Two students are reading a novel. Ashley reads 10 pages per day. Carly reads 8 pages per day , but she started early and is already on page 40. Write a system of equations to reprsent the situation, using d for days and p for pages.

Answer:

Step-by-step explanation:

36.7

Applying the Heron's formula, the area of the parallelogram = 36.7 square units.

Heron's Formula = √[s(s - a)(s - b)(s - c)], where:

A diagonal of a parallelogram cuts a parallelogram into two equal triangles.

Thus, we have two equal triangles in the parallelogram given.

Area of the parallelogram = 2(area of triangle)

Find the area of one triangle using the Heron's formula:

a = 5

b = 8

c = 11

s = (5 + 8 + 11)/2 = 12

Area of one triangle = √[12(12 - 5)(12 - 8)(12 - 11)]

= √[12(7)(4)(1)]

= √336

= 18.33 sq. units.

Therefore, area of the parallelogram = 2(18.33) = 36.7 square units.

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Answer:

The normal price is $90

Step-by-step explanation:

Let

x-----> the normal price

we know that

100%-10%=90%=90/100=0.90

so

0.90x=$81

Solve for x

x=$81/0.90

x=$90

Answer:

Moderate Negative Correlation

Step-by-step explanation:

I got 100% on Homework...

The strength of the correlation between the hours spent exercising and the hours spent playing video games moderate negative relationship.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

If Irina spends more time playing video games she will have less time to spend exercising, therefore, we can conclude that if she plays more video games the time spent on exercising will be less and vice versa. Thus, there exists a negative correlation coefficient between the two variables.

Since in a day there is limited time available, therefore, if time is spent on video games, there will be very less or no time left for exercising, hence, the relationship between the two is moderate and dependent.

Hence, the strength of the correlation between the hours spent exercising and the hours spent playing video games moderate negative relationship.

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Answer:

Either x = 2 or y = 6, depending on the original line

Step-by-step explanation:

So, if the original line is horizontal, our new line is vertical, and all vertical lines in a graph is x = some number. To pass through the point (2, 6), x has to equal 2, since the point's x-coordinate is 2.

On the other hand, if the original line is vertical, our new line is horizontal, which is y = some number. Our point's y-coordinate is 6, so our line should be that y = 6.

It's A, x=2. I hope i helped!!

Answer:

Step-by-step explanation:

A regular polygon is defined to be a convex polygon with congruent sides and congruent angles.

Convex means that all interior angles are less than 180 degrees.  However, if all interior angles are equal, the polygon has to be convex.

Final answer:

A regular polygon is a convex shape with sides and angles that are all congruent, exemplified by the faces of an icosahedron or an equilateral triangle.

Explanation:

A regular polygon is defined to be a convex polygon with congruent sides and congruent angles. This means that all sides are the same length and all interior angles are equal in measure, which contributes to the polygon's symmetry. As an example from three-dimensional geometry, an icosahedron is a symmetrical, solid shape with 20 faces, each of which is an equilateral triangle.

Answer:

4.4 is the answer hope it help you

Answer:

4.4 is the answer round it to the nearest ten

Answer:

[tex]\frac{inches}{minute}[/tex]

Change the feet to minutes by multiplying by 12, and change the hour to minutes.

Speedy: [tex]\frac{240}{60}[/tex]

Slowpoke: [tex]\frac{80}{30}[/tex]

Cleo: [tex]\frac{96}{10}[/tex]

Speedy is the fastest.

[tex]\frac{feet}{hour}[/tex]

Change minutes to feet by dividing and change the minutes to hours by multiplying.

Hope this helps and have a great day!!!

[tex]Sofia[/tex]

The fully simplified product of (b-2c)(-3bc) has 2 terms and a degree of 3. The number of negative terms in the simplified product depends on the values of b and c, which are not provided.

When simplifying the expression (b-2c)(-3bc), we use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis. However, since the two terms -2c and -3bc will multiply to produce a term with a higher degree than b times -3bc, the simplified expression does not have 4 terms, but rather only 2 terms. The correct simplified form is -3b^2c + 6c^2. There are two terms, and the highest degree of any term, which is the sum of the exponents of the variables in that term, is 3 (b^2c having degree 3, since 2+1=3).

