Here is a map of a town.
It has a scale of 2 cm to 7 km.
A centimetre ruler is shown on the map.
What is the real-life distance between the ice rink and the theatre?

Let x = length and y = width

You would have 2 lengths, so 2x and 3 widths, so 3y

Those need to equal total length of fence:

2x + 3y = 1200

The 3 widths would equal total fence minus the 2 lengths:

3Y = 1200-2x

Solve for y: y = 400 -2/3x

Area = length x width = xy. Replace y :

Area = x(400-2/3x) = 400x-2/3x^2

Differentiate:

400-4x/3 =0

4x/3 = 400

4x = 1200

X = 300

Y = 400-2/3(300) = 200

The dimension would be 300 ft x 200 ft

Answer:

There were 12 babies and 4 adults

Answer:

D

Step-by-step explanation:

Using the changing base formula, log base 2 raised to 7 can be written as log7/log2

The correct answer is D. log(7) / log(2).

To find the equivalent of log2(7), you can use the change of base formula for logarithms.

The change of base formula states that log base a of b is equal to log base c of b divided by log base c of a.

In this case, we want to find the equivalent of log2(7), so we can use the change of base formula with base 10 as follows:

log2(7) = log(7) / log(2)

Therefore, the correct answer is D. log(7) / log(2).

Learn more about logarithms click;

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Answer:

[tex]2.46\times 10^5[/tex]

Step-by-step explanation:

[tex]9.78 \times 10^5 - 732,000\\= 9.78 \times 10^5 - 7.32 000\times 10^5\\= 9.78 \times 10^5 - 7.32\times 10^5\\= 2.46\times 10^5[/tex]

Answer: 48 miles

Because north is straight from the starting point and you traveled 48 miles north so 48

Answer:

50 miles

Step-by-step explanation:

If you draw the shape

you'll roughly get the above mentioned one..

so it's a right angle triangle now

using Pythagoras relationship

48^2+14^2=x^2

2304+196=x^2

2500=x^2

x= 50

straight line distance aka displacement is 50 miles

Answer: 11:15 AM

Step-by-step explanation:

9:00 plus an hour and 15 minutes (75 minutes) makes it 10:15.  Then bake for an hour (60 minutes), makes it 11:15

Answer:

what she saisddddddddddd

Step-by-step explanation:

Answer:

(x+4)

Step-by-step explanation:

Since area is width times length, you can just factor the area to get the width and length

You factor to get (x+4)(x+7)

Since (x+7) is the length, (x+4) must be the width

Answer:

(x + 4) m

Step-by-step explanation:

[tex]Area \: of \: rectangle = length \times width \\ \\ width = \frac{Area \: of \: rectangle}{length} \\ \\ = \frac{ {x}^{2} + 11x + 28 }{x + 7} \\ \\ = \frac{ {x}^{2} + 7x + 4x + 28}{x + 7} \\ \\ = \frac{ x({x} + 7) + 4(x + 7)}{x + 7} \\ \\ = \frac{ ({x} + 7) (x + 4)}{x + 7} \\ \\ = (x + 4) \: m \\ \\ \red{ \boxed{\bold {\therefore \: width \: = (x + 4) \: m}}} [/tex]

Answer:

The roots (r) or the Zeros ( other name ) = -11 and -14

Step-by-step explanation:

Post in comments if u need step by step and Ill give to u :)

Answer: likely, pls mark me as brainliest if it helped u

Step-by-step explanation:

hcglnlkl gzfog dufkbicfhpffkgdhjdk

Answer:

(9x-2)(9x+2)

Step-by-step explanation:

81x^2 - 4

Rewriting as

(9x)^2 - 2^2

This is the difference of squares a^2 - b^2 = (a-b)(a+b)

(9x-2)(9x+2)

Answer:

(9x + 2)(9x - 2)

Step-by-step explanation:

To factor this expression, you can use a neat trick called difference of squares.

Difference of squares tells us:

a^2-b^2 = (a+b)(a-b)

Now look at the expression we have here:

81x^2 - 4

well, we know that 81 is 9^2, x^2 is literally x^2, and 4 is 2^2

So we can rewrite this as:

(9x)^2 - 2^2

By difference of squares that gives us:

(9x + 2)(9x - 2)

Answer:

The correct option is (B) 69.7%.

