Practice Sum

If y is inversely proportional to x and y=4 when x=3

i) Express y in terms of X

ii) Find the value of y when x=6​

Answer:

5.2x + 24.4

Step-by-step explanation:

1.2(x-3) + 4 (x+7)

=1.2x - 3.6 + 4x + 28

=5.2x + 24.4

Hope this helps..

Answer:

He has memorized 18 words

Step-by-step explanation:

(3/4)*24 = 18

Answer:

B

Step-by-step explanation:

Step 1: Find √11

√11 is between perfect squares √9 and √16

√9 < √11 < √16

3 < √11 < 4

So it is between 3 and 4

Step 2: Evaluate

√11 = 3.31662

Closest dot is B.

Answer:

16, 56, ...

Step-by-step explanation:

It looks like you have to put in each cell the multiplication of the row and the column, so the columns are 2, 7, 4 etc., and the row is always 8.

First cell: 2x8 = 16

Second cell: 7x8 = 56

and so on

It teaches you to apply the multiplication in a random sequence; you should be able to do this in your head.

Answer:

Where does the graph of the line y = x - 2 intersect the x-axis?

O A. (0, 2)

O B. (2,0)

O C. (0, -2)

0 D. (-2, 0)

C. ( 0 , -2 )

Step-by-step explanation:

I hope this helps

Follow // Followback

The line of y=x-2 intersects the x axis at (2,0).

To find the points where line intersect the x-axis.

Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs.

The x-axis is defined as being at y=0 (look at a graph, the x-axis intersects the y-axis at y=0). Therefore, all you need to do is put in 0 for y, and solve for x.

  y=x-2

 put in 0 for y

 0=x-2

add 2 to both sides

2+0=x-2 +2  

 x=2

Therefore the line of y=x-2 intersects the x axis at (2,0).

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Answer:

Hey there!

The question is basically asking for you to solve a fraction subtraction problem, and fill in the missing values as you solve.

The given problem is 2/3 - 1/2. However, we can't subtract right now, since the denominators are different.

2/3 can be expressed as 4/6, and 1/2 can be expressed as 3/6.

Thus, the missing denominator in line one is 6 and the missing numerator in line one is 3.

4/6-3/6=1/6.

Thus, the numerator in line two should be 1.

From top to bottom, the numbers in the three boxes should be 6, 3, and 1.

This can be a confusing topic, especially if you're just learning it. Let me know if you need additional help :)

Answer:

Step-by-step explanation:

9*60+36= 540+ 36= 576 minutes

so it is = 576/ 60 hours

Answer:

Solution : First Option

Step-by-step explanation:

This equation is quadratic as there is a " x^2 " term present. If you were to expand the equation,

x(x - 6) = - 5,

x^2 - 6x = - 5,

x^2 - 6x + 5 = 0

As you can see this resembles a quadratic equation. Your solution will be the first option, 1. The equation is a quadratic equation because there is an x^2 term

Answer:

The equation is an quadratic equation because there is an x^2-term 2

Step-by-step explanation:

Answer:

y=30

Step-by-step explanation:

f(-2)=18+3(-2)^2

f(-2)=18+3*4

f(-2)=18+12

f(-2)=30

Answer:

y= 6

Step-by-step explanation:

substitute x= -2 in the equation y=18+3x^2

from there you'll get your final answer

Answer:

-217

Step-by-step explanation:

Add them both together because it is asking for the "sum".

-354+137= -217

Answer:

10

Step-by-step explanation:

We can show this as:

Since

Then

The closest number in the list is 10 as all the rest are greater than 10

Second choice is the correct one

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[tex]\sqrt{90}[/tex]

[tex]= \sqrt{10}[/tex] (Decimal: 9.486833)

( I don't know it might be wrong )

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       Have a great day/night!

                  ❀*May*❀

Answer:

A and D

Step-by-step explanation:

3 - 5x > 2

= -5x > 2-3

= -5x > -1

= x < 1/5

Answer:

The correct answer is A. x = 1 or D. x = 7.

Step-by-step explanation

For this problem, we can substitute each of the values and see which ones make the inequality true.

Using x = 1

3 - 5(1) > 2

3 - 5 > 2

-2 > 2

This is not true, so this is not our solution. However, I will show the rest of the solutions anyways.

Using x = 0

3 - 5(0) > 2

3 - 0 > 2

3 > 2

This is true, so x = 0 is a solution to the inequality.

Using x = -1

3 - 5(-1) > 2

3 + 5 > 2

8 > 2

This is true, so x = -1 is a solution to the inequality.

Using x = 7

3 - 5(7) > 2

3 - 35 > 2

-32 > 2

This is not true, so x = 7 is not a solution to the inequality.