Therefore, the correct statements about the fully simplified product of (b-2c)(-3bc) are:

Answer:

  D.  (x + 7, y - 2)

Step-by-step explanation:

To get back the original after translating left 7 and up 2, you must translate right 7 and down 2. The transformation of choice D does that.

Answer:

5/16

Step-by-step explanation:

If Vanessa pulls out a 2 from the first bag, then the possibilities based on the second bag are:

X = 2*3 = 6

X = 2*4 = 8

X = 2*5 = 10

X = 2*6 = 12

Repeat this for the other values from the first bag.  If she pulls a 3, the possibilities are:

X = 3*3 = 9

X = 3*4 = 12

X = 3*5 = 15

X = 3*6 = 18

If she pulls a 4:

X = 4*3 = 12

X = 4*4 = 16

X = 4*5 = 20

X = 4*6 = 24

And finally, if she pulls a 5:

X = 5*3 = 15

X = 5*4 = 20

X = 5*5 = 25

X = 5*6 = 30

Of the 16 total combinations, 5 are greater than or equal to 12 and less than or equal to 15.

Therefore, P(12 ≤ X ≤ 15) = 5/16.

Answer:

4750

Step-by-step explanation:

475000/100 = 4750

4750 * 6 = 28500

4750 * 5 = 23750

28500 - 23750 = 4750

Answer:

4750

explanation:

Answer:

x = 12.5

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos ⁡θ= base/hypotenuse

cos⁡ 28=11/x

x=11/cos⁡28  

x=11/0.8829

x=12.45

Rounding off to nearest 10

x=12.5

Answer:

A) The equation in factored form is (4t + 1)(t - 2) = 0

B) The solutions of the equation are t = -1/4 and t = 2

C) It will take 2 seconds for the rocket to hit the ground

Step-by-step explanation:

* Lets study the information in the problem

- A child launches a toy rocket from the top of a slide

- The equation of the motion is -16² + 28t + 8 = 0, where t is the time

 of rocket to hit the ground

* Now lets solve the problem

- At first simplify the equation

∵ -16t² + 28t + 8 = 0

∵ Al the terms have a factor 4

- Divide all terms by 4

∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1

∴ 4t² - 7t - 2 = 0

- Lets factorize

∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket

∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket

∵ 4t + -2 = -8t ⇒ product of the extremes

∵ 1t × 1 = 1t ⇒ product of means

∵ -8t + 1t = -7t ⇒ middle term

∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)

∴ (4t + 1)(t - 2) = 0

A) The equation in factored form is (4t + 1)(t - 2) = 0

- Lets use the zero product property to solve the equation

∵ (4t + 1)(t - 2) = 0

- Equate each factor by 0

∵ 4t + 1 = 0 ⇒ subtract 1 from both sides

∴ 4t = -1 ⇒ divide both sides by 4

∴ t = -1/4

OR

∵ t - 2 = 0 ⇒ add 2 for both sides

∴ t = 2

B) The solutions of the equation are t = -1/4 and t = 2

C) We can not accept the answer t = -1/4 because there is no negative

    value for the time

∴ The answer is t = 2 only

* It will take 2 seconds for the rocket to hit the ground

Answer:

42

Step-by-step explanation:

The permutation for that set of data looks like this:

[tex]_{7}P_{2}[/tex]

The formula looks like this:

[tex]_{7}P_{2}=\frac{7!}{(7-2)!}[/tex]

which of course simplifies to

[tex]_{7}P_{2}=\frac{7!}{5!}[/tex]

which further simplifies down to the most basic simplification:

[tex]_{7}P_{2}=7*6[/tex]

since the 5*4*3*2*1 that goes after the 6 in the numerator cancels with the 5*4*3*2*1 in the denominator.

You could also check this on your calculator.  Hit "math", then arrow over to "Prob" and it's under nPr.

Explanation:

The altitude CH divides triangle ABC into similar triangles:

ΔABC ~ ΔACH ~ ΔCBH

Angle bisector AL divides the triangle(s) into proportional parts:

BL/BA = CL/CA

HD/HA = CD/CA

Of course, the Pythagorean theorem applies to the sides of each right triangle:

AH^2 +CH^2 = AC^2

DH^2 +AH^2 = AD^2

LC^2 + AC^2 = LA^2

AC^2 +BC^2 = AB^2

And segment lengths sum:

HD +DC = HC

AD +DL = AL

AH +HB = AB

CL +LB = CB

Solving the problem involves picking the relations that let you find something you don't know from the things you do know. You keep going this way until the whole geometry is solved (or, at least, the parts you care about).

