Which of the following expressions is equivalent to 2 exponent -4

The length of the third side is 14.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.

Given that,

a = 8

b = 12

Let the length of the third side be c,

Applying the Pythagorean theorem:

a² + b² = c²

8²+ 12² = c²

c² = 64+144

c² = 208

c = √208 = 14.42

Thus, the length of the third side is 14.

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The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.

In mathematics, an identity is a statement or equation that is true for all values of the variables involved. For example, the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, is an identity.

In summary, identities in mathematics are statement that are true for all values of variables, they are used to simplify expressions, solve equations and prove theorems, and they play an important role in the study of mathematical structures.

The 12 algebraic identities in mathematics are:

Commutative property of addition: a + b = b + a

Commutative property of multiplication: a x b = b x a

Associative property of addition: (a + b) + c = a + (b + c)

Associative property of multiplication: (a x b) x c = a x (b x c)

Distributive property: a x (b + c) = (a x b) + (a x c)

Identity property of addition: a + 0 = a

Identity property of multiplication: a x 1 = a

Additive inverse property: a + (-a) = 0

Multiplicative inverse property: a x (1/a) = 1

Transitive property: a = b and b = c then a = c

Substitution property: a + b = b + a

Reflexive property: a = a

It's worth noting that these are some of the algebraic identities which are frequently used in algebra and other related mathematical branches.

The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.

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Answer: The least number of bottles the trader can obtain is the greatest common divisor (GCD) of the number of liters in the two buckets.

We can use the Euclidean algorithm to find the GCD:

First find the remainder of 24 divided by 27, which is 24 % 27 = 0.

Since the remainder is 0, we know that the GCD of 24 and 27 is 27.

Therefore, the trader can obtain at least 27 bottles from the two buckets of beverages A and B.

Note that the GCD represents the size of the bottle and this is the least number of bottles that the trader can obtain.

Step-by-step explanation:

The number of students are enrolled in PE be 447.

A percentage expressed in decimal form is a proportion, but a proportion is not always a % expressed in decimal form.

A fraction expressed in a specific way is called a decimal. For example, you can write the fraction as 0.5 instead of 1/2, with the zero in the ones place and the five in the tenths place. The word decimal is derived from the Latin word decimus, which means tenth, and the number 10 (or decem).

From the given information, we get 30% of 1490

Convert 30% into a decimal and multiply by 1490

Convert 30 % into a decimal form: 0.3

Multiply 0.3 by 1490

= 0.3 × 1490

Simplifying the values, we get

0.3 - 1490

= 447

Therefore, the number of students are enrolled in PE be 447.

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Answer:

49.5°

Step-by-step explanation:

Draw a line b/w B and D, this will "cut" the angles of both down the exact middle making it much easier to work with now that you have 2 separate triangles

For example, angle A remains 36° but angle B becomes 54° and angle D becomes 76.5°. Now that you have B and D, just subtract 180 from both to get your C value. 180° - 54° - 76.5° = 49.5°

The area of the triangle is 27.9 sq.cm.

What is meant by area of triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area.

We have the lengths of two sides and the measure of the included angle. So, you can use the formula R = [tex]\frac{1}{2}[/tex]pr sin(Q), where p and r are the lengths of the sides opposite to the vertices P and R respectively.

Using the formula, the area, R= [tex]\frac{1}{2}[/tex] (9) (8.4) sin (132°).

R = 37.8 sin (132°)

R = 37.8 (0.74)

R = 27.9 (approx)

Hence, the area of the triangle is 27.9 sq.cm.

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Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.

In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.

The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.

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Answer:

x = 131

y = 131

Step-by-step explanation:

x = 180 - 49 (sum of angles on a straight line)

x = 131

y = x (corresponding angles)

y = 131

The missing value for x is 7.

The inverse variation relationship between two variables x and y is described by the equation y = k/x,

where k is a constant.

We can use this equation to find the missing value, using the information given.

