Multiply and combine like terms to determine the product of these polynomials:
(2x + 3)(5x − 6)

Answer:

380

Step-by-step explanation:

This is a bit nasty. It depends on how you read the 20 miles more and what you do with it. The best and most careful way to do it is do it a long way setting up the two equations carefully.

Second day

Let the time travelled = t

Let the speed travelled = 60 mph

d2 = 60*t

First Day

40*(t + 2) = d1

but d1 = d2 + 20 because he travelled 20 miles further on d1

40 * (t + 2) = d2 + 20

d2 however = 60*t

40*(t+2 ) = 60*t + 20          Remove the brackets

40t + 80 = 60t + 20           Subtract 20 from both sides

40t + 60 = 60t                   Subtract 40t from both sides

60 = 20*t                           Divide by 20

t = 60/20

t = 3 hours.

Day 2 = 60 + t = 180

Day 1 = 40*5  = 200

Total distance = 380

Where did that 20 miles go? It was just an observation about the difference in distance travelled between the 2 days.

The total distance the driver traveled in the two days is 260 miles

From the question, on the first day, the driver was going as a speed of 40 mph.

Let s be speed

∴ [tex]s_{1}= 40mph[/tex]

On the second day, he increased the speed to 60 mph

∴ [tex]s_{2}= 60mph[/tex]

From the statement- If he drove 2 more hours on the first day

Let time be t

Then

[tex]t_{1}= t_{2} + 2[/tex] hrs

and traveled 20 more miles

Let d be distance  

Then,

[tex]d_{1}= d_{2} + 20[/tex] miles

From the formula

Distance = Speed × Time

Then,

[tex]d = s \times t[/tex]

∴ [tex]d_{1} = s_{1} \times t_{1}[/tex]

From above,

[tex]d_{1}= d_{2}+20[/tex] miles

[tex]s_{1}= 40mph[/tex]

[tex]t_{1}= t_{2} + 2[/tex] hrs

Putting these into

[tex]d_{1} = s_{1} \times t_{1}[/tex]

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex] ...... (1)

But,

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

∴ [tex]t_{2}= \frac{d_{2} }{s_{2} }[/tex]

From above, [tex]s_{2}= 60mph[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{60}[/tex]

Put this into equation (1)

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex]

[tex]d_{2} + 20 = 40\times (\frac{d_{2}}{60} +2)[/tex]

[tex]d_{2} + 20 = \frac{2}{3}d_{2} +80\\d_{2} = \frac{2}{3}d_{2} +80-20\\d_{2} = \frac{2}{3}d_{2} +60[/tex]

Multiply through by 3

[tex]3\times d_{2} = 3\times \frac{2}{3}d_{2} +3 \times 60\\3d_{2} = 2d_{2} + 120\\3d_{2} -2d_{2} = 120[/tex]

∴ [tex]d_{2} = 120[/tex] miles

∴The distance traveled on the second day is 120 miles

For the distance traveled on the first day,

Substitute [tex]d_{2}[/tex] into the equation

[tex]d_{1}= d_{2}+20[/tex] miles

∴ [tex]d_{1}= 120+20[/tex]

[tex]d_{1}= 140[/tex] miles

∴ The distance traveled on the first day is 140 miles

The total distance traveled in the two days = [tex]d_{1} + d_{2}[/tex]

The total distance traveled in the two days = 120 miles + 140 miles

The total distance traveled in the two days = 260 miles

Hence, the total distance the driver traveled in the two days is 260 miles

Learn more here: https://brainly.com/question/23531710

If you can show that the following two items are true

then you have shown that triangle A'B'C' is a translated or shifted copy of triangle ABC. In other words, they are the same triangle.

Answer:

y = 1/2x + 5/2

Step-by-step explanation:

y = 1/2x + b

5 = 1/2(5) + b

5 = 5/2 + b

5/2 = b

9514 1404 393

Answer:

  y = 4

Step-by-step explanation:

The given points are on the horizontal line ...

  y = 4

This is the standard-form equation of that line.

Answer:

b = 2√3

a = 4

Step-by-step explanation:

Here taking 60 as reference angle

so

tan60 = p/b

[tex]\sqrt{3}[/tex]    = p/2

so p = 2√3

so

b = 2√3

so

[tex]h^2 = p^2 + b^2\\h^2 = (2\sqrt{3})^2 + 2^2\\h^2 = 12 + 4\\h^2 = 16\\h = \sqrt{16} \\h = 4[/tex]

a = 4

Answer:

Step-by-step explanation:

The numbers from 1 to 9999 can be shown in the form of:

Each of x, y, z represent the digits from 0 to 9, so 10 ways each.

For each of the forms we have:

Total of:

By the way this is applicable to any digit.

Max number of digits=4

Their can be 4ways to represent

Each form can repeat 3

Total repeating

Answer:

G

Step-by-step explanation:

you know its G just by the way it is

Answer:

n>-4

Step-by-step explanation:

8+n>4

n>4-8

n>-4

Answer:

-4

Step-by-step explanation

Subtract 8 from 4 to get -4.

N = -4

God Bless.

Nate had $3000 at the beginning.

The percentage is defined as a ratio expressed as a fraction of 100.

Let the original amount of money is P

Nate spent 12 % of his paycheck on car repairs

⇒ 12% of P = 12P/100

And he spent 25 % of the remainder on food.

⇒  0.25(88/100)P

He gave $ 1,320 of the remaining money to his parents

⇒ 1320  

If the usual price of the computer was $ 825 and the discount was 20 %

⇒ 825 - 0.20(825) = 660

P = 12P/100 + 0.25(88/100)P + 1320 + 660

P - 34P/100 = 1980

100P - 66P = 198000

P = 3000

Hence, Nate had $3000 at the beginning.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ2

Answer:

B

Step-by-step explanation:

Adjacent angles must have the same vertex, so if the middle letter of the three letters used to name each of the angles in a pair are not the same, the angles cannot be adjacent.

That eliminates choices A, C, and D.

Answer: B

Look in the picture first below. Each pair of angles with the same vertex marked in blue is a pair of adjacent angles. For two angles to be adjacent angles, they must be next to each other, have the same vertex, and one cannot be inside the other.

Now look in the second picture below. Each pair of angles marked in red is not a pair of adjacent angles. Some of them are not next to each other. Others have one angle inside the other.

Answer:

1.665e+21

Step-by-step explanation:

hope it help

make it as brininst

Answer:

[tex]10^{12}\left(5\cdot \:10^8\right)\left(3.33\cdot \:10^0\right)[/tex]

Exponent rule:  [tex]a^b\cdot \:a^c=a^{b+c}[/tex]

[tex]10^{12}\cdot \:10^8\cdot \:10^0=\:10^{12+8+0}[/tex]

[tex]5\cdot \:3.33\cdot \:10^{12+8+0}[/tex]

Now, add 12 + 8 + 0 =20

[tex]=5\cdot \:3.33\cdot \:10^{20}[/tex]

Multiply 5 × 3.33=16.65

[tex]=10^{20}\cdot \:16.65[/tex]

Convert to decimal form

[tex]10^{20}=1.0E20[/tex]

Multiply

[tex]16.65\cdot \:1.0E20=1.665E21[/tex]

OAmalOHopeO

Step-by-step explanation:

Asymptote: y = 2 y-intercept: (0,8)

Step-by-step explanation:

The given function is

f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)

x

+2

This function is of the form:

f(x) = a {b}^{x} + cf(x)=ab

x

+c

where y=c is the horizontal asymptote.

By comparing , we have c=2 hence the horizontal asymptote is

y = 2y=2

To find the y-intercept, we put x=0 into the function to get:

f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)

0

+2=6+2=8

Therefore the y-intercept is (0,8).

Answer:

10

Step-by-step explanation:

ans is 10

because 2×5 is 10

Answer:

2x5= 10

Step-by-step explanation:

5, 10,15,20

five 2 times is 10

Answer:

8 : 27

Step-by-step explanation:

Given the ratio of sides of 2 similar objects = a : b , then

ratio of volumes = a³ : b³

Here ratio of sides = 56 : 84 = 2 : 3 , then

ratio of volumes = 2³ : 3³ = 8 : 27

Answer:

Mike had 72 stamps

Ken had 120 stamps

Step-by-step explanation:

Given

[tex]M \to Mike[/tex]

[tex]K \to Ken[/tex]

[tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]

[tex]K + 24 = 3 * ( M - 24)[/tex]

Required

Find K and M

Make K the subject in: [tex]K + 24 = 3 * ( M - 24)[/tex]

[tex]K = 3 * ( M - 24) - 24[/tex]

Substitute [tex]K = 3 * ( M - 24) - 24[/tex] in [tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]

[tex]\frac{1}{5} * [3 * ( M - 24) - 24] = \frac{1}{3} * M[/tex]

Open brackets

[tex]\frac{1}{5} * [3M - 72 - 24] = \frac{1}{3} * M[/tex]

[tex]\frac{1}{5} * [3M -96] = \frac{1}{3} * M[/tex]

Multiply both sides by 15

[tex]3* [3M -96] = 5 * M[/tex]

[tex]9M -288 = 5M[/tex]

Collect like terms

[tex]9M -5M= 288[/tex]

[tex]4M= 288[/tex]

Divide both sides by 4

[tex]M= 72[/tex]

Substitute [tex]M= 72[/tex] in [tex]K = 3 * ( M - 24) - 24[/tex]

[tex]K = 3 * (72 - 24) - 24[/tex]

[tex]K = 3 * 48 - 24[/tex]

[tex]K = 120[/tex]

Answer:

The speed of the balloon is 0.16 m/s.

