Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph?

Answer:

Is there more information?  There is not enough to find the slope of a line.  I'll answer with an equation that works, but I suspect it won't be correct.

Step-by-step explanation:

If the only requirement is to have a line that goes through (4,3).  Then one could simply say:

y = 4

This is a horizonal line that goes through (3,4), and will always produce a y value of 4 regardless of x.  No, it will not pass through (4,3) since y is aleways 4, regardless of x.

If you wanted to get fancier, we could write a needlessly more complex equation:

y = (4/3)x

When x = 3, y = 4, so (3,4) is on this line.  But (4,3) is not.  y = (4/3)(4) means y = (16/3), not 4.

This would be the least common multiple of 3, 4, 5, and 9. We can start by listing the multiples of the biggest number, 9, and seeing if each of the numbers can be divisible by the smaller numbers.

9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180

180 would be the answer because it is the first number in our list that is divisible by 3, 4, 5, and 9.

The recursive formula for the given sequence is [tex]f(n+1)=f(n)-99.4[/tex]

Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula [tex]a_n = a_{n-1} + d[/tex]. [tex]a_n = a_{n-1}r[/tex] is the recursive formula for a geometric sequence.

We are given a sequence as:

99.4,0,-99.4,-198.8, and so on

We can see that the sequence is constantly getting decreased by -99.4

i.e. f(1)=99.4

Then, f(2)=f(1)-99.4

               =99.4-99.4

               =0

f(3)=f(2)-99.4

   =0-99.4

   =-99.4

Therefore, the recursive formula of the given series is [tex]f(n+1)=f(n)-99.4[/tex]

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Since this is an algebraic problem

  ⇒let's solve it like one

     [tex]2*3^{x+5} < 14\\3^{x+5} < 7\\ x+5 < log_37\\x < -5 + log_37\\x < -3.2288[/tex]

Answer: x < -3.2288

Hope that helps!

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The first scatter plot does not have a zero correlation.

Option(a) is correct.

A statistic called correlation gauges how much two variables change in connection to one another.

Correlation quantifies correlation but cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.

A scatterplot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.

Zero means there is no correlation between the two variables under comparison.

A 0 correlation indicates that there is no relationship between the two variables according to the correlation statistic. This merely indicates that there isn't a linear relationship, not that there isn't any link at all. The first scatter plot does not represent a linear relationship, thus, it has zero correlation.

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The distance between two slits is d =2.89*10^-7 m

Distance between slits,   d=2.89*10^-7 m

It is given that,

Wavelength, λ = 410nm= 410*10^-9 m

Angle, θ =45

We need to find the distance between two slits that produces first minimum. The equation for the destructive interference is given by :

dsinθ =(n+1/2) λ

For first minimum, n = 0

dsinθ =(1/2) λ

So, d is the distance between slits

d ={1/2 λ}sinθ

=2.89*10^-7 m

So, the distance between two slits is d =2.89*10^-7 m. Hence, this is the required solution.

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Answer:

x = 12

Step-by-step explanation:

sqrt(x+4) - 3 = 1

First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.

sqrt(x+4) = 1 + 3

sqrt(x+4) = 4

To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.

(sqrt(x+4))^2 = 4^2

x + 4 = 16

subtract 4 to finish up.

x = 12

Check:

sqrt(12 + 4) - 3 = 1

sqrt16 - 3 = 1

4 - 3 = 1

1 = 1 Check!

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Calculate discriminant :

[tex]\qquad \sf  \dashrightarrow \: 3 {x}^{2} + 6x - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 36 - 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} [/tex]

Now, let's calculate it's roots ( x - intercepts )

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} [/tex]

So, the intercepts are :

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} [/tex]

and

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} [/tex]

Answer:

[tex]\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)[/tex]

Explanation:

Given expression:

f(x) = 3x² + 6x - 1

Use quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0[/tex]

Here after finding coefficients:

Applying formula:

[tex]x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}[/tex]

[tex]x = \dfrac{ -6 \pm \sqrt{48}}{6}[/tex]

[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{6}[/tex]

[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}[/tex]

[tex]x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}[/tex]

[tex]x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}[/tex]

Applying the same-side interior angles theorem,

7. m∠4 = 50°; m∠5 = 130°

8. m∠2 = 15°; m∠8 = 15°.

The same-side interior angles theorem holds that, two interior angles on a side of a transversal are supplementary, that is they add up to 180 degrees.

According to the alternate exterior angles theorem, exterior angles that alternate each other along a transversal are congruent, that is they have equal measures.

7. m∠4 + m∠5 = 180 [same-side interior angles theorem]

Substitute

y + 2y + 30 = 180

3y + 30 = 180

3y = 180 - 30

3y = 150

y = 50

m∠4 = y = 50°

m∠5 = 2y + 30 = 2(50) + 30

m∠5 = 130°

8. m∠2 = m∠8 [alternate exterior angles theorem]

Substitute

x - 30 = 3x - 120

x - 3x = 30 - 120

-2x = -90

x = 45

m∠2 = x - 30 = 45 - 30 = 15°

m∠8 = 3x - 120 = 3(45) - 120 = 15°

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Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.

The z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:

Z = (X - mu)/sigma

The mean and the standard deviation are given as follows:

mu = 400, sigma = 50

The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:

X = 550:

Z = (X - mu)/sigma

Z = (550 - 400)/50

Z = 3

Z = 3 has a p-value of 0.9987.

X = 500:

Z = (X - mu)/sigma

Z = (500 - 400)/50

Z = 2

Z = 2 has a p-value of 0.9772.

0.9987 - 0.9772 = 0.0215 = 2.15% probability.

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The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.

Set 1: 12, 8, 10, 50

Set 2: 13, 9,8

To determine the mean for each set

Mean = totality of elements/number of elements

Mean of Set 1:

[tex]$=\frac{12+8+10+50}{4}[/tex]

[tex]$=\frac{80}{4}=20$[/tex]

Mean of Set 2:

[tex]$=\frac{13+9+8}{3}[/tex]

[tex]$=\frac{30}{3}=10$[/tex]

To determine the mean absolute deviation (MAD) of the data in each set.

M.A.D of Set 1:

[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]

[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]

M.A.D of Set 2:

[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]

[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]

The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.

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Answer:

Step-by-step explanation:

Beatrice's conclusion is wrong

All of these points are not on the same line, because are different parallel lines

The slope between (-2,-1) and (1,0) is equal to 1/2

Answer:

Beatrice is incorrect. All of these points are not on the same line because the slope between (-2,-1) and (1,0) which are coordinates fr each of the pairs above, are equal to 1/2

Step-by-step explanation:

Let m1 be first slope

[tex]m1 \: = \frac{y2 - y1}{x2 - x1}= \frac{0 - ( - 2)}{4 - ( - 2)}= \frac{0 + 2}{4 + 2} \\ = \frac{2}{4} = \frac{1}{2} [/tex]

Let m2 be second slope

m2 = (y2 - y1)/ (x2 - x1)

= (2-(-1)) / (4-(-2)

= (2+1) / (4+2)

= 3/6 =1/2

Thus, the slopes are different parallel lines because m1 =m2

The expressions which demonstrates the identity property of multiplication is; 25(1) = 25 option B

Identity Property of Multiplication states that any number multiplied by 1 does not change, that is, it is constant or remains the same

Check all options

25(0) = 25

0 = 25

Not true

25(1) = 25

25 = 25

True (identity property of multiplication holds)

25 + 0 = 25

25 = 25

True (Not identity property of multiplication)

25 + 1 = 25

26 = 25

Not true

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Answer:

1/3.

Step-by-step explanation:

P(event a occurs) = 3/9 = 1/3

P(event b occurs) = 3/9 = 1/3

P(a) ∩ P(b) = 1/3 * 1/3 = 1/9

P(b|a) = P(a) ∩ P(b) / P(a)

          =  1/9 / 1/3

          =  1/3.

The distance from Sang to Jazmin is 101 yards.

From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.

The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.

From;

c^2 = a^2 + b^2

c = √a^2 + b^2

c = √(20)^2 + (99)^2

c = 101 yards.

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Answer:

Step-by-step explanation:

A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.

Let x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.

  x + y = 500 . . . . . . quantity of new alloy needed

  0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy

These are the desired system of equations.