Answer:

Step-by-step explanation:

The question is not complete, i think the correct question is:

Kareem and Kira each opened a savings account today. Kareem opened his account with a starting amount of $770, and he is going to deposit $30 per month. Kira opened her account with a starting amount of $935, and she is going to deposit $45 per month. Let x be the number of months after today

Let us assume that each acre of land on Mars cost $107.

a) For Kareem account, she started with $770 and would deposit $30 per month. Let y represent the money deposited after x month. This can be represented by the equation:

y = 770 + 30x

Since each acre cost $107, 10 acre would cost $1070. Therefore $1070 is needed to be saved. To find the number of months, substitute y = 1070 and solve. Therefore:

1070 = 770 + 30x

1070 - 770 = 30x

30 x = 300

x = 300/30

x = 10

It would take 10 months for Kareem to buy 10 acres of land

b) For Kira account, she started with $935 and would deposit $45 per month. This can be represented by the equation:

y = 935 + 45x

Since each acre cost $107, 10 acre would cost $1070. Therefore $1070 is needed to be saved. To find the number of months, substitute y = 1070 and solve. Therefore:

1070 = 935 + 45x

1070 - 935 = 45x

45 x = 135

x = 3

It would take 3 months for Kira to buy 10 acres of land

Answer:

33000

Step-by-step explanation:

Substituting 250 for x and -120 for y, we get:

(250)^2 + 2(250) - (250)(120)  =  62500 + 500 - 30000, or

32500 + 500, or 33000

Answer:

Step-by-step explanation:

y = -1/2 x – 7

when x is 0

y = -1/2(0) - 7

y = - 7

(0,-7)

when y is 0

0 = -1/2 x - 7

1/2 x = -7

x = -7(2)

x = -14

(-14,0)

The graph of equation y = -1/2x – 7 is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

⇒ y = - 1/2x - 7

Hence, We get;

The graph of equation y = -1/2x – 7 is shown in figure with slope - 1/2 and y - intercept is - 7.

Thus, The graph of equation y = -1/2x – 7 is shown in figure.

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Answer:

There are 7,725 square feet of grass on the trapezoidal field

Step-by-step explanation:

Here in this question, we are interested in calculating the square feet of grass present on the trapezoidal field.

What this question is actually asking us is to calculate the area of the trapezoid-shaped grass field.

To calculate this area, what we need to do

simply is to use the formula for the area of a trapezoid.

Mathematically, the area of a trapezoid can be calculated using the formula;

Area of trapezoid = 1/2 * (a + b) * h

where a and b refers to the length of the parallel lengths of the trapezoid and h refers to the height of the trapezoid.

From the question;

a, b = 81ft and 125 ft

h = 75 ft

Substituting these values, we have :

Area = 1/2 * (81 + 125) * 75

Area = 1/2 * 206 * 75 = 83 * 75 = 7,725 ft^2

Answer:B&D

Step-by-step explanation:

Answer:

c) 135°

b) 72°

d) 90°

a) 115°

Step-by-step explanation:

A supplementary pair are two angles whose measures added is equal to 180°. Set an equation with the given values plus a number (the other angle) equal to 180:

c) [tex]x+45=180[/tex]

Solve. Subtract 45 from both sides:

[tex]x+45-45=180-45\\\\x=135[/tex]

The supplement is 135°

b) [tex]108+x=180[/tex]

Solve. Subtract 108 from both sides:

[tex]108-108+x=180-108\\\\x=72[/tex]

The supplement is 72°

d) [tex]x+90=180[/tex]

Solve. Subtract 90 from both sides:

[tex]x+90-90=180-90\\\\x=90[/tex]

The supplement is 90°

a) [tex]x+65=180[/tex]

Solve. Subtract 65 from both sides:

[tex]x+65-65=180-65\\\\x=115[/tex]

The supplement is 115°

:Done

Answer:

The last option log_7*(8x/9)

Step-by-step explanation:

You can use the rule of logarithms to solve this. In this expression you have addition and subtraction of logs so knowing that you can use multiplication and division to simplify this into a single log.

Step-by-step explanation:

As we can see, the line on the bottom is a perfectly straight 180º line, so the two angles, a and 50º are supplementary angles. Remember: Supplementary angles = 180º, and complementary angles = 90º.

Since this is a 180º line, all we have to do is to subtract 50 from 180 to get our angle a.

