1. Which of the following natural numbers are perfect squares? Give reasons in support
of your answer.
(i) 729
(ii) 5488
(iii) 1024
(iv) 243​

Answer:

See below

Step-by-step explanation:

70/100 + 4/10 is equivalent to 70/100 + 40/100 which equals 110/100.

68/100 + 6/10 is equivalent to 68/100 + 60/100 which equals 128/100.

6/10 + 12/100 is equivalent to 60/100 + 12/100 which equals 72/100.

4/10 + 34/100 is equivalent to 40/100 + 34/100 which equals 74/100.

None of them equal 75/100, however if you were looking for 74/100 or 72/100, check above.

Answer:

First we have the function f(x) = 27*x  - 67.5

It has an x-intercept at (a, 0)

This means that:

f(a) = 0 = 27*a - 67.5

Solving the above equation we can find the value of a.

0 = 27*a - 67.5

67.5 = 27*a

67.5/27 = a = 2.5

Now let's look at equation g(x).

It is a linear equation, remember that a linear equation can be written as:

g(x) = y = A*x + B

Where:

A is the slope, and B is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂. y₂), the slope can be written as:

A = (y₂ - y₁)/(x₂ - x₁)

In this case we can select any two points from the table, for example, I will use the second and third points:

(1, 39) and (2, 32.5)

Then the slope is:

A = (32.5 - 39)/(2 - 1) = -6.5/1 = -6.5

Then the equation is something like:

g(x) = y = -6.5*x + B

B is the y-intercept, to find this value, we can use one of the two points we used before.

For example, (1, 39) means that g(1) = 39

Then:

g(1) = -6.5*1 + B = 39

     = B = 39 + 6.5 = 45.5

Then the equation for g(x) is:

g(x) = -6.5*x + 45.5

Now, we know that g(x) has an x-intercept at (b, 0)

this means that:

g(b) = 0 = -6.5*b + 45.5

6.5*b = 45.5

b = 45.5/6.5 = 7

Then the difference between b and a is:

b - a = 7 - 2.5 = 4.5

b is equal to a plus 4.5

And the ratio is:

b/a = 7/2.5 = 2.8

b is 2,8 times larger than a.

Answer:

[tex]\frac{1}{5^6}[/tex]

Step-by-step explanation:

Given the expression (5⁻²)⁵ ₓ 5⁴

According to indices

(a^m)^n = a^{mn}

(5⁻²)⁵ = (5⁻¹⁰)

(5⁻²)⁵ ₓ 5⁴

= 5⁻¹⁰ ₓ 5⁴

= 5⁻¹⁰⁺⁴

= 5⁻⁶

Hence the equivalent expression is [tex]\frac{1}{5^6}[/tex]

Answer:

27

Step-by-step explanation:

Let :

Number of 40¢ = x

Number of 22¢ = 4x + 3

Total stamp value = $8.34 = (8.34 * 100) = 834¢

40¢x + 22¢(4x + 3) = 834¢

40x + 88x + 66 = 834

128x = 834 - 66

128x = 768

x = 768 / 128

x = 6

Number of 22¢ stamp:

4(6) + 3 = 24 + 3 = 27

Given:

The equation is:

[tex]12=5^x[/tex]

To find:

The logarithmic equation that is equivalent to the given exponential equation.

Solution:

According to the property of logarithm:

[tex]a=b^x\Leftrightarrow \log_b a=x[/tex]

We have,

[tex]12=5^x[/tex]

Here, [tex]a=12,b=5[/tex]. By using the above property of logarithm, we get

[tex]\log_{5}12=x[/tex]

[tex]x=\log_{5}12[/tex]

Therefore, the correct option is C.

Answer:

Option B --> (8, -5)

Step-by-step explanation:

To find the midpoint, we use the equation-

[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]

The coordinates given were (8, -2) (8, -8)

x1= 8,

x2 = 8

y1 = -2

y2= -8

Substituting these values in the equation:-

[tex]\frac{8+ 8}{2} , \frac{-2 + -8}{2}[/tex]

[tex]\frac{16}{2} , \frac{-10}{2}[/tex]

Coordinates of midpoint will be ---> (8, -5)

Answer:

x=3±√5/2

Step-by-step explanation:

Step-by-step explanation:

given

2x + y = 13

turning to y = ax + b we get

y = - 2x + 13

hope it helps :)❤

Answer:

Answer is B: (-sqrt(3/2 , -1/2)

Step-by-step explanation:

First convert radians to degrees

theta = (7pi/6)*(180/pi)

=210 degrees

Cos(210 degrees)= -sqrt3/2

Thats the x coordinate

sin(210 degrees)= -1/2

thats the y coordinate

Answer:

The corresponding point on the unit circle for the radian measure is [tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]

Step-by-step explanation:

What is unit circle?

A unit circle is typically drawn around the origin (0,0) of a X,Y axes with a radius of 1.

What is radian measure?

One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle.

The radian measure is,

α=[tex]\frac{7\pi }{8}[/tex]

Changing to degree measure,

[tex]\frac{7\pi }{6} *\frac{180}{\pi } \\=210^{o}[/tex]

The measure on the unit circle is,

(cos [tex]\alpha[/tex] , sin [tex]\alpha[/tex])=(cos 210 , sin 210)

                    =[tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]

Option A.

To know more about unit circle, radian measure here

https://brainly.com/question/10675916

#SPJ2

Answer:

1 second

Step-by-step explanation:

use the general quadratic formula

Answer:

Perimeter of Triangle sum of all sides.

=13 cm

Answer:

heres ur answer good luck

https://www.web-formulas.com/Math_Formulas/Geometry_Surface_of_Cube.aspx

Step-by-step explanation:

Answer:

the answer should be 98

Step-by-step explanation:

try it

Answer:8.7

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

2 * 8 = 16

Question: Which is an equivalent form of the expression 1800(1.2)-t?

Answer: 1800 (5/6)-t

Answer: B) established a strong, central government

Answer:

The emperor Chandragupta is established a strong, centralized government

Answer:

the answer is c

Step-by-step explanation:

inscribed angles made by same base should be equal

Answer:

B.

Step-by-step explanation:

Perpendicular lines intersect at exactly one point.

(perpendicular lines form an x with right angles)

Answer: C. J=5

Step-by-step explanation: Hope this help :D

Answer:

The answer is C I know that is right

Answer:

ML = 12.8

Step-by-step explanation:

24/6.4 = 48/ML

24ML = 307.2

ML = 12.8

Answer:

12.4

Step-by-step explanation:

rounded to 1dp

please mark as brainliest if correct

thank you

Answer:

12.4 is the answer.

Step-by-step explanation:

Answer:

72.5 km/h

Step-by-step explanation:

Multiply the km/h by how many hours your going at that speed/total number of hours on trip.

(90x(3.5/8))+(80x(2/8))+(70x(1.5/8))

39.375+20.5+13.125

72.5km/h

Answer:

683cm

Step-by-step explanation:

Pay attention next time

Answer:

[tex] \displaystyle A_{ \text{surface}} = 42cm ^{2} [/tex]

Step-by-step explanation:

we are given the base area of a cube

recall the surface area formula of a cube

[tex] \displaystyle A_{ \text{surface}} = 6( {a}^{2} )[/tex]

notice that, we are given the base area 7cm² in other words we are given a² i.e 7cm²

Thus substitute:

[tex] \displaystyle A_{ \text{surface}} = 6( 7 )cm ^{2} [/tex]

simplify multiplication:

[tex] \displaystyle A_{ \text{surface}} = 42cm ^{2} [/tex]

and we are done!

Answer:

Plz subscribe my Gaming channel Sameer Duos

Step-by-step explanation:

The correct answer is whole number

Answer:

$81.6

Step-by-step explanation:

(1,360.00)(6%)=81.6

Answer:

B) height = 5√3

Step-by-step explanation:

height² = 10² - 5² = 100 - 25 = 75

height = √75 = 5√3