y² - 2²z²

                              = 9y² - 4z²

c) (x + a)(x + b) =x² + (a+b)x + ab

105 * 98 = (100 + 5) (100 - 2)  {here, x = 100 ; a = 5 ; b = -2}

              = 100² + (5 +(-2) ) *100 + (5)*(-2)

              = 10000 + (3)*100 - 10

              = 10000 + 300 - 10

              = 10290

Answer:

7 slices

Step-by-step explanation:

1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.

Answer:

7

Step-by-step explanation:

Using the definition

n[tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]

where n! = n(n - 1)(n - 2)..... 3 × 2 × 1

Then

7[tex]P_{1}[/tex] = [tex]\frac{7!}{(7-1)!}[/tex] = [tex]\frac{7!}{6!}[/tex] ← cancel out the multiples 6 ×5 × 4 × 3 × 2 × 1 , then

7[tex]P_{1}[/tex] = 7

Answer:

10 digress when converted to nearest digree

Answer:

m∠DAB+m∠ADC=180

115+ 29 + m∠ADB=180

m∠ADB=180 - 115 -29

= 36°

Answer:

5, 12, 19, 26, 33

Step-by-step explanation:

Using the recursive rule and a₁ = 5 , then

a₂ = a₁ + 7 = 5 + 7 = 12

a₃ = a₂ + 7 = 12 + 7 = 19

a₄ = a₃ + 7 = 19 + 7 = 26

a₅ = a₄ + 7 = 26 + 7 = 33

The first 5 terms are 5, 12, 19, 26, 33

Given:

The given equation is:

[tex]-3t^2+24t=h[/tex]

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

[tex]-3t^2+24t=h[/tex]

The height of the ball is at least 36 feet above the ground. It means [tex]h\geq 36[/tex].

[tex]-3t^2+24t\geq 36[/tex]

[tex]-3t^2+24t-36\geq 0[/tex]

[tex]-3(t^2-8t+12)\geq 0[/tex]

Splitting the middle term, we get

[tex]-3(t^2-6t-2t+12)\geq 0[/tex]

[tex]-3(t(t-6)-2(t-6))\geq 0[/tex]

[tex]-3(t-2)(t-6)\geq 0[/tex]

The critical points are:

[tex]-3(t-2)(t-6)=0[/tex]

[tex]t=2,6[/tex]

These two points divide the number line in 3 intervals [tex](-\infty,2),(2,6),(6,\infty)[/tex].

Intervals      Check point           [tex]-3(t-2)(t-6)\geq 0[/tex]           Result

[tex](-\infty,2)[/tex]               0                       [tex](-)(-)(-)=(-)<0[/tex]         False

[tex](2,6)[/tex]                    4                       [tex](-)(+)(-)=+>0[/tex]            True

[tex](6,\infty)[/tex]                  8                        [tex](-)(+)(+)=(-)<0[/tex]        False

The inequality is true for (2,6) and the sign of inequality is [tex]\geq[/tex]. So, the ball is above 36 feet between 2 to 6 seconds.

[tex]6-2=4[/tex]

Therefore, the required inequality is [tex]-3t^2+24t\geq 36[/tex] and the ball is 36 feet above for 4 seconds.

Answer:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

9514 1404 393

Answer:

  22.09 ft²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr² . . . . where r is the radius, half the diameter

The slice, at 45°, is 1/8 of the circle, so the area of the slice is ...

  A = (1/8)π(15 ft/2)² = 225π/32 ft² ≈ 22.09 ft²

Answer:

[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]

Answer:

[tex]8\sqrt{5}[/tex]

Step-by-step explanation:

[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]

 [tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]

[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]

[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]

            [tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]

Answer:

180- 110= 70

70+x+90=180

160+x=180

180-160=x

20=x

Answer:

19: 5

Step-by-step explanation:

Total fruit  is 5+10+4 = 19

fruit: pears

19: 5

Answer:

19:5

Step-by-step explanation:

5+10+4= 19

Pears= 5

Answer:The answer is 1 3/8 (D)

Step-by-step explanation:

If you added the amounts of each tick mark (which would be 13 2/8), and then subtracted it by 16, it would be 2 6/8. 2 6/8 divided by two (because we need to find the length of both of the indentical meteors) would be 1 3/8.

Now, to make sure it is 1 3/8: 13 2/8 + 1 3/8 + 1 3/8 = 16.

It is confirmed, 1 3/8 (Answer D) is the correct answer.

(Also, I took this test and got it correct :D)

Step-by-step explanation:

Answer:

y = -1/4x +2

Step-by-step explanation:

First find the slope using two point

(0,2) and (4,1)

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

   = (1-2)/(4-0)

   = -1/4

The y intercept is 2

The slope intercept form of a line is

y= mx+b where m is the slope and b is the y intercept

y = -1/4x +2

Answer:

the equation of the line is y = -1/4x +2

Step-by-step explanation:

The first step is to see where the line intercepts on the y-axis, which is 2. The next step is to see what the slope is so because it goes down 1 right 4, you find out that the slope of the line is -1/4.

Hope this helps!

Answer:

b i think

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

I'm very sure

Answer:

CAUTION HERE !!!!!

if you suggested edits are accurate the solution would be...

[tex]\frac{3p^2 - 5p+9}{6p^2}[/tex]

that is not one of your choices, but is is almost identical to choice "D"

which is different by [tex]6px^2[/tex]  vs   [tex]6p^2[/tex]

which i think is your comment ????  

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

write question in short form

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

because line AB divided the triangle into two equal halves

Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]

Divide through by 2

[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]

Complete the square by adding the square of the half of the coefficient of x to both sides:

[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]

[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]

Take the square root of both sides

[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]

Hence the value of x is 6.58m

Answer:

You didn't give me any specifics about what you want me to solve or do.

Answer:

1 = 35p

6 = 35p×6

= 240p

Therefore, 6 bagels cost 240 p

Answer:

2/3 kilometers

Step-by-step explanation:

Add the two distances together

4/9 + 2/9 = 6/9

Simplify the fraction by dividing the top and bottom by 3

2/3

Answer:

Step-by-step explanation:

(4/9) + (2/9) = 6/9 = 2/3

Answer:

a(y_2)_b(y_2) =a_b)(y_2(

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

(x-h)^2 + (y-k)^2 = r^2

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

Answer:

Choice C.

[tex]y + 1 = - 2(x - 2)[/tex]

Step-by-step explanation:

When converting to

[tex]y = mx + b[/tex]

We are left with:

[tex]y = - 2x + 3[/tex]

Which fits both the x-intercept and y-intercept.

Answer:

the last one: x^3 + 5x^2 - 9x - 45 = 0

Step-by-step explanation:

You can solve all the other ones by simple factoring and/or calculator.

Since the last one has more than 3 terms, it's likely that you'll have to use group factoring to solve it.

Answer:

-3/5

Step-by-step explanation:

Pythagorean formula :

x^2 + y^2 = r^2

(-8)^2 + (-6)^2 = r^2

64 + 36 = 100

r^2 = 100

r= 10

sin is the y coordinate over the radius :

-6/10

-3/5