Find the equation of a line parallel to y = x – 3 that contains the point (-2, 1).
Yeah

The value of  [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex] is after simplification is C)-30

What is mixed fraction?

A mixed number combines an integer (whole number) with a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number). When a number contains both an integer (whole number) and a correct fraction, it is known as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).

Here the given expression is ,

=> [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex]

Now we need to convert them into improper fraction then,

=> [tex]\frac{15+3}{5}[/tex] × [tex]\frac{-(24+1)}{3}[/tex]

=> [tex]\frac{18}{5}[/tex] × [tex]\frac{-25}{3}[/tex]

=> 6 × -5 = -30

Hence the correct option is C)-30.

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Answer: b

Step-by-step explanation:

The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

transformation of functions

f(x) - f(x) -2

translate 2 units down

f(x) - f(x - 2)

translate 2 units right

f(x) - f(x) + 2

translate 2 units up

The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.

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A table which has a constant of proportionality between y and x of 0.9 include the following: B. table B.

In order to have a proportional relationship and equivalent ratios that is constant, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) based on the given parameters in each table:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 17/18

Constant of proportionality (k) = 0.94 (False).

For the variables x and y in table B, the constant of proportionality (k) is given by;

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 3.6/4 = 5.4/6 = 10.8/12

Constant of proportionality (k) = 0.9 (True).

For the variables x and y in table C, the constant of proportionality (k) is given by;

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 3.3/3

Constant of proportionality (k) = 1.1 (False).

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Answer:

[tex]x=8.5[/tex]

Step-by-step explanation:

By the definition of a midpoint, [tex]TU=UV[/tex].

[tex]6=2x-11 \\ \\ 2x=17 \\ \\ x=8.5[/tex]

The geometric series of the pattern is -512 for n = 9: -2, -4, 8-16,. is a geometric progression  and .

In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).

is a geometric progression  and r= 2.

is a geometric progression ai —2 and r= 2.

= —512

The place w Formulas are employed.

In this instance, we have  and n=9. These values are added to the formula above to get the following results:

an

9—1

-2. (256)

= —512

The initial terms in this series are:

8, -16...

The total number of terms in a geometric sequence makes up a geometric series. Using the initial term  and the common ratio r, it is possible to determine the nth partial sum of a geometric series as follows: .

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Answer:

6

Step-by-step explanation:

20 divided by 3 without any remainders, fractions, or decimals is 6.

Hope I helped!

Answer:

Step-by-step explanation:

Since 5 miles is approximately 8 kilometers, and Sawyer lives 12.7 kilometers from the soccer field, Sawyer lives farther than Jabar from the soccer field.

So Sawyer lives about 4.7 kilometers farther from the soccer fields.

Answer:

the answer is 1

Step-by-step explanation:

b(n) = -4 so b(n) is 2-4 then n is -1

b(n) = -2

n = -1

Answer:

Step-by-step explanation:

b(n) = -4 -2(n -1)

Find the 12th term in the sequence.

Put 12 where n is and evaluate.

The 12th term of the sequence is -2052.

The person must leave the money for  18.6 .

         [tex]A= P (1 +\frac{r}{n} )^{nt}[/tex]

        A =Amount = 2900

        P = Principal = 1000

        r = ratio =  5.75%

        2900 = 1000[tex](1 +\frac{5.75}{12} )^{12x[/tex]

        2900 = 1000 [tex](1 +\frac{575}{120000} )^{12x[/tex]

        2900 = 1000[tex](1 +\frac{23}{4800} )^{12x\\\\[/tex]

        2900 = 1000[tex](1 +\frac{4823}{4800} )^{12x\\\\[/tex]

       2900/1000 = 1000[tex](\frac{4823}{4800} )^{12x\\\\[/tex]

               29/ 10 = [tex](\frac{4823}{4800} )^{12x\\\\[/tex]

         12x = [tex]log _{\frac{4823}{4800} }\frac{29}{10}[/tex]

            [tex]x = \frac{log _{\frac{4823}{4800} }\frac{29}{10}}{12}[/tex]

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If the streetlights are spaced in the same way, there will be 48 streetlights on the 4-mile road.

First, we know that there are 18 streetlights evenly spaced on a 1.5 mile road.

Then the space between consecutive streetlights is:

1.5mi/18 = (3/36) mi = (1/12) mi

Now, the number of streetlights that we will have on a 4-mile road is given by the quotient between the length of the road and the distance between consecutive streetlights, it is:

N = 4mi/(1/12 mi) = 12*4 = 48

There will be 48 streetlights on a 4 mile road.

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The Z-Score associated on moving one standard devations to the right is equals to the 1.0, i.e., Z = 1.00. So, correct answer is option (c).

We have, The number of classes, n = 5

Mean of size of five classes,µ = 44

Standard deviations for five classes,σ = 8

The dynamic equation for conversion to z-scores in real-time is, Z = (Xᵢ - µ )/standard deviations (s)

Z-Score : A Z-Score is a metric that represents that how closely a value relates to mean of set of values. If Z score value is zero that means data point's scores are same as mean score.

Formula for Z- Score is Z = (X - µ)/σ

where, X ---> data values

µ --> mean of values

σ --> standard deviation

For 32, Z = (X - µ)/σ = (32 - 44)/8 = -1.50

For 42 , Z= (X- µ)/σ = (42 - 44)/8 = -0.25

For 48, Z = ( 48 - 44)/8 = 0.5

For 52, Z = ( 52 - 44)/8 = 1.0

For 54, Z = (54 - 44)/8 = 1.25

When we move One standard deviations to right , that means X = 44 + 8 = 52 , So the Z-Score for 52 is Z = 1.0. Hence, required value is 1.0.

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Complete question:

The dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. The dynamic equation shows the mathematical conversion to z-scores in real-time. Drag the vertical line to see the corresponding z-score for each possible class size,

Z =( Xᵢ - X)/s Created by Gary M. McClelland, Professor Emeritus | University of Colorado Boulder Cengage Learning. All Rights Reserved. 1. Make sure the green line is on the mean value of x= 44. Next, move the green line one standard deviation to the right. What Z-score is associated with this value?

a. ) Z-0.75

b) Z= 0.80

c) Z = 1.00

d) Z = 0.5

Answer:

x = - 2

Step-by-step explanation:

the magnitude of a vector < a, b, c > is

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

given vector < 1, 2, x > has magnitude of 3 , then

[tex]\sqrt{1^2+2^2+x^2}[/tex] = 3

[tex]\sqrt{1+4+x^2}[/tex] = 3

[tex]\sqrt{5+x^2}[/tex] = 3 ( square both sides to clear the radical )

5 + x² = 3² = 9 ( subtract 5 from both sides )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

since x is negative then x = - 2

Answer is B

y=16.9x+0.7

To Calculate line of best fit you can simply input the values into the stats function on your calculator and using the "Reg" function to get your values of the standard equation form of your line of best fit which is y=bx+a

b=16.9

a=0.7

Answer:

12

Step-by-step explanation:

2w + 4 = 28

2w = 24

w = 12

w = 12.

[tex]2w+4=28[/tex]

[tex]2w+4-4=28-4\\ \\2w=24[/tex]

[tex]\frac{2w}{2} =\frac{24}{2} \\ \\w=12[/tex]

To verify the answer, write the original expresion and substitute variable "w" by the calculated value (12). If the calculations equal the same number of both sides of the equal sign (=) then the answer is correct.

[tex]2(12)+4=28\\ \\24+4=28\\ \\28=28[/tex]

The same number appears on both sides of the equal sign. Hence, the answer is correct!

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Answer:

23.2wx - 13.2w

Step-by-step explanation:

4w (5.8x - 3.3) =

4w * 5.8x - 4w * 3.3 = distribute 4w to 5.8x and 3.3

4 * 5.8 *w * x - 4w * 3.3 =

23.2 * w * x - 13.2w  ==> simplify

23.2wx - 13.2w

Answer:

Below

Step-by-step explanation:

3 (x-12) = 15     divide both sides of the equation b y 3 to get :

x-12 = 5           now add 12 to both sides

x = 17       Done.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Solving for x or simplify this equation}[/tex]

[tex]\mathsf{3(x - 12) = 15}[/tex]

[tex]\huge\textbf{DISTRIBUTE 3 within PARENTHESES}[/tex]

[tex]\mathsf{3(x) + 3(-12) = 15}[/tex]

[tex]\mathsf{3x - 36 = 15}[/tex]

[tex]\huge\textbf{ADD 36 to BOTH SIDES}[/tex]

[tex]\mathsf{3x - 36 + 36 = 15 + 36}[/tex]

[tex]\huge\textbf{SIMPLIFY IT}[/tex]

[tex]\mathsf{3x = 15 + 36}[/tex]

[tex]\mathsf{3x = 51}[/tex]

[tex]\huge\textbf{DIVIDE 3 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{3x}{3} = \dfrac{51}{3}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT}[/tex]

[tex]\mathsf{x = \dfrac{51}{3}}[/tex]

[tex]\mathsf{x = 17}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 17}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Therefore , the solution to the given problem of expression comes out to be -8 * 10³.

A number must be substituted for each variable and arithmetic operations must be carried out in order to verify an algebraic expression. The response variable is equivalent to 6 in the illustration above because 6 + 6 equals 12. The variables can be replaced with their values if we know what they are, and the expression can then be evaluated.

Here,

Given : - 8,000

To write -8000 with a power of 10

Thus,

-8000 written into

=> -8 * 10³

So, we get -8 * 10³ as the scientific notation for the given expression

Therefore , the solution to the given problem of expression comes out to be -8 * 10³.

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The intercepts of the graph are

The polynomial is given as

G(x) = -2(3x+4)(x-1)(x-3)^2

Rewrite as

G(x) = -2(3x+4)(x-1)(x-3)²

The x-intercepts of a polynomial are the points at which the polynomial crosses the x-axis.

To find the x-intercepts, we need to set y = 0 and solve for x.

