What is the product?
(7x²)(2x + 5)(x² - 4x-9)
14x5 – x4 - 46x3 - 58x2 – 20x-45
14x6 – 56x5 – 91x4 - 140x2 - 315x2
14x? - 56x6 – 126x + 35x4 – 140X2-315x2
14x12 – 182x® + 35x4 – 455x2

Answer:

[tex]1 \dfrac{5}{7}\ mph[/tex]

Step-by-step explanation:

Let x mph be the current's rate.

Upstream:

Distance = 18 miles

Rate = 12 - x mph

Time [tex]=\dfrac{18}{12-x}[/tex] hours

Downstream:

Distance = 24 miles

Rate = 12 + x mph

Time [tex]=\dfrac{24}{12+x}[/tex] hours

Time is the same, so

[tex]\dfrac{18}{12-x}=\dfrac{24}{12+x}\\ \\18(12+x)=24(12-x)\\ \\216+18x=288-24x\\ \\18x+24x=288-216\\ \\42x=72\\ \\x=\dfrac{12}{7}=1 \dfrac{5}{7}\ mph[/tex]

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]

In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.

coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.

Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].

Final answer:

The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.

In the given equation, the fractional coefficient is 3/4, which is the fraction that multiplies the variable y.

Explanation:

The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.

In the equation 3/4y + 1/2 = 3 1/4, the fractional coefficient refers to the fraction that is multiplied by the variable y.

In this case, the coefficient is 3/4.

When working with algebraic expressions and equations, understanding how to identify and manipulate coefficients is essential for problem-solving.

The student's query seems to be aimed at identifying the coefficient of the variable in the equation. In algebra, fractions like 3/4 can be seen as coefficients when they are directly next to a variable.

No unit cancellations are needed here as the question pertains to pure algebra and not to unit conversions or applied mathematics.

Answer:make a graph

Step-by-step explanation:

Answer:

Part a) [tex]3x+5y=30[/tex]

Part b) see the explanation

Part c) see the explanation

Step-by-step explanation:

Part a) Construct a liner equation

Let

x ----> the number of bags of  tootsie rolls

y ----> the number of bags of lolly-pops

we know that

The number of bags of tootsie rolls bought multiplied by their price ($3) plus the number of bags of lolly-pops bought multiplied by their price ($5) must equal $30

so

The linear equation that represent this problem is

[tex]3x+5y=30[/tex]

Part b) Find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x s equal to zero

In this context, the y-intercept is the number of bags of lolly-pops that i can buy when the number of bags of tootsie rolls is equal to zero

For x=0

[tex]3(0)+5y=30[/tex]

[tex]y=6[/tex]

The y-intercept is the point (0,6)

so

I can buy 6 bags of lolly-pops and 0 bags of tootsie rolls

Find the x-intercept

The x-intercept is the value of x when the value of y s equal to zero

In this context, the x-intercept is the number of bags of tootsie rolls that i can buy when the number of bags of lolly-pops is equal to zero

For y=0

[tex]3x+5(0)=30[/tex]

[tex]x=10[/tex]

The x-intercept is the point (10,0)

so

I can buy 10 bags of  tootsie rolls and 0 bags of lolly-pops

Part c) Find the slope

we have

[tex]3x+5y=30[/tex]

isolate the variable y

[tex]5y=-3x+30[/tex]

[tex]y=-\frac{3}{5}x+6[/tex]

The slope is m=-3/5  ---> is negative because is a decreasing function        

That means ---> For every three less lollipops you get, you can have 5 more tootsie rolls

Answer:

F is the mid point of BC. (Proved)

Step-by-step explanation:

See the attached diagram.

Given AB ║ CD and EF is drawn to be parallel to AB.

So, EF ║ AB ║ CD .......... (1)

Now, in Δ ABD, E is the midpoint of AD and EG is parallel to AB.

So, G must be the midpoint of BD.

Now, in Δ BCD, G is the midpoint of DB and GF is parallel to CD. {From relation (1)}

So, we can write F is the midpoint of BC. (Proved)

[Since we know the theorem that if we joint the midpoints of two sides of a triangle then the line formed will be parallel to the third side.]

Answer:

The radius of the given equation is 2 .

Step-by-step explanation:

The equation of a circle whose center (h, k) and radius is r,

(x - h)² + (y - k)² = r² ..............................(i)

Here given that-

x² + y² + 21 = 10 x

x² - 10 x + y² + 21 = 0

( To making perfect square, add and subtract 25 ) -

x² - 10 x + 25 - 25 + y² + 21 = 0

(x² - 10 x + 25) + y² -4 =0

[As we know that -

(x - 5)² = x² - 10 x + 25]

(x - 5 )² + y² = 4

(x - 5)² + (y - 0)² = 4

(x - 5 )² + (y- 0)² = 2² ................................(ii)

On comparing equation (i) and(ii)-

r = 2

Hence the radius of the given equation is 2 and center is ( 5, 0).

