Question 2
2.1
A car travels for 1 hour 30 minutes and covers a distance of 150 km. How
long (In hours and minutes) will it take the car to cover a distance of 260 km
at the same average speed?

Answer:

x=4.285714286

Step-by-step explanation:

Let the number be x

Now we have,

→ [tex]32-7x=2\\\\[/tex]

→ [tex]32-2=7x\\\\[/tex]

→ [tex]30=7x\\[/tex]

→ [tex]x=\frac{30}{7} \\[/tex]

→ x=4.285714286

The solution to the trigonometric equation in the interval is given by:

[tex]x = \frac{\pi}{4}[/tex]

In this problem, the equation is given by:

[tex]\frac{1}{\sin{\theta}} = 2\cos{\theta}[/tex]

Applying cross multiplication, we have that:

[tex]2\sin{\theta}\cos{\theta} = 1[/tex]

Applying a trigonometric identity, we have that:

[tex]\sin{2x} = 1[/tex]

We have that on the interval [0, 2π), [tex]\sin{\left(\frac{\pi}{2}\right)} = 1[/tex]

Hence:

[tex]\sin{2x} = 1[/tex]

[tex]\sin{2x} = \sin{\left(\frac{\pi}{2}\right)}[/tex]

[tex]2x = \frac{\pi}{2}[/tex]

[tex]x = \frac{\pi}{4}[/tex]

For [tex]\frac{3\pi}{4}[/tex], we have that:

[tex]\sin{2x} = \sin{\left(\frac{3\pi}{2}\right)} = -1[/tex]

Hence only the first solution is correct.

More can be learned about trigonometric equations at https://brainly.com/question/24680641

Solution:

Given:

Let's substitute the values of Length, Breadth, and Height to obtain the volume of the tank.

Now, let's convert meters into liters.

Hoped this helped!

Answer:28.16

Step-by-step explanation:

A markup of 220% would bring 11 to 35.20, and a mark down of 20% would bring 35.20 to 28.16.

Your'e Welcome  (ФДФ) .

Answer:

230

Step-by-step explanation:

multiply 12 by 15 and add it onto the 50 to get your answer!

Have a good day!

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos²Θ = 1 - sin²Θ

Consider the left side

sin²Θ - cos²Θ

= sin²Θ - (1 - sin²Θ ) ← distribute parenthesis by - 1

= sin²Θ - 1 + sin²Θ

= 2sin²Θ - 1

= right side , thus verified

Answer:

Option B

Step-by-step explanation:

Given the following question:

53 oz = c?
[tex]1c=8oz[/tex]
[tex]53\div8=6.625[/tex]
[tex]6.625=\frac{6625}{1000}\div125=\frac{53}{8}[/tex]
[tex]\frac{53}{8} =53\div8=6\frac{5}{8}[/tex]
[tex]=6\frac{5}{8}[/tex]

Your answer is option B or "6 5/8 cups."

Hope this helps

Answer:

[tex]18=2^x[/tex]

Step-by-step explanation:

[tex]log_2(18)=x\\\\2^{log_2(18)}=2^x\\\\18=2^x[/tex]

Answer:

yards: 14080

miles: 8

that's basically it

Answer:

14080 yards

Step-by-step explanation:

A yard is 1/1760 mile, meaning 1 mile = 1760 yards.

5 miles + 3 miles = 8 miles

8 miles to yards = ?

8 x 1760 = 14080.

The Sims family drove 14.08k yds or 14080 yards.

Answer:

3

Step-by-step explanation:

7x² is the first term,

14x is the second term and

2 is the third term.

Answer:

10

Step-by-step explantion

Simplifying

2x + 3 + 25 = 3x + -17

Reorder the terms:

3 + 25 + 2x = 3x + -17

Combine like terms: 3 + 25 = 28

28 + 2x = 3x + -17

Reorder the terms:

28 + 2x = -17 + 3x

Solving

28 + 2x = -17 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

28 + 2x + -3x = -17 + 3x + -3x

Combine like terms: 2x + -3x = -1x

28 + -1x = -17 + 3x + -3x

Combine like terms: 3x + -3x = 0

28 + -1x = -17 + 0

28 + -1x = -17

Add '-28' to each side of the equation.

28 + -28 + -1x = -17 + -28

Combine like terms: 28 + -28 = 0

0 + -1x = -17 + -28

-1x = -17 + -28

Combine like terms: -17 + -28 = -45

-1x = -45

Divide each side by '-1'.

x = 45

Simplifying

x = 45

Answer:

Step-by-step explanation:

Exterior angle is same as sum of two remote interior angles:

Answer:

a) -6

b) -9

c) 27

Step-by-step explanation:

Since a=-3, plug in -3 for a and solve.

the answer is just 50° for both

Answer: 8 spools

Step-by-step explanation:

There are 12 apartments, and each apartment will need 60 meters of cable, so 12×60= 720 meters of cable needed.

If each spool only has 100 meters and he needs 720 meters, then 720÷100= 7.2. So he would need to purchase at least 8 spools, and will have 80 meters left over.

