A car and a bus were travelling towards each other at uniform speeds. They were 250 km apart at noon and passed each other at 2 p.m. If the speed of the car was 75 km/h, find the speed of the bus.

Answer:

x = [tex]\frac{3}{20}[/tex]

Step-by-step explanation:

Given

x + [tex]\frac{3}{2}[/tex] + (x - 1) = [tex]\frac{4}{5}[/tex]

Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10x + 15 + 10(x - 1) = 8

10x + 15 + 10x - 10 = 8

20x + 5 = 8 ( subtract 5 from both sides )

20x = 3 ( divide both sides by 20 )

x = [tex]\frac{3}{20}[/tex]

x + 3/2 + x - 1 = 4/5

Collect the same terms

x + x + 3/2 - 1 = 4/5

2x + 3/2 - 2/2 = 4/5

2x + (3 - 2)/2 = 4/5

2x + 1/2 = 4/5

2x + 0.5 = 0.8

Subtract both sides 0.5

2x + 0.5 - 0.5 = 0.8 - 0.5

2x + 0 = 0.3

2x = 3/10

Divide both sides by 2

2x ÷ 2 = ( 3/10 ) ÷ 2

x = 3/10 × 1/2

x = 3/20

_________________________________

3/20 + 3/2 + ( 3/20 - 1 ) = 4/5

3/20 + 30/20 + ( 3/20 - 20/20 ) = 4/5

(3 + 30)/20 + (3 - 20)/20 = 4/5

33/20 - 17/20 = 4/5

(33 - 17)/20 = 4/5

16/20 = 4/5

4 × 4 / 4 × 5 = 4/5

4/5 = 4/5

Thus we found the correct value of x .

And we're done...

Answer:

ones

Step-by-step explanation:

Answer:

i believe its 162

Step-by-step explanation:

hope it helped :>

Answer:

14/3

Step-by-step explanation:

4 and 2/3 = 4 2/3 = 4 + 2/3 = 4/1 + 2/3 = 12/3 + 2/3 = 14/3

Answer:

x = 2

Step-by-step explanation:

note that 4096 = [tex]8^{4}[/tex] , then

[tex]8^{2x}[/tex] = [tex]8^{4}[/tex]

Since bases on both sides are equal, both 8 , then equate the exponents

2x = 4 ( divide both sides by 2 )

x = 2

Answer:

x = 2

Step-by-step explanation:

[tex]8^{2x} = 4096[/tex]

Step 1 :- Write 4096 in the exponential form with the base of 8.

[tex]8^{2x} = 8^4 [/tex]

Step 2 :- Since the base of both equation is same , set the exponents equal.

2x = 4

Step 3 :- Divide both side by 2

[tex]{2x}{2} = \frac{4 }{2}[/tex]

x = 2

Answer:

4/3 =a

Step-by-step explanation:

10 − 3(2a − 1) = 3a + 1

Distribute

10 -6a +3 = 3a+1

Combine like terms

13 -6a = 3a+1

Add 6a to each side

13-6a+6a = 3a+6a +1

13 = 9a+1

Subtract 1 from each side

13-1 = 9a+1-1

12 = 9a

Divide by 9

12/9 = 9a/9

4/3 =a

a = 4/3

10 - 3( 2a - 1 ) = 3a + 1

10 - 3 × 2a -3 × -1 = 3a + 1

10 - 6a + 3 = 3a + 1

10 + 3 - 6a = 3a + 1

13 - 6a = 3a + 1

13 - 6a - 3a = 3a - 3a + 1

13 - 9a = 1

13 - 13 - 9a = 1 - 13

- 9a = - 12

-9a / - 9 = - 12 / - 9

a = 4/3

Answer:

0.4 or 0.40

Step-by-step explanation:

There are 10 total numbers. 4 of them are in set B.

So, 4/10 are in set B.

The probability is 0.4 because 4 divided by 10 is 0.4.

Answer:

[tex](13)\ 1 <x < 15[/tex]

[tex](14)\ 6 <x < 18[/tex]

Step-by-step explanation:

Question 13:

[tex]a,b = 8,7[/tex] -- the two sides

Using triangle inequality theorem, we have:

[tex]a + b > x[/tex]

[tex]a + x > b[/tex]

[tex]x + b > a[/tex]

So, we have:

[tex]a + b > x[/tex]

[tex]8 + 7 > x[/tex]

This gives:

[tex]15 > x[/tex]

[tex]a + x > b[/tex]

[tex]8 + x > 7[/tex]

Collect and evaluate like terms

[tex]x > -1[/tex]

[tex]x + b > a[/tex]

[tex]x + 7 > 8[/tex]

Collect and evaluate like terms

[tex]x > 1[/tex]

Ignore the inequality with a negative value.

So, we have:

[tex]x > 1[/tex] and [tex]15 > x[/tex]

Rewrite as:

[tex]1< x[/tex] and [tex]x < 15[/tex]

Merge

[tex]1 <x < 15[/tex]

Question 14:

[tex]a,b = 12,6[/tex] -- the two sides

Using triangle inequality theorem, we have:

[tex]a + b > x[/tex]

[tex]a + x > b[/tex]

[tex]x + b > a[/tex]

So, we have:

[tex]a + b > x[/tex]

[tex]12 + 6 > x[/tex]

This gives:

[tex]18 > x[/tex]

[tex]a + x > b[/tex]

[tex]12 + x > 6[/tex]

Collect and evaluate like terms

[tex]x > -6[/tex]

[tex]x + b > a[/tex]

[tex]x + 6 > 12[/tex]

Collect and evaluate like terms

[tex]x > 6[/tex]

Ignore the inequality with a negative value.

So, we have:

[tex]x > 6[/tex] and [tex]18 > x[/tex]

Rewrite as:

[tex]6< x[/tex] and [tex]x < 18[/tex]

Merge

[tex]6 <x < 18[/tex]

Answer:

Gradient of A: 2

Gradient of B: -1

Step-by-step explanation:

Gradient = change in y/change in x

✔️Gradient of A using two points on line A, (2, 5) and (0, 1):

Gradient = (1 - 5)/(0 - 2) = -4/-2

Simplify

Gradient of A = 2

✔️Gradient of B using two points on line B, (0, 5) and (5, 0):

Gradient = (0 - 5)/(5 - 0) = -5/5

Simplify

Gradient of B = -1

Answer:

ok

What do you want me to answer ?

Answer:

that thing is not seeing properly and you can capture it again and resend it

Answer:

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect

Step-by-step explanation:

???????? what is easy??

Answer:

3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]

Step-by-step explanation:

(f · g )(x) = 3[tex]x^{2}[/tex] · (x + 2) = 3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]  (Multiply the two terms by distributing)

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]

Adding 620 on both sides, we get

[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]

We need to find the y-value for [tex]x=57[/tex].

[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]

[tex]y=183.825+523.25[/tex]

[tex]y=707.075[/tex]

[tex]y\approx 707.1[/tex]

Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.

Answer:

ok so lets divide 90 by 15 to get 6 so she gets paid 6 per student and that means lisa gets paid 12 so lets just multiply

6*20=120 so mary gets paid 120

and lisa gets paid doable that so 420

but i don't know there base pay so the i can't answer this problem

Hope This Helps!!!

Answer: 8

Step-by-step explanation:

Hi!

[tex]3x^3-2y^3-6x^2y^2+xy=\\\\=3\cdot(\frac{2}{3})^3-2\cdot(\frac{1}{2})^3-6\cdot(\frac{2}{3})^2\cdot(\frac{1}{2})^2+\frac{2}{3}\cdot\frac{1}{2}=\\\\=3\cdot\frac{8}{27}-2\cdot\frac{1}{8}-6\cdot\frac{4}{9}\cdot\frac{1}{4}+\frac{1}{3}=\\\\=\frac{8}{9}-\frac{1}{4}-\frac{2}{3}+\frac{1}{3}=\frac{8}{9}-\frac{1}{4}-\frac{1}{3}=\frac{32}{36}-\frac{9}{36}-\frac{12}{36}=\boxed{\frac{11}{36}}[/tex]

Answer:

true

Step-by-step explanation:

complementary angles equal 90° and 34+56 is 90°

Answer:

True

Step-by-step explanation:

Complement angle means that the two angles add up to 90 degrees. We can check this by adding the two given angles together:

34+56=90

90=90

This means that this is true.

I hope this helps and have a great day!

Answer:

x = 6

HI = 29

Step-by-step explanation:

✔️HI = ½(AB) => Triangle Mid-segment Theorem

HI = 5x - 1

AB = 58

Plug in the values and solve for x

5x - 1 = ½(58)

5x - 1 = 29

Add 1 to both sides

5x - 1 + 1 = 29 + 1

5x = 30

Divide both sides by 5

5x/5 = 30/5

x = 6

✔️HI = 5x - 1

Plug in the value of x

HI = 5(6) - 1

HI = 30 - 1

HI = 29

Answer:

Probably 10

Step-by-step explanation:

10/5=2

Answer:

A. ^3√5 is the answer.

Step-by-step explanation:

5^( 1 / 3 ) = ^3√5

Answer:

5% = 1/20

15% = 3/20

6.5% = 0.065

25% = 0.25

7% = 0.07

Step-by-step explanation:

I hope this helps! Just ask me if you have any questions.

Have a nice dayy! :)

Answer:

.05  25%  .15  7% .065  100% 2000% .25

Step-by-step explanation:

Percentages to decimals :

example  

5% = .05

First remove the % sign: 5

Where is the decimal? Here : 5.00

Now move the decimal to the left two places. Fill the gaps with zeros : .05

Another way to do it is by divide the number by 100. Use a calculator if necessary.

Example 2: 6.5%

Move decimal two places to left: .065

Example 3: .56%

Move decimal to places to the left:  .0056

Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.

Example: .25 becomes 25%

                .07 becomes 07% or just 7%

The choose (C) 60

The measure of the angles of a triangle is 180, and this triangle is equilateral, so 180/3=60, each angle is 60°

Answer: x= 112°, y = 34°

Step-by-step explanation:

"Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle."

"The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points."

x = 180° - 68° = 112°

y = 68 ÷ 2 = 34°

Circle theorems source: https://revisionmaths.com/gcse-maths-revision/shape-and-space/circle-theorems#:~:text=Angles%20formed%20by%20drawing%20lines%20from%20the%20ends,the%20point%20on%20the%20circumference%20our%20triangle%20touches.

Answer:

13.97%

Step-by-step explanation:

Find her percent increase in pay by dividing 95 by 680:

95/680

= 0.1397

Multiply this by 100:

= 13.97

So, her percent increase in pay is approximately 13.97%