Step-by-step explanation:

The table provided represents the probabilities of a positive response to two government programs from citizens in eight cities.

The probabilities mentioned in the table are conditional probabilities, i.e. the probability of a positive response for program 1, given that the individual is from city x.

The probability a positive response for program 1 from an individual from Houston is 69.7%.

Then the conditional probability of a positive response for program 1, given that the individual is from Houston is 69.7%.

Thus, the correct option is (B).

Answer:

1. We'll be looking at g(x) and from the table when x = 3,000 Angela owes 44,600 dollars.

2. f(3) = 2000

   g(2000) = 45,000

3. g(3,500) = 44,400 and f(6) = 3,500 so the answer is 44,400 - 3,500 = 40,900.

4. From the table when f(x) = 2,500, x = 4.

5. From the table when g(x) = 44,200, x = 4,000.

Answer:

1. when f(x) = $ 3000 the loan still 44,600

2. f(3) means her saving in 3rd month. so f(3) is 2000 then g(2000) is 45000

3. g(3500) - f(6) = 44400 - 3500 = 40,900

4. based on table f(x), x is 4

5. based on table g(x) (the right one), x is 4000

Answer:

The correct answer is "B", we first need to add 40 to both sides of the equation.

Step-by-step explanation:

Since we have the following quadratic equation:

[tex]x^2 - 40 = 0[/tex]

The first step to solve it is to isolate the independent variable, "x". To do that we must add +40 on both sides of the equation, since that way the "-40" on the left will be gone in a way that maintains the validity of the equation as shown below:

[tex]x^2 - 40 = 0\\x^2 - 40 + 40 = 40\\x^2 = 40[/tex]

After this step we take the square root of both sides:

[tex]\sqrt{x^2} = \sqrt{40}\\x = \pm \sqrt{40}\\x = \pm \sqrt{4*10}\\x = \pm 2*\sqrt{10}[/tex]

Therefore the correct answer is "B".

Answer:

20

Step-by-step explanation:

Let Kayla's age be k.

Let Isaac's age be a.

Kayla is 6 years older than Raoul. This means that:

k = y + 6

lsaac is 4 years younger than Raoul. This means that:

a = y - 4

y = 12

=> k = 12 + 6 = 18

and

a = 12 - 4 = 8

The sun of Raoul's age and Isaac's age is:

12 + 8 = 20

Answer:

It is A)

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Answer: The answer is C

Answer:

476 Pi cm^2

Step-by-step explanation:

The surface area of a cone is given by the formula:

● Sa = Pi× r^2 + Pi×r×l

r is the radius and l is the slant heigth.

■■■■■■■■■■■■■■■■■■■■■■■■■■

We are given that:

● r = 14 cm

● l = 20 cm

Let's calculate Sa

● Sa = Pi×14^2 + Pi × 14 × 20

● Sa = 476 Pi cm^2

Answer:

PR is 9 units long.

Step-by-step explanation:

You can see that triangle YXZ and QPR are similar because they have 2 angles in common. This means that they have a scale factor between them. The scale factor between triangle YXZ and QPR happens to be 1/3, as you can see, side QP is 1/3 times of corresponding side YX. To find PR, you just need to check how long its corresponding side is. XZ is 27 units long, and 1/3 of 27 is 9 units.

Answer: 0.25 or 1/4

Step-by-step explanation:

1/2*2 = 1/2^2 = 1/4

Answer: an orchestra seating ticket cost $10

A mezzanine seating ticket cost $8

A balcony seating ticket cost $7

Step-by-step explanation:

Let x represent the price of an orchestra seating ticket.

Let y represent the price of a mezzanine seating ticket.

Let z represent the price of a balcony seating ticket.