There are probably some choices we're not being shown, but let's just do the whole procedure.

x² + 6x - 8 = 0

Step one: move the 8 to the other side.

x² + 6x = 8

Step two: add (6/2)²=9 to both sides.

x² + 6x + 3² = 8 + 9

Step three: Factor

(x + 3)² = 17

Step four: take the square root

x + 3 = ±√17

Step five: Solve for x,

x = -3  ± √17

Answer:

21 mini-muffins

Step-by-step explanation:

7 multiplied by 3 equals 21

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Tony bought a total of 21 mini-muffins. This was calculated by multiplying the number of packages he bought (7) by the number of mini-muffins in each package (3).

This question is about a mathematical operation called multiplication. Tony purchases 7 packages of mini-muffins. There are 3 mini-muffins in each package. To find the total number of mini-muffins Tony buys, multiply the number of packages he bought (7) by the number of mini-muffins in each package (3). This calculation is written as 7 * 3. Therefore, Tony buys a total of 21 mini-muffins.

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Answer: 1.0

Step-by-step explanation: Since a percent is a ratio that compares a number to 100, think of 100% as the ratio 100/100 or 100 divided by 100.

Now, dividing a number by 100 moves the decimal point two places to the left so 100 divided by 100 will move the decimal point two places to the left which will gives us 1.0 or simply just 1.

So 100% can be written as the decimal 1.0.

Answer:

1

Step-by-step explanation:

Byeeee, get a hundred!

Answer:

41

Step-by-step explanation:

Substitute in 5 and 7 into the correct spots:

(-3)(7)+2((8)(5)-9)

Multiply and simplify:

-21+2(40-9)

-21+2(31)

-21+62

41

:)

Answer:

50

Step-by-step explanation:

-21 + 16x - 9

-21 + 80 - 9

59 - 9

50

Answer:

The profit = $(3x - 75) where x = number of t-shirts sold

Step-by-step explanation:

School spirit club wants to raise money by selling t-shirts. one local company charges a fixed fee of $75 for creating the design and $5 for each shirt that they print.

We have to find the club's income if they sell each t-shirt for $8.

Let the number of t-shirts that the club sell be equal to x.

So the cost of making x t-shirts = 75 + 5x

If the club sells x t-shirts , then the money they earn = 8x

Profit = selling price - cost price

          = 8x - (75 + 5x)

          = $(3x - 75)

The club also needs to sell at least 25 t-shirts to make a profit and from then on makes a profit of $3 on each t-shirt they sell.

Answer:

3.375 miles

Step-by-step explanation:

3/4 can be changes to 0.75. SO multiply 4.5 times 0.75 to get your answer

Answer:

3.5 hours

Step-by-step explanation:

Given: Distance= 26.2 miles

           Speed= 12 km/h

First lets convert the unit of speed from kmh to mph.

Remember, 1 mile= 1.609 km

∴ For speed of 12 km/h= [tex]\frac{12}{1.609}= 7.45\ mph[/tex]

Speed= 7.45 mph

Next, find time taken by Allan to complete a Marathon.

[tex]Time= \frac{Distance}{speed}[/tex]

⇒ Time= [tex]\frac{26.2}{7.45}[/tex]

∴ Time= 3.516 hours ≅ 3.5 h (nearest tenth)

∴ Allan took 3.5 hours to complete marathon.

Allan takes approximately 3.5 hours to complete a marathon. This is determined by converting the marathon distance to kilometers and dividing it by his running speed.

To determine how long it takes Allan to complete a marathon, we need to convert the marathon distance from miles to kilometers and then find the time it takes based on his running speed.

1 mile is approximately 1.60934 kilometers, so:

26.2 miles × 1.60934 km/mile ≈ 42.164 km

Allan runs at an average speed of 12 kilometers per hour. The time (t) needed to complete the marathon can be calculated as:

t = distance / speed

t ≈ 42.164 km / 12 km/h ≈ 3.514 hours

Rounding to the nearest tenth of an hour, Allan takes approximately 3.5 hours to complete the marathon.

