Name the property of real numbers illustrated by each equation.
97(7)=100(7)-3(7)

The required distance between the third and first fret would be 64.390 mm.

Arithmetic functions are defined as adding, subtracting, dividing, and multiplying built-in functions.

- Subtraction operation: calculates the difference between the right-hand and left-hand operands.

for example 4 -2 = 2

+ Addition operation: on either side of the operator, additional significances are added.

For example 4 + 2 = 6

We have been given that the distance between the first and second frets is 33.641 mm.

The distance between the second and third frets is 31.749 mm.

So the distance between the third and first fret will be:

⇒ 33.641 + 31.749

Apply the addition operation, and we get

⇒ 64.390 mm

Therefore, the required distance between the third and first fret would be 64.390 mm.

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Answer:

Step-by-step explanation:

17.55 x 0.92 = $16.15

Answer:

C. Negative skew

Step-by-step explanation:

I did the test and got it right, plato / edmentum

Answer:

Step-by-step explanation: add the equations

2x² = 30

x² = 15

y² = 12 - 15

    = -3

x4 -y4 = 15² - (-3)²

           = 216

The equation of the circle for a circular irrigation field with radius 12 and center at (7 , -10) is (x - 7)^2 + (y + 10)^2 = 144.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circular irrigation field, substitute these values to the general form of the equation of the circle.

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

where (h , k) = (7 , -10)

r = 12

(x - 7)^2 + (y - -10)^2 = 12^2

(x - 7)^2 + (y + 10)^2 = 144

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Answer:

|2x + y - 3z|

Plug in the values

|-4 + 10 - 9|

= |-3|

= 3

Step-by-step explanation:

the answer is (3) because when all the letters are turned into numbers then solved it becomes [-4+10+(-9)] then you have to turn it into a positive because of the lines.

Answer:

y = 3x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 6) ← 2 points on the line

m = [tex]\frac{6-0}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

y = 3x ← equation of line

The next 2 terms if it is a geometric sequence is 360 and 480.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms.

Given:

The sequence in the form

[tex]f_{1} =120,[/tex]

[tex]f_{n} =f_{n-1}[/tex]         for n>2

According to given question we have

[tex]f_{1} =120,[/tex]

The formula would be:

[tex]f_{n} =f_{n-1}+f_{1}[/tex]         for n>2

[tex]f_{2} =f_{2-1}+f_{1} =f_{1}+f_{1} =240\\\\f_{3} =f_{3-1}+f_{1} =f_{2}+f_{1} =240+120=360\\\\f_{4} =f_{4-1}+f_{1} =f_{3}+f_{1} =360+120=480\\[/tex]

Therefore, the next 2 terms if it is a geometric sequence is 360 and 480.

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Exercise 1

5 3/4 + (-1/4)

Multiply 5 and 4 to get 20.

20 + 3/4 - 1/4

Add 20 and 3 to get 23.

23/4 - 1/4

Since the fractions 23/4 and 1/4 have the same denominator, subtract their numerators to subtract them.

23 - 1/4

Subtract 1 from 23 to get 22.

22/4

Reduce the fraction 22/4 to its lowest expression by extracting and canceling 3.

11/4

Exercise 2

-2/3 + 1/6

Convert -2/3 and 1/6 to fractions with like denominators.

- 2×2/3 × 2 + 1/6

Simplify

-4/6 + 1/6

Since -4/6 and 1/6 have the same denominator, add their numerators to add them together.

-4 + 1/6

Add −4 and 1 to get −3.

-3/6

Reduce the fraction -3/6 to its lowest expression by extracting and canceling 3.

-1/2

Exercise 3

-8/5 + (-3/4)

Convert -8/5 and 3/4 to fractions with like denominators.

-32/20 - 15/20

Since -32/20 and 15/20 have the same denominator, subtract their numerators to subtract them.

-32 - 15/20

Subtract 15 from −32 to get −47.

-47/20

Answer:

E

Step-by-step explanation:

Substituting x=0 into 1-x², we get:

[tex]\lim_{x \to 0} f(1-x^2)=\lim_{x \to 1} f(x)[/tex]

which does not exist.

The solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1

In this question, we have been given an equation.

2x / 3 - 1/2 = 2x + 5/6

We need to find the solution of given equation.

⇒ 2x / 3 - 1/2 = 2x + 5/6

⇒ (4x - 3)/6 = (12x + 5)/6

⇒ 4x - 3 = 12x + 5

⇒ 4x - 12x = 5 + 3

⇒ -8x = 8

⇒ x = -1

We need to check above solution.

so, substitute x = -1 in LHS of given equation.

LHS

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

= -2/3 - 1/2

= -(2/3 + 1/2)

= -[(4 + 3)/6]

= -7/6

Now, substitute x = -1 in RHS of given equation.

RHS

= 2(-1) + 5/6

= -2 + 5/6

= (-12 + 5)/6

= -7/6

For x = -1, LHS = RHS

Therefore, the solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1

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Answer:

                           18

7b² + 12b + 19 + -------

                           b - 1

Step-by-step explanation:

(7b³ + 5b² + 7b - 1) ÷ (b - 1)

1 | 7   5   7   -1

  ↓    7  12  19

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

  7    12   19  18

                           18

7b² + 12b + 19 + -------

                           b - 1

I hope this helps!

Answer: science

Step-by-step explanation:

The two segments having the same length are line VW and line YZ. Option D

A number line can simply be defined as a straight line with numbers that are  placed at equal intervals or segments along its length.

It is also known as a visual picture or representation of numbers.

