The area of this square is one hundred twenty-one square centimeters. What is the length of one side of this square?

Answer:

When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. This makes sense, since all the angles in the first quadrant are less than 90°. So, if our given angle is 33°, then its reference angle is also 33°.

When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle. So, if our given angle is 110°, then its reference angle is 180° – 110° = 70°.

When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°. So, if our given angle is 214°, then its reference angle is 214° – 180° = 34°.

When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle. So, if our given angle is 332°, then its reference angle is 360° – 332° = 28°.

The number of minutes to take for the light to travel from the sun to the earth is 7.93×[tex]10^{1}[/tex] minutes.

The distance between the earth and sun=9.52×[tex]10^{7}[/tex] miles

The speed of the light from sun=1.2×[tex]10^{6}[/tex] miles per minutes

Speed=Distance/Time

Time= Distance/Speed

Substitute the values in the equation

Time taken for the light to travel from the sun to the earth = The distance between the earth and sun ÷ The speed of the light from sun

Substitute the values in the equation

=9.52×[tex]10^{7}[/tex]÷ 1.2×[tex]10^{6}[/tex]

=(9.52÷1.2)×[tex]10^{7-6}[/tex]

=7.93×[tex]10^{1}[/tex] minutes

Hence, the time taken for the light to travel from the sun to the earth is 7.93×[tex]10^{1}[/tex] minutes

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Harold's total payment is  $5,841.50.

Percentage is the  fraction of a quantity that is expressed as a number out of hundred. The sign used to represent percentages is %. Percentages are a measure of frequency.

The total bill Harold would pay is the sum of the first $550, 25% of the remaining bill, 12% of the fee for prescription medications and the late payment fee since she paid after September 30.

Amount of total bill that Harold would pay = (100 - 75)% x (20,500 - 550)

25% x 19,950 = $4,987.50

Amount of the  prescription medications Harold pays : 12% x 450 = $54

Total bill - $550 + $4,987.50 + $54 + $250 = $5,841.50

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The probability of picking a dime and then a penny without replacement is  0.0651.

Probability is used to determine the odds that a random event would happen. The probability the event happens is 1 and the probability that the event does not happen is 0.

The more likely the event is to occur, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability of picking a dime and then a penny without replacement = (number of dimes / total number of coins) x (number of pennies / total number of coins - 1)

(19 / 73) x (18 / 72) = 0.0651

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Answer:

Jay paid £573.76 for the smart phone originally.

A numerical expression to represent the greatest total number of fish that could be in both aquariums is; Number in Tiger barb + number in giant danios

The Greatest number of fishes that could be in both aquariums is; 14

We are given that;

Tiger barbs = 30 gallon aquarium

Giant danios = 20 gallon aquarium

Greatest number of fishes that could be in both aquariums;

Tiger barb = volume / length

Tiger barb = 30 / 3

Tiger barb = 10 fishes

Giant danios = volume / length

Giant danios = 20 /5

Giant danios = 4 fishes

Hence, the greatest total number of fishes in both aquarium is :

Number in Tiger barb + number in giant danios

= 10 + 4 = 14

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Complete question is;

There are tiger barbs in a 30-gallon aquarium and giant danios in a 20-gallon aquarium

Use the rule to solve this problem. The rule for the number of fish in an aquarium is to allow 1 gallon of water for each inch of length.

Giant Danio=5 inch length

Tiger barb=3 inch length

What is the correct numerical expression that represents the greatest total number of fish that could be in both aquariums?

Answer:

C

Step-by-step explanation:

hope this helps!

The smallest angle on the line will be 36°

A line segment seems to be a straight line that connects two places. A line segment does indeed have a predetermined length. A ruler can be used to determine the shortest distance between the two points.

A straight angle in geometry is an angle with a vertex point of 180 degrees. It basically generates a straight line with sides that point in opposite directions first from the vertex. It is also known as "flat angles."

We know the the sum of the straight angle is = 180°

So,

(5a + 18) + (48 - a) + (8a -30 ) = 180°

5a - a + 8a + 18 +48 - 30 = 180°

12a + 36 = 180°

12a = 180 - 36

a = 12°

So putting the value of a in the equation:

(5a + 18) = 5 *12 + 18 = 78°

(48 - a) = 48 - 12 = 36°

(8a -30 ) =  96 - 30 = 66°

36° < 66° <78°

So the smallest angle on the line will be 36°

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The maximum distance Jameel can travel is 11.5 miles

The equation that determines the distance is given as

2 + 0.4(4m - 1) = 20

Subtract 2 from both sides of the equation

So, we have

0.4(4m - 1) = 20 -2

Evaluate the like terms

So, we have

0.4(4m - 1) = 18

Divide both sides by 0.4

So, we have

(4m - 1) = 18/0.4

Evaluate the quotients

So, we have

(4m - 1) = 45

Remove the bracket

So, we have

4m - 1 = 45

Add 1 to both sides of the equation

4m = 46

Divide both sides of the equation by 4

So, we have

x = 11.5

Hence, the maximum distance Jameel can travel is 11.5miles

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The slope of line gh is [tex]\frac{-9}{7}[/tex] .