Answer:

1. [tex]12x^2-13.4x-11[/tex]

- Degree: 2

- Number of terms: 3

2. [tex]7x^3+168[/tex]

 - Degree: 3

- Number of terms: 2

3. [tex]9x^4-9[/tex]

- Degree: 4

- Number of terms: 2

Step-by-step explanation:

For this exercise you need to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

1. Given:

[tex](4x + 2.2)(3x - 5)[/tex]

Apply the Distributive property:

[tex]=12x^2+6.6x-20x-11[/tex]

Add the like terms:

[tex]=12x^2-13.4x-11[/tex]

You can idenfity that:

- Degree: 2

- Number of terms: 3

2. Given:

[tex](-304 +503 - 12) + (7x^3 - 25 + 6)[/tex]

Add the like terms:

[tex]=187 + 7x^3 - 25 + 6=7x^3+168[/tex]

You can idenfity that:

- Degree: 3

- Number of terms: 2

3. Given:

[tex](3x^2 - 3)(3x^2 + 3)[/tex]

Apply Distributive property:

[tex]=9x^4-9x^2+9x^2-9[/tex]

Add the like terms:

[tex]=9x^4-9[/tex]

You can idenfity that:

- Degree: 4

- Number of terms: 2

The slope of the line is -4.

Work is provided in the image attached.

Answer:

[tex]m=-4[/tex]

Using the Slope Formula:

[tex]m= \frac{4+12}{5-9}=\frac{16}{-4} =-4[/tex]

Answer:

(-18, 2)

Step-by-step explanation:

To rotate a point by 90°:

R₉₀ (x, y) = (-y, x)

R₉₀ (1, 9) = (-9, 1)

To dilate by 2:

D₂ (x, y) = (2x, 2y)

D₂ (-9, 1) = (-18, 2)

Answer:

19 coach seats

Step-by-step explanation:

let the number of coach seats be C and number of first class seats be F

given that the total number of seats is 29,

C + F = 29 ---------(eq 1)

also given that each coach seat = $600, each 1st class seat is $1050 and a total of $21900 was collected,

600C + 1,050F = 21,900 -------(eq 2)

we have 2 equations and 2 unknowns, we can solve the system of equations by elimination

(eq 1) x 1,050 gives us:

1,050 (C + F) = 1,050(29)

1,050C + 1,050F = 30,450 ----- (eq 3)

by elimination, subtract eq 2 from eq 3

(1,050C + 1,050F) - (600C + 1,050F) = 30,450 - 21,900

1,050C - 600C = 8,550  

450C = 8550

C = 855 /450

C = 19

Answer:

$280

Step-by-step explanation:

Interest = Interest Rate x Principal x time

Interest = 0.04 x $3,500 x 2

Interest = $280

Answer:

Total cost to paint the room = £73.51

Step-by-step explanation:

Given:

Dimensions of the room = 6.8 m [tex]\times[/tex] 9.2 m

Cost of tin of paint = £11.75

A tin of paint covers an area = 20 [tex]m^2[/tex]

To find the cost of painting the room with two coats of paint.

Solution:

Area of the room = [tex]length\times width=6.8\ m\times 9.2\ m= 62.56\ m^2[/tex]

We will use unitary method to find the amount of paint required for the room.

If [tex]20\ m^2[/tex] of area is covered by 1 tin of paint.

For [tex]1\ m^2[/tex] of area, amount of paint required = [tex]\frac{1}{20}[/tex] of a tin

Then, for [tex]62.56\ m^2[/tex] amount of paint required = [tex]\frac{62.56}{20}=3.128[/tex] tins of paint.

For double coats twice paint must be required.

So, total amount of paint required for painting the room with two coats of paint = [tex]3.128\times 2=6.256[/tex] tins of paints.

Using unitary method to find total cost.

If 1 tin of paint costs = £11.75

6.256 tins of paint will cost = [tex]6.256\times \£11.75=\£73.508\approx\£73.51[/tex]

Total cost to paint the room = £73.51

Answer:

SAS Reflective property

Step-by-step explanation:

By reflexive property and SAS, we prove that ΔPYJ and ΔPXK are congruent.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, JP = KP and PX = PY.

∴ JX = KY.

Hence Z is the midpoint of JY and XK.

∴ JY = XK.

Reflexive property.

And the included ∠P is common to both the  ΔPYJ and ΔPXK.

Side angle side congruency.

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Answer:

1 quart blue + 1 1/2 quart red

Step-by-step explanation:

Given:

Ratio of blue paint : red paint = 1/3 : 1/2

simplifying this ratio into whole numbers by multiplying both sides by 2 and 3, we get:

(1/3) x (3x2) : (1/2) x (3x2)

2 : 3

From this we can determine the fractions of red and blue paint used in any total purple mix

fraction of blue paint = 2/(2+3) = 2/5 of purple mix

fraction of red paint = 3/(2+3) = 3/5 of purple mix

we are given that we want to make 2 1/2  (= 5/2) quarts of purple paint

hence

amount of blue paint

= fraction of blue paint in purple mix x total amount of purple paint

= (2/5) x (5/2) = 1 quart

amount of red paint

= fraction of redpaint in purple mix x total amount of purple paint

= (3 /5) x (5/2) = 3/2 quart = 1 1/2 quart

Answer: [tex]540[/tex]

We count the number of ways that some lane can be left empty, and subtract from the total:

Each driver has three choices, so it's [tex]3^6 = 729[/tex].

