The solution of the equation 2d - 6 = 5 is _____.

Answers

Answer 1

Answer: If you would like to solve the equation 2 * d - 6 = 5, you can do this using the following steps:

2 * d - 6 = 5
2 * d = 5 + 6
2 * d = 11 /2
d = 11/2
d = 5 1/2

The correct result would be 5 1/2.

Answer 2

Answer: $2d-6=5\n\nAdd\ 6\ on\ both\ sides.\n\n2d=11\n\nDivide\ by\ 2\ on\ both\ sides.\n\nd= (11)/(2)\n\nd=5(1)/(2)$

$\sf\ Answer:\ {\boxed{d=5(1)/(2)}}$

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Write the equation of each line in the indicated form 1. Standard form. Slope=8/3;(-2,0)

2. Point-slope form (-5,6) and(3,-10)

Answers

1. standard form is y=mx+b so I will use point slope to start
y-0=8/3(x+2), y=(8/3)x+(16/3)
2.Must solve for slope first, (y2-y1)/(x2-x1), -10--5/3-6= -5/-3= 5/3
so slope is 5/3, point slope is y-y1=m(x-x1), y-6=5/3(x+5)

Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Answers

It's a geometric sequence.

$300, 150, 75,... \n \n a_1=300 \n r=(a_2)/(a_1)=(150)/(300)=(1)/(2) \n \n S_n=(a_1 (1-r^n))/(1-r) \n \Downarrow \n S_5=(300(1-((1)/(2))^5))/(1-(1)/(2))=(300(1-(1)/(32)))/((1)/(2))=(300 * (31)/(32))/((1)/(2))=(75 * (31)/(8))/((1)/(2))=((2325)/(8))/((1)/(2))=(2325)/(8) * 2= \n=(2325)/(4)=581 (1)/(4)=581.25$

The answer is 581.25.

we have that

$300 + 150 + 75 +...$

Let

$a1=300\n a2=150\n a3=75$

we know that

$(a2)/(a1) =(150)/(300) \n\n (a2)/(a1)=0.5 \n \n a2=a1*0.50$

$(a3)/(a2) =(75)/(150) \n\n (a3)/(a2)=0.5 \n \n a3=a2*0.50$

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\n S5=300+150+75+37.5+18.75\n S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=(a_1 (1-r^n))/(1-r) \n\na_1=300 \n r=(1)/(2)\n\n S_5=(300(1-((1)/(2))^5))/(1-(1)/(2))\n\n=(300(1-(1)/(32)))/((1)/(2))\n\n=(300 * (31)/(32))/((1)/(2))\n\n=(75 * (31)/(8))/((1)/(2))\n\n=((2325)/(8))/((1)/(2))\n\n=(2325)/(8) * 2\n\n=(2325)/(4)\n\n=581 (1)/(4)\n\n=581.25$

therefore

the answer is

$581.25$

If its £18.75 per square metre of clear plastic how much will it cost to cover 2x notice boards 1 metre high and 1 metre wide ?

Answers

just double 18.75 because the total area needed to cover is 2 square meters

For the function f(x) = -2(x + 3)^2 -1, identify the vertex, domain, and range. A.) The vertex is (3, -1), the domain is all real numbers, and the range is y ≥ -1. B.) The vertex is (3, -1), the domain is all real numbers, and the range is y ≤ -1. C.) The vertex is (-3, -1), the domain is all real numbers, and the range is y ≤ -1. D.) The vertex is (-3, -1), the domain is all real numbers, and the range is y ≥ -1

Answers

ok so domain is all allowed numbers look at deonomenator and don't allow any numbers that will make it zero none that means domain=all real numbers vertex in form y=a(x-h)^2+k (h,k)=vertex we have y=-2(x+3)^2-1 h=-3 k=-1 vertex=(-3,-1) range the vertex opens down so max is y=-1 y≤-1 domain is all real vertex is (-3,-1) y≤-1 C

Which is a subset of {1, 2, 4, 5, 6}?{0, 1, 2}
{3, 4}
{5, 6, 7}
{2, 6}

Answers

{2,6} is a subset of set {1, 2, 4, 5, 6} which is correct option (D).

What is a set?

A set is defined as a group of objects in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent parts can be included in anything.

What is a Subset?

A subset is defined as part of a given set subset (another set or the same set). The set notation to represent a set A as a subset of set B is written as A ⊆ B.

Given set as :

{1, 2, 4, 5, 6}

There are 2⁵ = 32 subsets

(which you know because there are 5 numbers in the set).

{},{1},{2},,{ 4},{ 5},{ 6},

{1,2},{1, 4},{1, 5},{1, 6}

{2, 4},{2, 5},{2, 6},

{ 4, 5},{ 4, 6},{ 5, 6},

,{1,2, 4},{1,2, 5},{1,2, 6}

,{1, 4, 5},{1, 4, 6},{1, 5, 6}

,{2, 4, 5},{2, 4, 6},{2, 5, 6}

,{ 4, 5, 6} {1,2, 4, 5, 6},