The area of a rectangle is the product of its length and width. Both length and width are whole numbers. A rectangular poster has an area of 204 square inches. The width of the poster is greater than 10 inches and is prime. What is the width of the poster?

Answer:

Step-by-step explanation:

The standard form of a point slope equation of a line is expressed as shown;

y-y₀ = m(x-x₀) where;

m is the slope of the line

(x₀, y₀) is the coordinate of the point that lies in the line.

Comparing the standard equation given with the equation in question

y - 3 = 4(x + 7) to get the point on the line we will have;

y₀  = 3 and -x₀ = 7

for -x₀ = 7;

multiply both sides with a minus sign

-(-x₀) = -7

x₀ = -7

Hence the coordinate of the point required (x₀, y₀) is (-7, 3).

Answer: y=6

Step-by-step explanation:

The given number is y.

According to the question,

Step 1 . subtracts three from the number (y-3), then doubles it

i.e. Final number = 2(y-3)

Step 2 .  subtracts three again i.e. (2(y-3)-3), and doubles the number again

i.e. Final result  = 2(2(y-3)-3)

If the result is his original number y, then

2(2(y-3)-3) =y

⇒ 2(2y-6-3)=y   [ using distributive property]

⇒ 2(2y-9)=y

⇒ 2(2y)-2(9)=y [ using distributive property]

⇒ 4y -18=y

⇒ 4y -y= 18 

⇒ 3y= 18

⇒ y= 6    [Divide both sides by 3]

Hence,  y=6

Answer:

y = 6

Step-by-step explanation:

here, lets plug it into the equation.

((y - 3)2) - 3)2 = y

((6-3)2) - 3)2 = 6

6-3 = 3 * 2 = 6 - 3 = 3 * 2 = 6

Answer:

1) -2/3

2) 7/60

3) -11/10

4) 37/24

Step-by-step explanation: calculator

Answer:

1.= -2/10 2.298143

step-by-step explanation:

ansver

Answer from: Quest

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

Step-by-step explanation:

Answer:

between 7 and 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2340

Step-by-step explanation:

Formulae for sum of interior angles is 180(n-2)

Whereby n=number of sides

[tex]180(15 - 2) \\ 180(13) \\ = 2340degrees[/tex]

Answer:12

Step-by-step explanation:

In U.S. dollars, the equivalent money will be $100.74

Given is your dinner in London cost 82 British pounds

Then in U.S. dollars, the equivalent money will be equivalent to -

x = 82 pounds = 82 x 1.2286 = $100.74

x = $100.74

Therefore, in U.S. dollars, the equivalent money will be $100.74

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Answer:

28 times

Step-by-step explanation:

Create an equation where x represents the number of times the bus is used:

1.75x = 0.5x + 35

Solve for x:

1.75x = 0.5x + 35

1.25x = 35

x = 28

So, the bus has to be used 28 times for the prices to be the same.

Answer:

Step-by-step explanation:

The domain of any polynomial function, quadratics included, is "all reals."

The graph opens upward, so the y-value of the vertex is the minimum value of the range: y ≥ 2.

Answer:

60

Step-by-step explanation:

The sum of the angles of a triangle is 180

x+x+x = 180

3x= 180

Divide by 3

3x/3=180/3

x = 60

Answer:

60

Step-by-step explanation:

sum of measure of interior angles of a triangle is 180

x+x+x=180

3x=180

x=180/3

x=60

Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given that two fair dice are tossed.

Total outcomes as we toss two dice are given as:

{

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

}

Where (a, b) represents a is the outcome of the die rolled for the 1st time and b is the outcome of 2nd toss of the die.

Total number of outcomes = 36

The outcomes with sum = 7 are :

{(1, 6), (2, 5), (3, 4) , (4, 3), (5, 2), (1, 6)}

Number of outcomes = 6

Probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(sum=7) = \dfrac{6}{36}\\\Rightarrow \bold{P(sum=7) = \dfrac{1}{6}}[/tex]

Answer:

5/6 can´t be simplified

Step-by-step explanation:

Answer:

5i/6

Step-by-step explanation:

[tex]\frac{5}{6}i\\\\\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\\=\frac{5i}{6}[/tex]

Answer:

9+9

Step-by-step explanation:

9+9=18

23-5=18

Answer:

4

Step-by-step explanation:

Answer:

49.68

Step-by-step explanation:

you would just plug in 35400 for y so  you get 35400=312x+19900 and then you would subtract 19900 from both sides so you get 15500 and then divide that by 312 which is 49.68

Answer:

a. The domain of the function is {x | x is a real number greater than or equal to 0}.

Step-by-step explanation:

The graph shows

1) the domain of the function {x | x is a real number greater than or equal to 0}

The domain of the function of the graph is obtained by the x - values which range from 0-11 . Thus they are equal or greater than zero.

2) the y- intercept shows the profit that is made by selling a certain number of shirts.

3) the x- intercept shows the number of shirts sold

4) Benito increases the price at least after the profit of $25 is made because we see from the graph that there is a loss of $10 if one shirt is sold separately and the dot on the eight appears around $ 25.

