What package of toothpaste has the lower unit price?
Package Price Unit Price
6.2 oz $2.95
8.0 oz $3.13

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

What is partial fraction?

Partial fractions are the fractions used for the decomposition of a rational expression.

Given:

(4x + 40)/ (x + 2)(x + 6) = A/(x + 2) + B/(x + 6)

4x + 40 = A(x + 6) + B(x + 2)

4x + 40 = x(A+B) + 6A +2B

On comparing

4= A+B

A= 4-B

and, 6A +2B =40

3A + B =20

3(4-B) + B =20

12  - 3B + B =20

-2B = 8

B= -4

and, A= 8

Hence, StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

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Answer:

C.

Step-by-step explanation:

photo below

I honestly have no idea how to slove this question

For real,I don't know. OK

BTW,you nice,keep going

Answer:

spider : 5

beetle : 6

Step-by-step explanation:

Total number of legs --> 8 + 6 = 14 ( 1 set )

Number of sets that can fit --> 76 ÷ 14 = 5 R 6

Since each set has a beetle and a spider,

Number of spider -->5 × 1 = 5

Since there are additional 6 legs:

Number of beetles --> ( 5 × 1 )+ 1 = 6

We can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

An ordered pair on the X-Y plane is written as (x, y).

Here we also have the relation:

-x + 4y = 9

If we isolate y, we get:

4y = 9 + x

y = (9 + x)/4

Now, we can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

To get the particular ones you can replace the value of x, for example, if x = 0, then:

(x, (9 + x)/4 ) = (0, 9/4)

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The exact value of cos 7pi/8 is 0. 9988

It is important to note that the value for pi = 3. 142

= cos 7π

Substitute value of π

= cos(7× 3. 142)

= cos 21. 994

Divide 21. 994 by 8

= 2. 740

Let's find the vale of [tex]cos \frac{21. 994}{8}[/tex]

= [tex]cos (2. 749)[/tex]

= [tex]0. 9988[/tex]

Thus, the exact value of cos 7pi/8 is 0. 9988

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Answer:

[tex]h(-6)=-(-6)-4\\h(-6)=2[/tex]

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

(3+6)/2*4

Answer:

18 square feet.

Step-by-step explanation:

   a = 6 ft

   b = 3 ft

   h = 4 ft

a & b are the length of the parallel lines. h is the height between the parallel lines.

[tex]\sf \boxed{\text{\bf Area of trapezoid =$ \dfrac{(a+b)*h}{2}$}}[/tex]

                                  [tex]\sf =\dfrac{(6+3)*4}{2}\\\\=\dfrac{9*4}{2}\\\\= 9 * 2\\\\= 18 \ ft^2[/tex]

The translation of the given algebraic words to symbols is: C. 3(ab).

The algebraic word, "triple" connotes "3 times'. "Product" means multiplication. Therefore, we would have the following translation:

Product of ab = ab

Triple of ab = 3(ab).

Therefore, the algebraic words translated to symbols is: 3(ab).

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When a customer has a 6 pound Chihuahua, the cost that will be charged is $5.00.

a. If a customer has a 6 pound Chihuahua, how much would you charge?

It should be noted that from the information given, for dogs that weigh 0 to 15 pounds, the amount charged is $5.00.

b. If a customer has a 65 pound Labrador, how much would you charge?

It should be noted that for dogs over 45 pounds, the amount that's charged is $9.00

There, the amount charged will be $9.00.

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Answer:

Step-by-step explanation:

Out of every 20 students, there are 9 that gain admission to s.h.s.

Overall, there are 12,000 students. To find how many groups of 20 students there are, we divide 12,000 by 20. We get 600.

Since there are 9/20 students, we multiply 600 * 9. We get 5,400.

So, out of the 12,000 students, 5,400 gained admission.

Hope this helps.

The number of days Tayloe will take to travel 100 miles if he travels 35 miles every 2 days is 40/7 or 5 5/7 in fraction form.

A fraction is a representation of a part of the whole.

Written as a/b, read as "a by b", it functions as a number of parts of a total of b number of parts.

In the question, we are given that Tayloe travels 35 miles every 2 days to work.

Therefore, daily traveling done by Tayloe can be shown as a fraction, 35/2 miles.

The total traveling given to us is 100 miles.

Thus, the number of days Tayloe will take to travel 100 miles can be shown in fractional form as 100/(35/2) = (100*2)/35 = 40/7 or 5 5/7.

Thus, the number of days Tayloe will take to travel 100 miles if he travels 35 miles every 2 days is 40/7 or 5 5/7 in fraction form.

