Unit 1 : Algebra basics Homework 1: the real numbers

9.

J (0 , -10)

gradient/slope(m) = 2.

We're asked to find K if K is the X- Intercept.

At the x intercept... the corresponding y value is zero. This concept should be pretty clear.

Reason is...

At the Point where the line touches the x axis...If you trace the y value... It will be at point zero(0).

With this Knowledge

We're able to interprete that the points of K is

(x" , 0)

Where x" represents the x coordinate of K

So

J ( 0, - 10)

K ( x" , 0)

m= 2.

Applying the Gradient/Slope Formula

m = y₂ - y₁/x₂ - x₁

x₁ = 0 y₁ = -10

x₂ = x" y₂ = 0

Substituting

2 = 0 - ( -10)/ (x" - 0)

2 = 10/x"

x" = 10/2

x" = 5.

Coordinates of Point K is ( 5 , 0).

THIS IS YOUR ANSWER!.

10.

Total Time Taken = 16secs

10a). We're asked to calculate the rate of speed change for the first 5secs.

This is another way of saying "Calculate Acceleration" in the first 5sec of Motion.

Why?

Acceleration is the rate of change of speed or the rate at which speed changes.

acceleration = v - u/t

where v = Final Speed

u = initial Speed.

Looking at the graph

You see that

Initial speed(u) = 1m/s

Final Speed(v) = 9m/s

t = 5secs

Acceleration = 9 - 1/ 5

a = 8/5

a = 1.6m/s².✅

10b)

We're asked to calc "t" from the graph.

Given that the acceleration at "t" untill 16sec(end of motion) is 2m/s².

This simply means that Constant Acceleration was held from "t" to the end of the Motion.

Do not confuse Constant Acceleration for Constant Velocity.

At Constant Velocity... Acceleration is zero(0)

At Constant Acceleration...Velocity Changes Uniformly or at the same rate each second and this is what we're dealing with in this question.

Taking the same step as we used in calculating acceleration above

Given a= 2m/s²

a = v - u/∆t

Where ∆t means time change or difference.

From "t" to 16

The change in time is 16 - "t"

2 = 21 - 9/( 16 - t)

2 = 12/16-t

16-t = 12/2

16 - t = 6

t = 16 - 6

t = 10secs.✅

Have a great Day!.

Answer:

6

Step-by-step explanation:

90/7 divided by 1 3/4 is 7.34 so the closest one to it is 6

Answer:

6-2=1414

Step-by-step explanation:

6-2=1414

now

sub 6 from 2

4=1414

now divide 1414 by 4

1414÷4

[tex]1414 \div 4[/tex]

you will get the answer

Step-by-step explanation:

[tex] \frac{6}{14} - \frac{2}{14} \\ have \: same \: denomenator \: so \: we \\ \: can \: substract \: it \: directly \\ \frac{6 - 2}{14} \\ = \frac{4}{14} = \frac{2}{7} \\ thank \: you[/tex]

Answer:

1/4 I think is that answer

Answer:

true.........

20÷5=4..

20÷4=5

Answer:

Step-by-step explanation:

Answer:

[tex]y=6x-5[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept

We're given that the slope is 6. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=6x+b[/tex]

Now, to solve for the y-intercept, plug in the point (1,1) and solve for b:

[tex]1=6(1)+b\\1=6+b\\b=-5[/tex]

Therefore, the y-intercept of the line is -5. Plug this back into [tex]y=6x+b[/tex]:

[tex]y=6x+(-5)\\y=6x-5[/tex]

I hope this helps!

Answer:

well, only 87 people were asked. How did they get 482?

also, they should have asked the people in the library.

3b + 0.5a

the variables b and a are unknown values that represent the number of bananas and apples to be bought. These are next to each of its prices for it to be multiplied once we know the variable.

The costs of the fruits are to be added and you will end up with the total cost of fruits.

Answer: i give up typing essays ill just give it to you straight azure clicks per second is 8.5 or 17/2

bronze click per second is 9.5 38/4

crimsons time is 2.28 i guessed the closest and used a calulator good thing i learned this recently

clicks for desert is 34.9 or 35 not too clear but 34.9 is closer but you can choose i got this from guesing the division and i got 35/4.2 and 34.9/4.2

emeralds time is 0.40 3/.40 or 3/0.40

clicks for the last one or fuscia is 6 6/0.70 is well 8 gawd dammit you made me rite anotha essay

Answer:

Subtract 5 from input.