Only option a is true.

Graphs are used to show the relationship between related quantities.

From the given options, the true statement is:

c. The x-intercept represents the shirts he has to sell before making a profit.

From the given graph, we have the following observations.

1. The domain of the graph is [tex]x \ge 2[/tex]

The corresponding y-values are negative for x = 0  and 1.

Because the graph represents the profit function, no value of x must correspond to a negative y-value.

Hence, (a) is false

2. It is impossible to say that his price increases, after selling 50 shirts

The y values show profit from shirts; not the price of shirts

Hence, (b) is false

3. The x-intercept indicates when he'll make a profit

The graph crosses the x-axis at x= 2.

This means that, he has to sell at least 2 shirts, before making a profit.

Hence, (c) is true

4. The y-intercept is the cost of 1 shirt

The y values show profit from shirts; not the price of shirts

Hence, (d) is false

Based on the above analysis, we can conclude that (c) is true

Read more about graphs at:

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Its conjugate is

7 - i√2

Answer:

rational numbers

Step-by-step explanation:

They cannot be negative numbers because the product of two negative numbers is positive.

They cannot be prime numbers because the product of two prime numbers is not a prime number.

The product of two complex numbers can be a complex number, but it may also be a real number.

The product of two rational numbers is always rational.

Answer: rational numbers

Answer: $51

Step-by-step explanation:

If 15% discount is applied then 85% of the price will be the left to pay.

so 85% * 60   will give you the price of the shirt after the discount.

85% * 60 = 51

Answer:

Step-by-step explanation:51.00$

Answer:

12+x goes to 19

3x+y goes to 25

4y-10 goes to 6

1/2xy goes to 14

x=7 and y=4 all you have to do is substitute for example 12+x substituted it's 12+7 then just do the math. That's it.

Answer:

42 or 4^2

hope this helps

Answer:

4^12

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

that is to say 20 -15 because it went late =5

then 2.5×5

Answer:

10.5

Step-by-step explanation:

If the recipe is designed for 4 people than you would need 6 eggs for 8 people (8 is twice as many as 4 so you need twice as many eggs.) similarly, 14 is 3.5 times as many as 4 (14/4=3.5) so you would need 3x3.5=10.5 eggs.

Not sure how that works but I hope this helped!

Answer:

Perfect square trinomial: [tex]n^2+n+\dfrac{1}{4}[/tex]

Binomial squared: [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].

Step-by-step explanation:

The given expression is [tex]n^2+n.[/tex]

Here coefficient of n is 1.

Now, find square of half of coefficient of n.

[tex]\left(\dfrac{1}{2}\times 1\right)^2=\dfrac{1}{4}[/tex]

Now, add [tex]\dfrac{1}{4}[/tex] in the expression to make it perfect square trinomial.

[tex]n^2+n+\dfrac{1}{4}[/tex]

[tex]\Rightarrow n^2+n+\left(\dfrac{1}{2}\right)^2[/tex]

[tex]\Rightarrow \left(n+\dfrac{1}{2}\right)^2[/tex]      [tex]\because (a+b)^2=a^2+2ab+b^2[/tex]

Therefore, perfect square trinomial is [tex]n^2+n+\dfrac{1}{4}[/tex] and binomial squared is [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].

Answer:

b

Step-by-step explanation:

Answer:

I think it's 4y

Step-by-step explanation:

I think it's 4y is because if y = 0 they all work but 4y which is 0 while all the others are 4

Answer:

The side of the square is 15m

The side of the triangle is 20m

Step-by-step explanation:

P square = 4s  where s is the side length

P triangle = 3 x where x is the side length

x = s+5

The perimeters are equal

4s = 3x

Replace x with s+5

4s = 3(s+5)

Distribute

4s = 3s+15

Subtract 3s from each side

4s-3s = 15

s = 15

The side of the square is 15

x =s+5

  =15+5

   = 20

The side of the triangle is 20

Answer:

[tex]\Large \boxed{\mathrm{square: 15 \ meters}} \\\\ \Large \boxed{\mathrm{triangle: 20 \ meters}}[/tex]

Step-by-step explanation:

The perimeter of a square is [tex]\sf P=4s[/tex], where s is the side length.

The perimeter of an equilateral triangle is [tex]\sf P=3a[/tex], where a is the side length.

The side length of the equilateral triangle is 5 more than the side length of the square.

[tex]\sf a = s+5[/tex]

The perimeter of the square and equilateral triangle are equal.

[tex]\sf 4s=3(s+5)[/tex]

Expanding brackets.

[tex]\sf 4s=3s+15[/tex]

Subtracting 3s from both sides.

[tex]\sf s=15[/tex]

The side length of the square is 15 meters.

[tex]\sf a=15+5 \\\\\\ a=20[/tex]

The side length of the triangle is 20 meters.

Answer:

y=x-1

is the line equation

Step-by-step explanation:

As we know that general equation of line is given by

y=mx + c

m is the slope and c is is y intercept

Know m = 1 and point (x,y) as (5,4)

So plug in the values and solve for c

4=1*(5)+c

c=-1

So equation of line is

y=x-1