Answer:
2
Proof:
x^2 + 6x + 7 + 2 = x^2 + 6x + 9 = x^2 + 6x + 3^2 = (x + 3)^2
The value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2
What is trinomial?"It is a polynomial which consists of three terms."
What is square trinomial?"A trinomial with degree 2"The general form of square trinomial is [tex]ax^{2} +bx+c[/tex] where a ≠ 0What is perfect square trinomial?"A square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac"
For given question,
We have been given a square trinomial.
[tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex]
We need to find the number in the blank space, so that the given trinomial would be complete square.
Let 'm' be the required number.
So, the trinomial would be [tex]x^2 + 6x + (7 +m)[/tex]
Comparing above square trinomial with [tex]ax^{2} +bx+c[/tex],
we have a = 1, b = 6, c = 7 + m
We know, a square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac
⇒ b² = 4ac
⇒ 6² = 4 × 1 × (7 + m)
⇒ 36 = 4 × (7 + m)
⇒ 9 = 7 + m
⇒ m = 2
This means, we need to add 2 in the blank space.
So, the square trinomial would be,
[tex]x^2 + 6x + 7 + \underline {2}\\\\= x^2 + 6x + 9\\\\= (x + 3)^2[/tex]
Therefore, the value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2
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We want to construct a box with a square base and we currently only have 10m2 of material to use in construction of the box. Assuming that all material is used in the construction process, determine the maximum volume that the box can have.
Answer:
The maximum volume of the box is:
[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]
Step-by-step explanation:
Given
[tex]Surface\ Area = 10m^2[/tex]
Required
The maximum volume of the box
Let
[tex]a \to base\ dimension[/tex]
[tex]b \to height[/tex]
The surface area of the box is:
[tex]Surface\ Area = 2(a*a + a*b + a*b)[/tex]
[tex]Surface\ Area = 2(a^2 + ab + ab)[/tex]
[tex]Surface\ Area = 2(a^2 + 2ab)[/tex]
So, we have:
[tex]2(a^2 + 2ab) = 10[/tex]
Divide both sides by 2
[tex]a^2 + 2ab = 5[/tex]
Make b the subject
[tex]2ab = 5 -a^2[/tex]
[tex]b = \frac{5 -a^2}{2a}[/tex]
The volume of the box is:
[tex]V = a*a*b[/tex]
[tex]V = a^2b[/tex]
Substitute: [tex]b = \frac{5 -a^2}{2a}[/tex]
[tex]V = a^2*\frac{5 - a^2}{2a}[/tex]
[tex]V = a*\frac{5 - a^2}{2}[/tex]
[tex]V = \frac{5a - a^3}{2}[/tex]
Spit
[tex]V = \frac{5a}{2} - \frac{a^3}{2}[/tex]
Differentiate V with respect to a
[tex]V' = \frac{5}{2} -3 * \frac{a^2}{2}[/tex]
[tex]V' = \frac{5}{2} -\frac{3a^2}{2}[/tex]
Set [tex]V' =0[/tex] to calculate a
[tex]0 = \frac{5}{2} -\frac{3a^2}{2}[/tex]
Collect like terms
[tex]\frac{3a^2}{2} = \frac{5}{2}[/tex]
Multiply both sides by 2
[tex]3a^2= 5[/tex]
Solve for a
[tex]a^2= \frac{5}{3}[/tex]
[tex]a= \sqrt{\frac{5}{3}}[/tex]
Recall that:
[tex]b = \frac{5 -a^2}{2a}[/tex]
[tex]b = \frac{5 -(\sqrt{\frac{5}{3}})^2}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{5 -\frac{5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{\frac{15 - 5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{\frac{10}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{\frac{5}{3}}{\sqrt{\frac{5}{3}}}[/tex]
Apply law of indices
[tex]b = (\frac{5}{3})^{1 - \frac{1}{2}}[/tex]
[tex]b = (\frac{5}{3})^{\frac{1}{2}}[/tex]
[tex]b = \sqrt{\frac{5}{3}}[/tex]
So:
[tex]V = a^2b[/tex]
[tex]V =\sqrt{(\frac{5}{3})^2} * \sqrt{\frac{5}{3}}[/tex]
[tex]V =\frac{5}{3} * \sqrt{\frac{5}{3}}[/tex]
[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]
The maximum volume of the box which has a 10 m² surface area is given below.
[tex]\rm V_{max} = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
We want to construct a box with a square base and we currently only have 10 m² of material to use in the construction of the box.
The surface area = 10 m²
Let a be the base length and b be the height of the box.
Surface area = 2(a² + 2ab)
2(a² + 2ab) = 10
a² + 2ab = 5
Then the value of b will be
[tex]\rm b = \dfrac{5-a^2}{2a}[/tex]
The volume of the box is given as
V = a²b
Then we have
[tex]\rm V = \dfrac{5-a^2 }{2a}* a^2\\\\V = \dfrac{5a - a^3}{2}\\\\V = \dfrac{5a}{2} - \dfrac{a^3}{2}[/tex]
Differentiate the equation with respect to a, and put it equal to zero for the volume to be maximum.
[tex]\begin{aligned} \dfrac{dV}{da} &= \dfrac{d}{da} ( \dfrac{5a}{2} - \dfrac{a^3}{2} ) \\\\\dfrac{dV}{da} &= 0 \\\\\dfrac{5}{2} - \dfrac{3a^2 }{2} &= 0\\\\a &= \sqrt{\dfrac{5}{2}} \end{aligned}[/tex]
Then the value of b will be
[tex]b = \dfrac{5-\sqrt{\dfrac{5}{2}} }{2*\sqrt{\dfrac{5}{2}} }\\\\\\b = \sqrt{\dfrac{5}{2}}[/tex]
Then the volume will be
[tex]\rm V = (\sqrt{\dfrac{5}{2}} )^2*\sqrt{\dfrac{5}{2}} \\\\V = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]
More about the differentiation link is given below.
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Five ninths of what is equal to 30? 54 15 35 45
given the points (-4,8)and(6,-12)
1 Determine the midpoint of the line segment connecting the points.
2 Determine the distance separating the two points
Answer:
1.
[tex]midpoint = ( \frac{ - 4 + 6}{2} , \: \frac{ - 12 + 8}{2} ) \\ = (1, \: - 2)[/tex]
2.
[tex]distance = \sqrt{ {( - 4 - 6)}^{2} + {( - 12 - 8)}^{2} } \\ = \sqrt{500} \\ = 22.4 \: units[/tex]
Nicole works in a sporting goods store
and earns $324 a week and 5% of her
sales. One week Nicole earned $432.
What were her sales that week? Write
and equation and solve.
Answer:
2,160
Step-by-step explanation:
432-324=108 earnings based on sales
sales x 5%=108
sales=108/.05
sales=2,160
you sight a rock climber on a cliff at a 32° angle of elevation. your eye level is 5.5 feet above the ground and you are 1000 feet from the base of the cliff. what is the approximate height of the rock climber from the ground?
Answer:
630 feets
Step-by-step explanation:
From the triangle attached :
Using trigonometry, the height h, which is the height of climber to your eye level :
Tan θ = opposite / Adjacent
Tan 32 = h / 1000
h = tan 32 * 1000
h = 0.6248693 * 1000
h = 624.86935
Height from the ground :
624.86935 + 5.5
= 630.369 feets
= 630 feet
Please help me please !!
The times taken by 18 people to complete a puzzle are shown
No they aren't
___________
HELP ASAP PLZ will give u brainliest if u answer it first find the length of df
Answer:
3.75
Step-by-step explanation:
DF = 6/24 × 15 = 3.75
________________
Based on past experience, a bank believes that 8.9 % of the people who receive loans will not make payments on time. The bank has recently approved 220 loans. What must be true to be able to approximate the sampling distribution with a normal model
Answer:
To be able to approximate the sampling distribution with a normal model, it is needed that [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], and both conditions are satisfied in this problem.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they will make payments on time, or they won't. The probability of a person making the payment on time is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The sampling distribution can be approximated to a normal model if:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Based on past experience, a bank believes that 8.9 % of the people who receive loans will not make payments on time.
This means that [tex]p = 0.089[/tex]
The bank has recently approved 220 loans.
This means that [tex]n = 220[/tex]
What must be true to be able to approximate the sampling distribution with a normal model?
[tex]np = 220*0.089 = 19.58 \geq 10[/tex]
[tex]n(1-p) = 220*0.911 = 200.42 \geq 10[/tex]
To be able to approximate the sampling distribution with a normal model, it is needed that [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], and both conditions are satisfied in this problem.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP I WILL GIVE BRAINLIEST
Jeremy read 243 pages on Saturday. He read 53 fewer pages on Sunday.
How many pages did he read in all?
243 = the pages read on Saturday
243 - 53 = 190 = the pages read on Sunday
190 + 243 = 433 = total pages read
Answer = 433
A=1/2h(B+b);A=81,B=8,b=1 what is h
Answer:
81=1/2h×9,
81=1/18h
1458h=1
h=1/1458
Answer:
h=1/ 1458
hope it is helpful to you
i need help! plz (listing BRAINLIST and giving points) :D
Answer:
angle M = 60
angle Q = 70
Step-by-step explanation:
M 180/3 = 60
Q 180-40 = 140/2 = 70
in a rectangle how many opposite sides are equal
Answer and Step-by-step explanation:
This is for your other question in case you don't see it.
