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The system of the equation has x = 0.

The two equations are,

y = 2x + 6x + 4

y = -4x + 4

Now equating the equation, we have

2x + 6x + 4 = -4x + 4

8x + 4 = -4x + 4

12x = 0

x = 0

Therefore the system of the equation has x = 0.

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Answer:

[tex] {3}^{x} = 243 = {3}^{x} = {3}^{5} = 5[/tex]

The range of the function y=1/2x+3 when the domain is {-2, 0, 2, 4} is {-1 , 0.33 , 0.14 , 0.090}

We have given a function y = 1/2x+3 .....(1) and domain {-2, 0, 2, 4} .

In order to find the range putting x = -2 in equation (1) , we get

y=1/(2(-2)+3

y=1/-4+3

y=1/-1

y = -1

Putting x = 0 in equation (1) , we get

y=1/2(0)+3

y=1/0+3

y=1/3

y = 0.33

Putting x = 2 in equation (1) , we get

y=1/2(2)+3

y=1/4+3

y = 1 / 7

y = 0.14

Putting x = 4 in equation (1) , we get

y=1/2(4)+3

y=1/8+3

y= 1 / 11

y = 0.090

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Answer: m<8=97 degrees.

m<5=83 degrees

Step-by-step explanation:

m<8=m<2 ==> Angles 8 and 2 are alternate interior angles, meaning that they're equal.

m<8=97 degrees.

m<8+m<5=180 degrees ==> Both angles 8 and 5 add up to a straight line, and straight lines measure 180 degrees and are called straight angles.

97+m<5=180

97-97+m<5=180-97

m<5=83 degrees

The prime factorization of 200 using exponential notation is [tex]2^3 *5^2[/tex] that is correct option is (b)

First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.

1) [tex]200\div2=100[/tex] (Even number)

2)  [tex]100\div2=50[/tex](Even number)

3)  [tex]50\div2=25[/tex](Even number)

4)  [tex]25\div5=5[/tex](Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

5)  [tex]5\div5=1[/tex](Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

Now, we construct the prime factorization using exponential notation:

[tex]200=2^3\cdot5^2[/tex]

The prime factorization of 200 using exponential notation is [tex]2^3\cdot5^2[/tex] that is option (b)

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The prime factorization of 200 using exponential notation is 2^3*5^2  that is correct option is (b)

First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.

1)  200/2=100 (Even number)

2) 100/2=50  (Even number)

3)50/2=25  (Even number)

4) 25/5=5 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

5) 5/5=1 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

Now, we construct the prime factorization using exponential notation:

200=2^3*5^2

The prime factorization of 200 using exponential notation is 2^3*5^2  that is option (b)

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Answer:9870

Step-by-step explanation:

Answer:

Step-by-step explanation:

So we have our 9871

For rounding when a number is four and below if I am remembering correctly you drop the number down. If 5 and up you bump it up to the next number in front of it.

9871

7 = tens

7 > 5

9881

Answer:

Step-by-step explanation:

As we know that a-b=7 and ab=8(a times b is equal to 8) If we find the factors of 8 we know that 8 times 1 make 8 and if u try 8-1= 7 so 1 squared is 1 and 8 squared is 16 so 16+1=17

Answer:

A = 8

B = 1

A squared + B squared = 65

Step-by-step explanation:

8 - 1 = 7

A - B = 7

8 x 1 = 8

A x B = 8

8 x 8 = 64

1  x 1 = 1

64 + 1 = 65

A squared + B squared = 65

Answer:

(C) tan 3pi/2

Step-by-step explanation:

See image. You can use the Unit Circle to help you find these answers. The Unit Circle looks like scary math chaos pizza, but it really is just a great big giant answer key. It has all the trig answers on it.

(If you use your calculator instead be sure to change it to radian mode.)

See image.

Tangent for any angle is the y/x.

Only tan 3pi/2 is undefined.

At 3pi/2 the x and y are (0,1) so tangent is 1/0 which is undefined.

The value of the expression log₈32 by using the change of base formula is 1.67.

Given that the expression is log₈32.

We are required to find the value of the expression using change of base formula.

The change of base formula is basically used at a time when we have to re-write a logarithm operation as a fraction of logarithms with a new base to find the value of the logarithm.

The result given by it is [tex]log_{a}b[/tex]=log b/log a.

The expression is log₈32.

log₈32=log 32/log 8

=log [tex]2^{5}[/tex]/ log [tex]2^{3}[/tex]

=5log 2/3log 2

=5/3

=1.67

Hence we can say that the value of the expression log₈32 by using the change of base formula is equal to 1.67.

