Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1 key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.

Let x represent the number of key chains. Let y represent the number of thumb drives.

Which inequalities are among the constraints for this situation?

Select each correct answer.




x+y≥50

x≥5y

x≤5y

x+5y≤50

y≤25

Answer:

2/15

Step-by-step explanation:

How many marbles are in the bag

4blue + 3 green + 7 red + 1 yellow = 15 marbles

On the 1st draw:

 red/total  = 7/15

Since we keep the marble, there are only 14 marbles left

4blue + 3 green + 6 red + 1 yellow = 14

On the 2nd draw:

blue/total  = 4/14  = 2/7

To find the probability of the two draws, we multiply them together

1st draw * 2nd draw

7/15 * 2/7 = 2/15

Answer:

the ratio of the area is 3:5

Step-by-step explanation:

Find a common factor of 6 and 10 and then divide it, the common factor is 2

6 divided by 2 is 3

10 divided by 2 is 5

so your ratio area is 3:5

Hope this helps :)

Answer:

Please, see the attached files.

Step-by-step explanation:

Please, see the attached files.

Thanks.

Answer:

y > -1/6 x+1

Step-by-step explanation:

The graph line is dotted.  Dotted lines means greater than or less than.  ( <, >)

Solid lines means less than or equal to     or greater than or equal to   (≤,≥)

Since the graph is shaded above the line, that means y is greater than the line.  If it were shaded below the line,  y would be less than.

y > -1/6 x+1

Answer:

Equation in point-slope form=  [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]

Step-by-step explanation:

The given end points are B(−1,1) and C(−5,−7)

Mid point M of BC= [tex]\frac{-5-1}{2}[/tex] , [tex]\frac{-7+1}{2}[/tex]

Mid point M of BC = -3 , -3

Slope of BC =  [tex]\frac{-7-1}{-5+1}[/tex] = 2

Slope of bisector= m= [tex]\frac{-1}{2}[/tex]

Equation of perpendicular bisector : [tex]\frac{y+3}{x+3}=\frac{-1}{2}[/tex]

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

                                                          ⇒   2(y+3)= -(x+3)

                                                          ⇒  [tex]2y+x=-9[/tex]

Answer:

A = B

Step-by-step explanation:

This is because they are alternate exterior angles and they equal the same thing.

Answer: 5 hours

Step-by-step explanation:

$35 per hour is the rate

$25 is the flat fee

$200 is the maximum you can spend

⇒ 35x + 25 ≤ 200

            -25     -25

    35x          ≤ 175

  ÷35              ÷35

         x         ≤   5

Answer: x = 3

Those angle markings tell us that all three angles are the same measure (60 degrees). So this is an equilateral triangle with each side congruent to each other.

Pick 2 sides, equate the expressions, solve for x. I'm going to pick AB and AC to work with

AB = AC

6x - 3 = 3x+6

6x-3x = 6+3

3x = 9

x = 3

----------

This works with any pair of sides, such as AC and BC

AC = BC

3x+6 = 5x

6 = 5x-3x

6 = 2x

2x = 6

x = 3

----------

and let's do the last one to be complete (it's optional)

AB = BC

6x-3 = 5x

6x-5x = 3

x = 3

Either way, we get the same result each time.

[tex]\dfrac{4x^2-x}{16x^2-1}=\dfrac{x(4x-1)}{(4x)^2-1^2}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x(4x-1)}{(4x-1)(4x+1)}=\dfrac{x}{4x+1}\\\\Answer:\ \boxed{\dfrac{4x^2-x}{16x^2-1}=\dfrac{x}{4x+1}}[/tex]

By simplifying  (4x ² - x ) / (16 x² -1) we get :

= x / 4x + 1 .

The basic rules and steps for simplifying any algebraic expression are as follows:

Given equation, (4x ² - x ) / (16 x² -1)

Factorize 4x² - x ,

= x ( 4x - 1) / 16x² - 1

factorize 16x² -1,

= x (4x - 1) / (4x + 1 ) (4x - 1 )

By cancelling common factor 4x - 1,

= x / 4x + 1

Simplifying (4x ² - x ) / (16 x² -1)  =  x / 4x + 1 .

