Given a rectangle with the following dimensions: Area = 50 units Length = x + 10 units Width = x units Find the value of x.

Answer:

Step-by-step explanation:

Answer:

1. x = -4, y = -5

Chosen strategy was to substitute for y in the second equation since the first equation gives y in terms of x. This gives an equation in x which can be solved for x, then y can be found by substituting for x in the first equation

2.  x = -2, y = -3
Strategy used is to eliminate the x terms by simply adding the equations since the coefficients of x are the same but of opposite signs. Solve for y and use this value to solve for x by substituting in any one equation

3. x = -5, y = 6

Strategy used was to set the RHS of the equations equal to each other since both equations are  equations with y on the LHS. Solve for x then use this value to find y value

4. x = 0, y = 1

Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation

Step-by-step explanation:

Here is how I would answer this question. Remember there are multiple ways of solving a linear equation of two variables but looking at the equations and from experience, I have chosen the most efficient way (my opinion)

Q1.

y = x - 1     [1]
3x - 4y = 8  [2]

Since we are given y = x - 1 in Eq [1], an obvious strategy is to substitute for y in eqn [2]

=>  3x - 4y

=>  3x - 4(x-1)
=>  3x - 4x - 4(-1) =
=> 3x -4x + 4

=> -1x + 4

=> -x + 4

And we know that eqn [2] has 8 on the RHS

∴   -x + 4 = 8

Subtract 4 from both sides

-x + 4 - 4= 8 -4
-x = 4

Multiply by -1 both sides

x = -4

Substitute for x in equation [1] y = x - 1 to get
y = -4 - 1 = -5

Solution: x = -4, y = -5

Q2
3x + 2y = -12    [1}

-3x + 2y = 0     [2]

Here we can see the coefficients of x are the same but with opposite signs

Adding the two equations will eliminate the x terms and  allow us to solve for y which can be used then to solve for x

Adding [1] and [2] gives

3x + 2y + (-3x + 2y) = -12 + 0

4y = -12

y = -3

Substitute for y in equation [1]

=> 3x + 2(-3) = -12

=> 3x - 6 = -12

=> 3x = -12 + 6  (adding 6 on both sides

=> 3x = -6

x = -2

Solution x = -2, y = -3

Strategy used: Adding both equations to eliminate x terms since x coefficients are same but of different signs

Q3

y = 3x + 21  [1]

y = 2x + 16  ][2]

Since we have two expressions for y in terms of x, set the RHS of equations [1] and [2] to be equal and solve for x

=>  3x + 21 = 2x + 16

Subtract 2x from both sides

=> 3x - 2x  + 21 = 16

=> x + 21 = 16

Subtract 21 from both sides

x = 16 - 21  = -5

Substitute for x in equation [2]
y = 2x + 16

=> y =  2(-5) + 16

y = -10 + 16

y = 6

Solution: x = -5, y = 6

Q4

2x - 7y = -7   [1]

x + y = 1        [2]

We can make the coefficients of one of the variable in both equations the same and either add/subtract as necessary to eliminate one of the variable terms and solve for the other

Multiply [2] by 7 to get
7x + 7 y = 7   [3]

[1] and [3] have y coefficients same but of opposite signs so add [1] and [3] together

2x - 7y + (7x + 7y ) = - 7 + 7

2x + 7x - 7y + 7y = 0

9x = 0

x = 0

Sub for x in [2] x + y = 0 to get

0 + y = 1

or y = 1

Solution: x = 0, y = 1

Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation

Answer:

True

False

False

False

Step-by-step explanation:

1) a rhombus is a quadrilateral that has four equal sides.  The angles do not have to be 90°, but if they are 90°, it would be a square.

2) Rhombus has all four sides equal  A rectangle does not have to have all four side lengths equal.

3) A quadrilateral means that it is a four sides figure.  A rectangle is a 4 sided figure will parallel sides and opposite sides of equal length.

4) Parallelograms mean that the opposite sides have to be equal.  A rectangle is a parallelogram, but it does not have to be a square.

The final stock price will be equal to $87.57.

Percentage may be defined as a form of expressing a number as a fraction of hundred. To find the percentage of a number we divide the number by the total amount and then multiply the answer with hundred. We have the initial value of stock price as $83.60, and the stock price changed by 4.75%. Now, if we find 4.75% 0f $83.60 we get

(4.75/100) × $83.60 = $3.97 which is the change occurring in price. We add this amount in the initial amount and we get $83.60 + $3.97 = $87.57. If we look at the initial and final amount of stock, we see that Luis benefitted from the stock as he gained an amount of $3.97.

Learn more about Percentage at:

brainly.com/question/860173

#SPJ9

The probability of getting more than 52 girls in 100 births is 0.3446

This is further explained below.

Generally,  The ratio of females to boys per one hundred births is modeled here as:

[tex]\large X \sim Bin(n = 100, p = 0.5)[/tex]

Where

Bin shows binomial

n=sample size

p=sample proportion

The following is an approximation of this using the normal distribution:

[tex]\large X \sim N(\mu= np, \sigma^2 = np(1-p))\\\\\large X \sim N(\mu= 100*0.5 , \sigma^2 = 100*0.5*0.5)\\\\\large X \sim N(\mu= 50 , \sigma^2 = 25)\\\\\large X \sim N(\mu= 50 , \sigma = 5)[/tex]

In light of this, the formula for calculating the probability is as follows:

P(X > 52)

When we take into account the continuity correction factor, we obtain the following:

P(X > 52.5)

After transforming it into a regular variable according to the standards, the following is what we get:

P(Z > (52.5 - 50) / 5)

= P(Z > 0.5)

Taking this information from the usual normal tables, we get the following:

P(Z > 0.5) = 0.3085

in conclusion, the necessary probability in this scenario is 0.3085. It should be noted that we may do this without correcting the continuity, in which case:

P(X > 52)

[tex]= P(Z > (\frac{52 - 50}{ 5})[/tex]

= P(Z > 0.4)

= 0.3446

Hence, the necessary probability in this scenario is 0.3446.

Read more about probability

https://brainly.com/question/11234923

#SPJ1

The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up

The equations of the functions are given as

f(x) = 3x + 9

g(x) = 3x - 10

Let the translations from f(x) to g(x) be h and k

So, we have

g(x) = f(x + h) + k

This gives

f(x + h) = 3(x + h) + 9 + k

Open the brackets

f(x + h) = 3x + 3h + 9 + k

Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k

g(x) = 3x + 3h + 9 + k

This means that

3x + 3h + 9 + k = 3x - 10

Evaluate the like terms

3h + 9 + k = - 10

This gives

3h + k = - 19

Express -19 as -21 + 2

3h + k = -21 + 2

Express 21 as 3 * 7

3h + k = -3 * 7 + 2

By comparison, we have

h = -7 and k = 2

This means that the transformation is 7 units right and 2 units up

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

In the given figure, RL, LG and RG are line segments, which are portions of a line q connecting two endpoints.

Therefore, RL, LG and RG a are another name of line q.

LQ is not another name of line q.

So, option B is correct.

Using the graph, where the vertical axis represents ounces of food and horizontal axis represents the days bag was bought,

a. It took 24 days for the cat food to be 16 ounces

b. The weight of the bag before it was opened is 56 ounces,.

The graph represents the number of ounces of cat food that were left in the bag and the days it was bought.

The vertical axis represents the ounces of cat food bought while the horizontal axis represents the days since the bag was bought.

Therefore, according to the graph, the days the bag takes to contain 16ounces of cat food can be calculated as follows:

According to the y-axis, the ounces of cat food reduces as the days goes by.

If you trace 16 ounces of cat food to the horizontal side, it shows it took 24 days for the cat food to be 16 ounces.

The amount the bag weigh before it was open should be on zero's days.

Therefore, the amount of bag is 56 ounces before it was opened.

learn more on graphs here:https://brainly.com/question/24754667

#SPJ1

From the graph, the athlete spent 2 hours biking (from hour 1 to hour 3)

And, the athlete spent 3 hours running (from hour 3 to hour 6)

Then, the athlete spent equal amounts of time biking and running is false

The withdrawal of $170 can be represented as -$170.

Since withdrawal results in a deduction of the money from the total amount, Hence, it will be represented as a negative value.

To learn more about Integers, refer to:
https://brainly.com/question/1768255

#SPJ13

The number -32/95 belongs to the set of rational numbers.

Rational numbers may be defined as set of numbers which can be expressed in the form of p/q where q cannot be equal to zero. Irrational numbers may be defined as set of numbers which cannot be expressed in the form of p/q. Rational numbers can be of three types. Positive rational numbers are those in which either both the numerator and denominator are positive, or both are negative. Negative rational numbers are those in which either of numerator or denominator is negative. Zero is also a rational number which can be expressed in the form of p/q. Now, the number -32/95 is expressed in the form of p/q and the numerator is negative, so it is a negative rational number.