Step-by-step explanation:

10-5=5

8-5=3

6-5=1

Note:if you need to ask question let me know about it.

Answer:

a.18.9 miles is the answer

Answer:

The three numbers are 29, 31, and 33.

Step-by-step explanation:

Let's imagine that the three consecutive odd integers are 2x−1, 2x+1, and 2x+3. And we are told the sum is 93 right? So, let's equal the three numbers to 93.

2x − 1 + 2x + 1 + 2x + 3 = 93

6x + 3 = 93

     -3     -3

-----------------

6x = 90

/6    /6

----------------

x = 15

Now, plug in x into 2x−1, 2x+1, and 2x+3 to find the three numbers.

2x − 1                   2x + 1                 2x + 3

2(15) - 1                2(15) + 1             2(15) + 3

30 - 1                    30 + 1                 30 + 3

= 29                      = 31                      = 33

Answer:

30, 31, 32

Step-by-step explanation:

I hope this helps

Answer:

AC = 12

Step-by-step explanation:

AC = 3(4)

AC = 12

Answer:12

Step-by-step explanation:Ac  when ever there are 2 varibales together you multiply them.

Answer:

Just writing anything above these numbers

Step-by-step explanation:

Answer:

let t be winning time     t < 7.09 seconds

Step-by-step explanation:

let's first order the times from least to greatest:

7.09, 7.40, 7.75, and 7.86

Now, in order to have the winning time, the last runner must have a time less than the fastest runner so far. So, the winning time is less than 7.09 seconds.

Make sure to add units. I know that my teachers are REALLY picky about that, though yours may not care.

Answer:

If he can spend $400 +- $50 ($350 or $450) the maximum number of guests at $25 each is 18 and the minimum is 14. If there can be up to 7 guests, he should prepare to have at least 3 tables to ensure everyone gets a seat if he goes with the $450 option.

Step-by-step explanation:

Please mark Brainliest if this helped :)

Division is one of the four fundamental arithmetic operations. The minimum number of tables Ashton should reserve so everyone has a seat is 2.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Ashton's budget is $400±50. Therefore, the maximum and the minimum budget that Ashton can spend on the banquet are,

Maximum budget = $400 + $50 = $450

Minimum budget = $400 - $50 = $350

A.) Now, the maximum guest will cost the maximum budget, therefore, we can write

Maximum guest = Maximum budget / Budget per guest

                           = $450 / $25

                           = 18

Minimum guest = Minimum budget / Budget per guest

                           = $350 / $25

                           = 14

B.) Since the minimum number of guests that can come to the banquet is 14, and only 7 people can seat at a table, therefore, the minimum number of tables Ashton should reserve so everyone has a seat is 2.

Learn more about Division here:

https://brainly.com/question/369266

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Answer:

Step-by-step explanation:

Move all terms to the left side.

3x−x+2−12=0

Reduce like terms.

2x−10=0

Factor.

2(x−5)=0

Determine the roots from the equation. In this case, x=5 is the only solution to the equation.

Answer:

x = 5

Step-by-step explanation:

hope it is help full

mark me a brainlist

Answer:

1

Step-by-step explanation:

it just is

Answer:

50 gallons of red

30 gallons of blue

Step-by-step explanation:

5 parts of the whole must be red, 3 parts of the whole must be blue, and there are 5+3=8 parts in total.

therefore, 1 part = 80/8 = 10 gallons

red : 5 parts

5×10 = 50 gallons

blue : 3 parts

3×10 = 30 gallons

Answer:

[tex]8 + x = 2 + 8 \\ 8 + x = 10 \\ x = 10- 8 \\ \\ x = 2 \\ then8 + 2 = 2 + 8 \\ thank \: you[/tex]

Answer:

2

Step-by-step explanation:

8 + 2 = 10, so basically, 10 - 8 = 2. Meaning the missing number to when 8 is added to something to equal 10, would be 2.