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Look at the picture.

[tex\alpha+\beta=180^o[/tex] - supplementary angles

Therefore we hve the equation:

[tex](14x-6)+(15+5x)=180\\\\(14x+5x)+(-6+15)=180\\\\19x+9=180\qquad\text{subtract 9 from both sides}\\\\19x=171\qquad\text{divide both sides by 19}\\\\\boxed{x=9}[/tex]

The sum converges to 1000.

The [tex]n[/tex]-th partial sum of the series is

[tex]S_n=\displaystyle\sum_{i=1}^n100\left(\dfrac9{10}\right)^{i-1}=100\left(1+\dfrac9{10}+\left(\dfrac9{10}\right)^2+\cdots+\left(\dfrac9{10}\right)^{n-1}\right)[/tex]

Then

[tex]\dfrac9{10}S_n=100\left(\dfrac9{10}+\left(\dfrac9{10}\right)^2+\left(\dfrac9{10}\right)^3+\cdots+\left(\dfrac9{10}\right)^n\right)[/tex]

so that

[tex]S_n-\dfrac9{10}S_n=\dfrac1{10}S_n=100\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]

[tex]\implies S_n=1000\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]

As [tex]n\to\infty[/tex], [tex]\left(\dfrac9{10}\right)^n\to0[/tex], so we're left with

[tex]\displaystyle\sum_{i=1}^\infty100\left(\dfrac9{10}\right)^{i-1}=\lim_{n\to\infty}S_n=1000[/tex]

The given infinite series is a converging geometric series with an initial term of 100 and a common ratio of 9/10. Using the formula for the sum of an infinite geometric series, we find that the sum is 1000.

To evaluate an infinite sum, or a series, we need to recognize the series structure. The given series ∑^{∞}_{i=1} 100(9/10)^{i-1} is a geometric series where the initial term (a) is 100 and the common ratio (r) is 9/10.

A geometric series converges only when the absolute value of r is less than 1, which is true in this scenario. When it converges, the sum (S) of the infinite geometric series can be calculated using the formula S = a / (1 – r).

By plugging into this formula, we get: S = 100 / (1 - 9/10) = 100 / (1/10) = 1000.

Therefore, the sum of the infinite series ∑^{∞}_{i=1} 100(9/10)^{i-1} is 1000.

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The equation tells you that Henry swims 1.6·1 = 1.6 laps when x = 1 minute.

The table tells you Larry swims 4.5 laps in 2.5 minutes. Dividing these numbers by 2.5 tells you Larry swims 4.5/2.5 = 1.8 laps in 2.5/2.5 = 1 minute.

Henry's rate is 1.6 laps per minute; Larry's rate is 1.8 laps per minute.

___

1.8 is larger than 1.6, so Larry swims faster than Henry. That is, Larry swims farther in the same amount of time, or takes less time to swim the same distance.

Answer:

Third option

Step-by-step explanation:

You are correct, right angle forms a 90°

Hope that helps

Answer:

The third option.

Step-by-step explanation:

The first option is acute becuase the angle is less that 90 degrees.

The second options is obtuse because it is more than 90 degrees.

The third option is a right angles becuase it makes an 90 degree angle.

The fourth option is also obtuse because it is more than 90 degrees.

Answer:

Step-by-step explanation:

Alright, lets get started.

The original photo size is 4 inches wide and 6 inches tall.

So, the ratio of width and height will be = [tex]\frac{4}{6}=\frac{2}{3}[/tex]

The new enlarged photo will be of the same ratio means 2:3

The width of enlarged photo is given as 12 inches.

