Is 6.610 a rational number

Answer:

A dozen chocolate cookies cost $6

and a dozen oatmeal cookies cost $7

Step-by-step explanation:

Let's assume that cost of 1 dozen chocolate cookies = x

Let's assume that cost of 1 dozen oatmeal cookies = y

then we get equations:

9x+8y=110...(i),

and 9x+5y=89...(ii)

Solve equation (i) for x

9x+8y=110

9x=110-8y

[tex]x=\frac{110-8y}{9}[/tex]...(iii)

plug (iii) into (ii)

9x+5y=89

[tex]9\left(\frac{110-8y}{9}\right)+5y=89[/tex]

[tex]110-8y+5y=89[/tex]

[tex]9\left(\frac{110-8y}{9}\right)+5y=89[/tex]

[tex]110-3y=89[/tex]

[tex]-3y=89-110[/tex]

[tex]-3y=-21[/tex]

[tex]y=7[/tex]

plug y=7 into (iii)

[tex]x=\frac{110-8y}{9}=\frac{110-8(7)}{9}=6[/tex]

So the final answer is given by:

A dozen chocolate cookies cost $6

and a dozen oatmeal cookies cost $7

Answer:

for four copies the cost is $72

Step-by-step explanation:

52 + 5a = 24 + 12a

28 + 5a = 12a

28 = 7a

a = 4

52 + 20 = 72

for four copies the cost is $72

Answer:

$12.54

Step-by-step explanation:

First, you have to apply the sale to the original price. In this case, you would have to multiply 22 and 43% to get $9.46. Now, you have to subtract 9.46 from 22 to get 12.54.

ANSWER

[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} > 1[/tex]

EXPLANATION

The given non-linear function is a hyperbola with equation:

[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} = 1[/tex]

Since the boundary lines are dashed lines, the inequality should be either < or >.

Since the outer portion is shaded, the inequality is

[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} > 1[/tex]

Answer:

1. 48.5÷7

Step-by-step explanation:

4.85÷0.7

We can multiply both terms by 10 without changing the division problem

4.85 * 10 = 48.5

.7 * 10 = 7

48.5 ÷ 7 is the same as 4.85 ÷ .7

Answer:

No solution

Step-by-step explanation:

The given equation is [tex]3(x-8)=x+2x+7[/tex].

Kamal expanded first  and simplified the RHS to get: [tex]3x-24=3x+7[/tex]

He then subtracted 3x from both sides of the equation to get: -24=7

Since the last statement is false, it means the given equation is inconsistent.

Hence the equation has no solution.

Answer:Its No Solution i just took the Unit Test.

Step-by-step explanation:

ANSWER

A.

[tex]\frac{ {x}^{2} - 36}{ {x}^{2} - 9 } [/tex]

EXPLANATION

The rational expression is

[tex] \frac{x + 6}{x + 3} \times \frac{x - 6}{x - 3} [/tex]

Multiply the numerators and the denominators to get:

[tex] \frac{(x + 6)(x - 6)}{(x + 3)(x - 3)} [/tex]

Recall that:

[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]

We apply this difference of two squares property to get:

[tex] \frac{ {x}^{2} - {6}^{2} }{ {x}^{2} - {3}^{2} } [/tex]

[tex] \frac{ {x}^{2} - 36}{ {x}^{2} - 9 } [/tex]

Answer: Option A

Step-by-step explanation:

You need to multiply the numerator of the first fraction by the numerator of the second fraction and multiply the denominator of the first fraction by de denominator of the second fraction:

[tex]\frac{x+6}{x+3}*\frac{x-6}{x-3}[/tex]

[tex]=\frac{(x+6)(x-6)}{(x+3)(x-3)}[/tex]

By definition we know that:

[tex](a-b)(a+b)=a^2-b^2[/tex]

Therefore, you get:

[tex]=\frac{x^2-6^2}{x^2-3^2}[/tex]

[tex]=\frac{x^2-36}{x^2-9}}[/tex]

Answer:

The number of students per year increasing

Answer:

A. They are all congruent

Step-by-step explanation:

I can't seem to remember the name right now, but since X is the incenter and all of the segments are perpendicular, they are a certain kind of line segment whose name I can't remember where they are all congruent.

Answer:

A

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

The equation to solve is:

[tex]\frac{x}{1.2}=15[/tex]

This basically means, "what number" (x), divided by 1.2 would give us 15??