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Answer:

third option listed

Step-by-step explanation:

We know that Johnny does not ever stay/wait at the same distance from the wall, as that would look like a flat line (the y-value / distance would be unchanging, it would be constant)

So, the only possibly correct option is C, because all other options describe him pausing

But why is it not A? We know that at "0" y we are at the gym wall, and that each point is a point that he turns around and runs the opposite way. He first runs away, back, away, back, away, back--which we know because of the direction of the line over time. We also can tell that each period of "away, back" is the same distance, and it takes the same time to travel that distance, by looking at the length of each line.

hope this helps!! have a lovely day :)

Answer:

the 3rd answer option

Step-by-step explanation:

as we can see, time is on the x-axis.

(0, 0) means start of the action (0 seconds) with 0 distance to the gym wall.

then we see that for 2 seconds Johnny increases the distance to the gym wall up to 3 units (the line goes to (2, 3)).

then we see that for the next 2 seconds he returns to the gym wall (0 distance).

then for 3 seconds he increases the distance to the gym wall to 5 units. the line goes to (7, 5). and then for the next 3 seconds he returns to the gym wall (0 distance). then for 4 seconds he increases the distance to the gym wall to 7 units. the line goes to (14, 7). abd then for the next 4 seconds he returns to the gym wall (0 distance).

So he needs to sell $2,000 in merchandise.

We can assume that we have a proportional relation:

y = k*x

Where y is the commission and x is what Norman sells, then:

$15 = k*$200

k = $200/$15 = 0.075

$37.50 = k*$500

k = $500/$37.50 = 0.075

Then the relation is:

y = 0.075*x

If he wants a commission of $150, then:

$150 = 0.075*x

$150/0.075 = x = $2,000

So he needs to sell $2,000 in merchandise.

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Trigonometric ratios are defined as the ratio of different sides of a right angle triangle with respect to one angle of the right angled triangle.

Length of the wire = Hypotenuse of the triangle =  X

Base of the triangle = Distance from the bottom of the tower to the point where wire is attached on ground = 20 m

Angle b/w Hypotenuse and Base of triangle = 46°

cos(θ) = Base / Hypotenuse

cos(46) = 20 / X

X = 20 / cos(46)

X = 28.79 m

Hence, the length of the wire is 28.79 m.

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Three types of financial institutions and the services they offer include:

Commercial banks:

Insurance company:

Investment banks:

Commercial banks are one of the largest and they offer deposit services to people and companies. They then use these deposits to make loans.

Insurance companies act to protect their clients from financial losses arising from unforeseen circumstances. They also help with wealth accumulation if a claim is not made.

Investment banks are very important for stock issuance, and mergers and acquisitions where they act as financial advisors and facilitators.

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Answer:

this is the example answer.

Step-by-step explanation:

(Answers may vary.)

Bank: Wells Fargo is a commercial bank that provides services for individuals, small businesses, and corporations. The bank manages IRAs (traditional and Roth), which are retirement funds that invest in different stocks and bonds to earn interest. Traditional IRAs offer tax-deferred growth. An individual doesn't have to pay taxes on earnings until he or she is ready to make withdrawals (i.e., after retirement). Roth IRAs offer tax-deferred growth until retirement and tax-free withdrawals while in retirement. The bank offers merchant services for small businesses. The bank processes payments via credit cards, debit cards, checks, gift cards, and international payments. Wells Fargo also gives small businesses options on how to accept customer payments: online shopping carts, mobile apps, and onsite payment processing equipment.The bank offers affordable student loans to cover the cost of tuition, books, computers, and housing. Students are not required to make loan payments until six months after leaving school. The bank offers two types of interest rates on student loans: variable and fixed. Variable interest rates range from 3% to 8% and fixed rates range from 5% to 10%.

Credit union: Navy Federal Credit Union has more than 5 million members. It is available for anyone who is affiliated with the Armed Forces, Coast Guard, National Guard, or the Department of Defense, or anyone who has a family member who is already a Navy Federal member. It offers a fixed-rate home equity loan for members. Home equity loans use a borrower’s home as collateral for the loan. These loans are usually used to pay for major expenses such as home repairs, college education, medical bills, and so on. The borrower can borrow up to 100 percent of the home's property value, with the agreement that the fixed-rate loan will be paid off in 20 years (longest term available). This credit union guarantees no hidden closing costs on the loan. It offers motorcycle, boat, and leisure vehicle loans. The loans require zero down payment and promise to cover the cost of the vehicle/boat, taxes, title, and tags. This is a good loan for someone who has not saved any money prior to choosing to buy a vehicle.It also offers prepaid Visa cards, which are useful for students and young adults who are learning to control expenses. Unlike most prepaid cards, this credit union states there are no hidden monthly fees, activation charges, or purchase fees. The prepaid cards can be loaded up to $10,000 and are protected by the credit union's zero liability policy. There are spending limits associated with the program: an ATM withdrawal limit per day of $600 and a spending limit of $3,000 per day.