___

We can use the Pythagorean theorem to find AH right away, since we already know AD and DH.

DH^2 +AH^2 = AD^2

4^2 + AH^2 = 8^2 . . . . . . . substitute known values

AH^2 = 64 -16 = 48 . . . . . . subtract 16

AH = 4√3 . . . . . . . . . . . . . . take the square root

Now, we can use this with the angle bisector relation to tell us how CD and CA are related.

HD/HA = CD/CA

4/(4√3) = CD/CA . . . . . substitute known values

CA = CD·√3 . . . . . . . . . cross multiply and simplify

Using the sum of lengths equation, we have ...

CH = HD +CD

CH = 4 + CD

From the Pythagorean theorem ...

AH^2 +CH^2 = AC^2

(4√3)^2 + (4 +CD)^2 = (CD√3)^2 . . . . . substitute known values

48 + (16 +8·CD +CD^2) = 3·CD^2 . . . . . simplify a bit

2·CD^2 -8·CD -64 = 0 . . . . . . . . . . . . . . . put the quadratic into standard form

2(CD -8)(CD +4) = 0 . . . . . . . . . . . . . . . . factor

CD = 8 . . . . . only the positive solution is useful here

Now, we know ...

∆ADC is isosceles, so ∠ACH = ∠CAD = ∠DAH = ∠CBA

CH = 8+4 = 12

AC = 8√3 . . . . . = 2·AH

Then by similar triangles, ...

AB = 2·AC = 16√3

BC = AC·√3 = 24

f(x)+g(x)

f(x)=3x+2 and g(x)=4x

You have:

3x +2 + 4x

Combine like terms:

3x +4x = 7x

The answer becomes 7x +2

The correct option will be No, she made an error in step 2, she should have found y=0.5

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been Given the system of linear equations:

-3x + 2y = 8 --- eqn. 1

3x + 2y = -6 ---eqn. 1

First add both equations together

4y = 2

Now, divide both sides by 4:

y = 2/4

y = 0.5

Thus Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect due to an error has occurred here.

Therefore, the error made by Kaitlyn while solving the equations is in step 2. Her solution will be incorrect.

The correct option will be: No

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Answer:

The correct answer is letter C

Answer:

44.72 feet

Step-by-step explanation:

Assuming that the bottom of the tree and the ground makes a right triangle-- use the Pythagorean theorem.

x^2 + 40^2 = 60^2

x^2 + 1,600 = 3,600

x^2 = 2,000

x = 44.72 ft

Answer:

C

Step-by-step explanation:

On edge

Answer:

  see below

Step-by-step explanation:

The graph extends to the left more or less horizontally, approaching the line y=3. The only choice that expresses that is the third one.

27 dimes for my answer

hope it works

Answer:0.001

x=the number of workers taking the bus to work

p= probability of success =(15/100) = 0.15

q= probability of failure =1- p = 0.85

P(X=6) = 10C6(0.15)^6(0.85)^4

            = 0.001

Answer: 0.001

Step-by-step explanation:

Binomial probability formula :

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of exactly x successes in n trials.

Given : The probability of city workers take the bus to work =15%=0.15

The sample size :n= 10

Now, the probability that exactly 6 put of 10 workers take the bus to work :-

[tex]P(6)=^{10}C_6(0.15)^{6}(1-0.15)^{10-6}\\\\=\dfrac{10!}{6!(10-6)!}(0.15)^6(0.85)^4\\\\=0.0012486552627\approx0.001[/tex]

Therefore , the probability that exactly 6 workers take the bus to work = 0.001

Answer:

The first choice is the correct one

Step-by-step explanation:

That funny symbol is the Greek symbol for "the sum of".  Sum means to add, so whatever numbers we have we are definitely adding them.  The index goes from a starting point of 1 up to 4.  That's those 2 numbers, one below and one above the sum symbol.  The "n" in 7/n is what we are replacing with each number starting at 1 and ending at 4.  7/1, 7/2, 7/3, 7/4.  Those are the numbers, now just put them together with plus signs between them and you're done.