Answer:

2 rhombus

3 parallelogram

answer:

y = 3x + 5

steps-explanation:

given sample equation:

comparing to the formula of slope intercept form: y = mx + b

                                              [ where m is the slope and b is the y-intercept ]

we can determine here that the slope is 3 and -1 is the y-intercept.

but here we need only the slope.

in parallel, the slope is same: 3

formula:                  

using the formula:                     [ here known that y1 is -1 and x1 is -2 ]

Answer:

-10

Step-by-step explanation:

if negative meets a negative its gone come out as a positive

Answer:

1[tex]\frac{4}{15}[/tex] of straw

Step-by-step explanation:

The total amount of straw and hay together is, [tex]4 \frac{2}{3}[/tex].

and the total amount of hay alone is, [tex]3\frac{2}{5}[/tex]

All you need to do is subtract the hay from the total, which gives you, the answer above.

Problem 1

If you need to convert to a mixed number, then follow these steps.

27.2 = 27 + 0.2

27.2 = 27 + 1/5

27.2 = 27 & 1/5

27.2 pizzas is the same as 27 & 1/5 pizzas. In other words, you have 27 whole pizzas plus 1/5 of an extra one.

===========================================

Problem 2

The decimal 1.75 converts to the mixed number 1 & 3/4 because of the steps below.

1.75 = 1 + 0.75

1.75 = 1 + 3/4

1.75 = 1 & 3/4

In my opinion, it is optional to convert to a mixed number for either problem 1 or problem 2. So you can stick with 1.75 as the answer if you want.

===========================================

Problem 3

16 & 3/4 = 16 + 3/4 = 16 + 0.75 = 16.75

To get the unit rate, which is the cost per unit, we divide the total cost over the amount.

cost/amount = (2.89)/(16.75) = 0.1725373

which is approximate.

Round to the nearest penny to get a unit cost of $0.17 per fluid ounce, i.e. a unit cost of 17 cents per fluid ounce.

===========================================

Problem 4

We follow the same idea as problem 3.

4 & 3/5 = 4 + 3/5 = 4 + 0.6 = 4.6

unit cost = (total cost)/(amount)

unit cost = (7.56)/(4.6)

unit cost = 1.643478 dollars approximately

unit cost = 1.64 dollars approximately

===========================================

Problem 5

6 & 1/2 = 6 + 1/2 = 6 + 0.5 = 6.5

Like before, we'll divide the total cost over the total amount.

unit cost = (total cost)/(amount)

unit cost = (8.22)/(6.5)

unit cost = 1.264615 dollars approximately

unit cost = 1.26 dollars approximately

===========================================

Here's another way to look at the unit cost or unit rate.

Notice in problem 5 it says "cost per yard". This is the same as "cost per 1 yard" or "cost for each yard".

We can express the given info as the ratio

6.5 yards:$8.22

Now we want the "6.5 yards" to become "1 yard" to achieve the unit rate.

So we'll divide both parts by 6.5

6.5 yards:$8.22

6.5/6.5 yards:$8.22/6.5

1 yard: $1.26 approximately

For each yard, we'll spend $1.26

Problems 3 and 4 follow similar ideas. So this is why we divided the total cost over the total amount.

Answer:

third answer

Step-by-step explanation:

solve for and isolate x by moving over all other numbers to the left and then take the fifth power to make x^1/5 = to x

Answer:

9, 30, 27

Step-by-step explanation:

To find the perimeter, you must add up each side. In this scenario, we know that the perimeter is 66 feet. We also know the sides, which are n, 3n+3 and 4n-9.

So, we must add the sides to get 66 feet.

n+3n+3+4n-9=66

Combine like terms, and solve:

(n+3n+4n)+(3+-9)=66

8n+-6=66

8n-6=66

n=9

So if n=9, we can easily find the value of the other sides.

3(9)+3=30 feet.

4(9)-9=27 feet

So, the sides are 9, 30, and 27 feet (in order).

Answer:

3884.4 is what percent of 46.8 is 8300

Answer:

[tex]y = -\frac54x -7[/tex]

Step-by-step explanation:

Slope:

Y-intercept:

y = -5/4x -7

-Chetan K

Answer:

Step-by-step explanation:

im pretty sure its the 1st one

Linear functions are functions that change at a constant rate

The linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]

From the question, we have the following ordered pairs

(x,P(x)) = (2005,43%) and (2011,58%)

Start by calculating the slope (m)

[tex]m = \frac{P(x2) - P(x1)}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{58\% - 43\%}{2011 - 2005}[/tex]

Evaluate the differences

[tex]m = \frac{15\%}{6}[/tex]

Evaluate the quotient

[tex]m = 2.5\%[/tex]

The linear function is then calculated as:

[tex]P(x) = m(x - x_1)+ P(x_1)[/tex]

So, we have:

[tex]P(x) = 2.5\%(x - 2005) + 43\%[/tex]

Rewrite as:

[tex]P(x) = 0.025(x - 2005) + 0.43[/tex]

This gives

[tex]P(x) = 0.025x -50.125 + 0.43[/tex]

[tex]P(x) = 0.025x -49.695[/tex]

Hence, the linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]

Read more about linear functions at:

https://brainly.com/question/15602982

Answer:

[tex] \frac{ - 2 - 1}{4 - 0} \\ \\ \frac{ - 3}{4} \\ \\ \frac{3}{ - 4} [/tex]