A picture measures x cm by (x + 4) cm. It is enlarged by a scale factor of 3 to form a poster. The area of the enlarged poster is 1053 cm².
(i) Pauline made a wild guess, without making any prior calculation, that the value of x is 31. Without finding the actual value of x, verify whether her claim is correct.
(ii) Form an expression in terms of x and show that it reduces to x² + 4x - 117 = 0.
(iii) Calculate the perimeter of the original picture before the enlargement.

pls help me I need it by 25mins​

Answer:

100cm²

Step-by-step explanation:

The notepad is square.

The area of a square = length X width.

All the sides of a square are the same length.

Therefore, the area of the notepad = 10 X 10 which equals 100.

Don't forget the units!

The units for area is cm².

The units for volume is cm³.

This is area so your answer is 100cm².

Hope this helped, have a nice day!

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.

Given that:

Pules Rs 4000 per night but will decrease the amount by R100 per person occupying the chalet.

Number of People          Cost per night

          1                                       4000

          2                                       3900

          3                                      3800

          4                                       3700

          5                                       3600

          6                                       3500

          7                                       3400

          8                                       3300

          9                                       3200

          10                                      3100

let C be cost per night and n be the number of people of staying in chalet.

equation:   C=  4000-100(n-1)

      for n=1: C= 4000- 0=4000

            n=2, C= 4000-100(1)= 3900

The graph is attached below:

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Answer:

[tex]a)~5(x-4)(x+1)[/tex]

Step-by-step explanation:

[tex]~~~5x^2 -15x -20\\\\=5(x^2 -3x -4)\\\\=5(x^2 -4x +x -4)\\\\=5\textbf{[}x(x-4) +(x-4)\textbf{]}\\\\=5(x-4)(x+1)[/tex]

Answer:

75

Step-by-step explanation:

becAUSE IF YOU TEST IT THATS UR ANSWER

The solutions to the equation -2x = 2^x are (1,2) and (2,4)

The attached graph represents the missing part of the question

The equations are given as:

f(x) = -2x

g(x) = 2^x

The solution to -2x = 2^x is the points where the graphs of f(x) and g(x) intersect

From the attached graph, the points of intersection are:

(1,2) and (2,4)

Hence, the solutions to the equation -2x = 2^x are (1,2) and (2,4)

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Answer:

6x-6x56 =-2016

Step-by-step explanation:

You have to subtract, then multiply by 56 to get -2016, as it shows a negative.

The slope of EF, FG, GH, and HE is 4, -1/4, 4, and -1/4 respectively. And the length of sides EF, FG, GH, and HE will be √68, √68, √68, and √68 units respectively.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

The points E(-4, 6), F(-6, -2), G(2, -4) , and H(4, 4) form quadrilateral EFGH.

Then the slopes are calculated below.

Slope of EF = (6 + 2)/(-4 + 6)

Slope of EF = 8/2

Slope of EF = 4

Slope of FG = (-4 + 2)/(2 + 6)

Slope of FG = -2/8

Slope of FG = -1/4

Slope of GH = (4 + 4)/(4 - 2)

Slope of GH = 8/2

Slope of GH = 4

Slope of HE = (6 - 4)/(-4 - 4)

Slope of HE = -2/8

Slope of HE = -1/4

Then the distance between the point will be

EF² = (-6 + 4)² + (-2 - 6)²

EF² = (-2)² + (-8)²

EF² = 4 + 64

EF = √68

FG² = (2 + 6)² + (-4 + 2)²

FG² = (8)² + (-2)²

FG² = 64 + 4

FG = √68

GH² = (4 - 2)² + (4 + 4)²

GH² = (2)² + (8)²

GH² = 4 + 64

GH = √68

FG² = (4 + 4)² + (4 - 6)²

FG² = (8)² + (-2)²

FG² = 64 + 4

FG = √68

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Answer:

15days.

Step-by-step explanation:

total amount=$85

renting amount=$10

amount per day=$5

to find the number of days the trimmer was rented it will be;

total amount-renting amount ÷$5

$85-$10÷$5

$75÷$5

=15days

Answer:

65

Step-by-step explanation:

The answer is Y

Step-by-step explanation:

You have to compare the numbers with conditions both in Rows and Columns.

Answer:

23cm

Step-by-step explanation:

If you multiply like terms you will get the answers. Then you add last to get 23cm

The required length ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).

Given that,
Package that had a length of 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3.

How much ribbon would be needed to go around the package in centimeters is to be determined.

Perimeter is the measure of the figure on its circumference.

The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.

Quantity of ribbon = perimeter of the rectangular package
                            = 2 * length + 2* width
                            = 2 * (2x^2+3x-5/x^2+x-3) + 2(x^2-x-5/x^2+x-3)
                            = 2 (3x^2 + 2x -10) / (x^2 + x - 3)

Thus, the required length of  ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).

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Let V be the volume of the tank. The tap fills the tank at a rate of V/(4 hours), or V/4 per hour. The hole empties the tank at a rate of V per hour. If both the tap and hole work together, the net rate of water flow is V/4 - V or -3V/4 per hour.

Starting with a full tank, the volume v of water at time t is given by the function

v(t) = V + (-3V/4) t

Solve v(t) = 0 to find the time it takes to empty:

V - 3V/4 t = 0

V = 3V/4 t

t = V / (3V/4) = 4/3

So it takes 4/3 hours = 80 minutes to empty a full tank.

