The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Note that the answer to the above expression is c = 19.35 or x = -32.35. This is resolved using the  Quadratic Formula.

Given

(13+c) * c = 620

⇒ 13c + c² = 620

⇒ c² + 13c -620 = 0 .......................1

We now have a quadratic equation above which we shall solve as follows:

For the above expression   (1)

a = 1, b = 13 and c = -620

that is

1c² + 13c + (-620) =0

Applying the Quadratic Formula = [tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

Rather than say c =  we say x to avoid confusion

[tex]$x = \frac{-13 \pm \sqrt{13^2 - 4(1)(-620)}}{2(1)}$[/tex]

[tex]$x = \frac{-13 \pm \sqrt{169 + 2480}}{2}$[/tex]

[tex]$x = \frac{-13 \pm \sqrt{2649}}{2}$[/tex]

Therefore

x (or c as you would recall) = (-13 + 51.7)/2 or -13 - 51.7)/2

Thus, c = 19.35 or x = -32.35.

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answer is in the photo. lmk if you want the solution steps.

There are 20 pink flowers in Mr. Elliot's garden.

We can start by using the information provided to figure out how many flowers are not red or purple. We know that 1/8 of the flowers are red, and 1/4 of them are purple, so:

(1/8) * 128 flowers = 16 red flowers

(1/4) * 128 flowers = 32 purple flowers

So, 16 + 32 = 48 flowers are red or purple.

This means that 128 - 48 = 80 flowers are not red or purple.

Then we know that 1/4 of the remaining flowers are pink, so:

(1/4) * 80 flowers = 20 pink flowers

So, there are 20 pink flowers in Mr. Elliot's garden.

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The 4 types of multiplication properties are

Properties of multiplication : the four properties of multiplication are the following :

1) Commutative property of multiplication : The commutative property of multiplication says that when we multiply numbers, the answer remains the same even if the order of the numbers changes. Example : Consider two numbers 3 and 8. Then 3× 8 = 8× 3.

2) Associative property of multiplication :

The associative property of multiplication says that if we want to multiply any three numbers together, the answer will always be the same regardless of the order in which we multiply the numbers. Example: Consider any three numbers say 2, 3 and 7 we get, 2 ×( 3×7) = 2×21 = 42.

3) Distributive property of multiplication :

The distributive property of multiplication says that multiplication can be distributed over addition, just like subtraction. Example : Consider the calculation, 2×(3+1) = 2×3 + 2× 1 = 8.

4) Identity Property of multiplication :

The Multiplication Identity Property says that if we multiply any number by 1, the answer will always be the same number. For example, 1 × 3 = 3× 1 = 3

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Answer: 3/2

Step-by-step explanation:

To find the slope of the line, we are going to look at that change in rise (meaning the change of the y values) over the change in the run (meaning the change of the x values). The easiest way to do this is to pick two points on the line and use the slope equation: (y2-y1)/(x2-x1). I will pick two points at random, though multiple can work to find the slope.

point one: (1,-3) *it is easiest to make the first point to the left of point two*

point two: (3,0)

now, use the equation to solve.

(0 - -3)/(3-1) = (0+3)/(3-1) = 3/2

Hope this helps!

Alison spends $48 less on the five t-shirts. Typically, the rate is expressed as a percentage.

Typically, the rate is expressed as a percentage. Multiply the rate by the starting cost to determine the discount. Subtract the discount from the original price to obtain the sale price.

Therefore, a sale price of $70 will be achieved with a 30% discount on a $100 list price. The phrase can also mean simply the price at which anything sells. For instance, if a piece of art sells for $10 million, that price set a record.

Typically, the rate is expressed as a percentage. Multiply the rate by the starting cost to determine the discount. Subtract the discount from the original price to obtain the sale price.  

40% * 16 = 4.0 * 16 = 64 - 16 = 48 = $48.

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The  expression can be used to find the total cot of the meal with the gratuity is 1.18P

A gratuity is an amount of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

A party of 8 had a bill of p.

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people.

Since there are 8 people so, gratuity will be applied on the bill

Since bill is of amount p

So, gratuity of 18 % of p =  18% of  P  

                                          = 18/100 ×P

                                         = 0.18P

Now the total bill after adding gratuity : P+0.18P= 1.18P

Hence the total cost of the meal with the gratuity is $1.18p.

Therefore the  expression can be used to find the total cost of the meal with the gratuity is 1.18P

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Answer:

Answer: Option 4
The only one where m∠C = m∠D

Step-by-step explanation:

If you rotate the triangle on the right enough to align them then you will see that with the given information the third choice is the correct one.

Even without that process if m∠A = m∠E and m∠B = m∠F then for the two triangles to be similar, ∠C, the remaining angle of ABC and ∠D the remaining angle of DEF must be equal

So ∠C = ∠D is a must for the two triangles to be similar

Only the fourth option has this as one of the entries

The corresponding sides and angles are m∠C = m∠D

Similar figures are zoomed in or zoomed-out (or just no zoom) version of each other. They are scaled versions of each other, and by scale, we mean that each of their dimension(like height, width, etc linear quantities) are constant multiple of their similar figure.

Even without that process if m∠A = m∠E and m∠B = m∠F then for the two triangles to be similar, ∠C, the remaining angle of ABC,

Also, ∠D the remaining angle of DEF must be equal

Therefore, ∠C = ∠D is a must for the two triangles to be similar

Hence,  m∠C = m∠D

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Answer:

(a + 8)(a - 5)

Step-by-step explanation:

a² + 3a - 40 =

= (a      )(        )

Find two numbers that multiply to -40 and add to 3.

They are 8 and -5.

= (a + 8)(a - 5)

solution :

a²+3a-40

find the roots (2 numbers in which you can add and multiply to give 3a and 40)

(a-5) (a+8)

substitute the roots with 3a and multiply 40 by a²

a²-5a+8a-40a²

a(a-5) +8(a-40a²)

(a-5) (a+8)

We are aware that x2(a+b)x+ab=0 is one such equation if a and b are the roots of a quadratic equation.

In other words, if a times the square of the phrase after b plus b times the same expression not squared plus c equals 0, then you have an equation with the quadratic form. The original equation will change to a quadratic equation if the value in the () is replaced with a variable like t.

Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

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To work out the value of k, we can use the given information that fg(2) = 12. We know that fg(x) is the composition of two functions f and g, so we can write fg(x) = f(g(x))

In this case, fg(2) = f(g(2)) = f(k*2^2) = f(4k)

We know that fg(2) = 12. So we can substitute this value into the equation above:

12 = f(4k)

Since we are only interested in the value of k, we can set the equation equal to 12 and solve for k.

12 = 4k

k = 12/4

k = 3

Therefore, k = 3 is the value of k in the function g(x) = kx^2

Sine law  work's for acute angles ,obtuse angles and right triangles.

Sine Law states that "When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.It is given by :

[tex]\frac{a}{sin A}= \frac{b}{sin B}= \frac{c}{sin C}[/tex]

The Law of Sines is valid for obtuse triangles as well as acute and right triangles, because the value of the sine is positive in both the first and second quadrant—that is, for angles less than 180°. You can use this relationship to solve triangles given the length of a side and the measure of two angles, or given the lengths of two sides and one opposite angle.

Sine law  work's for acute angles ,obtuse angles and right triangles.

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Answer:

See picture attachment.

Hope this helps :)

Sam' speed for the first 15 minute of her journey is 80km/hr.

Speed refers to the rate of change of an object’s position in any direction. It is measured as the ratio of distance to the time (period in which the distance was covered). It is a scalar quantity. The formula for speed is given by:

Speed = Distance/ Time

Based on the provided travel graph,

Distance d = 20 km

Time t = 15 min = 15/60 = 0.25 hr

Hence,

Speed = d/t = 20/0.25 = 80km/hr

The speed in the first 15 minutes of Sam’s journey is 80km/hr.

Note: The question is incomplete. The complete question is: Sam drives his car on a journey. The travel graph for the first 15 minutes of his journey. Work out Sam' speed for the first 15 minute of her journey. Give your answer in km/h.

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Answer:

x = 83

Step-by-step explanation:

This question tests on the concept of Angle Properties

Properties required: Sum of Angles in a triangle.