Learn more about Rational numbers at:

brainly.com/question/17572421

#SPJ9

Considering the definition of an equation and the way to solve it, if there are 21 students in the club and the T-shirt order costs a total of $187, each T-shirt cost $7.

An equation in mathematics is defined as an equality established between two expressions in which known elements and unknowns or unknown values appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the cost of each T-shirt, and knowing that:

the equation in this case is:

21x + 40= 187

Solving:

21x= 187 - 40

21x= 147

x= 147 ÷ 21

x=7

Finally, each T-shirt has a cost of $7.

Learn more about equations:

brainly.com/question/28247651

#SPJ1

If The printing company charges a certain amount for each shirt plus a setup fee of 40$. 21 students in the club and the t-shirt order costs a total of $187,Then each t shirt cost 7.

Two or more expressions with an Equal sign is called as Equation.

Given that, The printing company charges a certain amount for each shirt plus a setup fee of 40$. 21 students in the club and the t-shirt order costs a total of $187,

We need to find how much money dose each t-shirt cost.

Let x be the money for each t shirt.

By given data let us form a equation.

21x + 40= 187

Subtract 40 from both sides

21x=187-40

21x=147

Divide both sides by 21

x=7

Hence the cost each t shirt is 7.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

[tex]n-2=10n+42\\n-10n=42+2\\-9n=44\\\frac{-9n}{-9} =\frac{44}{-9} \\n=-\frac{44}{9}[/tex]

Hope this helps.

2 hours Eugene needs to travel before they are 290 km apart.

Given,

Average speed of Adam = 65 km/h

The average speed of Eugene = 80 km/h

Both travel in the opposite direction

Solution:

Let x be hours taken.

S = d/t

65 x+  80 x = 290

145x = 290

x = 2 hr

To learn about time, refer

https://brainly.com/question/17146782

#SPJ13

Answer:

answer c=3p in different ways.

Step-by-step explanation:

so the first one I think you put muliplys of 3..annd the second one you put a graph of 3

Answer:

Yes, it is possible

Step-by-step explanation:

Take a function y= f(x). When it is reflected across the x-axis the x-coordinates do not change but the y coordinates become the negative of the pre-image

In other words reflection f'(x) of f(x) over the x-axis is y = -f(x)

If we reflect f'(x) over the x-axis then the resultant reflection is

f''(x) = -f'(x) = -(-f(x)) = f(x)

So we get the original image after two consecutive reflections along the x-axis

Answer:

(x, y) to (-y,-x)

Step-by-step explanation:

You have to find the reflection which is the opposite so the opposite of x is -x the opposite of y is -y!

The number of seasoning batches required by the teacher is 4.

Given, there are 26 students in a class.

The teacher is adding 1 batch of hawaiian popcorn seasoning to 13 cups of popcorn.

Each student gets 2 cups of popcorn.

If 26 students are getting 2 cups of popcorn, then the total cups required by the students will be :

26×2

= 52 cups.

Now, one batch of seasoning is consumed by 13 cups.

how many batches of seasoning will be required for 52 cups = ?

⇒ 13 cups + 13 cups + 13 cups + 13 cups = 52 cups

Hence 4 batches of seasoning is required for 26 students to get two cups each popcorn with seasoning.

Therefore 4 batches of seasoning the teacher used.

Learn more about Solving equations here:

brainly.com/question/1214333

#SPJ1

Answer:

6.3

Step-by-step explanation:

Answer:

How do I take 20 % off a price?

Take the original price.

Divide the original price by 5.

Alternatively, divide the original price by 100 and multiply it by 20.

Subtract this new number from the original one.

The number you calculated is the discounted value.

Enjoy your savings!

Step-by-step explanation:

Answer:...

Step-by-step explanation:

Answer:

Yearly fee of $48 is better

Step-by-step explanation:

It is obvious. We know that a year have 12 months so if we compare between the $30 per months deal (which is $360 a year when we multiple it with 12) and the $48 a year deal, the difference is $312 which is a lott.

If Maria only want to use it for a month then its fine but if she want to use it more than 1 month, she definitely should choose the no 2 deal because if she even only rent it for 2 months using the no 1 deal ($30+$30=$60), the no 2 deal ($48) is far more better with a $12 difference.

Part A: Just like the top we know that its costs $34 per month and we need to know how much it would costs for 12 months/a year. So we just have to multiple it with 12=$408. Now which is better $495 or $408? Of course its $408 right? Maria could save $87 with renting the trombone than buying the trombone.

