[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}[/tex]
c=9 makes the given expression a perfect square trinomial.
The given expression is:
[tex]x^{2} +6x+c[/tex]
We can rewrite it as:
[tex]x^{2} +2*x*3 + c[/tex].....(1)
What is the expansion of [tex](a+b)^2[/tex]?The expansion of [tex](a+b)^2[/tex] is [tex]a^{2} +2ab+b^{2}[/tex]
Comparing (1) with [tex]a^{2} +2ab+b^{2}[/tex]
We get
a=x
b=3
c=b²
So, c=3² =9.
So, c=9 makes the given expression a perfect square trinomial.
Hence, c=9 makes the given expression a perfect square trinomial.
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Mia and Carlos are hiking on a trail where they start 16 miles apart. If Mia can average 2.3 miles per hour while hiking and Carlos can average 2.5 miles per hour. How long will it take for them to meet up?
Answer:
I'm not sure but if this is on a calculus paper, this may put you on the right track?
Step-by-step explanation:
definate integral from 2.3 to 2.5 would equal 3.2, i don't know what to do with that information but i hope that helps you.
Evaluate 2-(-4) + (-g) where y= 7.
Answer:
-1Step-by-step explanation:
2 - (-4) + (-y)
Substitute y = 7 to the expression:
2 - (-4) + (-7) = 2 + 4 - 7 = 6 - 7 = -1
Please show the steps as well.
Answer:
x = 4Step-by-step explanation:
Rewrite the equation as
[tex]2^{x -1}=8\\[/tex][tex]2^{x -1}=2^3[/tex]Powers are equal if bases are same
[tex]x -1=3[/tex][tex]x=3+1[/tex][tex]x=4[/tex]~Hello! I will try to help you!
[tex] \Rightarrow \sf {2}^{x - 1} = 8[/tex]
»Convert the number 8 to a power of 2, then:-
[tex] \Rightarrow \sf {2}^{x - 1} = {2}^{3} [/tex]
»Because the bases on the right and left are the same, we will cross out the bases to produce a linear equation.
[tex] \Rightarrow \sf \cancel2 {}^{x - 1} = { \cancel2}^{3} [/tex]
»Let's find the value of x in the above equation!
[tex] \Rightarrow \sf x - 1 = 3 \\ \Rightarrow \sf x = 3 + 1 \\ \Rightarrow \bf x = 4[/tex]
With this it's done!
1 doller bill and a 10 doller bill and for quarters makes what?
Answer:
12$
Step-by-step explanation:
1 plus 10 from the singular dollar bill and the 10 dollar bill now we have 11 then we add one because there are 4 quarters which are 1 dollar that is why we have 12 dollars
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
answer "Less than"
Step-by-step explanation:
a) 1 2/3 = 5/3 = 1.666 ...
b) 1 5/6 = 11/6 = 1.833 ...
a < b
Answer:
1 5/6 > 1 2/3
Step-by-step explanation:
=> 1 5/6 = (1*6)+5/6
=> 1 5/6 = 6+5/6
=> 1 5/6 = 11/6
so like that, 1 2/3 = 5/3
now the denominators should be the same
for that,
5*2/3*2 = 10/6
11/6 and 10/6
=> 11/6 > 10/6
=> 1 5/6 > 1 2/3
ILL GIVE BRAINLIEST. ANSWER ASAP
Answer:
283 m^2
Step-by-step explanation:
To find the area of a circle, you need to times pi, in this case 3.14, by the radius,9.5 here, squared.
A= π (r^2)
2x+5=12 pleas and thank you :D
Answer:
x= 7/2
Step-by-step explanation:
move the constant 2x+5=12 to make it 2x=12-5.
subtract 12-5= 7
2x=7 divide both sides
x=7/2
i did try my best hope this helps :)
Name the image of C(6, –4) under a rotation 90 counter-clockwise about the origin.
a. C(–4, –6)
b. C(6, 4)
c. C(–6, –4)
d. C(4, 6)
Answer:
d.) (4,6)
Step-by-step explanation:
(-y,x) is the formula for a 90 counter-clockwise rotation.
So, it's (4,6)
royalred just started production of a new synthetic motor oil they have overhead costs of $21,804.00 a month plus manufacturing costs of $4.99 per quart of oil the oil sells for $7.36 per quart and the company's profit per month can be determined by the function p(x)=2.37x-21,804, where x is the number of quarts of oil sold over which of the following intervals will the company be making a profit
a: 2,962, 10,580
b: 9,201, 18,860
c: 2,932, infinite
d: 9,200, infinite
Considering the given profit function, it is found that the interval of values of x for which the company makes a profit is:
d: 9,200, infinite.
What is the profit function?Considering x as he number of quarts of oil sold, the monthly profit function is given by:
p(x) = 2.37x + 21,804.
The company makes a profit if p(x) > 0, hence:
p(x) > 0
2.37x + 21,804 > 0
x > 21,804/2.37
x > 9,200.
Which means that option D is correct.
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You are deciding between First National Bank and Liberty Bank. They both offer checking and savings accounts. First National charges a $10 fee to receive checks and charges $2.50 per ATM transaction. Liberty Bank has no check fee but charges $3.25 per ATM transaction. How many times do you need to be charged an ATM fee before you are paying the same amount of money in fees at both banks?
Step 1: Define your variables - Look at the question statement. What are you being asked to find?
Step 2: Write 2 equations that use those unknown variables
Step 3: Solve the system of equations
Step 4: State your solution. What does it mean in the context of the word problem?
Someone Help me please
geometry help me please
Answer:
2448
Step-by-step explanation:
because 12×12=144×17=2448
log2 (10x+5) - log2 5 =5
PLEASE SOLVE AND SHOW WORK
THANKS A TON
Answer:
[tex]\sf x =15.5[/tex]
Step-by-step explanation:
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5[/tex]
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)[/tex]
[tex]\sf log_2\left\dfrac{(10x+5)}{5} =log_2 (32)[/tex]
[tex]\sf 2x+1 =32[/tex]
[tex]\sf 2x+1 -1=32-1[/tex]
[tex]\sf 2x =31[/tex]
[tex]\sf x =15.5[/tex]
Answer:
Step-by-step explanation:
[tex]log_{a}[/tex] [tex]x_{1}[/tex] - [tex]log_{a}[/tex] [tex]x_{2}[/tex] = [tex]log_{a}[/tex] [tex]\frac{x_{1} }{x_{2} }[/tex]
[tex]log_{a}[/tex] x = b ⇒ [tex]a^{b}[/tex] = x
~~~~~~~~~~~~~~
[tex]log_{2} (10x+5)[/tex] - [tex]log_{2} 5[/tex] = 5
[tex]log_{2} \frac{10x+5}{5}[/tex] = 5
[tex]\frac{10x+5}{5}[/tex] = [tex]2^{5}[/tex]
10x + 5 = 32 × 5
2x + 1 = 32
x = 15.5
HELP!:
x^2 + 6x + 9 = ?
This is a factorizing question!! I need help, quickly!
Answer:
nasa pic yung answer
Step-by-step explanation:
hope its help
correct me if im wrong
Answer:
x=-3 x=-3
Step-by-step explanation:
You have the equation x^2+6x+9=0. So we are tying to find two terms that add to 6 but multiply to 9. Those numbers are 3 and 3. So now we have x^2+3x+3x+9=0. Then factor it to get (x+3) and (x+3) then to isolate x do x+3=0, x=-3 (move 3 to the other side to get x=-3).
Please help me with this
Answer:
11 cm
Step-by-step explanation:
1m = 100cm
By examining the graph carefully, we can see that the record in 1985 is 2.4 m. In 1970 it was slightly under 2.3 m. For it to be 15cm it would have to be 2.25m. For it to be 9 cm it would the record would have been above 2.3m.
why am I still in ambitious?! I have over a thousand points and 5 brainlest and you only need about 250 points and 5 brainlest?! what is going on ????
Answer:
has the app crashed, if not i dont know
Just need help, can't remember how to solve it.
A building has a height of 16 1/4 meters. Each floor in the building has a height of 3 1/4meters.
How many floors are in the building?
Answer:
5
Step-by-step explanation:
16 1/4 divided 3 1/4
Solve 4g - 5 ≤ 11 for g.
Answer:
g ≤ 4
Step-by-step explanation:
4g - 5 ≤ 11
Add 5 on both sides,
4g ≤ 11 + 5
4g ≤ 16
Divide 4 on both sides,
g ≤ 4
The mass of an ant is 5 x 10-3 grams. The mass of a bee is 1 x 10-¹ grams. Based on this information, how many ants equal the mass of a bee?