-2(3x+4)(x-1)(x-3)² = 0

Divide through by -1

(3x+4)(x-1)(x-3)² = 0

Now we can solve for each factor equal to zero:

3x+4 = 0, x = -1.33

x-1 = 0, x = 1

x-3 = 0, x = 3

So the x-intercepts are -4/3, 1, 3

The y-intercept of a polynomial is the point at which the polynomial crosses the y-axis.

For this polynomial, we have

G(0) = -2(30+4)(0-1)(0-3)² = -2(4)(-1)(9) = 72

So the y-intercept is (0, 72)

See attachment for the graph

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The exact value of cos (-pi/3) can be found using the unit circle or the angle addition formula.

Using the unit circle, we know that the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is cos(-pi/3) and y-coordinate is sin(-pi/3).

On the unit circle, the angle of -pi/3 is the same as the angle of 2pi/3 (since the unit circle has a period of 2pi), therefore the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is -1/2.

Alternatively, using the angle addition formula:

cos (-pi/3) = cos(pi - pi/3) = cos(pi) * cos (pi/3) - sin(pi) * sin(pi/3) = -1/2

So, the exact value of cos (-pi/3) is -1/2.

Answer:

Below

Step-by-step explanation:

Use the distance formula  ( a modification of Pythagorean theorem)

d^2 = ( x1-x2)^2 + (y1-y2)^2

  d^2 = (-7-2)^2 + (-6-4)^2

    d =  sqrt (181) =~ 13.454

When a fair coin is tossed nine times, there is a 0.090 (rounded off to the nearest thousandth) chance that at most one will land on heads.

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number between 0 and 1, where about 0 represents how likely the event is to occur and 1 represents certainty. A probability is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the total number of outcomes to the proportion of occurrences in a whole set of equally likely options that lead to a specific occurrence.

given

binomial probability ⁿCₓ[(p)ˣ(q)ⁿ⁻ˣ]

where p= probability of tail = 1/2 (favorable outcome)

q = probability of head = 1/2: (1 - p)

n = total outcome = 9

x = 4

ⁿCₓ[(p)ⁿ(q)ⁿ⁻ˣ] = ⁹C₄[(1/2)⁴(1/2)⁵]

=  [1/16 x 1/32]

= (512)

126/512 = 0.24609

≈ 0.090 nearest thousandth rounded off .

When a fair coin is tossed nine times, there is a 0.090 (rounded off to the nearest thousandth) chance that at most one will land on heads.

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Answer:

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

Step-by-step explanation:

y = 3x^3 - 4  ==> solve for x

y + 4 = 3x^3  ==> isolate x by adding 4 on both sides

(y + 4)/3 = x^3  ==> divide 3 into both sides

x = [tex]\sqrt[3]{(y + 4)/3}[/tex] ==> isolate x by taking the cube root on both sides

y = [tex]\sqrt[3]{(x + 4)/3}[/tex] ==> switch both x and y

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

Answer:

$20,400

Step-by-step explanation:

You just have to multiply 680,000 by 0.03 (since 3% is equivalent to 0.03)

If triangle ABC has the following measurements, than the measure of side c is 25.08

What is triangle ?

A triangle in which it contains three sides and three angles and the sum of three angles be 180 degrees.
Given ,

a = 17

b = 23

C = 76 degrees.

So,

we know that,

c = [tex]\sqrt{a^{2}+b^{2}-2abcosc }[/tex]

c = [tex]\sqrt{17^{2} + 23^{2} - 2*17*23*cos76 }[/tex]

c = [tex]\sqrt{289 + 529 - 884*cos76}[/tex]

c = [tex]\sqrt{818-189}[/tex]

c = [tex]\sqrt{629}[/tex]

c = 25.08

hence , If triangle ABC has the following measurements, than the measure of side c is 25.08

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Answer: y = 40

Step-by-step explanation:

we know 5x=40 so the 2 bottom angles combined are 80

so you have 2y+20=100

2y=80

y=40

Answer:

x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2

Step-by-step explanation:

Solve for x:

x^2 - 5 x + 7 = 0

Subtract 7 from both sides:

x^2 - 5 x = -7

Add 25/4 to both sides:

x^2 - 5 x + 25/4 = -3/4

Write the left hand side as a square:

(x - 5/2)^2 = -3/4

Take the square root of both sides:

x - 5/2 = (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2

Add 5/2 to both sides:

x = 5/2 + (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2

Add 5/2 to both sides:

Answer: x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2

Answer:

x=2.28

Step-by-step explanation:

7x +y=11 we substitute y by ( -5)

7x +(-5)=11 (+)×(-)= --

7x-5=11

7x=11+5 when we move -5 to the opposite it become +5

7x =16

x=16 ÷7

x=2.28

Answer:

B. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means that there are 10³ cubic decimeters in a cubic meter.

Step-by-step explanation:

When we cube a number, we multiply the number by itself twice.

Therefore a cubic meter is:

To calculate the number of cubic decimeters in a cubic meter, we need to cube the number of decimeters in a meter.

Given there are 10 decimeters in a meter, then there are 10³ cubic decimeters in a cubic meter: