Solve a) with Substitution and b) with Elimination (check attached picture)

By factorizing, we have

[tex]x^2 + 5xy - 6y^2 = (x - y) (x + 6y) = 0[/tex]

so that

[tex]x - y = 0 \implies \boxed{y = x}[/tex]

or

[tex]x + 6y = 0 \implies \boxed{y = -\dfrac x6}[/tex]

Answer:

In [tex]$(a+b)^{2}$[/tex] is obtained by addition therefore result is trinomial while in (a-b)(a + b) the middle terms are canceled out of each other therefore result is binomial.

Step-by-step explanation:

Explanation

Answer:

7

Step-by-step explanation:

Whenever you shifting an exponential function to the left/right, you're going to generally have the equation: [tex]y=2^{x-k}[/tex] where k is the shift. So in this case we can think of x+3 as x and k as 10, since the shift is 10. This gives you the equation: (x+3) - 10, which simplifies to x-7, meaning the k value in this case is going go be 7. You can also think of it as already being shifted 3 units to the left, and you shift it 10 units to the right, that means this new function will be shifted 7 units to the right relative to the origin. This means the k=7.

Step-by-step explanation:

so in this case

x-4

y-2

z-5

average=x+y+z/no of values

= 4+5+2/3

=11/3

=3.6

Answer:

36 miles and 10 miles

Step-by-step explanation:

area = length × width

A = LW

W = unknown = x

L = 26 ft more than width = x + 26

A = LW

360 = (x + 26)x

360 = x² + 26x

x² + 26x - 360 = 0

(x + 36)(x - 10) = 0

x + 36 = 0  or  x - 10 = 0

x = -36 or x = 10

We discard the solution x = -36 since the width of a rectangle cannot be a negative number.

W = x = 10

L = x + 26 = 10 + 26 = 36

Answer: 36 miles and 10 miles

Answer:

Step-by-step explanation:

c = b·sin(C)

c= 10Sin(45

c=7.071

So the side length opposite to the 45 degree angle is 7.071 :)

https://www.calculator.net/triangle-calculator.html

^this website is perfect for questions like these^

Good luck with the rest of your work!

Answer: 1

Step-by-step explanation:

To find slope: (y1-y2)/(x1-x2)

y1 = -4

y2=-6

x1 = -5

x2 = -7

-4 --6 = -4 + 6 = 2

-5--7 = -5+7 = 2

2/2 = 1

so, the slope is 1

The best accuracy for the transformation is; Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.

In a translation transformation, all the points in the object are moved in a straight line in the same direction. The size, the shape and the orientation of the object remain the same.

In this question, the points on triangle A are: (-1, 0), (-2, 4) and (-1, 4).

Marcus' translation is as follows:

The points are the same of triangle B, hence the statement is accurate. According to the order of the translations, the second statement is correct.

Read more about Transformations at; https://brainly.com/question/4289712

#SPJ1

The value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. This a can be obtained by solving the linear inequality by taking terms with x to one side of the inequality similar to solving of linear equation.

Given that  

         3x + 3 - x + (-7) > 6

         3x - x > 6 + 7 - 3

         2x > 10

          x > 5

Hence the value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. The correct option is c.

Learn more about solving of inequality:

brainly.com/question/11897796

#SPJ4

The 6th term of the sequence is 4

The given parameters are:

a1 = -4096

a4 = 64

The nth term of the sequence is:

a(n) = a1 * r^(n-1)

So, we have:

a4 = a1 * r^3

This gives

r^3 = a4/a1

Substitute the known values

r^3 = 64/-4096

Evaluate

r^3 = -1/64

Take the cube roots

r = -1/4

The 6th term is

a(6) =a1 * r^5

This gives

a(6) = -4096 * (-1/4)^5

Evaluate

a(6) = 4

Hence, the 6th term of the sequence is 4

Read more about sequence at:

https://brainly.com/question/5721539

#SPJ1

19 : 125 = 0.152, and because there is a finite amount of digits after the decimal, this is a terminating decimal. (if anything's wrong just message)

hi hermes

According to graph, GMT time when the plane flew over the beacon was 9:24.

While looking closely at the graph on x axis , one will notice that each hour is divided into 5 parts and hence each part has 12 minutes. looking at y axis, one may find that each part on y axis resembles 20miles. Hence at 280 miles away from Bristol, The GMT time is 9:24.

