Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
Need help on square roots.​

Answer:

  (D)  t^4

Step-by-step explanation:

You have defined ...

  a3 = a2·a1

  a4 = a3·(a2·a1) = a3²

  a5 = a4·(a3·a2·a1) = a4² = (a3²)² = a3⁴

Then if a3 = t, a5 = t⁴

Let's begin by understanding the given sequence and the pattern it follows.
We are given the initial terms:
a1 = 3
a2 = 5
For n > 2, the next term is defined as the product of all preceding terms. Therefore,
a3 = a1 * a2
a4 = a1 * a2 * a3
and so on.
Now, let's generalize this for any term an where n > 2. According to the problem, an = t.
The term immediately after an would be an+1, which equals the product of all preceding terms:
an+1 = a1 * a2 * a3 * ... * an-1 * an
Since an = t, and every term before it has been multiplied to give t (by definition of the sequence), we have:
an+1 = t * t
an+1 = t^2
Now, let's find an+2. This term is the product of all preceding terms, which now includes an+1:
an+2 = a1 * a2 * a3 * ... * an-1 * an * an+1
From above, we know an = t and an+1 = t^2. Hence:
an+2 = t * t^2
an+2 = t^3
Therefore, the value of an+2 in terms of t is t^3. The correct answer is (C) t^3.

Answer:

65

Step-by-step explanation:

Jake measured the height of the Great Sphinx of Giza by using a mirror and the Law of Reflection. Doubling the height of the mirror gives us an approximation of the statue's height.

In order to measure the height of the Great Sphinx of Giza, Jake used the concept of the Law of Reflection.

He placed a mirror on the ground and walked backwards until he could see the top of the statue in the mirror.

If his eyes were 5.5 feet above the ground, the mirror's height would be equal to half the height of the statue.

Since Jake's eyes are at a height of 5.5 feet, the distance from the ground to the top of the mirror should also be 5.5 feet.

Therefore, the height of the Great Sphinx of Giza can be calculated by doubling the height of the mirror, which gives us 11 feet.

So, the approximate height of the statue is 11 feet.

Answer:

 =57.89%

Step-by-step explanation:

The total number of golf ball is 4+8+7 = 19

P (red or yellow) = number of red or yellow

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

                                total number of golf balls

                           = 4+7

                              -----

                              19

                         =11/19

Changing this to a percent means changing it to a decimal and multiplying by 100%

                        = .578947368 * 100%

                         =57.8947368%

Rounding to two decimal places

                         =57.89%

The probability of drawing a red or yellow golf ball from the box can be calculated by dividing the total number of red and yellow balls (11) by the total number of balls in the box (19), resulting in a probability of 11/19 or approximately 57.89%.

To calculate the probability of drawing a red or yellow golf ball from the box, we first need to figure out the total number of balls in the box. This is found by adding up the number of each color of balls: 4 red balls + 8 green balls + 7 yellow balls = 19 total balls.

Next, we consider the total number of red and yellow balls, which is 4 red + 7 yellow = 11.

To find the probability, we divide the number of desired outcomes (red or yellow balls) by the total number of outcomes (total balls). So, the probability is 11/19.

To express this as a percentage rounded to two decimal places, we can multiply the result by 100, which gives us approximately 57.89%. So, there is a 57.89% chance of drawing a red or yellow ball from the box.

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Answer:

Step-by-step explanation:

Check the picture below.

Answer:

15

Step-by-step explanation:

70 = 4 x (a + 2.5)

70 = 4a + 10

70-10 = 4a

60 ÷ 4 = a

15= a

Answer:

the three options i chose:

A. n and k are on plane A and s

C. p is the inteersection of n and g

D. those 3 lines are noncollinear

Answer:

The correct options are A, C and D.

Step-by-step explanation:

From the given figure it is clear that points N and K lie on the line f, and line f is the intersection line of plane A and S.

So, points N and K are on plane A and S. Option A is correct.

Points P and M lie on the line n, and line n is not the intersection line of plane B and S.

We clearly see that point M is not on the plane S.

So, option B is incorrect.

Point P is the intersection of line n and line g.

So, option C is correct.

Point M and P lie on line n and point P and Q lie on line g.

