Find the term that must be added to the equation x2+6x=7 to make it into a perfect square.

The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Given that the area of rectangle is 169 [tex]inches^{2}[/tex].

We have to find the smallest perimeter and dimensions of the rectangle.

let the length of rectangle be x inches and breadth be y  inches.

We know that area of rectangle is the product of its length and breadth. So,

Area=xy

169=xy

y=169/x

Perimeter of rectangle =2(x+y)

Put the value of y=169/x in the perimeter.

P=2(x+169/x)

P=2x+338/x

Differentiate both sides with respect to x.

dP/dx=2-338/[tex]x^{2}[/tex]

Again differentiate it with respect to x.

[tex]d^{2} P/dP^{2}[/tex]=676/[tex]x^{3}[/tex]

Because the second derivative is greater than 0 so the perimeter is minimum.

Put dP/dx=0 to get the value of x.

dP/dx=0

2-338/[tex]x^{2}[/tex]=0

2=338/[tex]x^{2}[/tex]

[tex]x^{2}[/tex]=169

x=[tex]\sqrt{169}[/tex]

x=13

Put the value of x in y=169/x

y=169/13

=13

To calculate the perimeter, put the values of x and y in P=2(x+y)

P=2(13+13)

=2*26

=52 inches.

Hence The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Learn more about perimeter at https://brainly.com/question/397857

#SPJ1

Answer:

y = -3x - 28

Step-by-step explanation:

y = mx + b is the slope-intercept of a line.  To write an equation in this form.  I need to find the slope (m) and the y-intercept (b).  Yay!  They gave us the slope (m).  It is -3.  Now we just need to figure out the y.  We can do that by plugging in the slope (-3) and using the x (-8) and the y (-4) that they gave us from the point to solve for b.

y = mx + b

-4 = -3(-8) + b  Multiple -3(-8) Remember a negative times a negative is a positive.

-4 = 24 + b  Now subtract 24 from both side of the equation

-28 = b  Now we can write the equation

y = mx + b

y = -3x + (-28) or y = -3x -28.  Adding a negative is the same as subtracting a positive.

The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

The given figure is a kite with two intersecting lines that are perpendicular to each other.

Since the lines are perpendicular to each other, hence;

m<1 = 90 degrees

For the measure of m<2

m<2 + 90 + 27 =180

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63degrees

Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees

Learn more on kites here: https://brainly.com/question/12160818

#SPJ1

Answer:

[tex]\frac{5x+2}{(x-4)(x+7)}[/tex]

Step-by-step explanation:

to obtain a common denominator

multiply the numerator/denominator of the first fraction by x + 7

multiply the numerator/denominator of the second fraction by x - 4

= [tex]\frac{2(x+7)}{(x-4)(x+7)}[/tex] + [tex]\frac{3(x-4)}{(x-4)(x+7)}[/tex]

simplify and add numerators leaving the common denominator

= [tex]\frac{2x+14+3x-12}{(x-4)(x+7)}[/tex]

= [tex]\frac{5x+2}{(x-4)(x+7)}[/tex]

Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR   (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.

Answer: 4

Step-by-step explanation:

The points are (-1, 1) and (5, 5).

So, the difference in the y coordinates is [tex]5-1=4[/tex].

The net change between the x-coordinates and y-coordinates on the graph is 6 units and 4 units respectively.

The coordinates from the given graph are (5, 5) and (-1, 1).

Given two points, (a, f(a)) and (b, f(b)) on the graph of f(x), the net change is the difference between the two f(x) values. Thus, net change is given by f(b)−f(a).

Here, the change in x-coordinates is 5-(-1) = 6

The change in y-coordinates is 5-1 = 4

Therefore, the net change between the x-coordinates and y-coordinates on the graph is 6 units and 4 units respectively.

To learn more about the net change between the coordinate points visit:

https://brainly.com/question/28716901.

#SPJ2

The diagonal of the rectangle solid is [tex]\sqrt{50[/tex]

The dimensions are given as:

3,4,5

The diagonal is calculated as:

[tex]d = \sqrt{3^2 + 4^2 + 5^2[/tex]

This gives

[tex]d = \sqrt{50[/tex]

Hence, the diagonal of the rectangle solid is [tex]\sqrt{50[/tex]

Read more about diagonal at:

https://brainly.com/question/654982

#SPJ1

It is a good practice for a server or bartender to not take patrons' drink orders too quickly

A bartender a person who prepares or serves alcoholic and some non-alcoholic beverages from behind a bar.

Below are some of the duties or responsibilities of a bartender:

So therefore, it is a good practice for a server or bartender to not take patrons' drink orders too quickly

Learn more about bartenders or servers:

https://brainly.com/question/14722415

#SPJ1

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

An equation is an expression that shows the relationship between two or more variables and numbers.

The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:

y = ax² + bx + c

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

The correct answer is A:3

Step-by-step explanation:

Answer:

I don't understand the array of numbers as written in the question.