Step-by-step explanation:

CD = 300 m

Let AD = x

AB = y

time, t = 3 min

Triangle, ADC

[tex]tan 15 = \frac{AD}{BC}\\\\0.27 \times 300 = x \\\\x = 80.4 m[/tex]

Triangle, BCD

[tex]tan 20 = \frac{BD}{BC}\\\\0.36 \times 300 = x + y \\\\x + y = 109.2 m[/tex]

So, y = 109.2 - 80.4 = 28.8 m

Speed = 28.8/180 = 0.16 m/s

Answer:

Step-by-step explanation:

He bought a total of 5 tickets, some child, some adult. This is the NUMBER equation.

# of adult tickets + # of child tickets = 5 tickets

Now for the COST equation. Each child ticket costs $2, so the expression for that is 2c; each adult ticket costs $8, so the expression for that is 8a. He spend a total of $22:

$2c + $8a = $22

Money and the number of tickets are NOT THE SAME so they cannot be put into the same equation. They won't add or subtract because they're not like.

Your system is choice A

Answer:

56.57

Step-by-step explanation:

See attached photo for steps

EDIT: I forgot to add 3.14, I am so sorry

Answer:

56.52

Step-by-step explanation:

Answer:

θ = 51.7

SOH-CAH-TOA

CAH: COS = ADJ/HYP   cos(θ) = 19.4/29.3

θ = 48.5

93.2 + 48.5 + x = 180

x = 38.3

90 + 38.3 + θ = 180

θ = 51.7

Step-by-step explanation:

Answer:

here's the answer to your question about

Given:

The height of a basketball is given by the function:

[tex]h(x)=-0.5x^2+3x+6[/tex]

where x is the horizontal distance from where it is thrown.

To find:

How far away from the basket should the player stand in order for the ball to go in the basket (10 feet high) on its way down.

Solution:

We have,

[tex]h(x)=-0.5x^2+3x+6[/tex]

Putting [tex]h(x)=10[/tex], we get

[tex]10=-0.5x^2+3x+6[/tex]

[tex]10+\dfrac{1}{2}x^2-3x-6=0[/tex]

[tex]\dfrac{1}{2}x^2-3x+4=0[/tex]

Multiply both sides by 2.

[tex]x^2-6x+8=0[/tex]

Splitting the middle term, we get

[tex]x^2-4x-2x+8=0[/tex]

[tex]x(x-4)-2(x-4)=0[/tex]

[tex](x-2)(x-4)=0[/tex]

[tex]x=2,4[/tex]

In the given function the leading coefficient is negative, so the given function represents a downward parabola. It means, first the function is increasing after that the function is decreasing.

So, the value of the function is 10 at [tex]x=2[/tex] (its way up) and at [tex]x=4[/tex] (its way down.

Therefore, the player should stand 4 units away from the basket in order for the ball to go in the basket (10 feet high) on its way down.

Area = Side^2

Area =( 4x + 2 )^2

Area = (4x)^2 + 2(4x)(2) + (2)^2

Area = 16x^2 + 16x + 4

Thus the correct answer is option B .

Answer:

32 newspapers

Step-by-step explanation:

6.4 / 0.2 = 32

Answer:

32 papers

Step-by-step explanation:

Take the total amount and divide by .20

6.40 / .20

Multiply the top and bottom by 10

64/2

32

Answer:

Step-by-step explanation:

I hope these are people in vehicles travelling toward each other.

80 mh * t + 40 mph * t = 420 miles

The two vehicles are going to travel a total of 420 miles. B will cover a lot more ground than A, but together they will make 420 miles

80t + 40t = 420

120t = 420

t = 420/120

t = 3.5

So after driving 3.5 hours, the two cars will meet.

Answer:

3596

Step-by-step explanation:

Use long multiplication to evaluate.

Answer:

3596

Step-by-step explanation:

(58*10) = 580

580*6 = 3480

58 * 2 = 116

3480 + 116 = 3596

Answer:

5x10^-2 option B

Step-by-step explanation:

Answer:

5x10^-2

the second one.

Answer:

17

Step-by-step explanation:

2f + 4f + 2 - 3 when f = 3

1) first we multiply 3 wherever f is

2 x 3 + 4 x 3 + 2 - 3 (solve)

6 + 12 + 2 - 3

18 + 2 - 3

20 - 3

17

Answer:

6+12+2-3=17

Step-by-step explanation:

Answer:x=3

Step-by-step explanation:

4x+3=x+9

4x-x=(-3)+9

3x=6

x=6:3

x=2