Know more about graph numerical

https://brainly.com/question/16608196

#SPJ4

Answer:

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

Step-by-step explanation:

Strictly speaking, we need to know the point of [tex]f(x) = 3x[/tex] intersecting [tex]f(x) = 9[/tex]. In other words, we need to solve the equality:

[tex]3x = 9; \\ x = \frac{9}{3}; \\ x = 3[/tex]

Here it is.

Concluimos que hay 8 libros de aritmética.

Sabemos que la relacion entre el número de libros de aritmetica y el total de libros es de 4 a 9.

Es decir, sí el número total de libros es N, entonces (4/9)*N de esos libros son de aritmética.

Sea X el número de libros de aritmética. Sabemos que hay 10 libros de algebra, entonces el número total N es:

N = 10 + X

Y usando la relación de arriba, podemos escribir:

X = (4/9)*N = (4/9)*(10 + X)

Ahora podemos resolver esto para X.

X*(9/4) = 10 + X

X*(9/4) - X = 10

X*(5/4) = 10

X = (4/5)*10 = 8

Concluimos que hay 8 libros de aritmética.

Sí quieres aprender más sobre algebra:

https://brainly.com/question/723406

#SPJ1

Answer:

900 liters of water is pumped in 1 hour

Step-by-step explanation:

Time taken to pump 15 liters of water =  1 minute.

Time taken to  pump 1 liters of water  = 1/15 minute

[tex]\sf \text{Time taken to pump 900 liters of water=$\dfrac{1}{15}*900$}[/tex]

                                                             = 60 minutes

                                                             = 1 hour

Answer:

120 different ways

Step-by-step explanation:

The formula to count the permutation since the order the matters: nPr = n! / (n - r)!, where n is the total number and r is the total number of chosen.

1) Substitute values into the formula. SMILE has 5 letters, and we choose 5.

5P5 = 5! / (5 - 5)!

5P5 = 5! / 0!

Zero factorial (0!) is always 1.

So, 5P5 = 5! / 1

5! = 5 × 4 × 3 × 2 × 1

5! = 120

Therefore, 5P5 = 120 / 1, which is 120. We can arrange the word SMILE in 120 different ways.

Answer:

The given lines are parallel.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (0,6) and (3,-24). Whereas, line 2 passes through (-1,19) and (8,-71).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{-24-6}{3-0} \\&m_{1}=\frac{-30}{3} \\&m_{1}=-10\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{-71-19}{8-(-1)} \\&m_{2}=\frac{-90}{9} \\&m_{2}=-10\end{aligned}$$[/tex]

Since, both slopes are equal.

Therefore, the lines are parallel.

Based on the translated image and the original triangle ABC, the true statements are:

The pre-image of triangle ABC and the image are shown to have sides that are congruent because they are exactly the same. This is why triangle A¹B¹C¹ is a slide of triangle ABC.

In order to form the image, the translation must have been such that each point of the preimage moved the same number of units.

Find out more on translations at https://brainly.com/question/27894131.

#SPJ1

Answer:

a, d, g

Step-by-step explanation:

i took da test

Answer:

If they worked together it would take 4 hours for the machines to produce 100 widgets

Step-by-step explanation:

w = widgets     hr = hour     ph = per hour

Old machine - 50w = 5hr = 10ph

New machine - 30w = 2hr = 15ph

Old machine - 20w = 2hr

New machine - 30w = 2hr

     I hope this helped!

Answer:

(7, 4)

Step-by-step explanation:

[tex]\text{Let the coordinates of B } = x_{B} , y_{B} \\\text{Let the coordinates of A} = x_{A} , y_{A} \\\text{Let the coordinates of midpoint M} = x_{M} , y_{M}[/tex]

By the midpoint formula,
[tex](x_{M},y_{M}) = (\frac{x_{A} + x_{B}}{2} , \frac{y_{A} + y_{B}}{2} )[/tex]

[tex]x_{M} = \frac{x_{A} + x_{B}}{2} \\y_{M} = \frac{y_{A} + y_{B}}{2} \\[/tex]

We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So
[tex]5 = \frac{3 + x_{B}}{2} \\\\\\textrm{Cross-multiplying } 10 = 3 + x_{B}} \textrm{ or } x_{B} = 10-3 = 7\\[/tex]

[tex]6 = \frac{8 + y_{B}}{2} \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_{B}} \textrm{ or } y_{B} = 12-8 = 4\\[/tex]

So coordinates of B are (7,4)

Work Shown:

f(x) = x + 10

f(x+1) = x+1 + 10 .... replace every x with x+1

f(x+1) = x + 11

Any sample proportion that is more than 1.96 standard errors from the population proportion will result in a confidence interval that includes p.