Three points are collinear if they are lie on a straight line.

Since points M, P and Q are not collinear, therefore they are noncollinear.

So, option D is correct.

Line d intersects plane A at point L.

So, option E is incorrect.

Answer:

ASA

Step-by-step explanation:

Answer: the ASA Postulate

Step-by-step explanation:

In the given picture , we have two triangles ∆LKM and ∆JKM , in which we have

[tex]\angle{LKM}\cong\angle{JKM}\\\\\angle{LMK}\cong\angle{JMK}[/tex]

[tex]\overline{KM}\cong\overline{KM}[/tex] [common]

By using ASA congruence postulate , we have

∆LKM and ∆JKM

ASA  congruence postulate tells that if two angles and the included side of a triangle are congruent to two angles and the included side of other triangle then the triangles are congruent.

Answer:

87 gift bags

Step-by-step explanation:

Answer:

6 pens

2 pencils

1 eraser in each gift bag

Most number of Gift Bags = 27.

Step-by-step explanation:

There will be some bags left over. The limiting factor is the erasers. At most, you can have 27 erasers and therefore 27 gift bags.

171 pens: 171/27 = 6 (you have to round down). The number of pens left over is 9.

(27*6 = 162)    

171 - 162 = 9

63 Pencils: 63/27 = 2 pencils per gift bag. There will be

63 - 2*27

63 - 54

9 pencils will be left over.

Answer:

95% of students are between 14 and 18 years old

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=16[/tex]

The standard deviation is:

[tex]\sigma=1[/tex]

The z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=14 the Z-score is:

[tex]Z_{14}=\frac{14-16}{1}=-2[/tex]

For x=18 the Z-score is:

[tex]Z_{18}=\frac{18-16}{1}=2[/tex]

Then we look for the percentage of the data that is between [tex]-2 <Z <2[/tex] deviations from the mean.

According to the empirical rule 95% of the data is less than 2 standard deviations of the mean.  This means that 95% of students are between 14 and 18 years old

Answer:

△ABC ~ △DEF

Step-by-step explanation:

the AA (angle angle) postulate is a postulate that says two triangles can be similar if they have two congruent angles. using this postulate with how each triangle has a 90° angle and ∠F is congruent to ∠C, we can determine that △ABC ~ △DEF.

The correct answer is C. OBC DE because of the definition of similarity in terms of similarity transformations.

A similarity transformation is a transformation that maps a figure onto a similar figure. A similar figure is a figure that has the same shape as the original figure, but may be a different size and orientation.

A rigid transformation is a transformation that maps a figure onto a congruent figure. A congruent figure is a figure that has the same size and shape as the original figure.

Since a series of rigid transformations maps F onto C where F is congruent to C, then the rigid transformations must have preserved the shape and size of F. This means that the rigid transformations must have been similarity transformations.

Therefore, the statement "OBC DE because of the definition of similarity in terms of similarity transformations" is true.

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Answer:

D. 70 degrees.

Step-by-step explanation:

Because the 2 triangles are similar corresponding angles are congruent.

So m < P = m< X = 66 degrees.

And since there are 180 degrees in a triangle:

m < W = 180 - (m < V + m < X)

= 180 - (44 + 66)

= 70 degrees.

The measure of the angle ∠W is 70°.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is that two sides of a triangle measure 7 feet and 19 feet.

Since the triangles VWX and triangle NOP are similar, we can say that the corresponding angles of both triangles is same.

∠W = ∠O

Also -

∠O + ∠N + ∠P = 180

∠O = 180 - 110

∠O = 70°

∠W = ∠O = 70°

Therefore, the measure of the angle ∠W is 70°.

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Answer:

The preferred p-value among the options offered is 0.001. The reason is because p-value represents the minimum probability of committing the type I error, that is, the probability of rejecting the null hypothesis, with the information contained in the sample, given that this hypothesis is true. The p-value of 0.001 is the lowest value proposed for this probability. Therefore, it supports more evidence that the null hypothesis is false.

Step-by-step explanation:

The preferred P-value among the options provided is 0.001.

0.001 is the preferred p-value simply because it shows the minimum probability of committing an error, it also implies that the probability of rejecting the null hypothesis based on the information presented in the sample, considering that the hypothesis is true.  