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Answer:   [tex]2\text{x}^4, \ 2\text{x}^7, \ 2\text{x}^{10}, \ 2\text{x}^{13}[/tex]

===========================================================

Explanation:

The first term is [tex]a_1 = 2\text{x}[/tex] and the common ratio is [tex]r = \text{x}^3[/tex]

To get the second term, we multiply the first term by that common ratio

[tex]a_2 = a_1*r = 2\text{x}*\text{x}^3 = 2\text{x}^4[/tex]

Repeat a similar idea for the third term

[tex]a_3 = a_2*r = 2\text{x}^4*\text{x}^3 = 2\text{x}^{4+3} = 2\text{x}^7[/tex]

and the fourth term is

[tex]a_4 = a_3*r = 2\text{x}^7*\text{x}^3 = 2\text{x}^{7+3} = 2\text{x}^{10}[/tex]

The fifth term is

[tex]a_5 = a_4*r = 2\text{x}^{10}*\text{x}^3 = 2\text{x}^{10+3} = 2\text{x}^{13}[/tex]

Something to notice: The exponents of the first five terms are: 1, 4, 7, 10, 13. The sequence of exponents is arithmetic even though the original underlying sequence is geometric.

The reason why the exponent sequence is arithmetic is because we keep multiplying by [tex]\text{x}^3[/tex], and hence we keep adding 3 to each exponent to get the next exponent.

-----------------------------------------

To summarize, the first five terms are:

[tex]2\text{x}, \ 2\text{x}^4, \ 2\text{x}^7, \ 2\text{x}^{10}, \ 2\text{x}^{13}[/tex]

We will ignore the first term 2x since your teacher wanted you to find the next four terms after that first term (i.e. term2 through term5).

Answer: x = 2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given equation,

→ 5(2x + 1) = 25

Solving for the value of x,

→ 5(2x + 1) = 25

→ 10x + 5 = 25

→ 10x = 25 - 5

→ x = 20/10

→ [ x = 2 ]

Hence, the value of x is 2.

There are 0 or no real solutions for the equation 4x²=-4x-4.

So,

Given the equation: 4x²=-4x-4

Then,

No factor for this equation.

Therefore, there are 0 or no real solutions for the equation 4x²=-4x-4.

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Answer:

0.03773584905

or 0.04

Step-by-step explanation: if this was not what you were looking for,

Answer: Shape A is congruent to Shape B because If you were to rotate one of the two and flip it, it would  match.

Step-by-step explanation:

hope it helps :)

Answer:

Thabo had 51 crayons at the start.

Step-by-step explanation:

Sam has three times as many crayons as Thabo. Then

x = 3y.

If Sam gives 17 crayons to Thabo, then he will have twice as many crayons as Thabo. Then

(x-17) = 2(y+17).

Thabo had 51 crayons to start with.

Given that Sam has three times more crayons than Thabo does. He will have twice as many crayons as Thabo if he gives him 17 of them.

We need to determine the number of crayons Thabo had in starting.

Let's use algebra to solve this problem step-by-step.

Let's assume that Thabo starts with "x" crayons.

According to the given information:

Sam has three times as many crayons as Thabo, which means Sam has 3x crayons.

If Sam gives Thabo 17 crayons, he will have (3x - 17) crayons left.

Thabo will have (x + 17) crayons after receiving the 17 crayons from Sam.

Now, the second condition states that if Sam gives Thabo 17 crayons, he will have twice as many crayons as Thabo.

Mathematically, it can be expressed as:

2(x + 17) = 3x - 17

Let's solve this equation to find the value of x:

2x + 34 = 3x - 17

Subtract 2x from both sides:

34 = x - 17

Now, add 17 to both sides:

x = 51

So, Thabo had 51 crayons to start with.

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Answer:

(3 3/4) : (3/4) = 5/1 = 5

Step-by-step explanation:

The situation which is represented by the inequality (7x + 50 > 4x + 100) is: A. Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

In this scenario, the number of week for saving money by each person is represented by the variable x. Therefore, the situation which is represented by the inequality (7x + 50 > 4x + 100) is that "Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?"

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The face of the rhombus ( length of one side) is found to be 13 cm.

A rhombus is a special parallelogram because it meets the definition of a parallelogram, which is a quadrilateral to two pairs of parallel sides.

As per the given question;

The circumference of the rhombus is 52 cm.

Let us consider the one side of the rhombus is of length 'x'.

As, we known that the sides of the rhombus are equal.

Thus,

4x = 52

x = 52/4

x = 13.

Therefore, the face or the length of the one side of the rhombus is found as 13 cm.

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37 • 2 • (0 + 1/2 ) - Inverse property of addition

37 • 2 • 1/2 - Commutative property of addition

37 • 1 - Inverse property of multiplication.

37 - Identity property of multiplication.

Algebraic expressions include at least one variable and at least one operation addition, subtraction, multiplication or division.

We have,

37 • 2 • (-5+ 5+ 1/2)

= 37 • 2 • (0 + 1/2 )  -Inverse property of addition

The inverse property of addition states that:

a + (-a ) = 0 where a ∈ R

= 37 • 2 • 1/2 - Commutative property/Identity property of addition

The commutative property of real numbers states that:

a + b = b + a where a,b ∈ R

= 37 • 1 - Inverse property of multiplication.