A reasonable domain and range of the function is as follows:

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

By critically observing the given sequence, we can reasonably and logically deduce that it follows the following function rule:

f(x) = -5(2)^{x - 1}

When x = 1, we have:

f(x) = -5(2)^{1 - 1}

f(x) = -5(2)^{0}

f(x) = -5

When x = 2, we have:

f(x) = -5(2)^{2 - 1}

f(x) = -5(2)^{1}

f(x) = -10

When x = 3, we have:

f(x) = -5(2)^{3 - 1}

f(x) = -5(2)^{2}

f(x) = -5(4)

f(x) = -20

When x = 4, we have:

f(x) = -5(2)^{4 - 1}

f(x) = -5(2)^{3}

f(x) = -5(8)

f(x) = -40

When x = 5, we have:

f(x) = -5(2)^{5 - 1}

f(x) = -5(2)^{4}

f(x) = -5(16)

f(x) = -80

Therefore, a reasonable domain and range of the function is given by:

Domain is equal to {1, 2, 3, 4, 5, ....}

Range is equal to {-5, -10, -20, -40, -80, ....}

Read more on domain here: https://brainly.com/question/14583155

#SPJ1

The statement that best describes the depth of the fish based on the given equation is: C. From the starting position of 3 meters below sea level, the fish is descending 7 meters per second.

A negative slope implies a negative constant rate of a linear equation. In slope-intercept form, the linear equation is expressed as y = mx + b, where the constant rate is represented as "m", while the starting value is represented as "b".

In the given scenario, the equation y = -7x - 3 models the depth, y, the fish swims below the sea level at x number of seconds.

This implies that:

The starting value (b) = -3, represents the starting position of the fish, which is 3 meters below the sea level.

-7 is the constant rate of the linear equation, which is the rate at which the fish is descending below the  sea level, which is: 7 meters per second. The best statement is therefore: C.

Learn more about linear equation on:

https://brainly.com/question/9101988

#SPJ1

Answer: 35 = a number

Step-by-step explanation: okay so since the number is being decreased wd know that that is subtraction. so what minus 8=27? well how about we add those two numbers to get the whole? so whats 8+27? 35. Hope this helped

Answer:

Step-by-step explanation:

35

X is the number of lillipops

y is the cost

the first point on the graph is 1 unit away from origin through x axis and 0.75 unit unit away from origin through y axis

so, x = 1 , y =0.75

The second coordinate is 2 unit away from origin through x axis and 1.5 unit away from origin through y axis

Answer: 0.75

Step-by-step explanation:

The value of x is -3.

Given,

[tex]m \angle{DRS}= x+143 \\m \angle{QRS}= 167\\m \angle{QRD}= x+30[/tex]

[tex]m \angle{DRS} +m \angle{QRD} = m\angle{QRS}[/tex]

x+143+x+30 = 167

2x = 167-173

2x = -6

x = -3

We add the two angles in it to find the value of x.

What are angles?

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Angles' Components

Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.

Arms: The angle's two sides are linked at a single end. The arms of an angle are OA and OB.

Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.

The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.

Learn more about Angles visit: https://brainly.com/question/7116550

#SPJ1

Answer:

15/100×400=60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

son 60 porque

400/10=40 entonces 40=10% entonces 5% es 20

40+20=60

Answer:

x = 7 km

Step-by-step explanation:

Perimeter of a polygon is  P = sum of the sides of a polygon

In this figure we are given all the sides except one designated as x and the perimeter

We can add up all the sides and solve for x

Sum of sides = 4 + 3 + 12 + 9 + x

Perimeter = 35

=> 4 + 3 + 12 + 9 + x = 35

=> 28 + x = 35

=> x = 35 - 38 = 7

The possible range of angle x is   x < 44

given data

In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘

In △ D E F , D E = 7 , E F = 12 and m ∠ D E F = ( 2 x − 6 ) ∘

A C > D F

Solution for angle x is gotten from the clue in A C > D F

This means that angle included by m ∠ A B C = 82 ∘ is greater than the angle included by m ∠ D E F = ( 2 x − 6 ) ∘

We therefore say that

82 ∘ >  ( 2 x − 6 ) ∘

82 + 6 > 2 x

88 > 2 x

divide both sides by 2

88 / 2 > 2 x / 2

44 > x

x < 44 degrees

Hence option g is the correct answer

Read more on inequalities here: https://brainly.com/question/25944814

#SPJ1