Answer:

8.4

Perimeter=a+b+c

3.2+4.2+3.-2

= 8.4

The perimeter of the triangle will be 5 + √17.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees. The sum of all the sides of the triangle will be known as the perimeter of the triangle.

A triangle DEF with vertices D (3,2), E (4,2), and F (3,-2).

Distance between DE will be

DE² = (4 - 3)² + (2 - 2)²

DE² = 1

DE = 1

Distance between EF will be

EF² = (3 - 4)² + (-2 - 2)²

EF² = 1 + 16

EF = √17

Distance between DF will be

DF² = (3 - 3)² + (-2 - 2)²

DF² = 16

DF = 4

Then the perimeter of the triangle will be

P = DE + EF + DF

P = 1 + √17 + 4

P = 5 + √17

The perimeter of the triangle will be 5 + √17.

More about the perimeter of the triangle link is given below.

https://brainly.com/question/25813512

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it's most likely c but i could be wrong

Answer:

first statement

Step-by-step explanation:

64 < 77 < 81 , then

[tex]\sqrt{64}[/tex] < [tex]\sqrt{77}[/tex] < [tex]\sqrt{81}[/tex] , that is

8 < [tex]\sqrt{77}[/tex] < 9

Thus [tex]\sqrt{77[/tex] is to the left of 9 on the number line

Answer:

OPTION A IS CORRECT.

BRAINLIST PLEASE!!!

Step-by-step explanation:

Hi there!

According to the question;

nth term (tn) = 3n+8

a).

T1 = 3*1+8

= 11

b).

t7 = 3*7+8

= 29

c).

t14 = 3*14+8

= 50

Therefore, t1 = 11, t7 = 29, t14 = 50.

Hope it helps!

Answer:

11, 29, 50

Step-by-step explanation:

To find the appropriate term , substitute the term number into the rule, that is

(a) t₁ = 3(1) + 8 = 3 + 8 = 11

(b) t₇ = 3(7) + 8 = 21 + 8 = 29

(c) t₁₄ = 3(14) + 8 = 42 + 8 = 50

Answer:

Step-by-step explanation:

The asymtope's equation is y = 3

Just use dy/dx to find the gradient of the curve at this point and sub in y = 3 :)

Please mark as brainliest (I really need it) :)

Answer:

D because it costs less for 7 hours

Answer:

The company that would give you the best deal would be Company D.

Step-by-step explanation:

Company A:

First you set up as an equation.

y=25x+50

I used 25x because 25 represents the hourly rate and x represents the hour it increases.

y=25(7)+50

We have to substitute 7 in for x because it says "If you had planned for 7 hours".

Multiply 25 and 7. You should get 175.

y=175+50

Add 175 and 50. You should get 225.

y=225.

You do the same thing for the rest of the problems.

Company B:

y=30x+40

y=30(7)+40

y=210+40

y=250

Company C:

y=20x+60

y=20(7)+60

y=140+60

y=200

Company D:

y=5x+150

y=5(7)+150

y=35+150

y=180

The company that would give you the best deal would be Company D.

Answer:

Step-by-step explanation:

ans:- 144 inches squared

ur welcome..

Answer:

144

Step-by-step explanation:

12*12=144

squares have all the same sized sides.

Answer:

x=8 y=4

Step-by-step explanation:

eliminate x: make x of two equation equal to each other

2(-3x+9y=12) : -6x+18y=24 ___[1]

-3(2x-8y=-16) : -6x+24y=48 ___[2]

[2]-[1]= 6y=24

substitute y to any equation;

2x-8y=-16

2x-8(4)= -16

2x= -16+32

2x= 16

Answer:

x=14 and y=6

Step-by-step explanation:

-3x+9y=12.............(i)×2

2x-8y=-16..............(ii)×3

Multiplying equation (i) by 2 and equation (ii) by 3 and adding (i) and (ii)

-6x+18y=12

6x-24y=-48

-----------------

0-6y=-36

or, -6y=-36

So,y=6

From (i)

-3x+9y=12

or,-3x+9×6=12

or,-3x+54=12

or,-3x=12-54

or,-3x=-42

So,x=14

Answer:

a = d/4 - b/c

Step-by-step explanation:

Subtract b/c from both sides. We can subtract a fraction

so

a = d/4 - b/c

Step-by-step explanation:

ANS is 3.47

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