Therefore, the p-value 0.001 is the lowest value proposed for this probability and it also corresponds to the sample of evidence that supports the alternative hypothesis which shows the method is effective.

Hypothesis testing refers to an act in statistics in which an analyst test the assumption as regards to a population parameter.

The methodology to be used by analysts is based on the nature of the data that are used and the purpose of the analysis

An analysts test a sample to accept or reject a null hypothesis. The outcome of the tests will reveal the analysis if his primary hypothesis is true or not. If the analysis of the tests is not true, it then means the analysts will have to formulate a new hypothesis and do the analysis again.

It implies the analysts will continue to repeat the process until the analysis shows the data hypothesis is true.  

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KEYWORDS:

The 60% of adults who like pizza was found by dividing the adults who like pizza ( 0.36) by the total adults ( 0.60): 0.36 / 0.6 = 0.6 = 60%

To find the percent of children that like pizza divide 0.29 by 0.40:

0.29 / 0.40 = 0.725 = 72.5%, which is about 70%

The answer would be C. A greater percentage of children (about 70%) prefer pizza.

The percentage of children that prefer pizza are about 70%, which is Option(c) .

A relative figure reflecting hundredth parts of any quantity is called a percentage.

Children who like pizza = 0.29

Total No. of children = 0.40

Percentage of children who like pizza = (0.29 / 0.40) * 100

Percentage = 72.5% (about 70%)

The percentage of children who like pizza are about 70%(Option - c)

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Answer:

GCF -The greatest real number shared between two integers. On the other hand, the Lowest Common Multiple (or LCM) is the integer shared by two numbers that can be divided by both number.

Step-by-step explanation:

Answer:

[tex]y-1=3(x-4)[/tex] -----> equation into point slope form

[tex]y=3x-11[/tex]  -----> equation into slope intercept form

[tex]3x-y=11[/tex] -----> equation in standard form

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

step 1

Find the slope of the line passing through ( 7 , 11 ) and ( 10 , 20 )

The slope m is equal to

[tex]m=(20-11)/(10-7)=3[/tex]

step 2

Find the equation of the line with m=3 that passes through (4,1)

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y-1=3(x-4)[/tex] -----> equation into point slope form

Convert to slope intercept form

[tex]y=mx+b[/tex]

isolate the variable y

[tex]y=3x-12+1[/tex]

[tex]y=3x-11[/tex]  -----> equation into slope intercept form

Convert to standard form

[tex]Ax+By=C[/tex]

[tex]3x-y=11[/tex] -----> equation in standard form

The slope of the given line passing through (7, 11) and (10, 20) is 3. Since parallel lines have equal slopes, the line passing through (4, 1) will also have a slope of 3. Plugging in the slope and point into the slope-intercept form, we find the equation of the line to be y = 3x - 11.

To find the equation of the line that passes through the point (4, 1) and is parallel to another line, we first need to determine the slope of the given line that passes through (7, 11) and (10, 20).

The slope of a line is found by taking the difference in the y-coordinates divided by the difference in the x-coordinates between two points on the line, which is often expressed as Δy/Δx or (y2-y1)/(x2-x1).

The slope of the line passing through (7, 11) and (10, 20) is calculated as follows:
Δy = 20 - 11 = 9

Δx = 10 - 7 = 3

Slope (m) = Δy/Δx = 9/3 = 3

Since parallel lines have the same slope, the line passing through (4, 1) will also have a slope of 3.

The equation of a line in slope-intercept form (y = mx + b) can then be used, where 'm' is the slope and 'b' is the y-intercept.

As we have the slope and a point on the line, we can substitute them into the equation to solve for 'b'.

The equation will look like this:
y = mx + b

1 = 3(4) + b

1 = 12 + b

b = 1 - 12

b = -11

The equation of the line that goes through (4, 1) and is parallel to the line through (7, 11) and (10, 20) is therefore y = 3x - 11.

Answer:

[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]

Step-by-step explanation:

[tex]\sin(\theta)+1=\cos(2\theta)[/tex]

Applying double angle identity:

[tex]\cos(2\theta)=1-2\sin^2(\theta)[/tex]

Doing so would give:

[tex]\sin(\theta)+1=1-2\sin^2(\theta)[/tex]

We need to get everything to one side so we have 0 on one side.

Subtract 1 on both sides:

[tex]\sin(\theta)=-2\sin^2(\theta)[/tex]

Add [tex]2\sin^2(theta)[/tex] on both sides:

[tex]\sin(\theta)+2\sin^2(\theta)=0[/tex]

Let's factor the left-hand side.

The two terms on the left-hand side have a common factor of [tex]\sin(\theta)[/tex].

[tex]\sin(\theta)[1+2\sin(\theta)]=0[/tex].

This implies we have:

[tex]\sin(\theta)=0 \text{ or } 1+2\sin(\theta)=0[/tex].

We need to solve both equations.

You are asking they be solved in the interval [tex][0,2\pi)[/tex].

[tex]\sin(\theta)=0[/tex]

This means look at your unit circle and find when you have your y-coordinates is 0.

You this at 0 and [tex]\pi[/tex]. (I didn't include [tex]2\pi[/tex] because you don't have a equal sign at the endpoint of [tex]2\pi[/tex].

Now let's solve [tex]1+2\sin(\theta)=0[/tex]

Subtract 1 on both sides:

[tex]2\sin(\theta)=-1[/tex]

Divide both sides by 2:

[tex]\sin(\theta)=\frac{-1}{2}[/tex]

Now we are going to go and look for when the y-coordinates are -1/2.

This happens at [tex]\frac{7\pi}{6}[/tex] and [tex]\frac{11\pi}{6}[/tex].

The solution set given the restrictions is

[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]

Answer:

Step-by-step explanation:

1. The multiplier for the first equation can be found by the ratio ...

  -(second equation x-coefficient)/(first equation x-coefficient)

  = (-2/3)/(1/5) = -10/3

This tells you that multiplying the first equation by -10 and the second equation by 3 will make the x-terms cancel. Matches selection A.

__

2. Adding the two equations shown gives ...

  (-2x -8y) +(2x +y) = (-60) +(-45)

  -7y = -105

  y = -105/-7 = 15 . . . . matches selection C.

__

3. Using the rule shown in question 1, the multiplier for the first equation will be ...

  -(second equation y-coefficient)/(first equation y-coefficient)

  -12/(3/4) = -16

Multiplying the first equation by -16 gives ...

  -16(-5x +3/4y) = -16(12)

  80x -12y = -192 . . . . no matching answer choice

(Sometimes, the problems have errors in their answers. This is one of those times. Choice A will probably be graded as correct, even though it is not.)

Answer:

(14.7 , 16.9)

Step-by-step explanation:

it is given that [tex]\bar{x}=15.8[/tex] tons

σ=3.8 tons

n=49

at 95% confidence level α=1-.95=0.05

[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=z_{0.025}\\[/tex]

=1.96 ( from the standard table)

at 95% confidence level the coefficient interval for μ is

[tex]\bar{x}\pm z_\frac{\alpha }{2}\times \frac{\sigma }{\sqrt{n}}[/tex]

[tex]15.8\pm 1.96\times \frac{3.8}{ \sqrt{49}}[/tex]

[tex]15.8\pm 1.1[/tex]

(14.7, 16.9)

Answer:

Because it's an odd function, the "tails" go off in different directions.  Also, because it's a negative function, the left starts from the upper left and the right goes down into negative infinity.  If it was a positive, the tails would be going in the other directions, meaning that the left would come up from negative infinity and the right would go up into positive infinity.

Step-by-step explanation:

Answer:

C on Edge: As x--> -∞, y-->+∞ and as x-->+∞, y-->-∞

:) Have a good day / night Everyone and stay safe!

Answer:

  B.  10.71 cents

Step-by-step explanation:

Benito's other expenses total ...

  $809 +170 +57 = $1036

so his gas expense is ...

  $1822 -1036 = $786

Then the per-mile cost is ...

  $786/(7340 mi) ≈ $0.10708/mi

Benito's gas cost averaged 10.71¢ per mile.

Answer is B) 10.71 cents.

You just add Benito's operating expenses togther, like so:

809 + 170 + 57 = $1036 so far.