Now, we count the ways where at least 1 lane is left empty:

But we have double-counted the situations where two lanes are left empty. Since each driver only has one choice, there are [tex]3(1^6)[/tex] situations we overcount. This leaves [tex]729 - (192 - 3) = 540[/tex] ways to fill all three lanes.

Also, you took this question directly from Alcumus. The source is AoPS Staff they wrote this problem, and might request this post be taken down since you technically are not allowed to post Alcumus problems on the internet or their own forums.

Answer:

The cars are travelling ar the speed 45 mph.

Step-by-step explanation:

Let the two cars are moving at the speed of x mph.

Now, Car A reaches its destination in 15 minutes i.e. [tex]\frac{15}{60} = 0.25[/tex] hours.

Therefore, Car A travels in 15 minutes by 0.25x miles.

Again, Car B reaches its destination in 35 minutes i.e. [tex]\frac{35}{60} = 0.583[/tex] hours.

Therefore, Car B travels in 35 minutes by 0.583x miles.

Given that, (0.583x - 0.25x) = 15

⇒ 0.333x = 15

⇒ x = 45 mph

Therefore, the cars are travelling ar the speed 45 mph. (Answer)

The cars travel at a speed of 3/4 miles per minute.

To find the speed of the cars, we can use the formula Speed = Distance/Time. Let's assume that Car A's speed is x miles per minute. Since Car B travels 15 miles farther than Car A and takes 35 minutes to reach its destination, Car B's speed would also be x miles per minute. Now, using the given information, we can set up two equations:

x * 15 = x * 35 - 15

Simplifying the equation, we get:

15x = 35x - 15

20x = 15

x = 0.75

Therefore, the cars travel at a speed of 0.75 miles per minute or the fraction 3/4 miles per minute.

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Answer:

21.04

Step-by-step explanation:

Start by adding the hundredths category.  0.09 + 0.05 = 0.14,  this means that your hundredths column will be a 4,  and you will carry the 1 over to the tenths.

Now add your tenths.  0.0 + 0.9 + 0.1 = 1.0,  which means that your tenths column is a 0.  Carry the 1 over to the whole numbers.

Now add your whole numbers.  7 + 13 + 1 = 21.  Combine your terms and you get 21.04

Final answer:

21.04

Explanation:

To find the sum of 7.09 and 13.95, we simply add the two numbers together, aligning the decimal points vertically.

Putting it all together, we get 21.04 as the final sum.

X is a right angle so 90 degrees.

The B will be equal to C so B is 47 degrees.

The Y is 180 degrees - X - C so Y is 43 degrees.

Hope this helps.

Answer:

40x-24y

Step-by-step explanation:

Option E

The numerator of fraction is 21

[tex]2\frac{5}{8}[/tex] is to be written as improper fraction in lowest terms

To find: numerator of fraction

An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).

To convert a mixed fraction to an improper fraction, follow these steps:

[tex]2\frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8}[/tex]

Thus the numerator of fraction is 21. Option E is correct

Answer:

A. 17 , 11

f(4)=3(4) + 5

=17

f(x)= 38

38 = 3x + 5

38 - 5 = 3x

33 = 3x

x =11

Answer:

Anil would take 10 days and Sunil would take 15 days to complete the work.

Step-by-step Explanation:

To Determine:

How many days they took to complete the work?​

Information Fetching and Solution steps:

Let is consider,

The number of days taken by Anil to complete the required work = d.

The number of days taken by Sunil to complete the required work = d + 5

Work done by Anil in one day = 1÷d

Work done by Sunil in one day = 1÷ (d+5)

Work done together by Anil and Sunil for one day = 1/d + 1/(d+5)

                                                                                    = (d+5+d)/d(d+5)

                                                                                    = (2d+5)/d(d+5)  

Work done together by Anil and Sunil for 4 days = 4×(2d+5)/d(d+5) ....[A]

Work done by Sunil in 5 days = 5÷ (d+5)  ....[B]

By adding equation [A] and [B], we can determine the complete work

[A] + [B] = 1

((4×(2d+5)/d(d+5))) + (5÷ (d+5)) = 1

8d+20+5d=1d(d+5)

13d+20=d²+5d

−d²+8x+20=0

(−d−2)(d−10)=0

d=−2 or d=10

As number of days can not be negative. So, d = 10. Therefore,

The number of days taken by Anil to complete

the required work = 10 days

The number of days taken by Sunil to complete

the required work = d+5 = 15 days

Hence, Anil would take 10 days and Sunil would take 15 days to complete the work.

Keywords: days, work

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Subtract the length of the tail from the whole length.

3/5 - 1/5 = 2/5

The answer is 2/5

3/5  -  1/5  = 2/5

so your answer is 2/5