This problem does not ask for the solution, but it is easily found using substitution for x.

  x = 500 -y

  0.65(500 -y) +0.90y = 0.75(500)

  (0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)

  y = 500(0.10/0.25) = 200

  x = 500 -200 = 300

300 grams of 65% copper and 200 grams of 90% copper are needed.

Step-by-step explanation:

g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.

so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.

now, we look at the graphic.

for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.

but we are looking for a c that has only one solution (one value of x to create that result).

c = 1 ?

let's imagine a horizontal line through y = 1.

we see, it cuts the function also 3 times. 3 solutions.

c = -1 ?

a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions

but c = 3 !

a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !

and that is therefore our answer.

Considering the given box plots, we have that:

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

Hence, for class A, we have that:

Then:

Hence, for class B, we have that:

Then:

Hence the correct options are given as follows:

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The height is changing by 0.5 units per minute as evident in the given table.

It follows from the task content that the table given indicates that at, 0min, the height was 150.

While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.

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The 5.25 m combined height of John, Jim, and Joe, the 12 cm height difference between John and Jim and the 0.09 m difference in height between Jim and Joe, indicates that solution to the word problem is Joe was 1.73  meters tall

A word problem is a presentation of a math problem using verbal description rather than numbers, variables and operators.

The combined height of John, Jim and Joe = 5.25 m

John's height = Jim's height - 12 cm = Jim's height - 0.12

Jim's height = Joe's height + 0.09 m

Let h represent Joe's height, we get;

Jim's height = h + 0.09

John's height = h + 0.09 - 0.12 = h - 0.03

John's height = h - 0.03

The sum of the heights is therefore; h + h + 0.09 + h - 0.03 = 3·h + 0.06

The sum of their heights = Their combined height = 5.25 meters

Therefore; 3·h + 0.06 = 5.25

h = (5.25 - 0.06)/3 = 1.73

Joe's height, h = 1.73 meters

Jim's height = 1.73 + 0.09 = 1.82

Jim's height = 1.82 meters

John's height = 1.73 - 0.03 = 1.7

John's height is 1.7 meters

Joe was 1,73 meters tall

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Using a linear function, we have that:

a) The costs are:

i. C(x) < $1.3.

ii. C(x) > $2.3.

b) The times are:

i. Less than 9 minutes.

ii. At least 16 minutes.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the y-intercept is of 0.3, while the slope is of 0.2, hence the cost for a call of x minutes is:

C(x) = 0.3 + 0.2x.

For calls shorter than 5 minutes, the costs are:

C(x) < 0.3 + 0.2 x 5

C(x) < $1.3.

For calls longer than 10 minutes, the costs are:

C(x) > 0.3 + 0.2 x 10

C(x) > $2.3.

The cost is less than $2.10 for calls of less than x minutes, found as follows:

0.3 + 0.2x < 2.1

0.2x < 1.8

x < 9.

The cost is greater or equal to $3.50 for calls of at least x minutes, found as follows:

0.3 + 0.2x >= 3.5

0.2x >= 3.2

x >= 16.

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The correct ratios are: cos 27=23/RT, sec 27= 23/10.4 and cot 63 = RT/10.4

What is trigonometry  ratio in tringle?

In triangle RST, angle T= 90° and angle R= 63°

As the total of all angle in any triangle is 180°, so the measure of the angle S = 180°- (90°+63°)

S= 180°- 153°

S= 27°

According to the rule of trigonometric ratios,

cos(θ) = [tex]\frac{hypotenuse}{opposite}[/tex]

sec(θ) = [tex]\frac{hypotenuse}{adjacent}[/tex]

cot(θ) = [tex]\frac{adjacent}{opposite}[/tex]

In respect of angle R (63°), side RS(23) is hypotenuse , ST(10.4) is opposite and RT is adjacent.

cos(63°) = [tex]\frac{23}{10.4}[/tex]

sec(63°) = [tex]\frac{23}{RT}[/tex]

cot(63°) = [tex]\frac{RT}{10.4}[/tex]

Now, in respect of angle S(27°), hypotenuse is RS(23), adjacent is ST(10.4) and opposite is RT.