20 ants equals to mass of the bee if the mass of an ant is 5 x 10-3 grams and the mass of a bee is 1 x 10-¹ grams.
Ratio and proportionGIven the following parameters from the question
Mass of an ant = 5 x 10⁻³ grams
Mass of the bee = 1 * 10⁻¹ grams
Find the ratio of both masses
Ratio = 1 x10⁻¹ /5 x 10⁻³/
Ratin = 0.1/0.005
Ratio = 20
This shows that 20 ants equals to mass of the bee
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what is the answer i need help
Answer:
[tex]588mm^3[/tex]
Step-by-step explanation:
Each side of the blue pyramid is 3 times the size of the red pyramid.
Instead of just dividing by 3 for the volume we must divide by 9 instead because we're working in cubes.
a. Find the slope of the line that passes through these points.
The slope is
(Type an integer or a simplified fraction.)
b. Is the slope between (1,4) And (3,12) the same as the slope between (3,12) and (4,16)?
Explain.
O A. Yes. Both slopes are equal to
(Type an integer or a simplified fraction.)
O B. No. The slope between (1,4) and (3,12) is equal to (4,16)
. The slope between (3,12) and
th
slope formula : [tex]\bold{ \sf \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
a. coordinates : (3,12) and (4,16)
[tex]\sf \rightarrow \dfrac{16-12}{4-3}[/tex]
[tex]\sf \rightarrow \dfrac{4}{1}[/tex]
[tex]\sf \rightarrow 4[/tex]
b. coordinates : (1,4) and (3,12)
[tex]\sf \rightarrow \dfrac{12-4}{3-1}[/tex]
[tex]\sf \rightarrow \dfrac{8}{2}[/tex]
[tex]\sf \rightarrow 4[/tex]
⇒ A. Yes. Both slopes are equal to 4
show work please and no links
Answer:
man it’s one in the morning and your picture is blurry a f
Step-by-step explanation:
Write an equivalent expression.
- 2(8+79)
Choose the correct answer below.
OA. -2(8 + 7g) = - 16 + 7g
OB. – 2(8 + 7g) = 7g - 16
OC. – 2(8 + 7g) = - 2 - 14g
OD. -2(8 +79) = - 16 - 14g
-
-
Please help
Answer:
D
Step-by-step explanation:
You just have to expand and you'll get the answer.
What are the solution(s) for the quadratic equation?
Y=x^2-2x+1
[tex]\\ \rm\rightarrowtail x^2-2x+1=0[/tex]
[tex]\\ \rm\rightarrowtail x^2-x-x+1=0[/tex]
[tex]\\ \rm\rightarrowtail x(x-1)-1(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail (x-1)(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail x=1[/tex]
5 × 1 1/4
Do you know the answer?
Answer:
6 1/2 (mixed) or 25/4 (improper)
Step-by-step explanation:
Firstly, I made the mixed number an improper fraction; 5/4
Then I did the equation;
5/1 x 5/4 = 25/4
25/4 is 6.25 when divided, then made it a fraction; 6 1/4
Hope this helps!
Proving the Sum of the Interior Angle Measures of a Triangle Is 180°
Answer:
okay that is great.......?
answer:
the full answers for it
Step-by-step explanation:
HELP SOMEONE please review the image :D
What is the absolute deviation of 30 in this data set?
{26, 35, 27, 30, 22}
2
3
5
8
Answer:
The answer is 2
Step-by-step explanation:
I took the k12 test. Hope this helps!
The correct answer is 2
What is mean absolute deviation?The mean absolute deviation is a measure of variability that indicates the average distance between observations and their mean.How to calculate the MAD (Mean absolute deviation)?Take the sum of the absolute value Divide the sum of the absolute value by the total number of values in the data set. Substract the mean after dividing the sum of the absolute value by the total number of values in the data set.
Now , taking the data {26,35,27,30,22}
Adding the data
26+35+27+30+22 = 140
Now , Divide 140 by the total number of values in data set is 5
Therefore, 140/5 = 28
The mean is 28
Now substract the mean from the absolute deviation of 30
that is 30-28 = 2
Hence , The absolute deviation of 30 is data set is 2.
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the gravitational potential energy of an object is given by the formula p= mfg. which equation is correctly solved for the height, h?
a. h= p + mg
b. h= p-mg
c. h= p/(mg)
d. h=pmg
Step-by-step explanation:
c. h= p/(mg)
HOPE it helps