What is the area of the smaller figure, in square centimeters?
04
08
O 20
O 40

The true about the sum of the two polynomials- 6s^2t – 2st^2 and 4s^2t – 3st^2 is The sum is a binomial with a degree of 3.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

Now the given polynomials are,

6s^2t – 2st^2 and 4s^2t – 3st^2

Now adding these two polynomials we get,

Sum of polynomials = 6s^2t – 2st^2 + 4s^2t – 3st^2

Taking alike terms together,

= 6s^2t + 4s^2t – 2st^2 – 3st^2

Now simplifying we get,

= 10s^2t – 5st^2

Here we see that the highest power of a variable is 2.

Thus this sum of polynomials is a binomial.

Now sum of the powers of variable s and t = 2 + 1 = 3

Thus, Degree of the sum of polynomials is 3.

Thus, the true about the sum of the two polynomials- 6s^2t – 2st^2 and 4s^2t – 3st^2 is The sum is a binomial with a degree of 3.

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limx→0sinaxcosbxsincx=limx→0(cosbx⋅sinaxax⋅cxsincx⋅ac)=ac

Answer:

j + 3 ≤ 12

Hope this helps :)

Solution, Explanation, & Check part below

Step-by-step explanation:

1. Isolate variable by doing the inverse operation which is subtracting 3 on both sides of the equation.

j + 3 ≤ 12

- 3 - 3

j ≤ 9

j can be any number that is less than 9 or equal to 9.

Check:

9 + 3 ≤ 12

12 ≤ 12

12 is equal to 12 ✓

Given that Jupiter takes 9.9259 hours to rotate on its axis and has a tangential speed of 12,293 m/s, then its radius is 69,912 km.

Tangential speed is defined as the measure of the circumference of the circular path the object is moving along divided by the value of the amount of time it took to complete one rotation.

tangential speed = C/t

where C = circumference

t = time it took to complete one rotation

Given that Jupiter takes 9.9259 hours to rotate on its axis and has a tangential speed of 12,293 m/s, solve for the circumference of Jupiter.

C = tangential speed x time

C = 12,293 m/s (9.9259 hours)(3600s/hr)

C = 439,268,719.3 m

Using the formula for circumference, solve for the radius of Jupiter.

C = 2πr

r = C / 2π

r = 439,268,719.3 m/2π

r = 69,911,788.03 m

r = 69,912 km

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Answer:

D. 69,912 km

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

[tex]\frac{x}{8}[/tex] = 3 ( multiply both sides by 8 to clear the fraction )

x = 8 × 3 = 24

Answer: 24

Step-by-step explanation:

x/8 = 3

x = 3x8

x = 24

By Euclid's axioms we proved that AC=BD

Things which are equal to the same thing are also equal to one another.

If equals be added to equals, the wholes are equal.

If equals be subtracted from equals, the remainders are equal.

Things which coincide with one another are equal to one another.

The whole is greater than the part.

given that , B is in between A and C

and C is between B and D

and also given that AB=CD

let AC=AB+BC .......(1)

    BD=BC+CD ........(2)

   subtract 1-2

we get, AC-BD=AB+BC-BC-CD

  AC-BD=AB-CD

we know AB=CD so we get

  AC-BD=0

 AC=BD

Hence, Proved

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Answer:

We established that AC=BD using Euclid's axioms.

Step-by-step explanation:

Things that are equivalent to one another are also equivalent to the same object.

The wholes are equal if equals are added to equals.

The remainders are equal when equals are subtracted from equals.

Things are equivalent to one another if they occur simultaneously.

A component cannot possibly equal the whole.

given that , B is in between A and C

and C is between B and D

and also given that AB=CD

let AC=AB+BC .......(1)

   BD=BC+CD ........(2)

  subtract 1-2

we get, AC-BD=AB+BC-BC-CD

 AC-BD=AB-CD

we know AB=CD so we get

 AC-BD=0

 AC=BD

Hence, Proved

Answer: 84 2/3

Step-by-step explanation:

x-66 2/3=18

x=18 + 66 2/3

x=18 + 66 + 2/3

x=84 + 2/3

x=84 2/3

Answer:

Step-by-step explanation:

The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.

Let 30minutes = 0.5 hours.

Let x represent the time for which the marshal has ran.

On this note, the robber must have galloped at; (x +0.5) hours.

Hence, it follows from the task content that if they are at the same distance from the bank; we have;

14(x+0.5) = 16(x)

14x + 7 = 16x

7 = 2x

x = 7/2 = 3.5 hours.

= 3.5 × 60minutes = 210minutes.

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We need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).

It is given that Δ MNO with right angle at point M has legs of lengths a and 2a .

We have to position the triangle on coordinate plane.

What is a right angled triangle ?

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

As per the question ;

The triangle is a right angle triangle, so it's two sides can be located

on axis.

Place the right angle of the triangle Δ MNO at M.

i.e., M will have coordinates (0,0)

The origin will allow the two legs to be along the x and y-axes , so position the triangle in the first quadrant.