We can cross multiply and simply solve for x:

[tex]\frac{x}{1.2}=15\\x=1.2*15\\x=18[/tex]

Correct answer x = 18

Answer:

x=18

Step-by-step explanation:

x/1.2=15

Multiply each side by 1.2

x/1.2 * 1.2 =15 * 1.2

x = 18

Answer:

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]

We have

[tex]AD=16,\ CD=x,\ DB=9[/tex]

Substitute:

[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex]          cross multiply

[tex]x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12[/tex]

bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.

so.. .we can just use the medium and small proportions.

Check the picture below.

Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

r - radius

We have r = 11. Substitute:

[tex]C=2\pi(11)=22\pi[/tex]

[tex]\pi\approx3.14\to C\approx(22)(3.14)=69.08[/tex]

The answer is B.

Hope this helps :)

whenever you have say a multiplication of a binomial or any polynomial, you can simply multiply each term of one by the other's terms, namely

(a+b)*(c+d+e)  => a(c+d+e) + b(c+d+e), and then add like-terms.

[tex]\bf \stackrel{length}{(6x+1)}\stackrel{width}{(3x+1)}\implies 6x(3x+1)+1(3x+1)\implies (18x^2+6x)~~+~~(3x+1) \\\\\\ 18x^2+6x+3x+1\implies \stackrel{\textit{adding like-terms}}{18x^2+9x+1}[/tex]

If the probability of even is 1/4 that is a quarter. A quarter of 120 is 120/4= 30 times

Answer:

[tex]r=\frac{7}{3}[/tex]

Step-by-step explanation:

When given the equation

[tex]\frac{r}{72} =\frac{3}{9}[/tex]

We must multiply each side by 72 in order to isolate r.

[tex]r =\frac{3}{9}*\frac{7}{1} \\\\r=\frac{21}{9} \\\\r=\frac{7}{3}[/tex]

Step-by-step Answer:

There is a total of 10 coins, 5 dimes, 2 quarters and three pennies.

By picking a coin, it could be any that shows up out of the 10, so the probability of picking any coin in particular is 1 / 10.

If there are 5 dimes, the probability of picking ANY one particular dime is 1/10, so with 5, the probability of picking ANY of the five dimes is 5/10 = 1/2.

Going along the same line of thought, the probability of picking any of quarters and pennies would be 2/10+3/10 = 5/10 = 1/2 as well.

Answer: Option B

B. [tex]\frac{9}{26}[/tex]

Step-by-step explanation:

We have the following equations:

[tex]2x + \frac{4}{3}y = 1[/tex]       (1)

[tex]y -\frac{9}{13}x=9[/tex]          (2)

Let us call "a" the coefficient of the variable x in the first equation and call "b" the coefficient of the variable x in the second equation.

Then we must multiply the number "a" by a value z such that when adding [tex]az + b[/tex] the result is zero.[tex]a = 2[/tex]

[tex]b = -\frac{9}{13}[/tex]

So

[tex]2z-\frac{9}{13} = 0[/tex]

We solve the equation for z

[tex]2z=\frac{9}{13}[/tex]

[tex]z=\frac{9}{26}[/tex]

The first equation must be multiplied by a value of [tex]\frac{9}{26}[/tex]

Answer:

[tex]\boxed{27^{\circ}}[/tex]

Step-by-step explanation:

BD is a diameter of the circle, so

mDE + mAE + mAB = 180°

 63° + mAE +  90°  = 180°

          mAE + 153°  = 180°

          mAE            =    27°

The measure of arc AE is [tex]\boxed{27^{\circ}}[/tex]

Answer:

28

Step-by-step explanation:

3+5^2

3+25

28

Answer:

28

Step-by-step explanation:

5^2=5*5

5*5=25

25+3=28

Let y equal to

the total fare and x is the mile of taxi ride. So the equation is

Y = 0.55x + 1.75

Since Susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

X = 15 miles of

taxi ride

So the system of

inequality is

10 < 0.55x +

1.75

X > 2

Answer:

d = 576

Step-by-step explanation

Think of the two different speeds as belonging to 2 different cars going to the same place, taking the same route and going to the same place.

Let the time traveled by the fast car = t

Let the time traveled by the slower car = t+4

Let the rate of travel of the slow car = 36 mph

Let the rate of travel of the fast car = 48 mph

===========

d = 36*(t + 4)

d = 48 * t

Since the distance is the same, they can be equated.

48t = 36(t + 4)           Remove the brackets.

48t = 36t + 144          Subtract 36t from both sides.