The inverse property of real numbers states that:

a + 1/a = 1 where a ∈ R

= 37 - Identity property of multiplication.

The identity property of multiplication of real numbers states that:

a x 1 = a where a ∈ R

Thus,

37 • 2 • (0 + 1/2 ) - Inverse property of addition

37 • 2 • 1/2 - Commutative property of addition

37 • 1 - Inverse property of multiplication.

37 - Identity property of multiplication.

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The complete question is:

For the following problem, match the name of the number property that was used to get to each step from the previous step.

37 • 2 • (-5+ 5+ 1/2)

37 • 2 • (0 + 1/2 )

37 • 2 • 1/2

37 • 1

37

identity property of addition

commutative property

inverse property of multiplication

inverse property of addition

identity property of multiplication

The correct unit price is $1.24 per pair of padded gloves such that the contractor's unit price is incorrect because total cost was divided by number of dozens bought instead of the number of units in 6 dozens

How many units are in a dozen?

The dozen of pairs of padded  gloves contains 6 pairs of padded  gloves, in other words, the number of units in 6 dozens is 6 dozens multiplied by 12 units in a dozen

number of units in 6 dozens=6*12

number of units in 6 dozens=72

unit price=total cost/number of units in 6 dozens

unit price=$89.28/72

unit price=$1.24

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Answer:

-2g-2f

Step-by-step explanation:

Hope it helps you

Answer: -2g-2f

Step-by-step explanation: Combine like terms

-3g+2f+g-4f

-2g-2f

The equation of the circle where the given parameters are Center = (6, 15) and Radius = 2 is (x - 6)^2 + (y - 15)^2 = 4

The given parameters are

Center = (6, 15)

Radius = 2

Rewrite the above parameters properly as

Center, (h, k) = (6, 15)

Radius, r = 2

The equation of the circle is represented as

(x - h)^2 + (y - k)^2 = r^2

Substitute the known values in the above equation

So, we have

(x - 6)^2 + (y - 15)^2 = 2^2

Evaluate the exponent of 2

So, we have

(x - 6)^2 + (y - 15)^2 = 4

Hence, the equation of the circle where the given parameters are Center = (6, 15) and Radius = 2 is (x - 6)^2 + (y - 15)^2 = 4

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Complete question

Write an equation of the circle with Center = (6,15) and Radius = 2

The required factor for the given expression is (x + 4)(3x - 1).

In mathematics, factorization or factoring refers to the process of composing a number or other mathematical object from numerous factors, usually smaller or simpler counterparts.

The given expression is 3x² + 11x - 4.

To factor a general quadratic expression of the form ax² + bx +c, we need to consider the product "ac" and find two factors for this number such that their sum is equal to b. during this case, a = 3, b = 11, and c = -4..

Therefore we need to consider the product ac = 3 × (-4) = -12.

Consider the 2 factors 12 and -1 for the product -12.

Then we have the sum is equal to 12 + (-1) = 12 - 1 = 11.

Therefore the expression 3x² + 11x - 4= 3x² + 12x + (-1)x -4= 3x² +12x - x - 4= 3x(x + 4) - (x + 4)= (x + 4)(3x - 1)

Therefore, the required factor for the given expression is (x + 4)(3x - 1).

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Victoria's debt to income ratio is 0.51 when her monthly expenses are compared to her monthly salary

What is debt to income ratio?

The debt to income ratio compares the monthly expenses(monthly obligations) of Victoria to her monthly salary to determine the portion of her salary that would be used in paying her bills

debt to income ratio=monthly expenses/monthly salary

monthly expense=1280

monthly salary=2,500

debt to income ratio=1280/2,500

debt to income ratio=0.51

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Answer:

Below in bold.

Step-by-step explanation:

(√5)² * (√3)²

= 5 * 3

= 15

(∛9))³  (√30)²

= 9 * 30

= 270

A number that can be expressed in scientific notation will be (2 × 10³) × 4 × 10².

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may also be referred to as standard form, scientific form, or standard index form.

Always set the base to 10. The exponent must be an integer that is non-zero, therefore it can either be positive or negative. The coefficient's absolute value is more than or equal to 1, but it must be less than 10.

It should be noted that the number that can be expressed in scientific notation will be (2 × 10³) × 4 × 10². This will be:

= (2 × 10³) × (4 × 10²)

= 8 × 10^5.

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The inequality that represent the possible length of the third side is

                    7 < x < 17

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the measure of the third side of the triangle.

We have been given measure of two sides which are 5 and 12. Then the possible length for the third side has two condition

Let the third side be x unit.

First condition,      x + 5 > 12

                              x > 7

Second condition,  12+ 5 > x

                                  17 > x

Hence the inequality that represent the possible length of the third side is

                    7 < x < 17

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Answer:

(- 1 , 1 )

Step-by-step explanation: