find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2​

Answer:

i) A = (3, 3), B = (12, 6), C = (6, 52) : Not orthogonal, ii) A = (-10, 5), B = (12, 16), C = (6, 52) : Not orthogonal, iii) A = (-8, 3), B = (12, 8), C = (18, 4) : Not orthogonal, iv) A = (12, -14), B = (-16, 21), C = (-11, 25) : Orthogonal, v) A = (-12, -19), B = (20, 45) : Impossible orthogonality, vi) A = (30, 20), B = (-20, -15) : Impossible orthogonality.

Step-by-step explanation:

The statement indicates that segments AB and BC must be orthogonal. Vectorially speaking, this can be expressed by using the following expression from Linear Algebra:

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = 0[/tex]

[tex](AB_{x}, AB_{y})\bullet (BC_{x},BC_{y}) = 0[/tex]

[tex]AB_{x}\cdot BC_{x} + AB_{y}\cdot BC_{y} = 0[/tex]

Now, let is evaluate each choice:

i) A = (3, 3), B = (12, 6), C = (6, 52)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 6) - (3, 3)[/tex]

[tex]\overrightarrow {AB} = (12-3, 6-3)[/tex]

[tex]\overrightarrow {AB} = (9, 3)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (6, 52) - (12, 6)[/tex]

[tex]\overrightarrow {BC} = (6 - 12, 52 - 6)[/tex]

[tex]\overrightarrow {BC} = (-6, 46)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (9, 3)\bullet (-6, 46)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (9)\cdot (-6) + (3) \cdot (46)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 84[/tex]

AB and BC are not orthogonal.

ii) A = (-10, 5), B = (12, 16), C = (6, 52)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 16) - (-10, 5)[/tex]

[tex]\overrightarrow {AB} = (12+10, 16-5)[/tex]

[tex]\overrightarrow {AB} = (22, 11)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (6, 52) - (12, 16)[/tex]

[tex]\overrightarrow {BC} = (6 - 12, 52 - 16)[/tex]

[tex]\overrightarrow {BC} = (-6, 36)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (22, 11)\bullet (-6, 36)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (22)\cdot (-6) + (11) \cdot (36)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 264[/tex]

AB and BC are not orthogonal.

iii) A = (-8, 3), B = (12, 8), C = (18, 4)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 8) - (-8, 3)[/tex]

[tex]\overrightarrow {AB} = (12+8, 8-3)[/tex]

[tex]\overrightarrow {AB} = (20, 5)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (18, 4) - (12, 8)[/tex]

[tex]\overrightarrow {BC} = (18 - 12, 4 - 8)[/tex]

[tex]\overrightarrow {BC} = (6, -4)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (20, 5)\bullet (-6, -4)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (20)\cdot (-6) + (5) \cdot (-4)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = -140[/tex]

AB and BC are not orthogonal.

iv) A = (12, -14), B = (-16, 21), C = (-11, 25)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (-16,21) - (12, -14)[/tex]

[tex]\overrightarrow {AB} = (-16-12, 21+14)[/tex]

[tex]\overrightarrow {AB} = (-28, 35)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (-11,25) - (-16, 21)[/tex]

[tex]\overrightarrow {BC} = (-11+16, 25-21)[/tex]

[tex]\overrightarrow {BC} = (5, 4)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (-28,35)\bullet (5, 4)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (-28)\cdot (5) + (35) \cdot (4)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 0[/tex]

AB and BC are orthogonal.

v) A = (-12, -19), B = (20, 45)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

vi) A = (30, 20), B = (-20, -15)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

Answer:

51.339

Step-by-step explanation:

Hello,

At the beginning Holly has $500

After one year

   he will get 500*(1+6.75%)=500*1.0675

After n year (n being real)

   he will get

   [tex]500\cdot1.0675^n[/tex]

and we are looking for n so that

   [tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]

so we need 51.339 years

Hope this helps

Answer:

The answer is option 2.

Step-by-step explanation:

Quadratic function is always written in the form of ax² + bx + c where the highest power of x is 2.

In the options above :

Option 1 is Cubic function.

Option 2 is Quadratic function.

Option 3 and 4 are Linear function.

Answer:

I guess....

Step-by-step explanation:

option 2............

Answer: min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Step-by-step explanation:

The five-number summary for this data set consists  of  min, Q1,

median, Q3, max.

Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.

Minimum value = 12

Maximum value = 37

since , number of observations = 10 (even)

So , Median = Mean of middle most terms

Middle most terms = 22, 25

Median =[tex]\dfrac{22+25}{2}=23.5[/tex]

First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)

= middle most term

= 17

Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)

= middle most term

= 30

Hence, five-number summary for this data set :

min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Answer:

[tex]x = -5[/tex]

Step-by-step explanation:

We can simplify this equation down until x is isolated.