Financial service company: First Financial advertises itself to be a leading provider of bad credit auto loans. It markets to individuals and companies who have bad credit ratings and cannot qualify for loans with banks and credit unions.It offers auto loans for anyone who earns $1,500 if the borrower’s credit score is less than 650. People who have filed bankruptcy can also obtain loans. The company’s website does not quote an interest rate or loan term.It offers business loans to high-risk merchants with bad credit. The website does not quote interest rates or loan terms.It offers merchant cash advances, which provide quick cash for businesses. The site does not provide detailed information about this service.

Answer:

187

Step-by-step explanation:

Least common multiple:

To find the required number,

30 =  2 * 3 * 5

36 = 2 * 2 * 3 * 3 = 2² * 3²

45 = 2 * 3 * 3 = 2 *3²

LCM = 2² * 3² * 5

        = 4 * 9 * 5

        = 180

Required number = 180 + 7

                             = 187

The plane reaches its destination at 12h10 minutes if the plane leaves town A for town B.at 0540hours

For legal, commercial, and social purposes, a time zone is a region that observes a uniform standard time. Instead of strictly following longitude, time zones tend to follow the borders between countries and their subdivisions.

We have:

A plane leaves town A for town B.at 0540hours.If the journey takes 6.5hours

05h40min

Total time takes = 6 hours and 30 minutes

= 5 hours + 40 minutes + 6 hours + 30 minutes

= 11 hours + 70 minutes

= 12 hours 10 minutes

or

= 12h10 minutes

Thus, the plane reaches its destination at 12h10 minutes if the plane leaves town A for town B.at 0540hours

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P(1) = P(-1)

P(1) = 3 - a + b
P(-1) = -3 + a + b

-> 3 - a + b = -3 + a + b
-> 3 - a + b + 3 - a - b = 0
-> 6 - 2a = 0
-> a = 3.

P(2) = 24 - 2a + b -> 24 - (2a - b) = 16 -> 2a - b = 8
-> 6 - b = 8
b = -2.

So, a = 3 and b = -2

Recheck : P(1) = 3 - 3 + (-2) = -2
P(-1) = -3 + 3 + (-2) = -2 => P(1) = P(-1) (true)

P(2) = 24 - 6 + (-2) = 16.

Answer:

  14 pounds

Step-by-step explanation:

The given equations can be solved for y by substituting for x. The first equation is convenient for writing x in terms of y.

  x = 20 -y . . . . . . . subtract y from the first equation

  7(20 -y) +5.5y = 119 . . . . . substitute for x in the second equation

  140 -1.5y = 119 . . . . . . . . simplify

  21 = 1.5y . . . . . . . . . . . add 1.5y -119 to both sides

  14 = y . . . . . . . . . . . .divide by 1.5

14 pounds of soy nuts should be used in the mixture.

__

Additional comment

There are many ways to solve a system of two linear equations. The attachments shows a matrix solution using a suitable calculator. It tells us that x=6 and y=14, as we found above.

The number that produced a rational number when added to 1/5 is D. -2/3.

A rational number is a number that can be written as a ratio (or fraction) of two integers.

For example, when 1/5 is added to -2/3, it produces a rational number, -7/15, that remains as a fractional value.

Thus, the number that produced a rational number when added to 1/5 is D. -2/3.

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The property that Antonio has used is what is called the Subtraction property of equality.

This is the property that tells us in mathematics that is a number is subtracted from an inequality, they would still remain the same.

2x + 1 = 11 is the same thing as also writing  2x = 10. The difference is that the like terms were on the same side.

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From the markings on the diagram, we can tell E is the midpoint of BC and D is the midpoint of AC. We can apply the triangle midsegment theorem: ED = ½BA. Substituting in the expressions for the lengths and solving for x, we get x = 5. Now, since BE = x, then BC = 10.

Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem, we can find the value of x:

ED = ½BA

x + 2 = ½(4x - 6)

2x + 4 = 4x - 6

4x - 2x = 6 + 4

2x = 10

x = 10/2

x = 5.

BC = x + x

BC = 5 + 5

BC = 10.

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Thw statement that's true for the function g is g(-13) = 20.

From the information given, the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

In this case, g(-13) = 20. Here, x = -13 is in the domain and 20 is also in the range. Therefore, this is true for g.

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Answer:

A linear relationship can be represented by a straight-line graph and by an equation of the form y=mx+b. In the equation, m is the slope of the line, and b is the y-intercept. Used to track changes over short and long periods of time. When smaller changes exist, this graph is better to use than bar graphs.