48t - 36t = 144           Combine

12t = 144                     Divide by 12

t = 144/12

t = 12

Therefore the faster car takes 12 hours to get where it is going.

d = 48 * t

d = 48 * 12

d = 576

For this case we have to:

x: It is the variable that represents the quantity of paint bottles

y: It is the variable that represents the number of boxes of colored pencils

So, we have:

[tex]2x + 3.50y[/tex]

If you can not spend more than $ 42 then we have:

[tex]2x + 3.50y\leq42[/tex]

Then you can buy 10 boxes of colored pencils and 3 of paint bottles at a cost of $ 41

[tex]2 (3) +3.50 (10)\\6 + 35 = 41[/tex]

You can buy 5 boxes of colored pencils and 12 of paint bottles at a cost of $

[tex]2 (12) +3.50 (5)\\24 + 17.5 = 41.5[/tex]

You can buy 7 boxes of colored pencils and 8 of paint bottles at a cost of $

[tex]2 (8) +3.50 (7)\\16 + 24.5 = 40.5[/tex]

Answer:

[tex]2x + 3.50y\leq42[/tex]

Answer:

See the procedure

Step-by-step explanation:

we know that

To find the population density per m² of each of the above species, divide the amount of each species by the total area

so

Ferns

[tex]\frac{30}{15}=2\frac{ferns}{m^{2}}[/tex]

Grass plants

[tex]\frac{150}{15}=10\frac{grass\ plants}{m^{2}}[/tex]

Oaks Trees

[tex]\frac{6}{15}=0.4\frac{oaks\ trees}{m^{2}}[/tex]

ANSWER

[tex]y = - \frac{3}{x + 2} [/tex]

EXPLANATION

The given parent function is:

[tex]y = \frac{1}{x} [/tex]

When this function is vertically stretched by a factor of 3, then we have

[tex]y = \frac{3}{x} [/tex]

A reflection across the y-axis transforms the function to;

[tex]y = - \frac{3}{x} [/tex]

When the resulting function is shifted to the left, the transformed function becomes;

[tex]y = - \frac{3}{x + 2} [/tex]

Answer:

i think its -2

because the object increased in size but nothing else changed the slope stays the same the slope is the same as the original shape

if i am wrong i apologize  

Step-by-step explanation:

The slope of the rectangle will be the same as ABCD option (B) -2 is correct, which is the slope of the ABCD.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

Rectangle ABCD is dilated by a scale factor of 2 with the origin as the center of dilation, resulting in the image A′B′C′D′.

As we know, if dilate the rectangle by factor 2 the slope of the sides will not change.

Thus, the slope of the rectangle will be the same as ABCD option (C) -2 is correct, which is the slope of the ABCD.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ2

For the first one: 8.35, 8.357, 8.36, 8.361

For the second one: 12.013, 12.130, 12.301, 12.310

From least to greatest

Answer:  [tex]24\sqrt{3}in^2[/tex] or  [tex]41.56in^2[/tex]

Step-by-step explanation:

You can find the area of a regular hexagon with the following formula:

[tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex]

Where "s" is any side of the regular hexagon.

For this hexagon you know that the length of each side is 4 inches. Then, you must substitute [tex]s=4in[/tex] into the formula  [tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex].

Therefore, the area of this regular hexagon is:

 [tex]A_{(hexagon)}=\frac{3\sqrt{3}(4in)^2}{2}[/tex]

 [tex]A_{(hexagon)}=24\sqrt{3}in^2[/tex] or [tex]A_{(hexagon)}=41.56in^2[/tex]

Answer:

the answer is 24 square root 3

Step-by-step explanation:

Answer:60

Step-by-step explanation:40/8 =5 so that means he can walk 5 dogs per hour and if you times 5 by 12 you get 60 as your answer.

Answer:

Ken can walk 60 dogs in 12 hours.

Step-by-step explanation:

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other, the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:

a ⇒ b

c ⇒ x

So, [tex]x=\frac{c*b}{a}[/tex]

In this case it is direct magnitudes, so that the three direct rule can be applied as follows: if Ken can walk 40 dogs in 8 hours, how many Ken dogs can he walk in 12 hours?

[tex]number of dogs=\frac{12 hours*40 dogs}{8 hours}[/tex]

number of dogs= 60

So, Ken can walk 60 dogs in 12 hours.

Answer: Anything greater than 4. (5, 6, 7, etc.) Which can be represented as x>4

Step-by-step explanation: Solve this as an equation. Draw a line through the inequality line. Add 4 to the 0, so it's now x>4. The x must be greater than 4.

Answer:

The answer is 40(1.25 – t) C.

Step-by-step explanation:

That's the answer for e2020 students!!

Answer:

c

Step-by-step explanation:

big brain