what is an equation of the line that is perpendicular to y-4 = 2(x-6) and passes through the point (-3, -5)

Answer:

  [tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

Invert the denominator and multiply.

  [tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]

Answer:

[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.

Answer:

The point (–3,–6) is not  in the solution set of the system of inequalities below.

x ≤ –3 y < 5∕3x + 2

Step-by-step explanation:

Given point (-3, -6)

inequality

x ≤ –3

It means that value of x should be less than or equal to -3

since in point (-3,-6) , -3 is point for representing x which is equal to -3 and hence satisfy the criteria for valid value of x,

thus, -3 lie in the solution set of inequality x ≤ –3

lets now see for y = -6

to do that we will put x = -3 in the given below inequality

y < 5∕3x + 2

y < 5∕3*-6 + 2

y < -10 + 2

y < - 8

Thus, inequality suggests that value of y should be less than -8.

but here y is -6, if we see number line -6 is greater than -8 and hence does not belong to the solution set  y < 5∕3x + 2 when x = -3

Thus, the point (–3,–6) is not  in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2

Answer:

F(10) = 14.41 Billion

The total number of hamburgers that will have been sold by 2013 is 14.41 billion.

Step-by-step explanation:

The exponential function representing the total number of hamburgers sold by a national fast-food chain which grows exponentially can be expressed as;

f(t) = p(a)^t

In 2003, t = 0 and f(0) = 3 Billion

f(0) = p = 3 billion

The initial value p = 3 billion

In 2010, t = (2010-2003) = 7

f(7) = p(a)^7 = 9 billion

3(a)^7 = 9

a^7 = 9/3 = 3

a = 3^(1/7)

Therefore, the function f(t) is;

f(t) = 3(3)^(t/7) .......2

In 2013, t = (2013 - 2003) = 10

Substituting t = 10 into equation 2;

f(10) = 3(3)^(10/7)

F(10) = 14.41195997001 Billion

F(10) = 14.41 Billion

The total number of hamburgers that will have been sold by 2013 is 14.41 billion.

Answer:

On Monday the temperature was 35 - 4 = 31°. On Tuesday, it was 31 + 2 = 33° and on Wednesday it was 33 - 5 = 28° F.

Answer:

{ 4,8}

Step-by-step explanation:

The intersection is what the sets have in common

{1, 4, 8, 12}∩ {2, 4, 6, 8}

{ 4,8}

Answer:

{4, 8}

Step-by-step explanation:

The intersection of sets are the terms that appear in both sets. In this case, the only numbers that appear in both sets are 4 and 8.

Answer:

The confidence level for this case is 96% or 0.96, then the significance level would be:

[tex]\alpha = 1-0.96 =0.04[/tex]

And then [tex]\alpha/2 =0.02[/tex]. We need to find a critical value who accumulates 0.02 of the area on each tail and we got:

[tex]z_{\alpha/2}=\pm 2.054[/tex]

Step-by-step explanation:

The confidence level for this case is 96% or 0.96, then the significance level would be:

[tex]\alpha = 1-0.96 =0.04[/tex]

And then [tex]\alpha/2 =0.02[/tex]. We need to find a critical value who accumulates 0.02 of the area on each tail and we got:

[tex]z_{\alpha/2}=\pm 2.054[/tex]

Answer:

AB || DC                               Given

∠ABE ≅ ∠CDB                    Alternate interior angles are congruent

BC || AE                                Given

∠CBD ≅ ∠BEA                     Alternate interior angles are congruent

ΔAEB is similar to ΔCBD    AA Similarity Postulate

BC / EA = BD / EB               Similar sides are proportional

Answer:

There are 65 dimes. There are 55 nickels.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of dimes

y is the number of nickels.

There are a total of 120 coins in the bag

This means that x + y = 120.

The total value of the coins is $9.25.

The dime is worth $0.10 and the nickel is worth $0.05. So

0.1x + 0.05y = 9.25

System:

[tex]x + y = 120[/tex]

[tex]0.1x + 0.05y = 9.25[/tex]

From the first equation:

[tex]y = 120 - x[/tex]

Replacing in the second:

[tex]0.1x + 0.05y = 9.25[/tex]

[tex]0.1x + 0.05(120 - x) = 9.25[/tex]

[tex]0.1x + 6 - 0.05x = 9.25[/tex]

[tex]0.05x = 3.25[/tex]

[tex]x = \frac{3.25}{0.05}[/tex]

[tex]x = 65[/tex]

[tex]y = 120 - x = 120 - 65 = 55[/tex]

There are 65 dimes. There are 55 nickels.

Answer:

(y1+y2)/2

Step-by-step explanation:

adding and dividing by the total is the way to calculate the average

Answer:  It will not create a perpendicular bisector.