In frequentist records, a confidence interval is more than a few estimates for an unknown parameter. A self-belief interval is computed at a chosen self-belief stage; the ninety-five% self-assurance stage is maximum commonplace, however other tiers, which include ninety% or ninety-nine%, are now and again used.

The confidence stage is the share of instances you expect to get near the identical estimate if you run your test again or resample the populace in an identical manner.

The confidence c programming language includes the higher and lower bounds of the estimate you anticipate locating at a given stage of confidence.

As an instance, in case you are estimating a 95% self-belief c language around the mean share of lady toddlers born every 12 months primarily based on a random sample of babies, you may find a top certain of zero.56 and a decrease certain of zero.48. those are the top and decrease bounds of the self-belief c programming language. The self-assurance level is 95%.

Learn more about sample proportion here: https://brainly.com/question/24232216

#SPJ4

A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.

To gauge the strength of the linear link between two variables, correlation coefficients are used.

A value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.

A zero correlation coefficient means there is no correlation between the two variables under comparison.

A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.

Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.

Learn more about correlation coefficient here:

brainly.com/question/4219149

#SPJ4

The store charged $24 for each pair of socks as the selling price.

Profit is the financial gain that is earned by a business or an individual after deducting all expenses from revenue. In other words, it is the amount of money that remains after all costs of producing and selling a product or service have been subtracted from the total revenue earned.

Revenue refers to the total amount of income earned by a business or an individual from the sale of goods or services during a specific period of time. It is the total amount of money that a business receives from its customers in exchange for its products or services.

In the given question,

Let's start by calculating the total revenue from the sale of 25 pairs of socks

Since the profit is 25% of the revenue, we can set up the equation:

Profit = 0.25 * Revenue

$150 = 0.25 * Revenue

Revenue = $150 / 0.25

Revenue = $600

The total revenue from selling 25 pairs of socks is $600.

To find the price per pair of socks, we can divide the revenue by the number of pairs:

Price per pair = Revenue / Number of pairs

Price per pair = $600 / 25

Price per pair = $24

Therefore, the store charged $24 for each pair of socks.

To know more about profit and revenue, visit:

https://brainly.com/question/15293328

#SPJ1

The measure of ab and df are 3cm and 7.5cm respectively

In order to determine the missing sides, we need to take the ratio of the similar sides as shown:

1) ab/de = ac/df

ab/de = ab+bc/df

Substitute the given values

ab/2 = ab+4.5/2+3

ab/2 = ab+4.5/5

2(ab+4.5) = 5ab
2ab+9=5ab

3ab = 9

ab = 3cm

Hence the measure of ab is 3cm

2) ae/ce = bf/df

24/9 = 20/df

24df =. 9(20)

24df = 180

df = 7.5cm

Hence the measure of ab and df are 3cm and 7.5cm respectively

Learn more on similar shapes here: https://brainly.com/question/11920446

#SPJ1

There are 104 cars in the parking lot.

According to statement there are between 90 and 115 cars on the lot.

So, {X| 90 < x < 115} (This renders an infinite solution set finite)

AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.

X ∈ {96, 104, 112,}

AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.

x = (96+104+112)/3

x = 104

There are 104 cars in the parking lot.

Learn more about ELIMINATION METHOD here https://brainly.com/question/13729904

#SPJ4

Answer:

The expression for the statement using absolute value notation is [tex]|x|\geq 100[/tex]

Step-by-step explanation:

It is given in the question that the distance from city A to city B is at least  100 miles.

It is required to express the statement using absolute value notation.

To express the statement using absolute value notation, deduce the statement in the form of an equation.

x represents the distance from city B to A city .

Deduce the statement in the form of an equation
[tex]|x|\geq 100[/tex]