So, cos(27°) = [tex]\frac{23}{RT}[/tex]

sec(27°) = [tex]\frac{23}{10.4}[/tex]

cot(27°) = [tex]\frac{10.4}{RT}[/tex]

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The correct option is A.

When the data are nominal or ordinal.

There are three types of correlation:

1. Positive and negative correlation

2. Linear and non-linear correlation

3. Simple, multiple, and partial correlation

There are different types of correlation one can use based on the types of variables being examined.

Spearman’s rho is a superb choice when you have nominal or ordinal data because Pearson’s isn't appropriate. Ordinal data have a minimum of three categories and the categories have a natural order. for instance , first, second, and third during a race are ordinal data.

Two variables can have some quite relationship, i.e., change in one may cause a change within the other.

If a change within the value of one variable causes a simultaneous change in the other variable in the same or opposite direction, then it’s termed as correlation, or these variables are said to be correlated. Keeping these in mind the answer to this question is When the data are nominal or ordinal

When the data are nominal or ordinal.

So the option no A is correct.

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I understand that the question you are looking for is:

There are different types of correlation one can use based on the types of variables being examined. When conducting an analysis, when do you need to use spearman’s rho instead of Pearson's r ?

A. When the data are nominal or ordinal.

B. When the data are ratio or interval.

C. When the data are random.

D. Spearman's rho should never be used for correlations.

Answer:

a7=4/3 or a7=-4/3

Step-by-step explanation:

using the geometric sequences formula

an=ar^n-1

a2=ar

a4=ar³

when a2=324 and a4=36

324=ar...........(1)

36=ar³............(2)

from equation (1) a=324/r substitute in equation (2)

we have :

36=324/r *r³

36=324r²

r²=36/324

r²=1/9

r=±1/3

substitute when r=±1/3 in (1)

324=a(±1/3)

a=±972

so the 7th term is

when r=±1/3

we have

a7=ar^6

a7=±972(±1/3)^6

a7=972/729

a7=4/3 or a7=-4/3

The distance from the center of the ellipse to where the spots are located will be 2 feet.

What is Distance?

The distance from the center of the ellipse to where the spots are located will be -

= 5 - 3

= 2 feet.

Therefore, the distance from the center of the ellipse is 2 feet.

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The solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x- y = 3

y - x = 1

Make y the subject in the second equation, by adding x to both sides of the equation

y - x + x = x + 1

This gives

y = x + 1

Substitute y = x + 1 in 2x- y = 3

2x- x - 1 = 3

Evaluate the like terms

x = 4

Substitute x = 4 in y = x + 1

y = 4 + 1

Evaluate

y = 5

Hence, the solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5

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The perimeter of the shape is 52 cm

The shape is given as:

Regular pentagon

The length of the sides are

Length = 12 cm

So, the perimeter of the regular pentagon is

P = 5* Length

This gives

P = 5 * 12cm

Evaluate

P = 60 cm

When the square of sides 6cm is removed from the regular pentagon, the perimeter becomes

P = 60cm - 6cm

Evaluate the difference

P =52 cm

Hence, the perimeter of the shape is 52 cm

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The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

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Answer:

d>0

Step by Step Explanation:

Let's solve your inequality step-by-step.

5+d>5−d

Step 1: Simplify both sides of the inequality.

d+5>−d+5

Step 2: Add d to both sides.

d+5+d>−d+5+d

2d+5>5

Step 3: Subtract 5 from both sides.

2d+5−5>5−5

2d>0

Step 4: Divide both sides by 2.

2d/2>0/2

d>0

Answer:

3

Step-by-step explanation:

You could put 3 because 5+3 is greater than 5-3.

(3x² - 7x + 14) + (5x² + 4x - 6)

Match 3x² and 5x² to get 8x².

Combine −7x and 4x to get −3x.

Subtract 6 from 14 to get 8.

Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".

(2x² - 5x -3) + (-10x² + 2x + 7)

Combine 2x² and -10x² to get −8x².

Combine −5x and 2x to get −3x.

Add −3 and 7 to get 4.

Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".

(12x² - 2x - 13) + (-4x² + 5x +9)

Combine 12x² and -4x² to get 8x².

Combine −2x and 5x to get 3x.

Add −13 and 9 to get −4.

Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".