Suppose new height of enlarged photo is H, so

[tex]\frac{12}{H}=\frac{2}{3}[/tex]

Cross multiplying

[tex]2H=36[/tex]

Dividing 2 in both sides

[tex]H=18[/tex] inches

So the height of new enlagred photo will be 18 inches.  :   Answer

Hope it will help :)

Tienes que usar la fórmula cuadrática:

(-b +/- √(b^2-4ac))/2a

Primero identificas los valores de a,b y c en kx^2-3x+2=0

K=a, b=-3, c=2

Luego sustituis en la fórmula y te queda:

(3+/-√(9-8k))/2k

Para que las raíces Sena reales se tienen que cumplir que 9-8k>=0

Answer:

Step-by-step explanation:

Therefore discriminant = b^2-4ac =0

b=-k, a=3,c=2

b^2-4ac= (-k)^2-4*3*2=0

k^2-24=0

k^2=24

k= +/- 2sqrt(6)

Answer:

197

Step-by-step explanation:

Initial population of rabbit is 139

after 2 years , rabbit population is 556

For exponential growth use y=ab^x

where a is the initial population

x is the time period

b is the growth rate, y is the final population

a= 139 is already given

when x=2, the value of y = 557

plug in all the values  in the formula and find out 'b'  

[tex]y=ab^x[/tex]

[tex]557=139(b)^2[/tex]

Divide both sides by 139

[tex]\frac{557}{139} =b^2[/tex]

take square root on both sides

b=2.00180 and b=-2.00180

growth factor cannot be negative

So b= 2.0018

The equation y=ab^x  becomes

[tex]y=139(2.0018)^x[/tex]

To find population after 6 months

1 year = 12 months

so 6 months = 0.5 years

we plug in 0.5 for x

[tex]y=139(2.0018)^{0.5}[/tex]

y= 196.66

so population after 6 months = 197

Answer:

x=5.

Step-by-step explanation:

set 7x-4=31 and solve.

Answer:

B)

X=5

Step-by-step explanation:

7x-4=31

+4 on both sides

7x=35

divide by 7 on both sides

x= 5

The expression that represents the total paid by the company is 295 + 15d.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given,

The fee for a food booth is $200 plus $5 per day.

Total cost for d days will be = 200 + 5d

The fee for a game booth is $95 plus $10 per day.

Total cost for d days will be = 95 + 10d

Total cost for d days = (200 + 5d) + (95 + 10d)

⇒ 200 + 95 + 5d + 10d

⇒ 295 + 15d

Hence "The expression that represents the total paid by the company is 295 + 15d".

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Step-by-step explanation:

We have been given the linear regression equation for a data set is y=-2.8x+70.8 where y is the temperature in degrees Fahrenheit and x is the number of hours since 8 am.

We can see that our given line is in slope-intercept form: [tex]y=mx+b[/tex], where, m = Slope of line and b = y-intercept.  

Upon comparing our given equation with slope intercept form we can see that the slope of the equation (m) is -2.8. The slope represents that temperature is dropping at a rate of 2.8 Fahrenheit per hour after 8 am.

The perimeter of any polygon is equal to the sum of the length of all sides of this polygon.

Therefore:

Answer:

So, we know that sides are 29, 15 and 4xy long. The perimeter would be

[tex]P=29+15+4xy[/tex]

Now, we sum like terms

[tex]P=44+4xy[/tex]

[tex]P=44+4xy[/tex]

Answer:

22.5

Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

[tex]s_{n}=\frac{n}{2}(2a+(n-1)d)[/tex]

Where,

Substituting these into the formula, we get the 10th partial sum to be:

[tex]s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5[/tex]

So the sum of the first 10 terms is 22.5. Third answer choice is right.

Answer is 22.5  so c :)

Answer:

Length 19.11 and width 5.89.

Step-by-step explanation:

Let the length be x and width be y metres.

Then,  using the  Pythagoras theorem:-

x^2 + y^2 =  20^2 = 400....................(1)

The perimeter = 50 so:-

2x + 2y = 50

Dividing through by 2:-

x + y = 25 .............................(2)

So  y = 25 - x

Substitute for y in  equation (1):-

x^2 + (25 - x)^2 = 400

x^2 + 625 - 50x + x^2 = 400

2x^2 - 50x + 225 = 0

x = 19.11 , 5.89,     x = 19.11 as its the length

and y = 25 - 19.11 = 5.89  ( from equation (2).

