Answer:
13 , 6.
Step-by-step explanation:
A equation is given to us and we need to find out the value of x . The given equation to us is ,
[tex]\sf\implies \dfrac{ x -9}{\sqrt{x+3}}= 1 [/tex]
Cross multiply ,
[tex]\sf\implies x - 9 =\sqrt{ x +3} [/tex]
Squaring both sides ,
[tex]\sf\implies (x - 9)^2 = x + 3 [/tex]
Simplify the whole square ,
[tex]\sf\implies x^2+9^2-2.9.x = x +3 \\ [/tex]
[tex]\sf\implies x^2+81 - 18x = x -3[/tex]
Add 3 and subtract x on both sides ,
[tex]\sf\implies x^2 -18x-x +81-3=0[/tex]
Simplify ,
[tex]\sf\implies x^2 -19x +78=0 [/tex]
Split the middle term of the quadratic equation,
[tex]\sf\implies x^2-13x-6x+78=0 [/tex]
Take out common ,
[tex]\sf\implies x( x -13)-6(x-13)=0[/tex]
Take out ( x -13 ) as common ,
[tex]\sf\implies ( x -13)(x-6)=0 [/tex]
Equate both factors to 0 ,
[tex]\sf\implies \boxed{\pink{\sf x = 13,6}}[/tex]
Hence the value of x is 13 or 6 .
Simplify[tex]\frac{9x^{16} }{6(x^{2} )^{3}x^{2} } }[/tex]
Answer:
[tex]\displaystyle \frac{3x^8}{2}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex] Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex] Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{9x^{16}}{6(x^2)^3x^2}[/tex]
Step 2: Simplify
Exponential Rule [Powering]: [tex]\displaystyle \frac{9x^{16}}{6x^6x^2}[/tex]Exponential Rule [Multiplying]: [tex]\displaystyle \frac{9x^{16}}{6x^8}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{9x^8}{6}[/tex]Simplify: [tex]\displaystyle \frac{3x^8}{2}[/tex]Figure out the pattern, and write the next number.
2,6,21,88
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answer:
h= 60
g= 120
m= 147
k= 33
Step-by-step explanation:
We know that all three lines are straight an continuous, so, at any given point the angles should add up to 180 degrees.
This immediately helps with angle h:
120 + h = 180
h = 60
As well as m:
33 + m = 180
m = 147
There are two ways to solve the next part:
First and most familiar way:
h + g = 180
60 + g = 180
g = 120
and:
m + k = 180
147 + k = 180
k = 33
The other way that I prefer is that the angles opposite of each other when two lines intersect are equal. I don't know if that makes sense, it's hard to explain in this format.
Which one correct answer??
What is the question of it ?
Convert the following fraction to a decimal.
1/3
A. 0.3
B. 0.03
C. 0.303
D. 3.9
Answer:
Option A, 0.3
Step-by-step explanation:
Step 1: Convert the fraction into a decimal
Technically, 1/3 is an irrational number meaning that it never ends. However, if we round it, it would round to 0.3 since 1/3 = 0.3333333.....
Answer: Option A, 0.3
A sales firm receives an average of three calls per hour on its toll-free number. For any given hour, find the probability that it will receive at least three calls. Use the Poisson distribution.
Answer:
At most 3 calls: 64.7%
At least 3 calls: 57.7%
5 or more calls: 18.5%
Step-by-step explanation:
y=5/3x + 3 in ordered pairs
Answer:
(3,8) ; (-3,-2) ; (6,13)
Step-by-step explanation:
A linear equation in Slope Intercept Form is given to us and we need to write the ordered pairs for x and y . The given equation is ,
[tex]\rm\implies y =\dfrac{5}{3}x + 3 [/tex]
For finding the ordered pairs , substitute different values of x to get different values of y.
Put x = 3 :-
[tex]\rm\implies y =\dfrac{5}{3}\times 3 + 3 [/tex]
[tex]\rm\implies y = 5+ 3 [/tex]
[tex]\rm\implies y =8[/tex]
Put x = -3 :-
[tex]\rm\implies y =\dfrac{5}{3}\times -3 + 3 [/tex]
[tex]\rm\implies y = -5+ 3 [/tex]
[tex]\rm\implies y =-2[/tex]
Put x =6 :-
[tex]\rm\implies y =\dfrac{5}{3}\times 6 + 3 [/tex]
[tex]\rm\implies y = 10+ 3 [/tex]
[tex]\rm\implies y =13[/tex]
Therefore ,
[tex]\small\implies\boxed{\rm\blue{ Odered \ Pairs \ = (3,8) ; (-3,-2) ; (6,13) }}[/tex]
2 2/3 +2 2/3 + 2 2/3 +2 2/3
Answer:
10.6666666667 is your answer
just round this to the nearest tenth
9514 1404 393
Answer:
10 2/3
Step-by-step explanation:
Multiplication works nicely on problems involving repeated addition:
2 2/3 +2 2/3 + 2 2/3 +2 2/3 = 4 × (2 2/3) = 4×2 +4×2/3 = 8 +8/3
= 8 + 2 2/3 = 10 2/3
In a sample of 56 bags of fertilizer, the average weight was found to be 17.2lb with a standard deviation of 0.7. Give a point estimate for the population standard deviation of the weight of the bags of fertilizer.