Answer:

None of these answers are correct

Step-by-step explanation:

neither of them are rays.

a ray goes from the center to the edge of a circle.

From simplification of the given algebra, the correct answers are as shown below.

1) (a² - b)/(a³b²)

This reduces to;

(a²/(a³b²)) - b/(a³b²)

⇒ a/(ab²) - 1/(a³b)

2) The algebraic expression is;

(b - a)/a³b³

⇒ b/a³b³ - a/a³b³

⇒ 1/a³b² - 1/a²b³

3) The algebraic expression is;

(2 - ab²)/(a²b³)

⇒ (2/(a²b³)) - (ab²)/(a²b³)

⇒ 2/(a²b³)) - 1/(ab)

4) The algebraic expression is;

(2 - ab²)/(a²b³)

⇒ 2/(a²b³) - 1/ab

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The rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute

From the question, we are to determine the rate which is equivalent to the rate Paula walked

Using the formula,

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

From the given information,

Distance = 1/12 mile

Time = 5/3 minutes

Putting the parameters into the formula, we get

[tex]Rate =\frac{\frac{1}{12} }{\frac{5}{3} }[/tex]

[tex]Rate = \frac{1}{12} \div \frac{5}{3}[/tex]

[tex]Rate = \frac{1}{12} \times \frac{3}{5}[/tex]

[tex]Rate = \frac{3}{60}[/tex]

[tex]Rate = \frac{1}{20}[/tex] mile/minute

Hence, the rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute

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Answer:

[tex]x^{2} +8x+16[/tex]

Step-by-step explanation:

There are 2 ways to find the square of a binomial. You can use FOIL or use a formula. Just remember that the square of a binomial will always be a trinomial.

FOIL

Since we are squaring a binomial we can rewrite the expression as (x+4) * (x+4). FOIL stands for First, Outside, Inside, Last. This explains how to multiply out 2 binomials. This method will give you 4 different terms that can then be combined to find the answer.

First - multiply the first terms of each binomial

Outside - multiply the terms on the outside of both binomials

Inside - multiply the terms on the inside of both binomials

Last - multiply the last terms of each binomial

Now we can combine these terms to create the new polynomial [tex]x^{2} +4x+4x+16[/tex]. Then, combine like terms for the final answer: [tex]x^{2} +8x+16[/tex].

Shortcut

Another way to square binomials is to use the formula [tex]a^{2} +2ab+b^{2}[/tex], where a is the first term and b is the second term. So, for this formula, the binomial would look like (a+b).

So, we can apply this formula by plugging in x for a and 4 for b.

Then, multiply the middle term

Finally, square 4

This gives us the same final answer as the method above.

Step-by-step explanation:

(x+4)^2

you can also expand it

(x+4)(x+4)

x^2+4x+4x+16

x^2+8x+16

The number of years the money was invested with annual compounding is 3.45 years.

When an amount earn interest compounded annually, it means that both the amount invested and the interest earned increases in value once a year.

Number of years =  (In FV / PV) / r

Where:

(In 7255 / 6000) 0.055 = 3.45 years

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The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.

A cuboid is a three dimensional figure with six rectangular faces .

The  volume of the cuboid is given by

V = length * breadth * height

It is given in the question that

a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick , this will be in the shape of a cuboid

The volume of cement required = 8 * 4 * 0.25

= 8 cu.ft

The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.

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Answer:

The car would have traveled 25 km.

Step-by-step explanation:

Set up the Proportion [tex]\frac{50}{60} = \frac{x}{30}[/tex]. Solving that proportion gets you an answer of 25, getting you the answer 25 km in 30 minutes. I hope this helps! :)

Answer:

first ans =x-7

second ans= x+y/x-y

Step-by-step explanation:

I think you would get it and it doesn't need explanation.

Answer:

68077

Step-by-step explanation:

he had spent 68077 because by 59425+8652 makes 68077

Answer:

$25 - $10f

Step-by-step explanation:

Fishie's name is fishy.  

We know Mr. Fishie spent $15 on a tank.  His 10 fish cost 10*$f.  His total is:

Total =15 + 10*f

His change after 2 $20 would be:

$40 - ($15 - $10f), or

$25 - $10f

Answer:

He could work 10 hours as a lifeguard, and 5 hours as a tutor

Step-by-step explanation:

If he makes $16 an hour as a lifeguard

            and $18 an hour as a tutor,

He could work 10 times $16, to make $160 for 10 hours.

Now we subtract this from $250, this makes $90.

We know need to find out how many times 18 goes into 90, 5 times.

So we know that he could work 10 hours as a lifeguard and 5 hours as a tutor.

I hope this is right.

I hope this helps too, have a nice day!

Answer:

c. diameter

because when a line intersects the center and even touches the centre is called a diameter

hope it helps.

Answer:

C

Step-by-step explanation:

Diameter

Answer:

[tex]\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]

Key:

• [tex]-\left(a-b\right)=-a+b[/tex]

Step-by-step explanation:

[tex]\tan \left(2\theta\right)-\left(1-\tan ^2\left(\theta\right)\right)[/tex]

[tex]-\left(1-\tan ^2\left(\theta\right)\right)=-1+\tan ^2\left(\theta\right)[/tex]

[tex]=\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]