"Parameter" = Perimeter.

Look at the picture.

We have the perimeter = 50 m.

The perimeter is 2l + 2w (l - length, w - width). Therefore

2l + 2w = 50      divide both sides by 2

l + w = 25     subtract w from both sides

l = 25 - w.

Use the Pythagorean theorem:

[tex]l^2+w^2=20^2\to(25-w)^2+w^2=20^2[/tex]

Use (a - b)² = a² - 2ab + b²

[tex]25^2-2(25)(w)+w^2+w^2=400\\\\625-50w+2w^2=400\qquad\text{subtract 400 from both sides}\\\\225-50w+2w^2=0\\\\2w^2-50w+225=0[/tex]

Use quadratic formula:

[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]

We have:

[tex]a=2,\ b=-50,\ c=225[/tex]

Substitute:

[tex]\Delta=(-50)^2-4(2)(225)=2500-1000=1500\\\\\sqrt\Delta=\sqrt{1500}=\sqrt{100\cdot15}=\sqrt{100}\cdot\sqrt{15}=10\sqrt{15}\\\\w_1=\dfrac{-(-50)-10\sqrt{15}}{2(2)}=\dfrac{50-10\sqrt{15}}{4}=\dfrac{25-5\sqrt{15}}{2}\\\\w_2=\dfrac{-(-50)+10\sqrt{15}}{2(2)}=\dfrac{50+10\sqrt{15}}{4}=\dfrac{25+5\sqrt{15}}{2}[/tex]

[tex]l_1=25-w_1\\\\l_1=25-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50-25+5\sqrt{15}}{2}=\dfrac{25+5\sqrt{15}}{2}\\\\l_2=25-w_2\\\\l_2=25-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50-25-5\sqrt{15}}{2}=\dfrac{25-5\sqrt{15}}{2}[/tex]

[tex]Answer:\ \boxed{\dfrac{25+5\sqrt{15}}{2}\ m\times\dfrac{25-5\sqrt{15}}{2}\ m}[/tex]

Answer:At a company fish fry, 1/2 in attendance are employees.

Employees’ spouses are 1/3 of the attendance. What is

the percentage of the people in attendance who are not

employees or employee's spouses?

One half of X are employees.

One third of X are employee's spouses.

Step-by-step explanation:1/2 + 1/3 = 3/6 + 2/6 = 5/6

Then we subtract that fraction from one whole, or 1,

to see what fraction is left.  That is, we say

1 minus 5/6

which is

1 - 5/6

Now write 1 as 6/6

6/6 - 5/6

We get 1/6

So 1/6 is left.  Now we need to make that into

a percent by multiplying it by 100 and tacking on a "%"

1/6 × 100

1/6 × 100/1

100/6

50/3

16 2/3 %

So 16 2/3 % of the people in

attendance are neither employees

nor employee's spouses.

Now let's check:

1/2 are employees.  That's 50%

1/3 are wmployee's spouses. That's 33 1/3%

15 2/3 % are neither employees nor employee's spouses.

Add them up

50     %

33 1/3 %

16 2/3 %

--------

99 3/3 %

And 99 3/3% = 100%

16.67% of the people in attendance are neither employees nor their spouses.

To calculate the percentage of people who are neither employees nor their spouses, we need to consider the total attendance as 100%. Since half of the attendance, i.e., 50%, are employees and one third, i.e., about 33.33%, are spouses, we add these figures to find the combined percentage of employees and spouses. We then subtract this combined percentage from 100% to find the percentage of people who are neither.

Combined percentage of employees and spouses: 50% (employees) + 33.33% (spouses) = 83.33%

Now, to find the percentage who are neither employees nor spouses, we subtract the combined percentage from 100%:

Percentage of neither: 100% - 83.33% = 16.67%

Therefore, 16.67% of the people in attendance are neither employees nor their spouses.

