the length of a rectangle is four less than twice it’s width. If the width is 6 inches what is the length of the rectangle ?

Answer: See below

Step-by-step explanation:

1) For the first question, we have to multiply the width by the length to find the area of the whole rectangle:

(4x-4)(x+1)= 4x^2 -4

2) For the second question, we have to multiply the width by the length to find the area of the shaded area in the rectangle:

(2x+2)(x-1)= 2x^2-2

3) The total area of the unshaded part of the whole triangle equals the area of the whole rectangle minus the shaded area:

4x^2-4 - 2x^2 -2 = 2x^2 - 6

By the concept of Permutations and Combinations, we get:

Number of ways to distribute 5 dollar bills among three children = 21

and

Number of ways to distribute 5 dollar bills such that each child gets at least one dollar = 6

Given:

To find: (A) number of ways to distribute the dollar bills among the children

(B) number of ways to do the same if each child gets at least a dollar.

Finding:

By using the formula: [tex]\binom{n+r-1}{r-1}[/tex],

Number of ways to distribute 5 dollar bills among three children = [tex]\binom{5+3-1}{3-1} = \binom{7}{2}= \frac{7\times6}{2}[/tex] = 21 ways.

Similarly, upon modifying the above formula as: [tex]\binom{n-1}{r-1}[/tex],

Number of ways to distribute 5 dollar bills such that each child gets at least one dollar is =

[tex]\binom{5-1}{3-1}= \binom{4}{2}=\frac{4\times3}{2}[/tex] = 6 ways.

To learn more about permutations and combinations, refer to the link: https://brainly.com/question/11732255

#SPJ4

The objective observations are so important to science because they are helpful in removing bias.

Objective observations are simply the direct observation recorded by an observer. It does not contain any personal interpretation by the observer. So it can be considered as a bias less observation.

In a scientific study, objective observations are equal to facts. An objective observer will not have a predetermined mind. So that observation will not contain prejudice. That is why it is not biased. So an objective observation helps in removing bias. So they are important in Science.

The opposite of objective observation is subjective observation. In a subjective observation, there is a chance of personal interpretations.

Learn more about objective observation at https://brainly.com/question/19541874

#SPJ4

6x² is the total area, in square feet, covered by the wood panels.

What is area?

So based on this, we can say that The expression to represent the total area, in square feet,

So, the wood panels is to be considered as the 6 ×  x² = 6x²

Learn more about area

brainly.com/question/27683633

#SPJ4

Answer:

28x-4

Step-by-step explanation:

Given

length (l)= 9x-4

Breadth (b) = 5x+2

Now

Perimeter (P) = 2(l+b)

=2(9x-4+5x+2)

=2(14x-2)

=28x-4

The measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

An angle that has a measure that is less than 90 degrees is classified as an acute angle.

Given the diagram below, the angle that is formed by rays AO and CO is angle AOC. The instrument shows that angle AOC is exactly 30 degrees.

30 degrees is less than 90 degrees and can therefore be termed an acute angle.

Therefore, the measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

Learn more about acute angle on:

https://brainly.com/question/6979153

#SPJ1

[tex]\angle DAE \cong \angle DCF[/tex]

by CPCTC.

Answer:

-6a - 48

The distributive property states that for an expression a(b + c), it can be evaluated to ab + ac.

To distribute, expand the algebraic expression using the aforementioned policy.

[tex]-6(a+8)[/tex]

Multiply a and b together.

[tex]-6\times a=-6a[/tex]

Then, multiply a and c together.

[tex]-6\times8=-48[/tex]

Finally, add the two values together.

[tex]-6a+(-48)=-6a-48[/tex]

[tex]\boxed{\bold{-6a-48}}[/tex]

Hey there!

Distributive Property formula:

a(b + c)

= a(b) + a(c)

= a * b + a * c

= ab + ac

Your equation: -6(a + 8)

Solving:

-6(a + 8)

= -6(a) - 6(8)

= -6 * a - 6 * 8

= -6a - 48

Therefore, your answer should be:

-6a - 48

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

x= 29 which is Friday of that Month.

As 1st February 2008 is Friday

By adding 7 to the date we will get the next Friday Date of that month

i.e., 1 + 7= 8

i.e., 8 is Friday

Again if we will add 7 in 8 then we will get another Friday

so by adding again i.e., 8 + 7= 15 which is again Friday

Then 15 + 7 = 22 which is Friday.

adding again we will reach final to final answer 22+ 7 = 29 which is Friday

after adding 29 with 7 we will get 36 and as we know there are only 30/31 days in a month.

So, by adding 7 to the date we will reach the next week.

To know further to find the days of that month refer to the link given below:

   https://brainly.com/question/2096634

#SPJ4

Answer:

z divided by 4 is 12

48 divided by 4 is 12

Answer:

A - Domain - [0,9] , Range - [0,3] , It represents a function because it passes the (vertical line test).