As N is on the y-axis ;

Its x-coordinate will be 0 and the y-coordinate will be a , because the leg is a units long.

i.e., N will have coordinates (0,a)

As O is on the x-axis,

its y-coordinate will be 0 and the x-coordinate will be 2a , because the leg is 2a units long.

i.e.,

O will have coordinate (2a,0)

We can put these coordinates after placing the triangle in the first quadrant i.e., M (0,0) , N (0,a) & O (2a,0).

Thus , we need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).

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Based on the given task content, the number of members in the marching band if the band has fewer than 200 members is 195 members

When the band members are told to line up in rows of eight but five is left over. This means the overall number is an odd number.

When they are lined up in rows of six, but three are left over. So, eliminate numbers with 3, 5, 6 ,9, 0.

Finally they are lined up in rows of seven, but four are left over.

So, eliminate numbers with 7 also.

So, all eliminated numbers are : 2,3,4,5,6,7,8,9,10

Left numbers are 1.

Given is that the band has fewer than 100 members. So, it can be 71 ,81 ,91

199, 195, 193, 191

We can check with 81.

81/4 = 20 remainder 1

81/6 = 13 remainder 3

81/7 = 11 remainder 4

So, the answer is 81.

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The coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).

It is given that in ΔL K L , J has coordinates (0,0) and K has coordinates (2 a, 2 b) .

We have to find the coordinates of point L so that , ΔL K L is a scalene triangle.

What is a triangle ?

A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.

As per the question ;

The ΔL K L is a scalene triangle.

J has coordinates (0,0)

K has coordinates (2 a, 2 b) .

The possible coordinate of the point L will be (0,y) or (2a,y).

Let's check it.

Using the distance formula ;

JK = [tex]\sqrt{(2a-0)^2 + (2b -0)^2}[/tex]

JK = [tex]\sqrt{(4a^2 + 4b^2)}[/tex]

JK = [tex]2\sqrt{a^2 + b^2}[/tex]

Similarly ;

JL = [tex]\sqrt{0^2 + y^2}[/tex]

JL = y

And

KL = [tex]\sqrt{4a^2 + (2b - y)^2}[/tex]

The sides are all of different lengths, so , we can conclude that this is a scalene triangle.

Thus , the coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).

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Answer:

1.

Step-by-step explanation:

67 is a prime number so we write

67 = 1 * 67

The GCF of 67 and 146 is 1.

The surface area of earth is 514.4million [tex]Km^{2}[/tex] and the volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].

Radius of Earth = 6400 (approximately).

Earth is a sphere. So by using the formula of Surface Area of sphere we can calculate the Surface area of earth as follows,

Surface Area of Earth = 4[tex]\pi r^{2}[/tex] = 4 × (3.14) × [tex](6400)^{2}[/tex]

                                    =  4 × 3.14 × 40960000

                                    = 514457600 [tex]Km^{2}[/tex]

                                    = 514.4million [tex]Km^{2}[/tex]

The surface area of earth is 514.4million [tex]Km^{2}[/tex] .

Similarly, by using the formula of volume of sphere we can calculate the volume area of earth as follows,

Volume of Earth = (4/3)[tex]\pi r^{3}[/tex]

                           = (4/3)×(3.14)×[tex](6400)^{3}[/tex]

                           =(1.3333)(3.14)(2.6214 × [tex]10^{11}[/tex])

                           = 1.0975 × [tex]10^{12}[/tex] [tex]Km^{3}[/tex]

                           = 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex]

The volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].

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The correct option is d) 7.

A production function indicates the proportion of a combination of inputs (labor and capital) that produces a given amount of output. Firms determine the quantity produced given the output price level and the quantity of a combination of input factors provided by the prices of capital and labor. Dividing the output by the number of capital and labor units employed gives the average capital and labor production, respectively.

The production functions,

Q = 3 K + 4 L

k = 10

L = 10

Q = 3 ( 10 ) + 4 ( 10 )

Q = 30 + 40

Q = 70

Average capital production is calculated by dividing output (Q) by the amount of capital used to produce that output (K).

Average capital production = output / capital

= 70 / 10

= 7

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Answer: The answer would be x = -3 + 0.5y.

Step-by-step explanation: pls give me brainliest. may help w/ my depression.

The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

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The measure of ∠B rounded to the nearest whole number is 71°

From the question, we are to calculate the measure of ∠B.

In the given diagram, we have a right triangle.

In the right triangle,

The hypotenuse is 21

Adjacent is 7

From SOH CAH TOA,

We have that

sin θ = Opposite / Hypotenuse

cos θ = Adjacent / Hypotenuse

tan θ = Opposite / Adjacent

Thus,

we can write that

cos B = 7/21

cos B = 1/3

B = cos⁻¹(1/3)

B = 70.528

B ≈ 71°

Hence, the measure of ∠B rounded to the nearest whole number is 71°

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A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.

The percent of the given number 26 % of 500 is 130.

A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.

Let the equation be 26 % of 500

Percentage = (value/total value) × 100 %.

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

26 % of 500 = 26/100 of 500

26/100 × 500 = 130

Therefore, the percent of the given number 26 % of 500 is 130.