Answer:

Step-by-step explanation:

Set up a table for a distance = rate × time problem.  We are considering the trips taken on Monday and Tuesday.

                         d     =     r     ×     t

Monday

Tuesday

Now let's start filling in what we know.  First off, Fran went to her Mother's both days.  Unless her Mother moved overnight from Monday to Tuesday, the distance from Fran to her mom is the same both days, even though we don't know how far it is.  So we will just call that "d".

                           d     =     r     ×     t

Monday               d     =

Tuesday              d     =

Now we are told about the times it took to get there on both days.  Monday took 2.7 hours and Tuesday took 3 hours.  Filling in that:

                            d     =     r     ×     t

Monday                d     =           ×     2.7

Tuesday               d     =           ×     3

We're getting there.  Now let's look at rates.  Again, we don't know her rate (that's what we are solving for!) but we do know that she drove faster on Monday than Tuesday.  Tuesday she was 6 miles per hour slower than Monday.  Since we don't know Monday's rate, we will call it r.  Since we don't know Tuesday's rate, but only that it is 6 mph slower than Monday, we will call it r - 6

                            d     =     r     ×     t

Monday               d     =     r      ×     2.7

Tuesday               d     =    r-6   ×     3

Now we have our equations.  We know that d = rt.  Since the distances are the same, d = d, by the transitive property of equality, we can set the 2 expressions equal to each other:

2.7r = 3(r - 6) and solve for r:

2.7r = 3r - 18

-.3r = -18

r = 60

If r = 60, then that r value goes in for Monday.  That means that Tuesday is 60 - 6 which is 54

What was her average speed on Tuesday is 54 mph

Monday

Time = 2.7 hours

Date = r mph

Distance = 4.5r miles

Tuesday

Time = 3 hours

rate = r-6 mph

Distance = 3(r-6) miles

Hence:

Distance = distance

2.7r=3(r-6)

2.7r = 3r - 18

0.3r = 18

r =18/0.3

r 60 mph ( Monday rate)

r-6=60-3  (Tuesday rate)

r-6 = 54 mph (Tuesday rate)

Inconclusion  What was her average speed on Tuesday is 54 mph.

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Step-by-step explanation:

Having proven that the triangles are similar, we can write the proportion:

AP / CP = CP / MP

9 / CP = CP / 16

CP² = 144

CP = 12

Now, we can simply use Pythagorean theorem to find the other sides.

AC² = AP² + CP²

AC² = 9² + 12²

AC = 15

CM² = CP² + PM²

CM² = 12² + 16²

CM = 20

Answer: Option C

the approximate height of the souvenir of the Eiffel Tower to the nearest tenth is __13 in___.

Step-by-step explanation:

We know that each foot of height of the Eiffel Tower is equivalent to 1/80 inch of height of the souvenir.

The Eiffel Tower is 1,069 feet high.

Then the height of the souvenir the 1,069 times 1/80 in

[tex]h = 1,069 *\frac{1}{80}\\\\h=13.3\ in[/tex]

The answer is the option C

Answer: 42,504

There Are 42,504 Different Combinations For The Swimmers

Answer:i dont

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

correct options are A, C and D

Step-by-step explanation:

While formulating an equation the first step is to read the problem carefully and then draw a picture if needed and the third step is write each fact as a variable.

so the steps which are used when formulating are as follows

Read the problem

Draw a picture if needed

Write each fact as a variable expression

Answer:

C) An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?  

Step-by-step explanation:

Note that in this question:

x = amount of containers to be purchased.

50,000 =  the amount given

< means that the amount in total must be less than (& not equal to) 50000

1200 = the amount of the container cost.

C) is your best answer.

~

Answer:

It is C

Step-by-step explanation:

An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?

1,200x < 50,000

x < 41.67

Thus, only 41 containers can be purchased, so that the purchase remains under $50,000.

The statement "the expense must be less than $50,000" means that the total cost must be less than $50,000.

The answer is 80%

Correct me if I’m wrong

Answer:

x= 8.1

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos⁡ θ= base/hypotenuse

cos⁡ 36=x/10

0.8090=x/10

8.090=x

x=8.090

Rounding off to nearest 10

x=8.1