We have given two points G(-2,6) and H(5,-3) .

Putting [tex]x_1=-2,y_1=6[/tex] and [tex]x_2=-5 ,y_2=-3[/tex] in equation (1) , we get

          [tex]m=\frac{-3-6}{5-(-2)} \\\\m=\frac{-9}{5+2}\\\\m=\frac{-9}{7} \\[/tex]

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Answer:

The answer is C. 5π > 15

Step-by-step explanation:

5π = 15.7

15.7 is greater than 15

Answer: (4m+n)(4m-n)

Step-by-step explanation:

16m² -n²=

(4m)²-n²=

(4m)²+4mn-4mn-n²=

4m(4m+n)-n(4m+n)=(4m+n)(4m-n)

Answer:

[tex] = { \tt{16m {}^{2} - {n}^{2} }} \\ { \tt{ = {4}^{2} {m}^{2} - {n}^{2} }} \\ { \tt{ = (4m - n)(4m + n)}}[/tex]

Answer:

9,246,073,189

Step-by-step explanation:

Answer:

9,246,793,189

Step-by-step explanation:

its 9 billion which have nine zeros in behind

and others do it by yourself

The function of  f(x) = (x+4)³ + 3 is one-to-one  then the value of

[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex] and,

[tex]f^{-1} (2) = -2.7401[/tex]

The function f(x) = (x+4)³ + 3

Let us assume,

y = (x+4)³ + 3

A function is said to be invertible when it has an inverse. It is represented by [tex]f^{-1}[/tex]. Condition for a function to have a well-defined inverse is that it be one-to-one and Onto or simply bijective.

Then,

y = (x+4)³   and    y = 3

Therefore the inverse of y = 3 is the line x = 3

We can solve,

y = (x+4)³

The solution of Inverse function,

So,

[tex]\sqrt[3]{y} = x+4[/tex]

We can get,

[tex]x = \sqrt[3]{y} -4[/tex]

So the inverse of y is [tex]\sqrt[3]{x} -4[/tex]

f(x) = (x+4)³

So the inverse of f(x) is [tex]\sqrt[3]{x} -4[/tex]

Therefore, [tex]f^{-1}( x)[/tex] = [tex]\sqrt[3]{x} -4[/tex]

Then f(x) = 2

[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex]

We can substitute f(x) = 2

[tex]f^{-1} (2) = \sqrt[3]{2} -4[/tex]      

Since, ∛2 = 1.2599

We can substitute this value,

[tex]f^{-1} (2) = 1.2599-4[/tex]

[tex]f^{-1} (2) = -2.7401[/tex]

Therefore,

The value of ,

[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex] and,

[tex]f^{-1} (2) = -2.7401[/tex]

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The total weight of the envelop after n paper clips have been added is w(n) = 0.5n + 6.75

An equation is an expression that shows the relationship between two or more numbers and variables.

Let w(n) represent the total weight of the envelop with n paper clips. A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams. Hence:

w(n) = 0.5n + 6.75

The total weight of the envelop after n paper clips have been added is w(n) = 0.5n + 6.75

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The feet of rope that Larry has left will be 29 feet.

Total number of feet of the rope = 63 feet

Feet that were used = 15.56 + 18.13 = 16 + 18 = 34 feet

Therefore, the feet of rope that Larry has left will be:

= 63 - 34

= 29

Therefore, the feet of rope that Larry has left will be 29 feet.

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Answer: 29 feet

Step-by-step explanation:

The new coordinates after the dilation with scale factor 1/4 is

                             a' = (5/2 , 3/2)

To get the new coordinates when the point is dilated is to multiply the scale factor with the coordinates of the point.

According to the question we have been given that

    center of dilation = (0,0)

       Scale factor = 1/4

       coordinate of the point, a = (10,6)

To get the new coordinates we will multiply the given coordinates by the scale factor that is ,

          a' = 1/4*(10,6)

              = (10*1/4 , 6*1/4)

           a' = (5/2 , 3/2)

Hence the new coordinates after the dilation is a' = (5/2 , 3/2)

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The area of a square is the square of the length of a side is a^2.

The quantity of space occupied within the square can be used to calculate the size of a square using mathematics. We'll go over the equation for calculating the square's area below. It is mainly known for its geometric quadrilaterals. The simplest definition of a square is a regular polygon with four equal sides. A square has all the same facts and characteristics as regular polygons.

The number of square units that are anticipated to fill a square is used to describe the area of a square. The area is typically defined as the area included by the confines of a level article or 2D figure.

Mathematical Area of Square Formula = a×a=a^2.

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The x-intercepts of the parabola are  (-1,0) and (-5,0) and the coordinates of the vertex are  ( -3 , - 4 ).

A parabola is a graphical representation of a function of the form y=g(x) where g(x) is a quadratic polynomial of x.