Step-by-step explanation:

See attached image

Hi! ❄

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

The eccentricity of the conic section below is 1, since the given conic section is a parabola, and any parabola's eccentricity is 1.

Hope that made sense !!

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

[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]

Answer:

b

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] - 1 and a₁ = 2 , then

a₂ = 3a₁ - 1 = (3 × 2) - 1 = 6 - 1 = 5

a₃ = 3a₂ - 1 = (3 × 5) - 1 = 15 - 1 = 14

a₄ = 3a₃ - 1 = (3 × 14) - 1 = 42 - 1 = 41

a₅ = 3a₄ - 1 = (3 × 41) - 1 = 123 - 1 = 122

Using the together rate, it is found that it would take each person working individually 27 and 29 hours to paint the house.

The together rate is the sum of each separate rate.

In this problem, we have that the rates are given as follows:

Hence:

[tex]\frac{1}{d} + \frac{1}{d - 2} = \frac{1}{14}[/tex]

[tex]\frac{d - 2 + d}{d(d - 2)} = \frac{1}{14}[/tex]

d² - 2d = 28d - 28.

d² - 30d + 28 = 0

(d - 29)(d - 0.96) = 0.

Both d and d - 2 have to be positive, hence the solution is d = 29, and it would take each person working individually 27 and 29 hours to paint the house.

More can be learned about the together rate at https://brainly.com/question/25159431

#SPJ1

Answer:

300

Step-by-step explanation:

25 choose 2 (exactly how it sounds like)

= (25*24)/(2*1)=600/2=300

Answer:

30.

Step-by-step explanation:

2 digit Numbers which  have factor of  2:

2*3, 2*5, 2*7, 2*11, 2*13, 2*17, 2*19, 2*23, 2*29, 2*31, 2*37, 2*41, 2*43, 2*47.

That's 14.

Then there are the ones with factor 3:

3*5 ....... 3*31 = 9 numbers.

Then

5*7  to 5*19 = 5 numbers.

7*11 , 7*13 = 2 numbers.

Total is 14 + 9 + 5 + 2

=  30.

There are 30 2-digit numbers that are the product of two different primes.

To determine the number of 2-digit numbers that are the product of two different primes, we first need to identify the primes within the range of 10 to 99. The prime numbers within this range are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

To find the count of 2-digit numbers that are the product of two different primes, we can consider all possible pairs of these primes.

The numbers that yield 2-digit numbers with a multiple of 2 are:

(2, 5), (2, 7), (2, 11), (2, 13), (2, 17), (2, 19), (2, 23), (2, 29), (2, 31), (2, 37), (2, 39), (2, 41), (2, 43), (2, 47).

Total = 14

The numbers that yield 2-digit numbers with a multiple of 3 are:

(3, 5), (3, 7), (3, 11), (3, 13), (3, 17), (3, 19), (3, 23), (3, 29), (3, 31).

Total = 9

The numbers that yield 2-digit numbers with a multiple of 5 are:

distinct: (5, 7), (5, 11), (5, 13), (5, 17), (5, 19).

Total = 5

The numbers that yield 2-digit numbers with a multiple of 7 are:

Distincts: (7, 11), (7, 13)

Total = 2

Therefore, the total numbers of pairs are 14 + 9 + 5 + 2 = 30.

To learn more about multiplication;

https://brainly.com/question/19634536

#SPJ2

Depending on the number of teams, the possible numbers of students per team are in the set:

{2, 3, 4, 6, 9, 12, 18}

We know that there are 36 students divided equally into N teams.

Such that the number of teams is larger than 1 and smaller than 20.

Then we could have 2 teams, such that the number of students in each team is given by the quotient between the total number of students and the number of teams.

36/2 = 18

There are 18 students in each team.

Notice that the numbers of teams can only be factors of 36, where:

36 = 6*6 = 2*2*3*3

So the factors are:

2, 3, 2*3, 3*3, etc...

If there are 3 teams we have:

36/3 = 12 students per team.

If there are 6 teams we have:

36/6 = 6 students per team.

if there are 9 teams:

36/9 = 4 students per team.

If there are 12 teams:

36/12 = 3 students per team.

If there are 18 teams:

36/18 = 2 students per team.

These are all the possibilities.

If you want to learn more about factors:

https://brainly.com/question/219464

#SPJ1

The multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.

Therefore, the multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.

Know more about the multiplicative rule here:

https://brainly.com/question/17272828

#SPJ4

The conversion factor of the chicken recipe used at the banquet is 4.5.

An equation is an expression that shows the relationship between two or more variables and numbers.

Conversion factor = (new amount * portion size) / (old amount * portion size)

Hence:

Conversion factor = (60 * 3) / (10 * 4) = 4.5

The conversion factor of the chicken recipe used at the banquet is 4.5.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

At office 826 they will meet if they leave at the same time.

It is given that,

Agent J has recently been relocated from office 2013 to office 1. But his former office neighbor, Agent K is still in office 2014.