1. 2 pairs (aka 4 sides) of Opposite Sides are equal
2. AB and DC are parallel, and AD and BC are parallel
3. Angles BDC and ACD are equal, angles DAC and DBC are equal, the angles ADB and BCD are equal, angles CAB and DBA are equal
4. 4 right angles
5. AB and DC are equal, and AD and BC are equal
6. 4 Triangles
7. False
8. Diagonals of a rectangle.
#teamtrees #PAW (Plant And Water)
10. (10.04 MC)
What are the period and phase shift for f(x) = -4 tan(x − n)? (1 point)
T
Period: n; phase shift: x =
2
Period: n; phase shift: x = n
TT
Period: 2n; phase shift: x =
2
Period: 2n; phase shift: x = 0
Answer:
Period: [tex]\pi[/tex]
Phase shift: n
Step-by-step explanation:
Tangent function:
Has the following format:
[tex]f(x) = \tan{ax - n}[/tex]
In which the period is [tex]\frac{\pi}{x}[/tex] and the phase shift is n.
In this question:
[tex]f(x) = -4\tan{(x-n)}[/tex]
[tex]a = 1[/tex], and thus, the period is [tex]\pi[/tex], with a phase shift of n.
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $2,033.00, and the tax rate in the area is 7%, what was the pre-tax subtotal?
Answer:
i believe the pre-tax subtotal would be 1890.69
Step-by-step explanation:
the 2,033 represents 100%. to remove that 7% you would do
.93 • 2,033 which gives you 1890.69
A parking garage charges the following amount for cars parked in the garage:
For the first hour that a car is parked in the garage, there is no charge. After the first hour, for the next two hours that a car is parked in the garage, there is a $5 charge. After the third hour, the garage charges $2 for each additional hour that the car is parked in the garage. If a car is parked in the garage for a fraction of an hour, the garage will charge that fraction of the additional hourly rate.
1. If a car is parked in the garage for 30 minutes, how much will the garage charge? Explain your answer.
2. If a car is parked in the garage for 2 hours and 30 minutes, how much will the garage charge? Explain your answer.
3. If a car is parked in the garage for 5 hours, how much will the garage charge? Explain your answer.
4. If a car is parked in the garage for 5 hours and 30 minutes, how much will the garage charge? Explain your answer.
ANY INCOMPLETE OR INAPPROPRIATE ANSWERS WILL BE REPORTED AND DELETED. POINTS WILL BE DEDUCTED.
Answer:
20$ i think
Step-by-step explanation:
A fraction is a way to describe a part of a whole. If a car is parked in the garage for 5 hours and 30 minutes the charge will be $10.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Given that for the first hour that a car is parked in the garage, there is no charge. After the first hour, for the next two hours that a car is parked in the garage, there is a $5 charge. After the third hour, the garage charges $2 for each additional hour that the car is parked in the garage.
1.) Since the car is parked for 30 minutes only.
Charge = $0
Hence, No charge will be charged for 30 minutes.
2.) If a car is parked in the garage for 2 hours and 30 minutes.
Charge for 1 hour = $0
Charge for the next 1 hour and 30 minutes = $5
Hence, the charge will be $5.
3.) If a car is parked in the garage for 5 hours.
Charge for 1 hour = $0
Charge for the next 2 hour = $5
Charge for the next 2 hour = 2×$2 = $4
Charge = $5 + $4 = $9
Hence, the charge will be $9.
4.) If a car is parked in the garage for 5 hours and 30 minutes.
Charge for 1 hour = $0
Charge for the next 2 hour = $5
Charge for the next 2 hour 30 minutes = 2.5 ×$2 = $5
Charge = $5 + $5 = $10
Hence, the charge will be $10.
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I need help ASAP pls! I hate geometry
There are 1,453 souvenir paperweights that need to be packed in boxes. Each box will hold 17 paperweights. How many boxes will be needed?
Answer:
86 boxes
Step-by-step explanation:
trust me its right
Given that y varies directly as x when y = 2 and x = -12, find x when y = 5.
Answer:
x = -30
Step-by-step explanation:
Use the direct variation equation, y = kx
Plug in 2 as y and -12 as x, and solve for k:
y = kx
2 = k(-12)
-1/6 = k
So, the equation is y = -1/6x
Plug in 5 as y and solve for x:
y = -1/6x
5 = -1/6x
-30 = x
So, when y = 5, x = -30
Math problem please help thank youuuuuu
Answer:
the answer is ( -8,-8 )
Step-by-step explanation:
the first point is in -8 and the second point is also in -8 , therefore the answer is ( -8,-8 )
A student is running a 3-kilometer race. He runs 1kilometer every 2minutes. Select the function that describes the distance from the finish line after xminutes
Answer:
(0.5X) - 3 = Distance from the finish line
Step-by-step explanation:
Given that a student is running a 3-kilometer race, and runs 1 kilometer every 2 minutes, to determine the function that describes the distance from the finish line after X minutes, the following calculation must be performed:
1 = kilometers for every 2 minutes
X = every number of minutes
1/2 = 0.5 = kilometers per minute
(0.5X) - 3 = Distance from the finish line
Thus, if the student runs for 4 minutes, the equation would operate as follows:
0.5 x 4 - 3 = X
2 - 3 = X
-1 = X
Can y’all help me please?