Explanation:

If the compass is the same setting as the first arc and drawn from point B, the points of intersection of the arcs will pass through the midpoint of AB (thus creating a perpendicular bisector).

If you change the setting of the compass and draw an arc from point B, the points of intersection of the arcs will still create a perpendicular line but will not pass through the midpoint of AB (creating a perpendicular line but not a perpendicular bisector).

A perpendicular bisector divides a line segment into two equal segments.

If the compass setting is changed, the line will not be bisected.

To bisect a line, the positioning of the compass must be done as follows:

The above points are what is being done in the given construction.

Any step or setting other than that, would not create a perpendicular bisector.

Hence, if the compass setting is changed, the perpendicular bisector of the line would not be drawn.

Read more about perpendicular bisection at:

https://brainly.com/question/11050543

Answer:

When describing a property line drawn down the center of a creek bed

Answer:

answer is a 107 hope it halp u

Answer:

24.9

Step-by-step explanation:

To do this, we set cos(58) to 15/x.

Using a calculator and some math, we get x is about 24.9.

Here is why we do that:

Since cosine is adjacent over hypotenuse, and we have the adjacent but not the hypotenuse, we can use that to create an equation.

Hope this helped!

Answer:

a ≈ 2.2

Step-by-step explanation:

Using the Cosine rule in Δ ABC

a² = b² + c² - 2bc cos A

Here b = 3, c = 4 and A = 32° , thus

a² = 3² + 4² - (2 × 3 × 4 × cos32° )

    = 9 + 16 - 24cos32°

    = 25 - 24cos32° ( take the square root of both sides )

a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2

Answer:

y=25x+50

non proportional relationship

Step-by-step explanation:

The relationship is not proportional because as you go along in the function and divide y by x, the ratios do not equal each other. In order for it to be a proportional relationship the y/x ratio must be equivalent throughout the function.

Step-by-step explanation:

To find AC we use tan

tan ∅ = opposite / adjacent

From the question

15 is the opposite

AC is the adjacent

tan 55 = 15 / AC

AC = 15 / tan 55

AC = 10.503

Hope this helps you

Answer:

A: 10.5 m

Step-by-step explanation:

it's what i think it is, i may be wrong! hope this helps!!~

Answer:

Step-by-step explanation:

Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...

  y = (300 -2x)/3

And the enclosed area is ...

  A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)

This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.

The maximum area is enclosed when the dimensions are ...

  50 ft by 75 ft

That maximum area is 3750 square feet.

_____

Comment on the solution

The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).

Step-by-step explanation:

to be honest I'm not sure how to do

Answer:

[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]

Step-by-step explanation:

hello, we have two equation

(1) x + 4y = 22

(2) 2x + y = 9

let's multiply (1) by 2 and subtract (2)

2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35

<=> 2x + 8y -2x -y = 35

<=> 7y = 35

<=> y = 35/7 = 5

we replace this value in (1) and it comes

x + 4*5 = 22

<=> x = 22 - 20 = 2

so the solution is

x = 2 and y = 5

hope this helps

Answer:

(a)0.5

(b)0.17

(c)0.625

(b)0.375

Step-by-step explanation:

Pr(E)=0.6​

Pr(F)=0.2

[tex]Pr(E\cap F)=0.1.[/tex]

(a)Pr (E|F )

[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]

(b)Pr (F|E )

[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]

(c)Pr (E|F')​

Pr(F')=1-P(F)

=1-0.2=0.8

[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]

Therefore:

[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]

(d)Pr(E'|F')​

[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]

Therefore:

[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]

Answer:

  P = 20000×1.625^(n/4)

Step-by-step explanation:

An exponential equation can be written using the given data:

  value = (initial value)×(growth factor in period)^(n/(period))

Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...

  P = 20000×1.625^(n/4)

Answer:

The picture where the red image is the skinniest

Step-by-step explanation:

The graph P(x) denotes the graph of the parent graph for all the functions. And, It includes the vertex of (0,0) and points which are shown below:

x      f(x)

-2      2

-1       1

0       0

1         1

2       2

Now as we can see in the attached figure i.e it changed the function points i.e given below for l(x) = 12P(x)

x      f(x)

-2      24

-1        12  

0        0

1        12

2       24

This depicts that it has a skinner graph that includes redish graph

Answer:

20 teachers

Step-by-step explanation:

Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.

Answer:

5.35 more miles

Answer:

5.35 miles to the finish line

Step-by-step explanation:

Step one

13.1-7.75=

5.35

Answer:

A'(8, -10)

B'(6, -12)

C'(2, -4)

A"(8, -4)

B"(6, -2)

C"(2, -10)

Step-by-step explanation:

The location of the points are at:

A(8, 8) , B(10, 6) and C(2, 2).