B - (0,0)

C - I'm not sure about this question but, If i would guess, (0,0) (9,3).

Step-by-step explanation:

For question C i think It means maximum and minimum points on the graph.

Im sorry if you get any of it wrong.

Answer:

184

Step-by-step explanation:

Answer:

v < 2

Step-by-step explanation:

To solve this problem, start by adding 12 to each side of the inequality, to clear the -12 from the left side. 10 + (-12) is 2, so your answer is v < 2.

Hope this helps! Let me know if you have any confusion!

When the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

The general equation of the circle is [tex]x^{2} +y^{2}+2gx+2fy+c=0[/tex]

Where (-g,-f) is the coordinates of the circle

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

Divide the equation by 2

[tex]x^{2} +y^{2}-6x+4y-12=0[/tex]

Compare the equation with general form

2g= -6

g= -3

2f= 4

f= 2

The center of the circle (-g,-f) = (3,-2)

The radius of the circle = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]

Substitute the values in the equation

r= [tex]\sqrt{(-3)^{2}+2^{2}- (-24) }[/tex]

[tex]=\sqrt{9+4+24} \\=\sqrt{37}[/tex]

=6.08 units

Hence, when the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

Learn more about circle here

brainly.com/question/23799314

#SPJ1

Answer:

Geometric.

Step-by-step explanation:

For example

2, 4, 8, 16

where the common ratio is 4/2 = 8/4 = 16/8 = 2.

Answer:

42.5

Step-by-step explanation:

You have to multiply 7 times 5 equals 35. Then you multiply 7 times 2 which is 14 plus 3 equals 5. So you have 175 as the first number. Then you put a 0 under that number. You multiply 5 times 1 which is 5 and 2 times 1 which is 2. Now you have 250 as your second number.

Add 175 plus 250 which is 425 but you have to put the decimal between 2 and 5. Now you have 42.5

Hope that helps

The average rate of change for the function will be 234.

It is the average amount by which the function is modified per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 3ˣ + 17

The value of the function at x = 3 will be

f(x) = 3³ + 17

f(x) = 27 + 17

f(x) = 44

The value of the function at x = 6 will be

f(x) = 3⁶ + 17

f(x) = 729 + 17

f(x) = 746

Then the average rate of change for the function will be

Average rate = [746 - 44] / [6 - 3]

Average rate = 702 / 3

Average rate = 234

The average rate of change for the function will be 234.

More about the average rate change of a function link is given below.

https://brainly.com/question/23715190

#SPJ1

Answer:

184-70

=114

114/9.5

=12

Step-by-step explanation:

1. Needed points is 184 and rewards points was 70

2. So he need extra 114 points for free movie ticket

3. 114 divide by 9.5 which is earn piont for every time he buy ticket

The equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Marques has a points card for a movie theater. • He receives 70 rewards points just for signing up

Let x be the number of visits.

The linear equation can be framed as follows:

70 + 9.5x = 184

9.5x = 184 - 70

After solving the above linear equation in one variable:

9.5x = 114

x  = 12

Thus, the equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ5

Answer:

good luck broooooooooooo

Answer:

-1

Step-by-step explanation:

→ -4 + (6/2)

→ -4 +3 = -1

So, the answer is -1.

Answer:

2 [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

.10

change it to 10/100

reduce by 10

1/10

Answer: 2 1/10

Step-by-step explanation:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.

2 1/10

A translation along the directed line segment NB then a reflection over the vertical line about B so sequence A is correct therefore option (A) will be correct.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Given the triangle MNO and ABC

Now,

If we translate MNO along the directed line segment NB and reflect over B then M will coincide with A and N with B and O with C.

In sequence B if we reflect on MO then M will not coincide with A and it will not form a triangle ABC.

Hence "A translation along the directed line segment NB then a reflection over the vertical line about B".

To learn more about the transformation of graphs,

brainly.com/question/3099136

#SPJ4

The given question has missed an image, incomplete question is given in the image,

At 0.6% per year compound interest. Brian will get 6841.19 after 6 years.

The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest.

It is said that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely computed on the principal sum.

Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

Based on the given conditions, formulate: 6600×(0.6%+1) 6

Evaluate the equation/expression: 6841.19264

Round the number: 6841.19

Answer: 6841.19

To learn more about compound interest from given link

https://brainly.com/question/12325365

#SPJ9

Answer: 4/9 es racional - cualquier fracción adecuada x/y es un número racional. Expresado como un decimal, esto es igual a 0.4 recurrente (es decir, 0.44444...)

Step-by-step explanation: ¡Espero que esto ayude!

El número 4/9 es un número racional. Es una razón, o fracción, formada por dos números enteros, 4 y 9.

In a poll conducted by a certain research​ center, 1046 adults were called after their telephone numbers were randomly generated by a​ computer, and were able to correctly identify the random sampling.