Answer:
???????????????????????
I am need help and an explanation on how to read these graphs.
Answer:
A is the answer
Step-by-step explanation:
A
plz mark it brainlist
Suppose a + bi and c + di are complex numbers with b not equaling 0.
(a) Calculate (a + bi) + (c + di) and (a + bi)(c + di).
(b) Show that if both the sum and product are real numbers, then either the complex numbers are real numbers or conjugates.
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Answer:
(a) sum: (a+c) +(b+d)i
product: (ac -bd) +(bc +ad)i
(b) (b+d)=0 and (bc+ad)=0 ⇒ a=c, d=-b or b=d=0
Step-by-step explanation:
(a) Combining like terms the sum is ...
(a +bi) +(c +di) = (a+c) +(b+d)i . . . . sum
And the product is ...
(a+bi)(c+di) = ac +(ad+bc)i +bd·i²
Since i = √-1, i² = -1 and the product can be written as ...
(a+bi)(c+di) = (ac-bd) +(ad+bc)i . . . . product
__
(b) If both the sum and product are real numbers, then we have ...
b +d = 0
ad +bc = 0
The first equation tells us d = -b. Substituting that into the second equation, we get ...
a(-b) +b(c) = 0
b(c -a) = 0
The zero product rule tells us this will be true if and only if b = 0 or c = a.
if b = 0, then d = 0 and both numbers are real.
if c = a, then c+di = a-bi and the numbers are conjugates.
Hence, if both the sum and product are real, both are real numbers or they are conjugates.
Si una vara 2,15 mts de longitud da una sombra de 6,45 mts
Answer:
he casted 4.3. away
Step-by-step explanation:
Convert 0.181818 … to a fraction by writing the repeating decimal as an infinite geometric series. Show all of your work (please)
0.181818… = 18 (0.010101…)
… = 18 (0.01 + 0.0001 + 0.000001 + …)
… = 18 (1/100 + 1/100² + 1/100³ + …)
… = 18 (1 + 1/100 + 1/100² + 1/100³ + …) - 18
Then you have
[tex]0.181818\ldots = \displaystyle18\sum_{k=0}^\infty\frac1{100^k} - 18 = \frac{18}{1-\frac1{100}} - 18 = \boxed{\frac2{11}}[/tex]
What is the length of PO
These are similar triangles, therefore their sides are proportional.
36 / 24 = PO / 36
24PO = 1296
PO = 54
Hope this helps!
in order to apply the law of cosines to find the length of the side of a triangle, is it enough to know which of the following?
A. The area of a triangle
B. The lengths of two of the triangle's sides and the measure of the angle between them
C. At least two of the angles of the triangle and the length of one of its sides
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Answer:
B. The lengths of two of the triangle's sides and the measure of the angle between them
Step-by-step explanation:
The usual formulation of the law of cosines is something like this:
c² = a² +b² -2ab·cos(C)
where 'c' is the side opposite angle C, and 'a' and 'b' are the other two sides. That is, to use this formula directly, one needs two side lengths and the measure of the included angle.
_____
Additional comment
One can use the law of cosines to solve a triangle when any two sides and one angle are known. The use of the formula will give a quadratic in the unknown side length, if it is not the side opposite the known angle. As with the law of sines, if the angle is opposite the shorter of the two given sides, there may be two solutions for the length of the third side.
Answer:
The answer is B.)
Step-by-step explanation:
If POR ~ ASTU, what is the scale factor of APQR to ASTU?
A. 1/5
B. 1/4
C. 5
D. 4
Answer:
[tex]k = \frac{1}{5}[/tex]
Step-by-step explanation:
Given
The attached triangles
Required
The scale factor
From the attachment, we have:
[tex]TU = 4[/tex]
[tex]QR = 20[/tex]
So, the scale factor from PQR to STU is:
[tex]k = \frac{TU}{QR}[/tex]
[tex]k = \frac{4}{20}[/tex]
[tex]k = \frac{1}{5}[/tex]
If Tevin has 2 times as many dimes as nickels and they have a combined value of 100 cents, how many of each coin does he have?
dimes____
nickels____
Answer:
dimes- 8
nickels- 4
Step-by-step explanation:
dime=10 cents
nickels=5 cents
5 x 4 = 20
10 x 8 = 80
80 + 20 = 100
... please give brainliest ...
find all the missing measurement
Answer:
find all the missing measurementFind Y. round to the nearest tenth.