Answer:

x=4+√5 or x=4−√5

Step-by-step explanation:

Multiply both sides by x-4.

x2−8x+16=5

x2−8x+16−5=5−5(Subtract 5 from both sides)

x2−8x+11=0

For this equation: a=1, b=-8, c=11

1x2+−8x+11=0

x=

−b±√b2−4ac

2a

(Use quadratic formula with a=1, b=-8, c=11)

x=

−(−8)±√(−8)2−4(1)(11)

2(1)

x=

8±√20

2

x=4+√5 or x=4−√5

There are 28 ways for Mary to put the plants on the sills.

We can use the Binomial Theorem to solve this problem.

We have 6 plants and 3 sills, so we have6 + 3 − 1 = 8 total objects.

Since we have 8 objects, we can use the Binomial Theorem to expand [tex](x + y)^{8}[/tex].

The coefficient   [tex]x^{6} y^{2}[/tex] will be the number of ways for Mary to put the plants on the sills. We can expand [tex](x + y)^{8}[/tex]

using the Binomial Theorem:

[tex](x + y)^{8}=(\left\ {{8}\atop {0}} \right. )x^{8}+ (\left\ {{8}\atop {1}} \right. )x^{7}y+(\left\ {{8}\atop {2}} \right. )x^{6}y^{2} +(\left\ {{8}\atop {3}} \right. )x^{5}y^{3} +(\left\ {{8}\atop {4}} \right. )x^{4}y^{4}+(\left\ {{8}\atop {5}} \right. )x^{3}y^{5} +(\left\ {{8}\atop {6}} \right. )x^{2}y^{6} +(\left\ {{8}\atop {7}} \right. )x^{1}y^{7} +(\left\ {{8}\atop {8}} \right. )y^{8}[/tex]

Since we are only interested in the coefficient of [tex]x^{6} y^{2}[/tex] , we can ignore all terms that do not have [tex]x^{6}[/tex] and  [tex]y^{2}[/tex].

Therefore, we are left with [tex](\left\ {{8}\atop {2}} \right. )x^{6}y^{2}[/tex]

[tex](\left\ {{8}\atop {2}} \right. )=\frac{8!}{2!(8-2)!} =\frac{8!}{2!6!} =\frac{8*7*6!}{2!6!} =28\\[/tex]

Therefore, there are 28 ways for Mary to put the plants on the sills.

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Answer:

the second option: [tex]7x+4y=44[/tex]

Step-by-step explanation:

So when a line is parallel, it means that it has the same slope and a different y-intercept, it's important that there is a different y-intercept, otherwise it would be the same line, and the "two lines" would intersect at infinite points.

Anyways by looking at the graph you have two points (-8, 5) and (-4, -2). So the run in this case was 4 and the rise was -7. This is a slope of -7/4. So we have the equation: [tex]y=-\frac{7}{4}x+b \text{ where b}\ne-9}[/tex]. Since it passes through the point (8, -3) we can plug that in as (x, y) to solve for b (the y-intercept)

Plug in (8, -3) as (x, y)

[tex]-3=-\frac{7}{4}(8)+b[/tex]

Multiply the -7/4 and 8

[tex]-3 = -14+b[/tex]

add 4 to both sides

[tex]11 = b[/tex]

So this gives us the equation:

[tex]y=-\frac{7}{4}x+11[/tex]

Since it's asking for it in standard form you move the 7/4 x to the other side

Add 7/4x to both sides

[tex]\frac{7}{4}x+y=11[/tex]

Multiply both sides by 4 to cancel out the fraction

[tex]7x+4y=44[/tex]

The area of the rhombus WXYZ is 48 unit².

From the diagram:

Diagonal WY = 8 units, Diagonal XZ = 6 units, hence:

Area = 8 * 6 = 48 unit².

A rhombus is a special case of a parallelogram. In a diamond, the opposite sides are parallel and the opposite sides are equal in angle. In addition, all sides of the rhombus are the same length and the diagonal bisects at right angles. Diamonds are also known as diamonds.

The diagonals of the rhombus intersect at right angles to form a non-uniform triangle. The opposite angles are equal. However, if all angles of the diamond are 90 degrees, the diamond is said to be square.

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AB turns clockwise to coincide with BC.

To find the angle by which turns counterclockwise to coincide with is 243.9 degrees:

An angle -

So,

= ABD + DBC

= 33.3° + 30.6°

= 63.9°

b) If E is drawn directly opposite C.

EBC is a straight line, so the sum of angles =180°

ABE + ABD + DBC = 180°

ABE + 33.3° + 30.6° = 180°

ABE + 63.9° = 180°

ABE = 180 - 63.1

ABE = 116.9

Therefore, AB turns clockwise to coincide with BC.

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