180-50 = 130º

Our answer: a = 130º

Answer:500 cm

Step-by-step explanation:

Given

height of ethan = 180 cm

length of shadow =144 cm

Distance of ethan from lamp =256 cm

from diagram, we can write

[tex]\Rightarrow tan \theta =\frac{FC}{EC}\quad \ldots(i)[/tex]

[tex]\Rightarrow \tan \theta =\frac{AB}{BE}\quad \ldots (ii)[/tex]

From (i)  and (ii)  we get

[tex]\tan \theta =\frac{FC}{EC}=\frac{AB}{BE}[/tex]

[tex]\Rightarrow \frac{180}{144}=\frac{h}{144+256}[/tex]

[tex]\Rightarrow h=\frac{180}{144}\times 400[/tex]

[tex]\Rightarrow h=500\ cm[/tex]

So, height of lamp post AB is [tex]500\ cm[/tex]

Answer:

10 sqrt(10)

Step-by-step explanation:

sqrt(1000)

sqrt(100*10)

we know that sqrt(a*b) = sqrt(a) sqrt(b)

sqrt(100) * sqrt(10)

10 sqrt(10)

Answer:

-13

Step-by-step explanation:

See steps below:

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               Hi my lil bunny!

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                 [tex]\boxed{-13}[/tex]

Let's solve your equation step-by-step.

[tex]2(3x+6)=3(x-9)[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(3x+6)=3(x-9)[/tex]

[tex](2) (3x) + (2) (6) = (3)(^{x}) + (3) (-9)[/tex] (Distribute)

[tex]6x + 12 = 3x + -27[/tex]

[tex]6x + 12 = 3x -27[/tex]

Step 2: Subtract 3x from both sides.

[tex]6x + 12 - 3x = 3x - 27 - 3x\\3x + 12 = -27[/tex]

Step 3: Subtract 12 from both sides.

[tex]3x + 12 - 12 = -27 - 12\\3x = -39[/tex]

Step 4: Divide both sides by 3.

[tex]\frac{3x}{3} = \frac{-39}{3}\\x = -13[/tex]

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Answer:

All parts are attached below :)

Given that :-

→ N represent the number of bikes .

→ Weight of container including bikes is 250+23(n-1) pounds.

To Find :-

→ Weight of container when we have 20 bikes.

Solution :-

→ Weight = 250+23(n-1) pounds

Putting the value of n here .

→ Weight = 250+23(20-1)

→ Weight = 250 +23(19)

→ Weight = 250 + 437

An expression is defined as a set of numbers, variables, and mathematical operations. The container weight with 20 bikes in it will be 687.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given that the weight of the container in pounds, including the bikes, can be modeled using the expression 250 + 23 (n-1). Therefore, the container weighs 20 bikes in it will be,

Weight of container = 250 + 23(n - 1)

                                 = 250 + 23(20 - 1)

                                 = 250 + 23(19)

                                 = 250 + 437

                                 = 687

Hence, the container weight with 20 bikes in it will be 687.

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Q1

[tex]n > \frac{81}{2} [/tex]

Q2 D

sry I don't hv time to ans more

Answer:

Not possible.

Step-by-step explanation:

250 = 2 * 5 * 5 * 5

From this you write the square root as 5 * √10  so you would have to use a calculator to get any further.

Answer:

Length = 82.5 feet

Width = 17.5 feet

Step-by-step explanation:

The formula for the Perimeter of a rectangle = 2(Length + Width)

= 2L + 2W

We are told in the question that: Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard

Hence, The perimeter of the rectangular front yard = 200 feet

200 = 2( L + W).........Equation 1

Also, the length is 5 feet less than 5 times the width

L = 5W - 5

Hence,

200= 2(5W - 5 + W)

200 = 2(5W + W - 5)

200 = 2(6W - 5)

200 = 12W - 10

Collect the like terms

200 + 10 = 12W

210 = 12W

W = 210/12

W = 17.5 feet

Substitute 17.5 for W in Equation 1

200 = 2( L + W).........Equation 1

200 = 2( L + 17.5)

200 = 2L + 35

200 - 35 = 2L

2L = 165

L = 165/2

L = 82.5 feet

Therefore, the Length of the rectangular fence = 82.5 feet while the Width of the rectangular fence is 17.5 feet.

=> R.H.S

[tex] \frac{ \sin(4x) }{ \cos(2x) } = \frac{ \sin(2x + 2x) }{ \cos(2x) } [/tex]

[tex] = \frac{ 2 \sin(2x) \cos(2x) }{ \cos(2x) } [/tex]

[tex] = 2 \sin(2x) [/tex]

[tex] = 2(2 \sin(x) \cos(x) )[/tex]

[tex] = 4 \sin(x) \cos(x) [/tex]

R.H.S = L.H.S

PROVED!

Answer:

Below

Step-by-step explanation:

● 4 sin(x) cos(x) = sin(4x)/cos(2x)

Let's prove that:

● 4 sin(x) cos(x) cos(2x) = sin(4x)

It's easier to prove it than the first one

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 4 sin(x) cos(x) cos (2x)

● [2 sin(x) cos(x)] 2 cos(2x)

We khow that [2 sin(x) cos(x)]= sin(2x)

So:

● sin(2x) 2 cos(2x)

Based on the same relation

● sin(4x)

It's proved