Answer:
(A) [tex]5\frac{1}{4}*4\frac{1}{5}[/tex]
Step-by-step explanation:
The area of a parallelogram is the same as the area of a rectangle which is A=bh where b is the base and h is the height. Therefore, Erica can use the expression [tex]5\frac{1}{4}*4\frac{1}{5}[/tex] to find the area of the parallelogram.
hii please help me :)
Answer:
1.) A = (1/2bh) 4 + lxw
= 1/2 x 7 x 13 x 4 + 7 x 7
182 + 49 = 231cm2
l think u can use the formula to find the area of the other pyramids
The graph shows a 6-sided polygon on the coordinate plane. The polygon has k = 1.5. In the spaces below, enter the coordinates of B’ and C’.
Answer:
[tex]B' = (-3,-3)[/tex]
[tex]C' = (-4.5,-7.5)[/tex]
Step-by-step explanation:
Given
[tex]k = 1.5[/tex]
[tex]B = (-2,2)[/tex]
[tex]C =(-3,-5)[/tex]
Required
B' and C'
This is calculated as;
[tex]B' = k * B[/tex]
[tex]B' = 1.5 * (-2,-2)[/tex]
[tex]B' = (-3,-3)[/tex]
and
[tex]C' =k * C[/tex]
[tex]C' = 1.5 * (-3,-5)[/tex]
[tex]C' = (-4.5,-7.5)[/tex]
A random sample of 10 observations was selected from a normal population distribution. The sample mean and sample standard deviations were 20 and 3.2, respectively. A 95% prediction interval for a single observation selected from the same population is
Answer:
18.0167≤x≤21.9833
Step-by-step explanation:
Given the following
sample size n = 10
standard deviation s = 3.2
Sample mean = 20
z-score at 95% = 1.96
Confidence Interval = x ± z×s/√n
Confidence Interval = 20 ± 1.96×3.2/√10
Confidence Interval = 20 ± (1.96×3.2/3.16)
Confidence Interval = 20 ± (1.96×1.0119)
Confidence Interval = 20 ± 1.9833
CI = {20-1.9833, 20+1.9833}
CI = {18.0167, 21.9833}
Hence the required confidence interval is 18.0167≤x≤21.9833
a rectangular auditorium seats 2898 people. the number of seats in each row exceeds the number of rows by 17. find the number of seats
Answer:
There are 46 rows with 63 seats in each row
Step-by-step explanation:
I started looking for a whole number dividing seats and rows to make up the two pieces we need to multiply. I started backward from 70 (lucky guess) and then worked my way down to 63 and 46.
Now I was also looking for something more elegant in an algabraic formula and I stated with x being the number of rows and the seats being (x=17)
so I started with X(X+17)=2898 but that fif sot pan out other than to take me to x squared +17 = 2898 - subtract 17 from each side xsquared equals 2916
square root of 2916 is 54 which started my searching for a random number.
I got lucky
plz help i dont know what to do
ANSWER QUICK
Answer:
the last one is correct.............
Please help me it is due soon, please no links
Answer:
The length of the three sides [tex]5, \sqrt{58} , \sqrt{65}[/tex]
The triangle is not a right triangle
Step-by-step explanation:
A = (3, 2) , B = ( 6, 9) , C = (10, 6)
Find the lengths using distance formula.
[tex]distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]AB = \sqrt{(6-3)^2 + (9-2)^2} = \sqrt{9 + 49 } = \sqrt{58}[/tex]
[tex]BC = \sqrt{(10-6)^2 + (6-9)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
[tex]AC = \sqrt{(3-10)^2+(2-6)^2} = \sqrt{49 + 16} = \sqrt{65}[/tex]
Using Pythagoras theorem :
[tex](Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides[/tex]
Longest side is AC . So we will check if it satisfies Pythagoras theorem :
[tex]\sqrt{65} = \sqrt{58} + 5^2\\65 = 58 + 25\\[/tex]
65 ≠ 58 + 25
So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.
What I Can Do
Directions: How can we help minimize the amount of electricity and water
to be consumed in a month? List down at least 3 ways each. Write your
answers on a sheet of paper.
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