Given information from the question:

x + 44° + 53° = 180°

x = 180° - 44° - 53°

x = 180° - 97°

x = 83°

Therefore the value of x is 83.

Answer:64

Step-by-step explanation:

a) The probability of event occur is  [tex]\frac{1}{5}[/tex].

b) The probability of event not occur is  [tex]\frac{4}{5}[/tex].

What is probability?

The likelihood of an event happening is gauged by probability. It is difficult to provide a complete prediction for many events. We can only anticipate the likelihood of an event occurring by using it. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here The ratio of the odds of an event occurring are 1:4.

Then probability of that the event will occur is ,

=>P(event will occur = [tex]\frac{1}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Now the probability of that event not will occur is ,

=> P(event will not occur) = 1 -[tex]\frac{1}{5}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Hence the answers are a) [tex]\frac{1}{5}[/tex] and b) [tex]\frac{4}{5}[/tex].

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A limit is generally written as

[tex]lim _{x- > c} f(x) = L[/tex]

It is read as “the limit of f of x, as x approaches c equals L”

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly defined.

Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as:

[tex]lim _{x- > c} f(x) = L[/tex]

It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.

Let us take an example to fully understand how to write limits.

[tex]lim_{x- > 2} 2x + 2[/tex]

= 2(2) + 2 = 6

This is how to write and represent limits.

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The triangle with the given sides is a right triangle and therefore with acute angular measures.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: The sides of a triangle here as 24,10,26

Now we know that the hypotenuse is the greatest side of a triangle.

and thus the hypotenuse is the side 26

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given, the length of sides of a triangle are 10, 24 and 26.

We have to find whether the given triangle is the right triangle.

By pythagoras theorem,

a²+b²=c²

Substituting the values

10²+24²=26²

By further calculation

100 + 576 = 676

LHS = RHS

Therefore, the given triangle is a right triangle and a right angle triangle is a acute triangle.

Hence, The triangle with the given sides is a right triangle and therefore with acute angular measures.

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The age of the sample of the carbon material is 19042 years.

We have to note that the half life of the sample has to do with the time that it takes for us to have only half of the original amount of the isotopes that are in the sample to be present.

Using the formula;

0.693/[tex]t{\frac{1}{2} }[/tex] = 2.303/t log (No/N)

[tex]t{\frac{1}{2} }[/tex] = Half life of the sample

t = time taken

No = Number of atoms initially present

N = Number of atoms at time t

Then;

0.693/5730 = 2.303/t log (No/0.1No)

0.693/5730 = 2.303/t  * 1

1.21 * 10^-4 = 2.303/t

t = 2.303/1.21 * 10^-4

t = 19042 years

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First step to solve system of equations using elimination method is to equate the coefficient of the variable you want to eliminate first in opposite sign and add both the equations.

As given in the question,

Let us consider two system of equations :

ax + by = c ___(1)

bx + ay = c ___(2)

First step to solve the system of equation by elimination method is :

To eliminate variable x:

Equate the coefficient of x by multiplying 'b' by (1) and '-a' by (2) we get,

abx + b²y = cb  __(3)

-abx - a²y = -ac __(4)

Now in second step you can add equation (3) and (4) and eliminate x-term.

Therefore, the first step while solving system of equation using elimination method is to equate the coefficient of eliminated term in opposite sign.

The above question is incomplete , the complete question is:

What is the first step in solving a system of equations by elimination method?.

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The coordinate of the point after a rotation of 90° counterclockwise will be (-3, -7).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The point is given below.

⇒ (-7, 3)

The coordinate of the point after a rotation of 90° counterclockwise will be given as,

(x', y') = (-y, x)

(x', y') = (-3, -7)

The coordinate of the point after a rotation of 90° counterclockwise will be (-3, -7).

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Using fundamental counting principle, the total total number of outfits that can be worn is  6.

A way for keeping track of all the possible outcomes in a circumstance is the fundamental counting principle.

If there are n ways to carry out one activity and m ways to carry out another activity after that, then there are n m n times n methods to carry out both of these activities, according to this assertion.

The Fundamental Principle of Counting dictates how choices are made depending on options.

The Fundamental Principle of Counting makes it easier to apply the selection method, which considers all feasible alternatives and their combinations for calculating the probability.

Total number of pants = 2

Total number of shirts = 3

Total number of outfits that can be worn = 3 × 2

= 6

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$ 240,437.74 - the balance of her fund on her 17th birthday.

His daughter turned 10 years old. Her reward was 5000.

subsequently, she began getting monthly interest compounded at a rate of 15%

She would thus have 5000 (the deposit from her birthday) + 15% = 5750 in her account at the end of the first month.

The amount would have been 5750 + 15% = 6612.50 at the conclusion of the second month.

She would have 6612.50 + 15% + 5000 (quarterly deposit) at the conclusion of the third month, which equals 12,604.38.

When she becomes 17 years old, if you keep doing these calculations, she will have a fun

$1,832,087,983.19

Only 145,000, including the 5,000 deposit made on her father's 17th birthday, would have been made by her father.

I would be grateful if someone could let me know where I can earn 15% compounded monthly.

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Answer:The arrow diagram represents a relation between two sets of data, but it does not provide enough information to determine whether it is a function or not. A function is a relation in which each element of the first set (the domain) is related to exactly one element of the second set (the range). In order to determine if the relation shown in the arrow diagram is a function, we need to know if each element in the domain corresponds to only one element in the range. From the arrow diagram we can not determine that.

As we have a set of ordered pairs (27,39), (31,27), (60,130), (45,67) and (123,180) and there is no repetition of the x-values (domain) or y-values (range) in the ordered pairs, we can say that the relation shown in the arrow diagram is a function.

Step-by-step explanation:

Answer:

Let the two numbers be x and y

Given ,

[tex]x + y = 95 \: \: ...(1)[/tex]

Also ,

[tex]y = x + 15 \: \: ...(2)[/tex]

Substiting equation 2 in equation 1 ,

[tex]x + x + 15 = 95 \\ \dashrightarrow \: 2x + 15 = 95 \\ \dashrightarrow \: 2x = 95 - 15 \\ \dashrightarrow \: 2x = 80 \\ \: \: \: \: dividing \: both \: sides \: by \: 2 \: \\ \dashrightarrow \: \cancel\frac{2x}{2} = \cancel\frac{80}{2} \\ \\ \dashrightarrow \: \: \boxed{ x = 40}[/tex]

Now , y = x + 15

therefore ,

[tex] y = 40 + 15 \\ \dashrightarrow \boxed{ y = 55 } [/tex]

Hence ,

the two numbers are 40 and 55 .

hope helpful! :)

Answer:

[tex]m\angle1=2^\circ\\m\angle2=88^\circ[/tex]

Step-by-step explanation:

As both angles are complementary, meaning they add up to 90°, we can simply solve for x using this sum and find each individual angle measure:

[tex]m\angle1+m\angle2=90^\circ\\(x-9)^\circ+(8x)^\circ=90^\circ\\x-9+8x=90\\9x-9=90\\9x=99\\x=11\\\\m\angle1=(x-9)^\circ=(11-9)^\circ=2^\circ\\m\angle2=(8x)^\circ=(8\cdot11)^\circ=88^\circ[/tex]

For the given data, independent variable = time in hours, dependent variable = distance traveled in miles.

An independent variable is one that is tweaked or changed to explore its effects when performing an experimental study. It is called "independent" because it is unaffected by any other study variables.

These are also referred to as independent variables:

Various justifications (they explain an event or outcome)

elements that predict (they can be used to predict the value of a dependent variable)

Those on the right side are variables (they appear on the right-hand side of a regression equation).

These expressions are particularly useful in statistics when calculating how effectively a change in one independent variable can forecast or explain changes in the dependent variable.

Given, the data is -

(0, 0), (2, 100), (3, 140), (4, 140), (5, 200), (8, 360)

time in hours = {0,2,3,4,5,8}

distance traveled in miles = {0, 100, 140, 140, 200, 360}

independent variable = time in hours

dependent variable = distance traveled in miles

Yes, the given relation is a function.

x variable represents the input of the relation

y variable represents the output of the relation

Domain = {0,2,3,4,5,8}

Range =  {0, 100, 140, 140, 200, 360}

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