To make x² + 6x = 7 a perfect square, we add 16 to the equation.
In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.
The given equation can be shown as:
x² + 6x = 7,
or, x² + 6x - 7 = 0.
To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.
This can be shown as:
x² + 6x - 7 = 0,
or, x² + 2(x)(3) - 7 = 0, where we get b = 3.
Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.
Thus, we add 16 to both sides of the equation, to get:
x² + 2(x)(3) - 7 + 16 = 16,
or, x² + 2(x)(3) + 9 = 16,
or, (x + 3)² = 16, which gives us the required perfect square.
Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.
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How many 2 digit numbers are the product of two different primes
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.
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which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities
The multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.
What is the multiplicative rule?The multiplication rule is a method for calculating the likelihood of two events occurring at the same time (this is also one of the AP Statistics formulas). There are two rules for multiplication. P(A B) = P(A) P(B|A) is the general multiplication rule formula, while P(A B) is the specific multiplication rule (A and B).The multiplication rule is the multiplication of one event's probability by the likelihood of another occurrence. The law of independent assortment, Mendel's second law, stipulates that alleles of one gene segregate into gametes independently of alleles of another gene.Therefore, the multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.
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Use the drawing tools to form the correct answers on the grid.
Graph these equations:
Drawing Tools
2 Line
Show Instructions
-10 9 8 7 6 5 432
9
S
S
4
W
2
2
3
4
5
5 Fr
in
92
23
4
5678
9 10
Answer:
I don't understand the array of numbers as written in the question.
Step-by-step explanation:
See attached image
I thought of a number,double it,then decreased it by 17. Then I divided the results by 3 I got 15. What was my number
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.
ASAP help me 30 points
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.
I NEED IT NOW
Owen made 60% of the shots he attempted during his hockey practice. He made 18 shots. How many shots did Owen attempt during his hockey practice?
Leigh has information on how many customers purchase bagels at her coffee shop. With the bagel sales numbers from the past four months, she wants to
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.
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Question is incomplete as question should include the following:
What spreadsheet could Leigh use to predict the sales of next month?
Given the following system of equations for n≥2, find a5.
a1=2
an=3⋅an−1−1
Select one:
a. 41
b. 122
c. 365
d. 2,094
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
A hospital director is told that 79% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is not the expected percentage. A sample of 260 patients found that 195 were insured. At the 0.05 level, is there enough evidence to support the director's claim
The probability computed shows that there ia enough evidence to support the director's claim.
How to illustrate the probability?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.
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Through how many radians does the minute hand of a clock turn during a 3-minute period?
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.
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Two people can paint a house in 14 hours. Working individually one of the people takes 2 hours more than it takes the other person to paint the house. How long would it take each person working individually to paint the house?
( You are supposed to get a quadratic equation and then solve that, but I don't know how to get to it.)
Using the together rate, it is found that it would take each person working individually 27 and 29 hours to paint the house.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, we have that the rates are given as follows:
The together rate is 1/14.The separate rates are 1/d and 1/(d-2).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.
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What is the point slope equation of a line with slope -3 that contains the point (-8,-4)?
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 eccentricity of the conic section below is
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]
Create a linear equation for the following data:
Answer:
[tex]y = -3x+4[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
Step 1: Rate of ChangeA 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].
As a server or bartender, it is a good practice a. to have multiple interactions with patrons to evaluate their moods and needs. b. sample the patrons' drink to determine how strong they are. c. to not take patrons' drink orders too quickly upon arrival. d. to only serve the patrons one alcoholic drink every 90 minutes.
It is a good practice for a server or bartender to not take patrons' drink orders too quickly
Who is a bartender or server?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:
Greet customers and create a welcoming atmosphere.Use a till to take orders and payments.Handle cash.Serve drinks at the bar or at the table.Keep the bar clean and well stocked.Give advice on drinks to suit customers' tastes.Collect glasses and wash up.So therefore, it is a good practice for a server or bartender to not take patrons' drink orders too quickly
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I need help for upcoming test tomorrow, will give brainliest
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]
find the diagonal of a rectangle solid whose dimensions are 3,4,5 (please include explanation)
The diagonal of the rectangle solid is [tex]\sqrt{50[/tex]
How to determine the diagonal of a rectangle solid?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]
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If 3 cups of flour are needed to make 60 biscuits, how much flour is needed to make 95 of the same kind of biscuits
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
24 people go out for a meal.
13 have a starter, 15 have a pudding and 7 have both a starter and a pudding.
Show this information on a Venn diagram.
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.
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(n)
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.
Who is 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.
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This graph represents a quadratic function. An upward parabola on a coordinate plane vertex at (minus 2, 2) and passes through (minus 3, 5) and (minus 1, 5). What is the value of a in the function’s equation? A. 3 B. 2 C. -3 D. -2
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.
What is an equation?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.
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Answer:
The correct answer is A:3
Step-by-step explanation:
Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer
The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively
What is a kite?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
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(Determine the net change between the indicated points on the graph.
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).
What is the net change between the coordinate points?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.
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36 fifth graders are on a team with the same number on students on each team, if there are more then then 1 but less then 20 teams, how many students can be on each team?
Depending on the number of teams, the possible numbers of students per team are in the set:
{2, 3, 4, 6, 9, 12, 18}
How many students can be on each team?
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.
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determine whether the following pairs of line will be parallel perpendicular or neither x=y ;x=y+1
Answer:
parallel because they have the same slope
Step-by-step explanation:
There are 25 students in a class. How many ways can the teacher (randomly) pick two students for the lead roles in the class play?
Answer:
300
Step-by-step explanation:
25 choose 2 (exactly how it sounds like)
= (25*24)/(2*1)=600/2=300
Find the smallest perimeter and the dimensions for a rectangle with an area of 169 in2. Question content area bottom Part 1 The smallest perimeter for a rectangle with an area of 169 in2 is enter your response here in.
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.
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Given that zQ =zR and pv= PT, show that PQ = PR
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.
You’re catering a banquet and want to use a delicious chicken recipe that was a success with a previous client. However, the recipe makes 10, 4-oz portions, and you need to serve 60 people with 3-oz portions. Calculate the recipe conversion factor.
The conversion factor of the chicken recipe used at the banquet is 4.5.
What is an equation?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.
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Agents J and K work in a long hallway with 4000 equally-spaced, consecutive offices. The agents decide to walk toward each other so they can meet and have lunch together. Agent J has recently been relocated from office 2013 to office 1. His former office neighbor, Agent K, is still in office 2014. Assuming that Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute, what office will they meet at if they leave at the same time
At office 826 they will meet if they leave at the same time.
How many offices are there between agents J and K?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.
How much time is required for them to walk the whole distance?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.
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