So, there are  (2014 - 1) - 1 = 2012 offices in between them.

It is given that,

Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute.

So,

Per minute they cross

= 25 + 36

= 61 offices.  

Thus, the time required for crossing all the 2012 offices is,

= 2012/61

= 32.9 ≅ 33 minutes

Then,

They will meet at

1 + 25(33) = 826 office (or)

2014 - 36(33) = 826 office (Negative since opposite direction)

Therefore, both of them meet at office 826.

Refer similar problem here:

https://brainly.com/question/1267118

#SPJ4

Answer:

31.

Step-by-step explanation:

We have the equation:

(2x - 17) / 3 = 15     where x is the number to be found.

Multiply both sides by 3:

2x - 17 = 45

2x = 45 + 17 = 62

x = 31.

Answer:

[tex]y = -3x+4[/tex]

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

A linear equation means that the y value changes at a constant rate as x increases by 1.

To find the rate of change you need to plug 2 ordered pairs into the formula:
[tex]\frac{y1-y2}{x1-x2}[/tex]

(x1,y1) can be any data point on this table. To make it easy, we will make it (2,-2).

(x2,y2) can be any data point other than the previously chosen point. So, we will choose (-1,7).

If we substitute this into the formula, previously mentioned, we get:

[tex]\frac{-2-7}{2-(-1)}[/tex]

When we solve this, we get the rate of change as -3.

This will be the "m" value in the linear equation format:
"y = mx+b"

The b value is the y-value of the data when x = 0.

So to get the b-value, you need to plug in one ordered pair into the "y=mx +b" equation.

"m" was the rate of change, which we found in the previous step.

Let's use (2,-2) as the chosen ordered pair.

By substitution, we end up with:
[tex]-2=-3(2)+b[/tex]

If we solve this out, we get:
[tex]b = 4[/tex]

m was -3 and b is now 4.

So, putting this into the equation "y = mx+b"
We get our answer as [tex]y=-3x+4[/tex].

The probability computed shows that there ia enough evidence to support the director's claim.

From the information given, the hospital director is told that 79% of the emergency room visitors are insured.

p = 0.79

q = 1 - 0.79 = 0.21

The computation of the z value is -1.91. This is a two tailed test.

The p-value will be:

= P(Z < -1.91)

= 0.0562 under the distribution table.

In this case, the p value is less than 0.10, therefore, we reject the null hypothesis.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

To predict the bagel sales numbers for the next month, Leigh could use Predict trend.

Given that Leigh has information on how many customers purchase bagel at her coffee shop.

We are required to answer the spreadsheet Leigh could use to predict bagel sales number for the next month.

Spreadsheet is developed for windows, macOS, Android and iOS.It features calculation through functions. In this we can use mathematical functions,logical functions, etc.

Leigh could use predict trend to predict the sales number of bagels of next month.

Hence predict trend could be used by Leigh to predict the sales for the next month.

Learn more about spreadsheets at https://brainly.com/question/26919847

#SPJ4

Question is incomplete as question should include the following:

What spreadsheet could Leigh use to predict the sales of next month?

pi/5.

Think of a clock as a circle. The minute hand when it moves around the clock will have traveled 360 degrees or 2*pi radians, traveling 2*pi radians in 60 minutes. So3 minutes out of 60 minutes is 1/10.  So the minute hand travels 1/10 of 2*pi radians (multiply 1/10 and 2*pi to get your answer).

Therefore your answer is pi/5 which is the letter a.

Well, a Radian, simply put, is a unit of measure for angles that is based on the radius of a circle. What this means is that if we imagine taking the length of the radius and wrapping it around a circle, the angle that is formed at the center of the circle by this arc is equal to 1 Radian.

Learn more about radians at

https://brainly.com/question/19758686

#SPJ4

The term used to describe a customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a cross-channel shopper.

A cross-channel shopper is a consumer who uses various combination of both several channels for the same purchase.

The customer has checked the pair of boots online but rather purchased the same boots at Macy's instead of purchasing online.

Therefore, a cross-channel shopper uses different purchasing channel to purchase a product.

Learn more about consumer:

https://brainly.com/question/380037

#SPJ1

Answer:

parallel because they have the same slope

Step-by-step explanation:

Answer:

3 cups for 60 biscuits

60/3=20

1 cup for 20 biscuits

95/20=4.75

4.75 cups of flour

Hope This Helps!!!

Answer:4.75

Step-by-step explanation: If 3 cups equals 60 biscuits then how much with you need for 95 biscuits

60/3 equals 20 95/20 equals 4.75 just to make sure lets multiply

475x20 equals 9500 now put the decimal back in place   95.00

Answer:

large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 la

or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, Root Tissues

Identify the root tissues. Record your answer under "Slide 5" on your lab report.

Answer:

see image

Step-by-step explanation:

The two circles will represent "starter" or "pudding" people and the overlap are both, but also don't forget people who chose neither. There must be 3-neither people. Because 6+7+8 only add to 21 and the question said there were 24 people.