The given equation of the parabola is y = x² + 6x + 5

to find the x-intercepts we have to take the value of y at zero.

∴  x² + 6x + 5 = 0

or,  x² + 5x + x + 5 = 0

or, x (x + 5) + 1 ( x + 5 ) = 0

or, (x+5)(x+1)=0

either x=-5 or x=-1

Therefore the x-intercepts of the graph is (-1,0) and (-5,0)

Now to find the vertex of the parabola:

y =  x² + 6x + 5

or, y = x² + 2·x·3 + 3² - 4

or, y = (x + 3)² - 4

Therefore from the above equation we can say that the vertex of the parabola is at ( -3 , - 4 ).

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Answer: How in the world would anybody answer this

Step-by-step explanation: I don't know!

The equation with nontrivial linear combination is (16)4x + ( -48 )2x²+ (-8 )(8x-12x²) = 0

We can solve this problem following some steps.

Let's assume the value is A for blank one and it is B for blank two.

Now we can rewrite the equation as,

(16)4x + (A) 2x²+ (B)(8x-12x²) = 0

Or, 64x + 2Ax² + 8Bx - 12Bx² = 0

After rearrangement, we can write this equation as,

x ( 64 + 8B) + x²( 2A - 12B) = 0

We can consider the whole equation as zero, only when the coefficient of both x and x² is zero, To complete a nontrivial combination, we have to write,

∴ ( 64 + 8B) = 0 [ Coefficient of x ]

Or , 8B = -64

Or, B = -64/8 = -8

Again following the previous concept we can also write, ( 2A - 12B ) = 0

[ Coefficient of x² ]

Now, we should put the value of B = -8

∵ ( 2A - 12B ) = 0

Or, 2A + 96 = 0

Or, 2A = - 96

Or, A = - 48

So, the value of A is -48, and the value of B is -8

Now we can conclude,

(16)4x + ( -48 )2x²+ ( -8 )(8x-12x²) = 0

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Answer:

yes

Step-by-step explanation:

to solve this you must first find her rate

6 / 20 is her rate

you want to know how many she can do in ten minutes so we must find how many seconds are in 10 minutes

10 * 60 = 600

175 / 600 is the rate needed fro the test

now make them have the same denominator

6 / 20 is also 180 / 600

175/600 is less than 180/600 so yes she will finish the test in time

The value of the x in the linear equation is a 3/4.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

8 - (6 - 8x) = 4x + 5

Now we have to solve this

Then

8 - (6 - 8x) = 4x + 5

8 - 6 + 8x = 4x + 5

Now, rearrange the above written terms for the value of the x

2 + 8x = 4x + 5

4x = 3

x =3/4.

So, The value of the x in the linear equation is a 3/4.

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Answer: an=2(n-1)+1

Step-by-step explanation:

1,3,5,7, …

As the terms progress in the sequence, each term get increased by 2 to get to the next term. Hence, the change is linear and can be modeled with the function y=2(x-1)+1 where y=term value, x=term number and 1 is the first term in the sequence.

y=2(x-1)+1

an=2(n-1)+1 ==> n=term number while an=term value. an=nth term

The digit 3 in 5,630, is not 10 times the value of the digit 3 in 342. It's false.

It should be noted the question has to do with place value. In this case, the digit 3 in 5,630 gives a value of 30.

On the other hand, the digit 3 in 342 is 300.

Therefore, we can see that the digit 3 in 5,630, is not 10 times the value of the digit 3 in 342.

Therefore, the correct option is false.

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The digit 3 in 5,630, is 10 times the value of the digit 3 in 342. True or. false?

Answer:

It will be (x=1.y=6.z=-6

Answer:

Choice b

(x = 1,  y = 6, z = -6)  

Step-by-step explanation:

The system of equations is

3x + 4y  + 3z = 9     (1)
3x + 3y +  3z =  3      (2)

2x + 4y + 3z =  8      (3)

Subtract (2) from (1) to eliminate the 3x and 3y terms and solve for y

(1) - (2)

==> 3x + 4y  + 3z - (3x + 3y +3z) = 9 - 3

==> 3x + 4y + 3z - 3x - 3y - 3z = 6

(3x-3x) + (4y-3y) + (3z-3z) = 6

4y - 3y = 6

y = 6

Subtract (3) from (1) to isolate the x term

(3x - 2x) + (4y-4y) + (3z-3z) = 9 -8

x = 1

Divide equation (2) on both sides by 32 to eliminate the coefficients

Equation (2) ÷ 3

==> (3x + 3y + 3z) / 2 = 3/3

==> x + y + z = 1    (4)

Substitute the values of x and y in Equation (4)

1 + 6 + z = 1

7 + z = 1

Subtract 7 from both sides

==> z = 1-7 = 6

Answer:
(x = 1,  y = 6, z = -6)

Answer:-

Step-by-step explanation:

Step 1 1.2r = 0.6r-3

Step 2 .6r = -3

Step 3 -3 divided by .6 = -5

Answer: -5