Each sample has an equal chance of being chosen as part of the sampling technique known as random sampling. A randomly selected sample is intended to be a fair representation of the entire population.

In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a procedure for randomly choosing a sample.

Learn more about random sampling here

https://brainly.com/question/24466382

#SPJ4

Answer:

k = x^3+y^3+z^3

Step-by-step explanation:

Solve for k by simplifying both sides of the equation, then isolating the variable.

Hope this helps.

Answer is 32.5 because the other ones isnt it

Answer: Total number of employees are employed by the store = 15 employees.

Step-by-step explanation:

The ratio of Full time employees to Not Full time employees would be 1 to 4.

Let, Full time employees F =1      

Not Full time employees N =4

We can write:

                                F/N = ¼

Cross multiply to get:

                                 N=4F

If 5 more Full time employees were hired, then the ratio would be 2 to 3.

This would be mean there are no (F+5) Full time employees.

Also there are still Not Full time employees.

We can write:

                             (F+5) / N = 2/3

Cross multiply to get:

                              3(F+5) =2N

Expand to get:

                               3F+15=2N

Replace N with 4F to get:      

                               3F+15=2(4F)

Solve to get:

                              3F+15=8F

                              15=8F-3F

                              15=5F

                                F=3

So, there are presently 3 Full time employees.

How many employees does the store have?

Since           F=3,

we can use the equation N=4F

To help find the value of N Replace F with 3 to get:

                              N = 4(3)

Solve to get:

                               N=12

So, Full time employees F=3    

Not Full time employees N=12

Then, Total number of employees = F+N

                                                         = 3+12

                                                         = 15.

Hence, Total number of employees = 15 employees.

Learn more about event correlation here: brainly.in/question/15910549

#21179

Answer:

When i24 is increased by 25% the answer is 30

Answer:

True

Step-by-step explanation:

I'm assuming this is a true or false question, and so the answer is true. Because two negatives (-) equal a positive. So, 45,000 - (-800) actually is 45,00 + 800 because there was as subtraction sign and a negative sign.

Answer:

Step-by-step explanation:

45,000-(-800)=45,800

45,000-(-800) does =45,800

Answer:

[tex]\mathrm{Focus:\;\;} \left(-\frac{5}{3},\:2\right)[/tex]

[tex]\mathrm{Directrix:\;\;}x=-\frac{1}{3}[/tex]

Step-by-step explanation:

The standard equation for a parabola is

[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]

with vertex at (h, k) and a focal length of |p|

[tex]\mathrm{Rewrite}\:x=-\frac{3}{8}\left(y-2\right)^2-1\:\mathrm{in\:the\:standard\:form}[/tex]:

[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}[/tex]

[tex]x+1=-\frac{3}{8}\left(y-2\right)^2-1+1[/tex] or

[tex]x+1=-\frac{3}{8}\left(y-2\right)^2[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-\frac{3}{8}[/tex]
[tex]\frac{x+1}{-\frac{3}{8}}=\frac{-\frac{3}{8}\left(y-2\right)^2}{-\frac{3}{8}}[/tex]

[tex]\mathrm{Simplify}[/tex]
[tex]-\frac{8x}{3}-\frac{8}{3}=\left(y-2\right)^2[/tex]

[tex]\mathrm{Factor\:}-\frac{8}{3}[/tex]
[tex]\left(-\frac{8}{3}\right)\left(x+\frac{-\frac{8}{3}}{-\frac{8}{3}}\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{Simplify}[/tex]
[tex]\left(-\frac{8}{3}\right)\left(x+1\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{Factor\:}4[/tex]
[tex]4\cdot \frac{-\frac{8}{3}}{4}\left(x+1\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{Simplify}[/tex]
[tex]4\left(-\frac{2}{3}\right)\left(x+1\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{We\; can\; rewrite\:this\;as}[/tex]
[tex]4\left(-\frac{2}{3}\right)\left(x-\left(-1\right)\right)=\left(y-2\right)^2[/tex]

Comparing this with the standard form we get
[tex]\left(h,\:k\right)=\left(-1,\:2\right)[/tex]
[tex]\:p=-\frac{2}{3}[/tex]

The parabola is symmetric around the x-axis.

The focus lies a distance [tex]p[/tex] from the center [tex]\left(-1,\:2\right)[/tex] along the x axis

So focus is at
[tex]\left(-1+p,\:2\right)[/tex] [tex]=\left(-1+\left(-\frac{2}{3}\right),\:2\right)[/tex] [tex]=\bold{ \left(-\frac{5}{3},\:2\right)}[/tex]

The parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis at a distance -p from the center

[tex]x=-1-p[/tex]

[tex]x=-1-\left(-\frac{2}{3}\right) = \bold{-\frac{1}{3}}[/tex]