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The growth per year in Mountain Biking is 0.25 Million

In the year 2004 - 8 Million people participated

So, the slope point becomes (2004,8)

In the year 2006 - 8.5 Million people participated

So, the slope point becomes (2006,8.5)

Now we have points as :

[tex]X_1[/tex] = 2004

[tex]Y_1[/tex] = 8

[tex]X_2[/tex] = 2006

[tex]Y_2[/tex] = 8.5

Growth per year in the sport :

= [tex]Y_2[/tex] - [tex]Y_1[/tex] / [tex]X_2[/tex] - [tex]X_1[/tex]

= 8.5 - 8 / 2006 - 2004

= 0.5 / 2 = 0.25

Therefore, Growth per year in the sport is 0.25 Million per year

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Answer:

-(8/-4)² + 2 - 4³ = -66

Step-by-step explanation:

-(8/-4)² + 2 - 4³

Here we need to respect the order of operations.

So ,first we calculate what’s between parentheses :

8/-4 = -2

Then

-(8/-4)² + 2 - 4³ = -(-2)² + 2 - 4³

Then

We calculate the exponent :

(-2)² = (-2) × (-2) = 4

4³ = 4 × 4 × 4 = 64

Then

-(8/-4)² + 2 - 4³ = -4 + 2 - 64

Then

The expression -4 + 2 - 64 contains addition and subtraction.

So ,we start calculating from left to right :

-4 + 2 = -2

Then

-4 + 2 - 64 = -2 - 64 = -66

Conclusion :

-(8/-4)² + 2 - 4³ = -66

The value of – 90 7 50 written as a decimal number is -90. 14

Decimals are the types of numbers, having a whole number and the fractional part that is separated by a decimal point.

The dot present that is found between the whole number and fractions part is known as the decimal point.

Given the mixed fraction;

– 90 7 50

Let's convert to improper fractions;

 -4507  /50

Find the ratio

-90. 14

Thus, the value of – 90 7 50 written as a decimal number is -90. 14

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ΔJKL has sides that are of 70.37 units.

So,

The formula of perimeter: √(x₂−x₁)²+(y₂−y₁)²

Filling the values in the formula, we obtain:

Then, each side of the triangle will be: 70.37 units

Therefore, ΔJKL has sides that are 70.37 units.

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Step-by-step explanation:

remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).

1.

domain : -infinity < x < +infinity

range : -1 <= y < +infinity

due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...

2.

domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.

the only forbidden value of x is therefore

3x + 5 = 0

3x = -5

x = -5/3

so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)

range : -infinity < y < +infinity

3.

domain : -infinity < x < +infinity

range : 0 <= y < +infinity

due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.

4.

this is 1/(2x) as I understand it.

similar to 2. we must avoid at 1/0 situation.

so, x must not be 0. everything else is possible

domain : (-infinity < x < 0) OR (0 < x < +infinity)

range : -infinity < y < +infinity

5.

everything is allowed and possible.

domain : -infinity < x < +infinity

range : -infinity < y < +infinity

The conclusion based on this data is that C. The hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.

It should be noted that from the information, the change in plant height for each group over a two-week period was averaged and recorded.

It should be noted that as more fertilizer was added, the height of the plant reduced. This shouldn't be so.

Therefore, the conclusion based on this data is that the hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.

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Answer: C

Step-by-step explanation: Edge 2022

The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

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The numbers -28 = -28 are representing the reflexive property.

According to the Reflexive Property, x=x for every real number x. The meaning of the reflexive property is that the two expressions will have identical answers.

Suppose for square the two expressions for the length are 2x - 2 and ( 4x / 2 - 2 ). The two lengths of the square will have the same value.

2x - 2 = ( 4x / 2 - 2 ).

2x - 2 = 2x -  2

This is called reflexive property. Therefore, the numbers -28 = -28 are representing the reflexive property.

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Based on the fact that the right line is a reflection across the y-axis, the lines are the same, they are just in a different position.

What is a Reflection?

This refers to the rigid transformation type that is used to represent an image and does not change its size or length of it.

With this understanding, we can see that the pre-image and the image in a rigid transformation are congruent which makes the lines to be the same, even if they are in a different position.

Answer:

4

Step-by-step explanation:

The slope of the line with points p(x, y) and p′(x′, y′) is given by:

[tex] (\frac{x. \: - \: x}{y. \: \: - y } )[/tex]

[tex] (\frac{8 - ( - 4)}{5 - 2} )[/tex]

12/3

slope = 4

According to the question, to check whether the events are mutually exclusive or not mutually exclusive for the rolling pair of dice to get the total either as six or ten.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time .For instance, in any event nobody can run forward or backward together at the same time.

Rolling a pair of dice to get the sum as 6, then is not mutually exclusive.

The calculation is as shown below:

P(E) = 6+5-1/36

= 10/36

= 5/18

= 27.8 %

Now, rolling a pair of dice to get either the sum as 6 or 10.

P(6 or 10)

= P(6)+P(10)

= 5/36+ 3/36

= 8/36

= 2/9

= 22%

Hence, it is not mutually exclusive event because the calculated percentage is 22%.

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