Next, subtract the total amount he spent this last year (1822), with how much he spent so far (1036).

1822 - 1036 = $786

Finally, divide the final total with the 7340 miles he plans to drive.

786 ÷ 7340 = 0.10708

Answer is B) 10.71 cents.

☺☺☺☺

Answer:

  C.  70

Step-by-step explanation:

In the expansion of (a + b)^n, the k-th term is ...

  nCk·a^(n-k)b^k . . . . . k = 0 to n; nCk = n!/(k!(n-k)!)

Here, we have n=8, k=4, so the term of interest is ...

  8C4·x^4y^4 = (8·7·6·5)/(4·3·2·1)x^4y^4 = 70x^4y^4

The coefficient of the term is 70.

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

cosC = cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]

sinA = sin60° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Hence

cosC × sinA = [tex]\frac{\sqrt{3} }{2}[/tex]  × [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Since,

[tex]\sin \theta=\frac{Opposite leg of }\theta}{\text{Hypotenuse}}[/tex]

[tex]\cos \theta=\frac{Adjacent leg of }\theta}{\text{Hypotenuse}}[/tex]

Given,

In triangle ABC,

AB = 1 unit, AC = 2 unit, and BC = √3 unit

Thus, by the above formule,

[tex]\cos C = \frac{\sqrt{3}}{2}[/tex]

[tex]\sin A=\frac{\sqrt{3}}{2}[/tex]

[tex]\implies \cos C\times \sin A =  \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}= \frac{3}{4}[/tex]

Answer:

  c.  1 ≤ y ≤ 3; y ≥ -2x +2

Step-by-step explanation:

The shading between the solid lines y=1 and y=3 tells you that one of the inequalities is 1 ≤ y ≤ 3 (including the "or equal to" case). The shading above the solid diagonal line tells you that inequality will be y ≥ (something).

Choice C matches these observations.

Just fun I'm going to add something above the below.

You can write an equation for this without the parameter.

You have y=t+5 and x=2t.  If you multiply both sides of y=t+5 by 2 you should get 2y=2t+10 and guess what you can replace 2t with x since you have x=2t.  So you can write 2y=x+10 as your equation to represent the parametric version they have here.

This is a linear equation as our graph appears to be below.   Solve for y by dividing both sides by 2 gives you y=x/2  +5.  The slope is 1/2 and the y-intercept is 5.  If t is between -2 and 3 then x is between -4 and 6 since x is doubled t (inclusive here since we have those equal signs along with those inequalities).

So you could have just graph the line y=x/2+5 on the interval [tex]-4 \le x \le 6 [/tex]/

Anyways, I'm also going to look at this without the rewrite:

I'm going to make a table with 4 columns.  The first column is t.  The second is x(t), the third is y(t), and the fourth will be a list of points (x,y) our relation will go through).

t    |     x(t)        |     y(t)           |   (x,y)

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

-2       2(-2)=-4      -2+5=3          (-4,3)

-1        2(-1)=-2       -1+5=4           (-2,4)

0        2(0)=0         0+5=5           (0,5)

1         2(1)=2           1+5=6           (2,6)

2        2(2)=4          2+5=7          (4,7)

3        2(3)=6          3+5=8           (6,8)

Now I'm going to graph the points in the last column on a coordinate-plane.

The horizontal axis is your x-axis and the vertical axis is your y-axis. I did the x-axis going up or down by two's while the y-axis is going up and down only by one's.

Answer:

Hoomp means "we come".

Step-by-step explanation:

"Floos Beiling Hoomp" means "We come in peace"

"Moog Naline Floos" means "Peace, Love, and Freedom "

"Beiling Boog Vladi" means "In the last hour"

Comparing 1st two statements, we get Floos means peace.

Comparing 1st and 3rd statements, we get Beiling means in

So, Hoomp is "we come".

Final answer:

"Hoomp" means "we come".

Explanation:

The question at hand involves deciphering the meaning of a word from messages in a strange language received from a distant planet.

By analyzing the given messages and their translations, we can determine the meaning of individual words through comparison and elimination.

Here's a step-by-step explanation:

Comparing the first and second statements, we understand that "Floos" means peace. From the first and third statements, we deduce "Beiling" means in.