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Answer:
32.7°
Step-by-step explanation:
Solve the given equation for C, then fill in the given values and evaluate.
C = arccos((a² +b² -c²)/(2ab))
Y = arccos((50² +90² -55²)/(2·50·90)) = arccos(7575/9000) ≈ 32.7°
__
Y is angle A in the attached triangle solver.
Surface roughness of pipe. Refer to the Anti-corrosion Methods and Materials (Vol. 50, 2003) study of the sur- face roughness of coated interior pipe used in oil fields, Exercise 7.26 (p. 311). The data (in micrometers) for 20 sampled pipe sections are reproduced in the table on p. 391.
a. Give the null and alternative hypotheses for testing whether the mean surface roughness of coated interior pipe, H, differs from 2 micrometers.
b. The results of the test, part a, are shown in the MINITAB printout at the bottom of the page. Locate the test statistic and p-value on the printout.
The minitab report isn't given.
Answer:
H0 : μ = 2 um
H1 : μ ≠ 2 um
Step-by-step explanation:
The mean surface roughness of coated interior pipe is given as 2um.
This refers to the population mean, μ = 2 um
Therefore, the null hypothesis which usually aligns with the population mean value will be stated as :
H0 : μ = 2 um
The alternative hypothesis is used to test the claim that the mean surface roughness is different from 2 ; hence no direction is given, this is thus a 2 - tailed test
H1 : μ ≠ 2 um
A man invested N80 at a certain rate of simple interest. If at the end of 5 years the money amounted to N88, what was the rate of simple interest paid?
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Answer:
2%
Step-by-step explanation:
The amount of interest is the difference between the total amount and the principal amount:
N88 -N80 = N8 . . . . the amount of interest
The interest amount is given by the formula ...
I = Prt
Solving for r, we find ...
r = I/(Pt) = 8/(80×5) = 1/50 = 2%
The rate of simple interest paid was 2%.
MFP15017010 2021 Question 2 2.1 Calculate the following 2- and 3-digit numbers using strategic doubling: 34 2.1.2 340 2.13 277 214 00 (10) 2.15 500
Answer:
plz check ur school solution down.
Step-by-step explanation:
Solve the equation for x: 6-(4x-2)/5=x
A 42 gallon hot water tank hose 350 pounds of water what weight of water at 53 gallon tank hold
Answer:
441.66667 pounds
Step-by-step explanation:
divide 350/42 then multiply the quotient by 53
Please help!
Solve for x
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Answer:
x = 1
Step-by-step explanation:
The product of lengths to the two circle intercepts are the same for each secant.
7(7+9) = (8x)(8x+6x)
112 = 112x² . . . simplify
1 = x² . . . . . . divide by 112
x = 1 . . . . . . . take the square root (segment lengths are positive)
Part C of Jim and his dad are building a rectangular flower bed.
If Jim and his dad decide to decrease the width of the flower bed from 15 feet, what happens to its length?
PLEASE HELP ME IM HAVING TROUBLE WITH IT
Answer:
True
False
Step-by-step explanation:
BC are on the same line so, the new [tex]B^{1}[/tex][tex]C^{1}[/tex] will also be on the same. Just a different line than the original. The both move the same distance when dilated.
CD and the new [tex]C^{1}[/tex][tex]D^{1}[/tex] cannot be the same length. The dilation will increase their length by 1[tex]\frac{2}{3}[/tex]
Use all the six numerals 4, 5, 6, 7, 8 and 9 to form two 3-digit even numbers whose sum is smallest, and what is the sum?
Step-by-step explanation:
this Is hard to find.............
Answer:
The numbers should be even, it means the unit digits are 4, 6 or 8.
The numbers should be minimal, it means the hundred's digits are 4 and 5.
With this we have possible numbers:
4x6 and 5y8, here 6 and 8 could be exchanged.The options are:
496 and 578 or476 and 598 or498 and 576 or478 and 596The sum of the two numbers is:
1074Find the area of the shaded regions.
QUICKLY PLEASE
Answer:
the answer is 270° on this
Answer:
84.78
Step-by-step explanation:
Area of a circle is pi(radius)^2
In this case it would be (pi(radius)^2)270/360 since it's 3/4 of a circle.
So we replace the values and solve:
3.14(36)(270/360)= 84.78 square centimeters.
Problem
Combine the like terms to create an equivalent expression:
y−(−3y)
please someone explain to me how to do this?