First, we'll use the first set of points to find the constant k:

y = k/x

16 = k/3.5

16 * 3.5 = k

56 = k

Next, we'll use the constant k and the second set of points to find the missing x value:

y = k/x

8 = 56/x

8 * x = 56

x = 56/8

x = 7

hence x is 7

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Answer:

1. A. -1.43 corresponds to an area of approximately 0.0637 under the normal curve.

B. 0.58 corresponds to an area of approximately 0.7295 under the normal curve.

C. -1.55 corresponds to an area of approximately 0.0633 under the normal curve.

D. For z>1.34, the area under the normal curve is approximately 0.0916.

--------

2. A. The 35th percentile corresponds to a z-score of approximately -0.48

B. The first quartile (Q1) corresponds to a z-score of approximately -0.67

C. For 12% of the data to fall above it, the z-score would be approximately 1.28

----------

3.  A. To find the area under the curve for x< 31 inches, we need to convert 31 inches to a z-score using the formula: z = (x - mean) / standard deviation. For this case, z = (31 - 36) / 10 = -0.6, the area under the curve for this is 0.2744

B. To find the area under the curve for x> 49 inches, we need to convert 49 inches to a z-score, the z-score is (49 - 36) / 10 = 1.3, the area under the curve for this is 0.0968

C. The area under the curve for x = 40 inches is 0.3520

D. To find the height at which 70% of 5 year olds are below it, we need to use the inverse standard normal calculator, which gives us a z-score of 0.84162, we can then use this z-score to find the corresponding x value by using the formula x = mean + (z-score * standard deviation) which in this case would be 36 + (0.84162*10) = 42.4 inches

Answer:

L = 53.37 cm

Step-by-step explanation:

We have the relationship

M ∝ L³

We can rewrite this as an equation:
M = k · L³

where k, a constant, is known as the constant of proportionality

Given M = 100 kg when L = 20, we get

100 = k · 20³

100 = k · 8000

k = 100/8000 = 0.0125

If M = 1900 kg and k = 0.0125 we can plug in these values to get

1900 = 0.0125 L³

==>  L³ = 1900/0.0125

==> L³ = 152000

Therefore L = ∛152000

L = 53.36803 or

L = 53.37 cm  rounded to 2 DP

Answer:

380.00

Step-by-step explanation:

M=KL

100=20K

K=5

M=5L

1900=5L

L=380

On Solving the given quadratic equation , we get the zeros of the equation is x = 3 .

A quadratic equation is an algebraic equation of second degree in x. The standard form of a quadratic is written as ax² + bx + c = 0  , where "a" and "b" are coefficients, x is variable, and c is constant term.

The given equation is : p(x) = x² - 6x + 9 ;

to find the zero , we equate the given quadratic function to zero(0) .

On equating ,

we have ;  x² - 6x + 9 = 0;

⇒ x² - 3x -3x + 9 .....by split middle term method ;

⇒ x(x - 3) -3(x - 3) = 0;

⇒ (x - 3)(x - 3) = 0;

which means that x - 3 = 0 ,and x = 3 .

Therefore , the zero of the given quadratic function is x = 3 .

The given question is incomplete , the complete question is

What is the zero of p(x) = x² - 6x + 9 ?

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The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

What is circumference of circle ?

Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

We can use the formula C = 2πr to find the circumference of the original circle, where C is the circumference and r is the radius of the circle.

Given that the wire encloses an area of 38.5 cm square, we can use the formula A = πr^2 to find the radius of the circle.

A = 38.5 cm^2

πr^2 = 38.5 cm^2

r^2 = 38.5/π cm^2

r = (38.5/π)^0.5 cm

Now that we know the radius of the circle, we can find the circumference using the formula:

C = 2πr

Now, we can find the area of the square by squaring the length of one side of the square which is the circumference of the original circle

Area of square = C^2

Therefore, The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

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Given that the wire encloses an area of 38.5 cm square, we can use the formula A = πr^2 to find the radius of the circle.

A = 38.5 cm^2

πr^2 = 38.5 cm^2

r^2 = 38.5/π cm^2

r = (38.5/π)^0.5 cm

C = 2πr

Area of square = C^2

The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

Answer:

8 X 8 = 64

Step-by-step explanation:

The total area of the shape is equal to 102 cm².