From the number line shown, we have the following deductions;

From the above solutions, we can see that line

Line VW is equal in length to line YZ

Thus, the two segments having the same length are line VW and line YZ. Option D

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The probability for the arrow that land in the number 3 is 1/8.

Probability:

Basically, the word probability means the possibility of occurring the required event.

Given,

The spinner is divided into 8 equal sections.

Here we need to find if the arrow lands on a number, what is the probability that it will land on 3.

Let us consider that the spinner has 8 equal-sized sections numbered 1 to 8.

Since the sections have equal size, each section is equally probable.

The probability of falling on each section is therefore 1/8.

We know that, in the 8 sections,

There is only one 3 in this list.

So, the possibility of the event = 1

Hence, probability is

=> 1/8

Therefore, the probability for the arrow that land in the number 3 is 1/8.

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Answer: 154º

Step-by-step explanation: vertically opposite angles => xº = 154º

Answer:

x = 5

Step-by-step explanation:

[tex]12x = 70 - 2x[/tex]

[tex]14x = 70[/tex]

[tex]x = 5[/tex]

Answer:

Here :))

Step-by-step explanation:

The division will give a value of 0.15 × 10^10.

The information is to divide the quantity 1.365 times ten raised to the eighteenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.

This will be:

(1.365 × 10^18) / (9.1 × 10^8)

= 1.365/9.1 × 10^10

= 0.15 × 10^10

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Answer:

Let r be the number of rides and g be the number of games.

2.50g + 4.00r = 52.50

r = 2g

The equations are 2.5g +4r = 52.5 and g=2r.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cost of game = $2.50

Cost of ride = $4

let g be the number of games

and, let r be the number of rides taken

total they played = $52.50

So, the equation can be

2.5g +4r = 52.5

and,  number of rides she went on is twice the number of games she played.

So, g = 2r

Hence, The equations are 2.5g +4r = 52.5 and g=2r.

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Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. The given conclusion is deductive reasoning.

Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.

Given the statements,

From the given sentences, the first sentence is a general statement, the second statement is a specific statement. And, at the last, the third statement is a conclusion statement.

Hence, the given conclusion is deductive reasoning.

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According to the question, to calculate the probability of the event which states that tossing a coin to get either head or tail

The total number of a coin is [tex]1[/tex]

And total number of possibilities are {H,T}

Therefore, the total number of favorable outcomes in which either head or tail can come: [tex]1[/tex]

As per question, the probability can be written as:

P(h or t) = P(h) + P(t)

            [tex]= \frac{1}{2} +\frac{1}{2} =1 = 100%[/tex]

Hence, the probability of getting either head or tail is [tex]1[/tex].

The given event is mutually exclusive because it has [tex]100[/tex] percent which is close to tenth of a percent. And these two events cannot happen at the same time also, so they are mutually exclusive.

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.

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The weight of Callie's backpack is 7½ pounds which is calculated by multiplication of the number of times the bag is heavier with the weight of the bag.

Multiplication or product of two constants is defined as the number of times a particular constant is added . If we want to multiply a and b then their product is equal to b times a added.

a+a+a+a....... b times=ab

The multiplication is one of the four basic arithmetic operations that are used in mathematics and everyday lives.

Given the weight of Callie's bag is 2 ½ times the weight of Carl's backpack.

Therefore to calculate the the weight of Callie's backpack we multiply the weight of Carl's backpack with  2 ½.

Weight of Carl's backpack=3 pounds

Therefore weight of Callie's backpack= 2 ½×3 pounds= 7½ pounds

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Answer:

Step-by-step explanation:

semplify

8/12 = 2/3

B)

1/3 + 1/3 = 2/3

Tamika's number of visits required to earn a free movie ticket is 14 visits.

According to the question, the given data is;

Tamika has a points card for a movie theatre which are as follow;

Signup rewards = 20 points

Each visit reward = 10.5

Total points needed = 167

Let 'x' be the number of visits.

Total points earned for x number of visits: 10.5x.

Thus, the equation according to statement;

20 + (10.5 × x) = 167

10.5x = 167 - 20

10.5x = 147

x = 147/10.5

x = 14 visits.

Therefore, Tamika's number of visits required to earn a free movie ticket are 14 visits.

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Using the definition of slope, the points (3 , -5), (-3 , 3), and (0 , 2) are not collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

Getting the slope of each pair of points:

(3 , -5) and (-3 , 3)

m = (y2 - y1)/(x2 - x1)

m = (3 - -5)/(-3 - 3)

m = 8/-6

m = -4/3

(-3 , 3) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - 3)/(0 - -3)

m = -1/3

(3 , -5) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - -5)/(0 - 3)

m = 7/-3

m = -7/3

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is not equal with each other, then they are not collinear.

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Answer:

x = 2, x = -6

Step-by-step explanation:

Given quadratic function in vertex form:

[tex]f(x)=(x+2)^2-16[/tex]

The zeros of a function occur when f(x) = 0:

[tex]\implies (x + 2)^2 - 16 = 0[/tex]

Add 16 to both sides:

[tex]\implies (x + 2)^2 - 16+16 = 0+16[/tex]

[tex]\implies (x + 2)^2 =16[/tex]

Square root both sides:

[tex]\implies \sqrt{ (x + 2)^2} =\sqrt{16}[/tex]

[tex]\implies x+2= \pm 4[/tex]

Subtract 2 from both sides:

[tex]\implies x+2-2= -2 \pm 4[/tex]

[tex]\implies x= -2 \pm 4[/tex]

Therefore:

[tex]\implies x=-2+4=2[/tex]

[tex]\implies x=-2-4=-6[/tex]

The zeros of the given quadratic function are x = 2, x = -6.