A Short answer Question​

A parking lot's length is 4 yards longer than its width. The dimensions of the parking lot are width=9 and length =12.

Given that,

A parking lot's length is 4 yards longer than its width.

We have to determine the parking lot's measurements if the area is 117 square yards.

Let us take the width as x and we get the length as x+4.

We can write as,

x(x+4)=117

x²+4x=117

x²+4x-117=0

x²+13x-9x-117=0

x(x+13)-9(x+13)=0

(x+13)(x-9)=0

x+13=0    and     x-9=0

x=-13       and      x=9

Therefore, The dimensions of the parking lot are width=9 and length=12.

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the fuction f(x) is equal to:

now, to evaluate f(15) we have to replace x=15 so the equation is going to be equal to:

The coordinates of the point between points a to b are (5, -5/8)

We have the following endpoints on the segment

A = (-2, 2)

B = (6, -1)

The line ratio is given as the following fraction

Ratio, m : n = 7/8

Express the fraction as a ratio

So, we have

m : n = 7 : 8 - 7

Evaluate the difference

So, we have

m : n = 7 : 1

The coordinate of the point is then calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

Substitute the known values in the above equation

Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)

Evaluate the products in the above equation

So, we have

Point = 1/8 * (42 -2, -7 + 2)

Evaluate the sum and the difference

So, we have

Point = 1/8 * (40, -5)

Evaluate the products

So, we have

Point = (5, -5/8)

Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)

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Answer:A) 3

Step-by-step explanation:

(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

Given the time, the distance that the.womn drives will be 240 miles.

From the information illustrated, the woman drives out at 40 miles per hour, return over the same road at 30 miles per hour, and spends 8 hours away from home.

It should be noted that the average speed will be illustrated as:

= (2 × r1 × r2) / +r1 + r2)

= (2 × 40 × 30) / (40 + 30)

= 240/7

Since she drive for 7 hours, the distance will be:

= 240/7 × 7

= 240 miles.

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22 lots of 5-6 acres each can be created from the remaining area.

What is acres?
The imperial and US customary systems both utilise the acre as a unit of land area. One chain by one furlong (66 by 660 feet) is the traditional definition, which is exactly equal to 10 square chains, 1/640 of a square mile, 4,840 square yards (43,560 square feet), and 4,047 m² (or around 40% of a hectare). An acre may be stated to be exactly 4,046.8564224 square metres based on the international yard and pound agreement of 1959.

Out of  25 acres of land 6 2/3 acres can not be developed into lots.

Therefore land that is left = 25 - 6 2/3 acres

= 25 - 20/3 acres

= 55/3 acres

No.of 5/6 acre lots can the rest of the land be divided into = 55/3 / 5/6 lots

= 22 lots

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Answer:

No association

Explanation:

If there is a positive linear association, the graph would show something close to a straight line with a positive slope.

In the same way, if there is a negative linear association, the graph would be a straight line with a negative slope

If there is a nonlinear association we would see a curve.

Since all the data is dispersed in the graph, we can say that the best description of this relationship is No association.

Solution:

Given the a figure;

The figure is a square with the unshaded region is a semi circle.

The measure of the side lengths of the square is 25 ft

To find the area, A, of the shaded region, the formula is

Where

Substitute the values of the variables into the formula above

Hence, the answer is 379.56 ft² (nearest hundredth)

The correct option C { -3, 1, 2, 6} is the domain of the relation given.

For the given relation in the question;

The values which are input in the function is called domain.

In put values are -  { -3, 1, 2, 6}

Thus, domain of the given relation is  { -3, 1, 2, 6}.

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Answer: 8/33

Step-by-step explanation:

r = 0.242424....

100r= 24.2424....

100r - r = 99r

99r = 24

r = 24/99 = 8/33

If Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04  .

In the question ,

it is given that Jaya's account balance at beginning of month was $94.42 ,

first transaction +$31.87 ,

means Jaya deposited $31.87

So Account balance = $94.42+$31.87 = $126.29

Second transaction -$34.19 ,

means Jaya withdraw $34.19

So Account balance = $126.29-$34.19 = $92.10

third transaction -$58.47 ,

means Jaya withdraw $58.47

So Account balance = $92.10-$58.47 = $33.63

fourth transaction +$48.57,

means Jaya deposited $48.57

So Account balance = $33.63+$48.57 = $82.20

fifth transaction -$13.16 ,

means Jaya withdraw $13.16

So Account balance = $82.20-$13.16 = $69.04

Therefore , if Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04  .

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Answer:

  a)  x³, 1/x, x, sin(x)

Step-by-step explanation:

You want to know which list of functions has the same graph when reflected across both the y- and x-axes.

Reflection across the y-axis transforms the function to ...

  f(x) ⇒ f(-x)

Reflection across the x-axis transforms the function to ...

  f(x) ⇒ -f(x)

Hence, reflection across both axes transforms the function to ...

  f(x) ⇒ -f(-x)

A function that has the characteristic that f(x) = -f(-x) is an odd function. Its graph is symmetrical about the origin. We can check to see if the functions of interest match this definition of an odd function:

  x³ = -(-x)³ . . . . true

  1/x = -(1/-x) . . . . true

  x = -(-x) . . . . true

  sin(x) = -sin(-x) . . . . true

  cos(x) = -cos(-x) . . . . false

  e^x = -e^-x . . . . false

  |x| = -|-x| . . . . false

The basic functions that are odd are ...

  x³, 1/x, x, sin(x)

The value derived when 5 is divided by 312 is 62.40.

Division is the process of putting a number into distinct equal groups using another number.  The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other mathematical operations include addition, subtraction and multiplication.

312  ÷ 5 = 62.40

The long division is:

      62.4

5[tex]\sqrt{312}[/tex]

 - 30  

       12

     - 10

          20

        - 20

          00

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Okay, here we have this:

Considering the following equation:

Sale Price=Original Price*(100%-Percentage discount)

Replacing we obtain:

$1149=$1549*(100%-Percentage discount)

$1149/$1549=(100%-Percentage discount)

0.7417=100%-Percentage discount

Percentage Discount=100%-0.7417

Percentage Discount=1-0.7417

Percentage Discount=0.2583

Percentage Discount=25.83%

Finally we obtain that the discount percentage is 25.83%.

The larger number is 44 and the smaller number is 14.

The first step is to develop a system of equations using the information provided in the question.

y = 2x + 16 equation 1

x + y = 58 equation 2

Where:

y = larger number

x = smaller number

The next step is to substitute for y in equation 2 using equation 1.

x + 2x + 16 = 58

Combine similar terms:

x + 2x = 58 - 16

Add similar terms together:

3x = 42

Divide both sides of the equation by 3:

x = 42 / 3

x = 14

Substitute for x in equation 2:

14 + y = 58

y = 58 - 14

y = 44

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Option Negative 4 over fifteen times x plus four is equivalent to expression one third times the quantity 2 times x plus 12 end quantity minus 14 over 15 times x.

Firstly writing the mentioned expression in mathematical form -

Expression = 1/3(2x + 12) - 14x/15

Simplifying the expression by performing multiplication

Expression = 2x/3 + 12/3 - 14x/15

Taking LCM of these three denominator, we get 15

Expression = 2x×5 + 12×5 - 14x/15

Performing multiplication in numerator of the Right Hand Side of the expression

Expression = 10x + 60 - 14x/15

Performing subtraction

Expression = - 4x + 60/15

Rewriting the expression

Expression = - 4x/15 + 60/15

Performing division on extreme Right Hand Side of the expression

Expression = - 4x/15 + 4

Thus, the correct equivalent expression is option negative 4 over fifteen times x plus four.

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Thus total number of labor is 15.6

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. Basic algebraic expressions like 2x + 4 = 8 are created by performing operations on variables and constants, such as addition, subtraction, multiplication, and division. These algebraic expressions serve as the mathematical statements.

1 st week:

30% of 1200 hour = 360 hour

1 labor = 50 hour

y =360 hour

y= [tex]\frac{360}{50}[/tex]=7.2 technicians

Final two weeks : 2nd and 3rd week

50% of (1200hr - 360hr)= 50% of 840hr=420hr

1 labor = 50 hr

2 labor  = 100hr

x = 420 hr

x = 420×[tex]\frac{2}{100} =\frac{420}{50}[/tex]

=8.4 technicians

Thus total number of labor = x+y

= 7.2 +8.4

=15.6

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The perimeter of 180, the length and width of the rectangle with maximum area are 45 and 45.

Let x= the length and y= the width of the rectangle.

The area of the rectangle A=x y

2 x+2 y=180 because the perimeter is 180.

Solve for y

[tex]$&2 y=180-2 x \\[/tex]

[tex]$&y=90-x[/tex]

Substitute for y in the area equation.

[tex]$&A=x(90-x) \\[/tex]

[tex]$&A=90 x-x^2[/tex]

This equation describes a parabola that extends down. The maximum value of the area is at the vertex.

Rewriting the area equation in the form [tex]$a x^2+b x+c$[/tex]

[tex]$A=-x^2+90 x \quad a=-1, b=90, c=0$[/tex]

The formula for the x coordinate of the vertex is

[tex]$x=\frac{-b}{2 a}=\frac{-90}{2 \cdot-1}=45[/tex]

The maximum area exists found at x=45

and  [tex]$y=90-x=90-45=45$[/tex]

Given a perimeter of 180, the proportions of the rectangle with the maximum area are 45 × 45

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Answer:

[tex]y=\frac{1}{5}x^2+\frac{9}{5}x+4[/tex] or y = 1/5x^2+9/5x+4 (they are the same just different formats)

Step-by-step explanation:

In this case we are given the intercepts of the parabola (aka another name for a quadratic function). Since the intercepts are given, it makes the most sense to use intercept form.
The basic formula for intercept form is:
y=a(x-b)(x-c) where a, b, and c are all constants
b and c are the x intercept values.
plug in the values:
y=a(x-(-4))(x-(-5))=a(x+4)(x+5)

y=a(x+4)(x+5)   let's call this equation 1

unfortunately, there is still an "a" at the beginning, but that's where the y intercept is used.
Since (0,4) is a solution to the equation: y=a(x+4)(x+5), the values can be plugged into this equation to solve for a.
In this case, x = 0 and y = 4, so plug in those values

4=a(0+4)(0+5) = a(4)(5) = 20a
a = 1/5
Now, plug "a" back into equation 1
y=1/5(x+4)(x+5) this is the intercept form. However, the question ask for standard form, so it must be expanded

FOIL the parentheses (expand it) to get:
y=1/5(x^2+9x+20) = [tex]\frac{1}{5}x^2+\frac{9}{5}x+4[/tex]

A rotation is a rigid transformation, this means that the shape changes location but does not change its size. So even if triangle PQR was rotated to P'Q'R', the side lengths remain the same so that

PQ=P'Q'= 9

QR=Q'R'= 12

RP=R'P'= 7

The same happens with the angles

Q=∠Q'=35°

R=∠R'=48|°

180-()35+48= 97°

So

P'Q'=9

P'=97|°

Considering the given allowances, it is found that:

a) Tom's allowances are of $66,000, while Solomon's are of $40,000.

b) Tom's net income is of $151,500.

c) Solomon's net income is of $160,000.

An allowance is an exemption in the taxable income of a person, meaning that taxes are not paid over this amount.

Solomon is single, hence he only has the personal allowance of $40,000, and his net income will be of:

Solomon's net income = 0.75 x 160,000 + 40,000 = $160,000. (75% because 25% of the amount not claimed in allowances is paid in taxes).

Tom's allowances are given as follows:

Hence his total allowances are of:

$40,000 + $10,000 + $16,000 = $66,000.

His net income will be of:

Tom's new income = 0.75 x 114,000 + 66,000 = $151,500.

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Answer:

4.416 or rounded just 4

Step-by-step explanation:

23×12=276

276-223=53

53÷12=4.416

Answer:

3x-2y=10

2y=3x-10

Y=(3/2)x-5

Slope m=3/2

Answer:

See attachment.

Step-by-step explanation:

Slope-intercept form:

[tex]\boxed{y=mx+b}[/tex]

where:

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

Given inequality:

[tex]3x-2y < 10[/tex]

Rearrange the given inequality to make y the subject:

[tex]\implies 3x-2y+2y < 10+2y[/tex]

[tex]\implies 3x < 10+2y[/tex]

[tex]\implies 3x-10 < 10+2y-10[/tex]

[tex]\implies 3x-10 < 2y[/tex]

[tex]\implies 2y > 3x-10[/tex]

[tex]\implies \dfrac{2y}{2} > \dfrac{3}{2}x-\dfrac{10}{2}[/tex]

[tex]\implies y > \dfrac{3}{2}x-5[/tex]

Compare this with the slope-intercept form.  

Therefore:

When graphing inequalities:

To graph the given inequality using its slope and y-intercept:

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The domain for the rational function is the set of all real numbers except for 8, this is written as:

{x | x ∈ R, x≠8}

For any function f(x), the domain is the set of the possible inputs.

In this case, we have the rational function:

f(x) = (x - 3)/(x - 8)

Now, we start by assuming that the domain is the set of all real numbers, and then we remove all the problematic values.

Now, we can't divide by zero, so the value of x that makes the denominator zero needs to be removed, that is such:

x - 8 = 0

x = 8

So the domain is the set of all real numbers except for 8, this is written as:

{x | x ∈ R, x≠8}

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The steps of finding the line that best fits a data set are the following:

1.- Draw and label the axes of a graph

2.- Plot the data points

3.- Choose two points that best fit the data set

4.- Find the slope of the line through the points

5.- Substitute one point in the equation y = mx+b

6.- Solve for b

7.- Write the complete linear equation

So the answer is X1 = 5.51 and X2 = -0.85

The net force  acting on the object is 12.44 N.

In this problem, we are dealing with the magnitude of a vector, where A vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow showing the direction. A vector's magnitude  is the length of the vector. The magnitude of the vector a is signified as ∥a∥. Since we are provided with magnitudes of the three forces acting on the object which are (-8,5), (0,1), and (4, -7) So  we can represent them in terms of vectors which are :

F₁= -8i+5j

F₂= j

F₃ = 4i-7j

The magnitude of a vector is basically to add the individual horizontal and vertical components to get the horizontal and vertical components of the resultant force, then sum up the square of the  vertical components and horizontal of the resultant force and take the square root of the result.

F(net) =[tex]\sqrt{}[/tex]( F₁²+ F₂²+ F₃²)

  =[tex]\sqrt{}[/tex] ((-8)²+(0)²+(4)²) +((5)²+ (1)²+(-7)²)

 =[tex]\sqrt{}[/tex](64+16)+(25+1+49)

= 12.44  N

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Answer:

83

Step-by-step explanation:

3x³+2y-6

x= 3 and y = 4, we will plug in what x equals to for the x value, then we will plug in what y equals to for the y value

3(3³) + 2(4) - 6

now let's use order of operations (PEMDAS: parenthesis exponent multiplication division addition subtraction)

parenthesis first

3³ = 3·3·3= 27

3(27) + 2(4) - 6

there are no exponents so we will use multiplication

3·27 = 81

2·4=8

81 + 8 - 6

83

Remember that to find a distance between two numbers, we have to subtract the least number from the greater one. So, in this case, we have -4 and 5, where 5 is greater than -4.