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Next, we would determine the area of this irregular shape in parts as follows;

Area of rectangle 1 = 15 × 6

Area of rectangle 1 = 90 cm²

Area of rectangle 2 = 4 × 3

Area of rectangle 2 = 12 cm²

Total area of irregular shape = 90 + 12

Total area of irregular shape = 102 cm²

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If a circular mulch bed has a radius of 1.6 feet. A bag of mulch contains 2 cubic feet of mulch. The mulch's depth to an appropriate number of significant digits is: C. 0.25 foot.

The volume of the mulch bed is given by the formula for the volume of a cylinder:

V = π * r^2 * h

Where:

r = radius (1.6 feet)

h=  the height (the depth of the mulch).

Since we have 2 cubic feet of mulch, and want to spread it evenly over the bed, we can set 2 = π * r^2 * h and solve for h:

h = 2 / (π * r^2) = 2 / (π * 1.6^2)

h ≈ 0.25 feet

Therefore the depth of the mulch is approximately 0.25 feet.

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No, it is not. X square 22 X square is not a polynomial because it does not have the standard form of a polynomial which is ax^n + bx^n-1 + cx^n-2 + ... + z.

A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power.

Leading term and leading coefficient are terms used to describe the first term and its coefficient, respectively, in the polynomial's standard form.

A polynomial's standard form is denoted by the formula f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

According to the definition of a polynomial in standard form, exponents must be written in decreasing order.

The standard form of polynomials is used to facilitate calculations.

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The values of a and b  for the given equation  are 25,-25

What is Quadratic equation ?

Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .

Given ,

equation x^3 - 625 x  = 0

x^3 - 625x = 0

taking x common

x(x^2 - 625 ) = 0

x^2 - 625 = 0

(x+25 ) (x-25) = 0

It is in the form of a2-b2

hence it is equals to a+b * a-b

x = 25,-25 .

Hence, The values of a and b are 25,-25 respectively for the given equation.

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Answer

6x + 19

Step-by-step explanation:

First, set up the equation

x + 4x + 5 + 14 + x

Now simplify the like terms

6x + 19

Answer:

Growth

Growth

Decay

Decay

To solve the equation x - 10 = 90, you can add 10 to both sides of the equation to get:

x - 10 + 10 = 90 + 10

x = 100

Therefore, the solution to the equation is x = 100.

You can also check this solution by substituting it back into the original equation:

x - 10 = 90

100 - 10 = 90

90 = 90

This confirms that x = 100 is a valid solution to the equation.

9. You are solving for the variable, x. Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x, by adding 10 to both sides of the equation:

[tex]x - 10 = 90\\x - 10 (+10) = 90 (+10)\\x = 90 + 10\\x = 100[/tex]

a. Add 10 to both sides.

10. You are solving for the variable, x. Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x, by multiplying 5 to both sides of the equation:

[tex]\frac{x}{5} = 5\\ (\frac{x}{5}) (* 5) = 5 (*5)\\x = 5 * 5\\x = 25[/tex]

d. Multiply both sides by 5.

~

The 45-degree set square contains an angle of 90 degrees, and also 30/60 degree set square contains a right angle. The 45 degrees set square is utilised to draw vertical lines. With the help of set squares, we can sketch parallel lines and perpendicular lines, construct some standard angles, and so on.

Geometric tools are instruments utilised to draw different kinds of geometric shapes. In Maths, geometry is the most critical topic, in which we learn about the shapes of things. Different types of tools with different names are utilised to draw these geometric shapes while solving geometry problems.

Some of the most generally utilised geometric tools are:

Ruler

Compass

Protractor

Divider

Set-squares

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Answer: [tex]y=\frac{1}{3} x+6[/tex]

Step-by-step explanation:

To find the perpendicular line, we have to change the slope of the original, equation.

The slope of the perpendicular line is 1/3. We can plug in the new point. To find the equation.

[tex]8=\frac{1}{3}(6)+b[/tex]          [multiply]
[tex]8=2+b[/tex]               [subtract both sides by 2]
b=6

Final equation is [tex]y=\frac{1}{3} x+6[/tex]

Answer:

y = 1/3x + 6

Step-by-step explanation:

Because perpendicular lines have opposite and reciprocal slopes, we have to change our slope into a positive and flip it into it's reciprocal.

Now its: y = 1/3x + b

Next, we find b using slope intercept form.

8 = 1/3(6) + b

8 = 2 + b

6 = b

Place b into the equation.

y = 1/3x + 6

To find the greatest common factor (GCF) of a sum, list the prime factors of each term in the sum. The GCF is the product of the common prime factors raised to the lowest exponent.

To find the greatest common factor (GCF) of a sum, you can first list the prime factors of each term in the sum. The GCF is the product of the common prime factors raised to the lowest exponent.

For example, to find the GCF of 36x² + 18x² + 12x², you would list the prime factors of each term:

36x² = 2² × 3² × x²

18x² = 2 ×  3² ×  x²

12x² = 2² ×3 × x²

The GCF is 2 × 3 ×  x² = 6x²

To rewrite the sum using the GCF and the distributive property, you divide each term in the sum by the GCF, and then multiply the GCF by the sum of the quotients:

(36x² + 18x²  + 12x²) / (6x² ) = 6 + 3 + 2

6x² × (6 + 3 + 2) = 6x² ×  11

So the sum can be rewritten as 6x² × 11

You can also use the same method to find GCF of numbers as well.

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Answer: 3b-a+7

Step-by-step explanation:

9b-6b=3b

3b-7-a

Answer: 3b+7-a

Step-by-step explanation:

9b+7-6b-a

3b+7-a

Answer: (A) 16

must be less than 19

and more than 5

Step-by-step explanation:

The coordinates of the exponential equation are A ( 2 , 640 ) , B ( 3 , 512 ) and C ( 4 , 409.6 )

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the first point be A ( 0 , 1000 )

Let the second point be B ( 1 , 800 )

Now , the exponential equation be represented as A

y = abˣ   be equation (1)

Substitute the value of x = 0 and y = 1000

1000 = ab⁰

So , the value of a = 1000

Substitute the value of x = 1 and y = 800

800 = ab¹

b = 800/1000

b = 0.8

So , the equation is y = 1000 ( 0.8 )ˣ  

Now , at the point A , the value of x = 2

So , y = 1000 ( 0.8 )²

y = 1000 x 0.64

y = 640

So , the point is A ( 2 , 640 )

Now , at the point B , the value of x = 3

So , y = 1000 ( 0.8 )³

y = 1000 x 0.512

y = 512

So , the point is B ( 3 , 512 )

Now , at the point C , the value of x = 4

So , y = 1000 ( 0.8 )⁴

y = 1000 x 0.4096

y = 409.6

So , the point is C ( 4 , 409.6 )

Hence , the coordinates are A ( 2 , 640 ) , B ( 3 , 512 ) and C ( 4 , 409.6 )

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The cannonball will be at a height of 640 feet for the first time after 6.5 seconds.

Acceleration, is a rate at which velocity changes with time, in terms of both speed and direction.

The time it will take for the cannonball to reach a height of 640 feet for the first time can be found using the equation:

t = (vf - vi) / a

where:

t = time (in seconds)

vf = final velocity (in feet per second) = 0 (at the top)

vi = initial velocity (in feet per second) = 208

a = acceleration (in feet per second squared) = -32 (upwards)

Plugging in the values:

t = (0 - 208) / (-32) = 6.5 seconds.

So, the cannonball will be at a height of 640 feet for the first time after 6.5 seconds.

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[tex]( \frac{3}{5} ){}^{2} + 4 \times 3 - 2[/tex]

[tex] \frac{9}{25} {}^{} + 12- 2[/tex]

[tex] \frac{9}{25} {}^{} + 10[/tex]

[tex] \frac{9 + 10(25)}{25} [/tex]

[tex] \frac{9 + 250}{25} [/tex]

[tex] \frac{259}{25} [/tex]