[tex]2x - 3 + 3x = -28[/tex]

We can combine the like terms of x.

[tex]5x - 3 = -28[/tex]

Add 3 to both sides.

[tex]5x = -25[/tex]

Now we can divide both sides by 5.

[tex]x = -5[/tex].

So x = -5.

Hope this helped!

Answer:

x=-5

Step-by-step explanation:

first combine like terms

5x-3=-28

add on both sides

5x=-25

divide

x==-5

Answer:

16+x²

Step-by-step explanation:

Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5

Hi there! Hopefully this helps!

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

So, we know that 4 to the 4th power equals 256.

4 to the 4th power = 4 x 4 x 4 x 4.

So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.

4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or you could break the equation into parts.

For example, there are FOUR 4s in the equation.

4 x 4 = 16.

4 x 4 = 16.

16 x 16 = 256.

Now since we've added ANOTHER 4, it should look like this:

16 x 16 = 256.

256 x 4 = 1024.

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

inital height is 2 meters

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's note a and b the two numbers.

a = b - 5

[tex]a^2+b^2=157[/tex]

We replace a in the second equation and we solve it

[tex](b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0[/tex]

It means that the sum of the two roots is 5 and the product is -66.

because

     [tex](x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }[/tex]

And we can notice that 66 = 6 * 11 and 11 - 6 = 5

So let's factorise it !

    [tex]b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6[/tex]

It means that the solutions are

(6,11) and (-6,-11)

I guess we are after positive numbers though.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The graph D shows a line with slope zero.

Since graph A, B and C doesn't make horizontal line, it is not a zero slope/ horizontal line.

Graph D is a horizontal line. It doesn't depend on any y value. It is neither increasing nor decreasing.

Therefore, graph D shows a line with a slope of zero.

Learn more about slope here:

https://brainly.com/question/3493733

#SPJ2

Since "a line has a slope of zero when it does not have any vertical rise. It will be a straight horizontal line." the answer is D

Answer:

623

Step-by-step explanation:

Given that margin of error (E) = 3 unit, standard deviation (σ) = 29, sample size (n) = ?

a) The confidence (C) = 99% = 0.99

α = 1 - C = 1 - 0.99 = 0.01

α/2 = 0.01 / 2 = 0.005

From the normal distribution table, The z score of α/2 (0.005) is the critical value and it corresponds to the z score 0.495 (0.5 - 0.005) which is 2.58.

[tex]critical\ value = z_{\frac{\alpha}{2} }=z_{0.005}=2.58\\[/tex]

b) The margin of error (E) is given as:

The minimum sample size (n) is 623

Answer: all of them have one solutions

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let b represent the number of cups of butter needed.

Let s represent the number of cups of sugar needed.

Let o represent the number of cups of oat needed.

Let f represent the number of cups of flour needed.

The recipe calls for two times as many cups of sugar as butter. It means that

s = 2b

Two times as many cups of oats as sugar. It means that

o = 2s

Two times as many cups of flour as oats. It means that

f = 2o

If Duane puts in one cup of butter, it means that b = 1

Therefore,

s = 2 × 1 = 2 cups

o = 2s = 2 × 2 = 4 cups

f = 2o = 2 × 4 = 8 cups

Therefore, he needs to add 8 cups of flour

Answer: Let b represent the number of cups of butter needed. Let s represent the number of cups of sugar needed. Let o represent the number of cups of oat needed. Let f represent the number of cups of flour needed. The recipe calls for two times as many cups of sugar as butter. It means that s = 2bTwo times as many cups of oats as sugar. It means that o = 2sTwo times as many cups of flour as oats. It means that f = 2oIf Duane puts in one cup of butter, it means that b = 1Therefore, s = 2 × 1 = 2 cupso = 2s = 2 × 2 = 4 cupsf = 2o = 2 × 4 = 8 cups Therefore, he needs to add 8 cups of flour

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

See explanations in the attached document

Answer:

94.25 kg I think

Step-by-step explanation:

58/4 =14.5 kg per bushel

6.5 x 14.5=94.25 kg

Answer:

94.25

Step-by-step explanation:

First you need to find the unit rate which is 58/4 which equals to 14.5 then you multiply by 6.5 to find 94.25

Answer:

P [ Z > 21 ] = 0,5   or   P [ Z > 21 ] = 50 %

Step-by-step explanation:

Normal Distribution N(21;4)

The question here is what is the area of the bell shape curve. As 21 is a mean for this distribution is in the middle of the bell, so values bigger than 21 will have a probability of 0,5, and values smaller than 21 will have the same probability 0,5. We must remember that the whole area under the curve has an area of 1 ( or 100% )

Answer:

x = 1.5

Step-by-step explanation:

5(4x-10)+10x=4(2x-3)+2(x-4)

Distribute(5)

20x-50+10x=4(2x-3)+2(x-4)

Distribute(4)

20x-50+10x=8x-12+2(x-4)

Distribute(2)

20x-50+10x=8x-12+2x-8

Combine like terms

30x-50=10x-20

Subtract(10x)

20x-50=-20

Add(50)

20x=30

Divide(20)

x = 1.5

Hope it helps <3

Answer:

Step-by-step explanation:

5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)

Expand the terms

That's

20x - 50 + 10x = 8x - 12 + 2x - 8

Simplify

30x - 50 = 10x - 20

Group the constants at the right side of the equation

That's

30x - 10x = - 20 + 50

20x = 30

Divide both sides by 20

x = 3/2

Hope this helps you

Answer:

101.98 yards.

Step-by-step explanation:

Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).

Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).

The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.

tan(22.6) = x / 245

x / 245 = tan(22.6)

x = tan(22.6) * 245

x = 0.4162598242 * 245

x = 101.9836569

So, you are about 101.98 yards from the cabin.

Hope this helps!

Answer:

x = ±sqrt(7)

Step-by-step explanation:

x^2 - 8 = -1

Add 8 to each side

x^2 - 8+8 = -1+8

x^2 = 7

Take the square root of each side

sqrt(x^2) = ±sqrt(7)

x = ±sqrt(7)

Answer:

  0.12 g/cm³

Step-by-step explanation:

Density is the ratio of mass to volume. The volume of the brownie is the cube of its side dimension:

  V = s³ = (5 cm)³ = 125 cm³

Then the density is ...

  ρ = M/V = (15 g)/(125 cm³) = 0.12 g/cm³

The density of the brownie is 0.12 g/cm³.

Answer:

A. 1 milliliter

Step-by-step explanation:

1000 milliliters = 1 liter

0.001 liters = 1 milliliter

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

Option B

Because the average points scored in the night is more than that of the day

Step-by-step explanation:

Each number cube has 6 possible values, so there are 6⁴ = 1296 possible permutations.  Only 1 of those permutations is all ones.  Therefore, the probability is 1/1296.

Answer:

[tex]\boxed{\sf k=6}[/tex]

Step-by-step explanation:

[tex]\sf kx (x-2)+6=0[/tex]

Expand brackets.

[tex]\sf kx^2 -2kx+6=0[/tex]

This is in quadratic form.

[tex]\sf ax^2 +bx+c=0[/tex]

Since this is for equal roots:

[tex]\sf b^2 -4ac=0[/tex]

[tex]\sf a=k\\b=-2k\\c=6[/tex]

[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]

[tex]\sf 4k^2-24k=0[/tex]

[tex]\sf 4k(k-6)=0[/tex]

[tex]\sf 4k=0\\k=0[/tex]

[tex]\sf k-6=0\\k=6[/tex]

Plug k as 0 to check.

[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]

False.

So that means k must equal 6.

Answer:

8.2

Step-by-step explanation:

When you calculate it by 100, there are two zeros, so you move two decimals to the right.

This makes 8.2, and 8.2 will be the answer.

Another example could be... 0.082✖️10.

In this case, there is 1 zero, so you move the decimal to the right once, making it 0.82.

Hope this helps!!!

Answer:

8.2

Step-by-step explanation:

When you calculate it by 100, there are two zeros, so you move two decimals to the right.

so you will get 8.2

hope it helps you

Answer:

H0 :

a. mu is greater than or equal to $108.50

Ha:

c. mu is less than or equal to $108.50

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence

In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

Answer:

[tex]\boxed{x = 2\frac{2}{3} }[/tex]

Step-by-step explanation:

[tex]-1.3+4.6x = 0.3 +4x[/tex]

Collecting like terms

[tex]4.6 x -4x = 0.3+1.3[/tex]

[tex]0.6x = 1.6[/tex]

Dividing both sides by 0.6

x = 1.6 / 0.6

x = 2 2/3

Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ [tex]\r p , \ \r q[/tex], ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of [tex]\alpha[/tex] ​?

Answer:

a

   [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

   [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

   [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e                        [tex]\r q = 1- \r p[/tex]

b

   [tex]\alpha = 10\%[/tex]

Step-by-step explanation:

Here

    [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

    [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e  

      [tex]\r q = 1- \r p[/tex]

      [tex]\r q = 1- 0.12[/tex]

      [tex]\r q = 0.88[/tex]

     [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as

     [tex]\alpha = ( 100 - C )\%[/tex]

Where  [tex]C[/tex] is the confidence level which is given in this question as  [tex]C = 90 \%[/tex]

So  

    [tex]\alpha = ( 100 - 90 )\%[/tex]

    [tex]\alpha = 10\%[/tex]