The orchestra tickets cost $2 more than the mezzanine tickets. It means that

x = y + 2- - - - - - - 1

The mezzanine tickets cost $1 more than the balcony tickets. It means that

y = z + 1 - - - - - - -2

Twice the cost of an orchestra ticket is $1 less than 3 times the cost of a balcony ticket. It means that

2x = 3z - 1- - - - - - - - -3

Substituting equation 2 into equation 1, it becomes

x = z + 1 + 2

x = z + 3 - - - - - - - - - -4

Substituting equation 4 into equation 3, it becomes

2(z + 3) = 3z - 1

2z + 6 = 3z - 1

3z - 2z = 6 + 1

z = 7

x = z + 3 = 7 + 3

x = 10

y = z + 1 = 7 + 1

y = 8

Answer:

CSK = Chennai Super Kings

KKR = Kolkata Knight Riders

Answer:

324cm^3

Step-by-step explanation:

The formula for calculating volume of a triangular prism is 1/2× bhl (b : base, h : height, l : length)

1/2 × 6 × 9 × 12 = 324cm^3

This is the expression your question creates 13-6•x

Answer:

This can be written as (13-6)n. Hope this helps!

Step-by-step explanation:

Answer:

[tex]m=18[/tex]

Step-by-step explanation:

The equation given is [tex]D=\frac{m}{v}[/tex]

and also we have that [tex]D=\frac{6}{7}[/tex], thus:

[tex]\frac{6}{7}=\frac{m}{v}[/tex]

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

I think the question is missing which variable is defined as [tex]=m+3[/tex], so I will solve for [tex]v=m+3[/tex] since is the only other variable in the equation.

substituting [tex]v=m+3[/tex]  into [tex]\frac{6}{7}=\frac{m}{v}[/tex]:

[tex]\frac{6}{7}=\frac{m}{m+3}[/tex]

and we solve for m:

[tex](m+3)(6)=7m\\6m+18=7m\\18=7m-6m\\18=m[/tex]

m is equal to 18.

Answer:

6.49

Step-by-step explanation:

2.49 + 0.25(16)

2.49+4

6.49

Answer:

$6.49

Step-by-step explanation:

1 lb = 16 oz

His salad weighs 1 lb, 8 ounces which is the same as 16 ounces plus 8 ounces.

8 ounces cost $2.49

His salad weighs 16 ounces more than 8 ounces, so in addition to the $2.49, he needs to pay $0.25 per ounce for 16 extra ounces.

16 * 0.25 = $4.00

Total cost = $2.49 + $4.00 = $6.49

Answer:

V = 729 cm³

Step-by-step explanation:

side length a = 9 cm

face diagonal f = 12.727922061358 cm

solid diagonal d = 15.58845726812 cm

surface area S = 486 cm²

volume V = 729 cm³

Formula: V=a³

Answer:

Total paper required = 165 cm²

Step-by-step explanation:

Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid

Surface area of the rectangular prism = 2(lb + bh + hl)

(here l, b, h are the length, width and height respectively)

                                                               = 2(5×5 + 5×4 + 4×5)

                                                               = 2(25 + 20 + 20)

                                                               = 2×65

                                                               = 130 cm²

Area of the top of the prism = (side)²

                                              = 5²

                                              = 25 cm²

Lateral area of the square pyramid = 4 × Area of one lateral side

                                                          = 4 × [tex][\frac{1}{2}(\text{Base})(\text{Height})][/tex]

                                                          = 4 × [tex][\frac{1}{2}(5)(6)][/tex]

                                                          = 60 cm²

Total paper required = (130 - 25) + 60

                                   = 105 + 60

                                   = 165 cm²

Answer:

[tex]v=-3i+5j[/tex]

Step-by-step explanation:

In the representation of a vector we must take into account the coordinate in which its tip is located.

In this case the vector tip is at [tex](-3,5)[/tex] and starts at the coordinate origin.

When expressing a vector in the following form:

[tex]v = ai + bj[/tex]

the numbers [tex]a[/tex] and [tex]b[/tex] represent the components of the vector, that is, the vector measurements when projecting it onto the axes.

The number that accompanies i ([tex]a[/tex]) is the component of the vector on the x-axis, in this case it is 3 units:

[tex]a = -3[/tex]

And the number that accompanies j ([tex]b[/tex]) is the component of the vector in the y-axis, in this case 5:

[tex]b = 5[/tex]

thus, the result is is:

[tex]v=-3i+5j[/tex]