Answer:

The correct option is C.

Step-by-step explanation:

Let triangle ABC and XYZ are similar.

If two triangles are similar, then ratio of their corresponding sides are same.

Since ABC and XYZ are similar, therefore sides AB, BC and AC are corresponding to the sides XY, YZ and XZ respectively.

[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]

From the above equation we can conclude that

[tex]\frac{BC}{YZ}\neq \frac{AC}{YX}[/tex]

[tex]\frac{BC}{YZ}\neq \frac{BA}{XZ}[/tex]

[tex]\frac{AC}{XZ}\neq \frac{BA}{XZ}[/tex]

Therefore option A,B and D are incorrect.

Answer:  BC/YZ = AC/XZ

Step-by-step explanation:

Remember the end letters need to be the same. So if you look at your choices this is the only one that is in order   BC  AC

                                                                         YZ   XZ

took the test

E = 360/n

is the formula to use when computing the exterior angle E for any regular polygon with n sides. For an octagon, we have 8 sides meaning n = 8 leads to

E = 360/n = 360/8 = 45

The exterior angle of a regular octagon is 45 degrees

Repeat for n = 6 (hexagon) to get E = 360/n = 360/6 = 60. A regular hexagon has exterior angles of 60 degrees each.

We see that the regular octagon's exterior angles (45) are smaller than the regular hexagon's exterior angles (60)

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

Answer: less than (choice B)

Final answer:

The measure of each exterior angle of a regular octagon is less than the measure of each exterior angle of a regular hexagon since the sum of the exterior angles is always 360 degrees and there are more sides on an octagon to divide this sum. The correct option is: B- Less than

Explanation:

To determine whether the measure of each exterior angle of a regular octagon is greater than, less than, or equal to the measure of each exterior angle of a regular hexagon, we must first understand how to calculate the measure of an exterior angle in a regular polygon. The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides. Therefore, to find the measure of a single exterior angle, you would divide 360 degrees by the number of sides the polygon has.

For a regular hexagon, which has six sides, the exterior angle is calculated as 360 ÷ 6, which equals 60 degrees. For a regular octagon, which has eight sides, the exterior angle is calculated as 360 ÷ 8, which equals 45 degrees.

Comparing the two measurements, we can clearly see that the measure of each exterior angle of a regular octagon is less than the measure of each exterior angle of a regular hexagon.

Answer:

Add [tex]-x^2+2xy[/tex]

Step-by-step explanation:

The polynomial [tex]x^2+y^2-2xy+1[/tex] can be added to eliminate the x terms by adding the additive inverse. We add [tex]-x^2+2xy[/tex] which has the inverse sign value of the polynomial terms.

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

[tex]x^2-x^2+y^2-2xy+2xy+1[/tex]

When we simplify, this leaves [tex]y^2+1[/tex] without an x term.

Answer:

-x^2+2xy

Step-by-step explanation:

x^2 + y^2 -2xy + 1 +something  = y^2 +1

This will get rid of the x and x^2 terms

Subtract y^2 from each  side

x^2 + y^2 -y^2 -2xy + 1 +something  = y^2-y^2 +1

x^2 -2xy+1 +something  = 1

Subtract 1 from each side

x^2 -2xy+1 -1+something  = 1-1

x^2 -2xy+something  = 0

Subtract x^2 from each side

x^2 -x^2 -2xy+something  = 0-x^2

-2xy+something  = -x^2

Add 2xy to each side

2xy -2xy+something  = -x^2+2xy

something = -x^2+2xy

We need to add  -x^2+2xy

Remember a binomial is 2 terms

Answer:

The original price was $26.40

Step-by-step explanation:

Set up the equation(s) for this situation. The total price was for six shovels, three of which were discounted by 33.3% from the initially marked-down price X:

$102 = 3 * (X-$6) + 3 * ((X-$6) * (2/3))

102 = 3X - 18 + 3 * (2/3) * X - 3 * (2/3) * 6

102 = 5X - 30

X = $26.40