Reflection over y = -1:

For point A the y distance between the point and y = -1 line is 9 (8 - (-1)). The reflection of point a over y = -1 would give a point 9 units below y = -1 which is at -10.

The new A coordinate is at A'(8, -10)

For point B the y distance between the point and y = -1 line is 7 (6 - (-1)). The reflection of point a over y = -1 would give a point 7 units below y = -1 which is at -8.

The new B coordinate is at B'(10, -8)

For point C the y distance between the point and y = -1 line is 3 (2 - (-1)). The reflection of point a over y = -1 would give a point 3 units below y = -1 which is at -4.

The new C coordinate is at C'(2, -4)

Reflection over y = -7:

For point A' the y distance between the point and y = -7 line is 3 (-7 - (-10)). The reflection of point a over y = -1 would give a point 3 units above y = -7 which is at -4.

The new A coordinate is at A"(8, -4)

For point B' the y distance between the point and y = -7 line is 1 (-7 - (-8)). The reflection of point a over y = -7 would give a point 1 units above y = -7 which is at -6.

The new B coordinate is at B"(10, -6)

For point C' the y distance between the point and y = -7 line is 3 (4 - (-7)). The reflection of point a over y = -7 would give a point 3 units below y = -7 which is at -10.

The new C coordinate is at C"(2, -10)

Answer:

The 99​% confidence interval estimate of the mean body temperature of all healthy humans is between 98.53ºF and 98.87 ºF. 98.6ºF is part of the interval, so the sample suggests that the use of 98.6ºF as the mean body​ temperature is correct.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 104 - 1 = 103

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 103 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.624

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{0.66}{\sqrt{104}} = 0.17[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.7 - 0.17 = 98.53ºF.

The upper end of the interval is the sample mean added to M. So it is 98.7 + 0.17 = 98.87 ºF.

The 99​% confidence interval estimate of the mean body temperature of all healthy humans is between 98.53ºF and 98.87 ºF. 98.6ºF is part of the interval, so the sample suggests that the use of 98.6ºF as the mean body​ temperature is correct.

Answer:

The amount of salt in the tank after t minutes is

y= 16e^(t/100)kg

Step- by-step Explanation

The tank contain 3000L of the brine

The rate is 30L/ min

The solution is mixed thoroughly, therefore, the rate in= rate out

dy/dt= rate in to the tank= rate out of the tank

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

The sign of f is used to symbolize many things. In physics it is commonly used to mean frequency and in music it is used to symbolize forte, which means loud.

Answer:

29+/-2.26

= (26.74, 31.26) characters

Therefore the 95% confidence interval (a,b) = (26.74, 31.26) characters

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 29 characters

Standard deviation r = 6 characters

Number of samples n = 27

Confidence level = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

29+/-1.96(6/√27)

29+/-1.96(1.154700538379)

29+/-2.263213055223

29+/-2.26

= (26.74, 31.26) characters

Therefore the 95% confidence interval (a,b) = (26.74, 31.26) characters

Answer:

[tex]x =-24[/tex]

Step-by-step explanation:

Given

[tex](\frac{2}{3})(\frac{1}{2}x + 12) = (\frac{1}{2})(\frac{1}{3}x + 14) - 3[/tex]

Required

Solve for x

[tex](\frac{2}{3})(\frac{1}{2}x + 12) = (\frac{1}{2})(\frac{1}{3}x + 14) - 3[/tex]

Open all brackets

[tex]\frac{2}{3}*\frac{1}{2}x + \frac{2}{3}*12 = \frac{1}{2}*\frac{1}{3}x + \frac{1}{2}*14 - 3[/tex]

[tex]\frac{2 * 1}{3 *2}x + \frac{2 * 12}{3}= \frac{1 * 1}{2 * 3}x + \frac{1 * 14}{2} - 3[/tex]

[tex]\frac{1}{3}x + \frac{24}{3}= \frac{1}{6}x + \frac{14}{2} - 3[/tex]

[tex]\frac{1}{3}x +8= \frac{1}{6}x + 7 - 3[/tex]

Collect like terms

[tex]\frac{1}{3}x - \frac{1}{6}x =7 - 3 -8[/tex]

[tex]\frac{1}{3}x - \frac{1}{6}x =-4[/tex]

Solve fraction

[tex]\frac{2-1}{6}x =-4[/tex]

[tex]\frac{1}{6}x =-4[/tex]

Multiply both sides by 6

[tex]6 * \frac{1}{6}x =-4 * 6[/tex]

[tex]x =-4 * 6[/tex]

[tex]x =-24[/tex]

Answer:

Step-by-step explanation:

Given

Required

Solve for x

Open all brackets

Collect like terms

Solve fraction

Multiply both sides by 6