Therefore, given its unique presence in the first statement, "Hoomp" logically translates to "we come".

This question illustrates the process of deciphering language through pattern recognition and comparative analysis, which is a fundamental aspect of linguistics and communication studies.

Below is the formula for the circumference of a circle

C = 2πr

This question gives us the diameter. To find the radius (r) you would divide the diameter by two like so...

16.4/ 2  = 8.2

Plug what you know into the formula and solve...

π = 3.14

r = 8.2

C = 2(3.14)(8.2)

C = 6.28(8.2)

C = 51.496

In the question it asks to round to the nearest tenth like so...

51.5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

51.496 rounded to the nearest tenth is 51.5

Answer:

Step-by-step explanation:

The point (-3, 4) is in QII.  If we plot this point and drop an altitude then connect the point to the origin, we have a right triangle with side opposite measuring 4 units and side adjacent measuring |-3|.  The tangent of the reference angle is the ratio side opposite/side adjacent, so

[tex]tan\theta=-\frac{4}{3}[/tex]

Since secant is the reciprocal of cosine, let's find the cosine of the reference angle and then flip it upside down.  The cosine of the angle is the side adjacent (got it) over the hypotenuse (don't have it).  We can find the hypotenuse using Pythagorean's Theorem:

[tex]c^2=-3^2+4^2[/tex] s0

[tex]c^2=25[/tex] and

c = 5

The cosine of the angle theta is

[tex]cos\theta=-\frac{3}{5}[/tex]; therefore,

[tex]sec\theta=-\frac{5}{3}[/tex]

Answer:

r = 5m

Step-by-step explanation:

miles walked   money earned

0                             0

1              1*5          5

2             2 * 5       10

3             3 * 5       15

4             4 * 5        20

5             5 * 5        25

6             6 * 5       30

We multiply 5 by each mile walked to determine how much money was raised

r = 5m  where r is the money raised and m is the miles walked

Steps:

---> Re arrange equation to get the format: y = mx + c

---> Work out the perpendicular gradient from the first equation

----> Substitute the x and y coordinates of point (-1, 0) and the perpendicular      gradient into y = mx + c   and work out c

---> Finally, substitute the perpendicular gradient and the value for c into y =mx + c  to get the gradient of the perpendicular line:

__________________________________________

Rearranging equation into the format: y = mx + c:

[tex]5y = x - 5[/tex]                  (Just divide both sides by y)

[tex]y = \frac{1}{5}x -1[/tex]

___________________________________________

Working out the perpendicular gradient:

To work out the perpendicular gradient, we just take the negative reciprocal of the gradient of [tex]y = \frac{1}{5}x -1[/tex]

Note: negative reciprocal means we just flip the fraction and put a minus sign.

The regular gradient is: [tex]\frac{1}{5}[/tex]

So the perpendicular gradient is the negative reciprocal of [tex]\frac{1}{5}[/tex]

which is -5       (note: [tex]\frac{-5}{1}[/tex] is just 5-)

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Now lets substitute in the values for the gradient (m), the y coord (0) and x coord (-1) of the point (-1, 0)   into y = mx + c, and solve for c:

y = mx + c     (substitute in all known values)

0 = -5(-1) + c   (the -1 times -5 will make + 5)

0 = 5 + c        (subtract 5 from both sides to cancel out the + 5)

-5 = c

so c = -5

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Finally, just substitute in the perpendicular gradient and the value for c into y = mx + c   to get the equation of the perpendicular line:

y = mx + c        (substitute in the perp. gradient and c)

y = -5x - 5

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The equation to the line perpendicular to 5y = x - 5 through point (-1, 0) is :

C. y = -5x - 5

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A quicker way to get equation of the perpendicular line once you know the perp. gradient is to use the equation:

y - y1 = m (x - x1)

y1 is the y coordinate of (-1, 0)

x1 is the x coordinate of (-1, 0)

m is the perpendicular gradient.

y - y1 = m (x - x1)       (Substitute in values)

y - 0 = -5 ( x - - 1)       (simplify)

y = -5 (x + 1)              (expand the brackets)

y = -5x - 5