Answer:
a) 9^2
b) 9^(1/2)
c) 9^(3/2)
Step-by-step explanation:
It is perhaps easier to start by using 3^n.
3 = 3^1
27 = 3^3
81 = 3^4
Recognize that 3 = 9^(1/2) and replace 3 in each of the above. The applicable rule of exponents is (a^b)^c = a^(bc).
a) 81 = (9^(1/2))^4 = 9^2
b) 3 = 9^(1/2)
c) 27 = (9^(1/2))^3 = 9^(3/2)
Answer:
(a) 9^2
(b) 9^0.5
(c) 9^1.5
Step-by-step explanation:
We need to find n such that 9^n = value indicated.
Recall that n=2 is a square, so
(a) 9^2=9*9=81
Recall that n=0.5 (or 1/2) is a square root, because 9^0.5 * 9^0.5 = 9^1 = 9, so
(b) 9^0.5 = 3, because 3*3 = 9
Recall that multiplication of two powers with the same base is the sum of the exponents, e.g. 9^a * 9^b = 9^(a+b).
Therefore,
(c) 27 = 9*3 = 9^1 * 9^0.5 = 9^(1+0.5) = 9^1.5
The sum of two numbers is 12. When one number is subtracted from three times the other, the result is 4.
Find the numbers.
Answer:
1 2/3, 10 1/3
Step-by-step explanation:
x + y = 12
(3x - 1) = 4
let x = 12-y
substitute:
3(12-y) - 1 = 4
36 - 3y - 1 = 4
35 - 3y = 4
-3y = -31
y = 31/3 or 10 1/3
x = 11 3/3 - 10 1/3 which is 1 2/3
help me out please !!!!
Answer:
0.06 liters
Step-by-step explanation:
acid concentration of 65% means that it of 100 units of that solution 65 are acid, and the remaining 35 are water.
so, 100 units are 0.2 liters in this example.
that means that 65/100 × 0.2 = 0.13 liters are acid.
35/100 × 0.2 = 0.07 liters are water
we get a 50% concentration, when we have the same amount of water and acid in the solution (acid is only half of 50% of the solution).
the account of acid remains the same, as we are only adding water.
so, how much water do we need to get from 0.07 liters to 0.13 liters (the same as the already present acid) ?
0.13 - 0.07 = 0.06 liters
Somebody help me ASAP! I WILL GIVE BRAINLIEST IF YOU SOLVE THIS BY 12:40 PM PST
Answer:
B. {2/3, 1}Step-by-step explanation:
x²/5 - x/3 = -2/153x² - 5x = -23x² - 5x + 2 = 0x = (5 ± [tex]\sqrt{5^2 - 4*3*2}[/tex])/6x = (5 ± 1)/6x = 6/6 = 1 , x = 4/6 = 2/3Correct choice is B
Please factor and find the zeros of each relation. (19 marks)
E. y = 3x^2 + 12x
F. y = x^2 + 20x + 100
Answer:
Step-by-step explanation:
y=3x^2+12x = 3x (x+4)
zeroes: x={0, -4}
y = x^2+20x+100 = (x+10)^2
zeroes: x = -10 (twice)
or x={-10, -10}
Guys, someone got it wrong. Were back at 56..Please give me the correct answer, guys.
Answer:
8 + 6 = 14
14 x 4 = 56
56 x 1/2(basically just dividing by 2) = 28 mm2
Formula of area of a trapezoid:
B1(base 1) + B2(base 2) x H(height) x 1/2(basically just dividing by 2)
In this case, 8 is your base your other base is 6 and your height is 4.
Mrs. Davis has 96 bottles of water. If each bottle holds 1 pint of water, how many gallons of water does Mrs. Davis have?
Answer:
It’s 12.48 but if it is only a number and no decimals it will be 12.
Step-by-step explanation:
Tape Diagrams and Writing Equations
Write an algebraic equation for this tape diagram. Then determine the value of x. You may use a calculator.
Answer:
3x + 16 = 22.75
3 = 22.75 - 16
3× = 6.75
3 3
x= 2.25
Soshi’s rhombus has a base of 12 in and a height of 10 in. Jack’s rhombus has base and height measures that are double those of Soshi’s rhombus. Compare the area of Jack’s rhombus to the area of Soshi’s rhombus. Explain.
Answer:
360
Step-by-step explanation:
Will give 50 points!!
Simplify your answer and write it as a proper fraction, improper fraction, or whole
number.
tan (H)=
Answer:
4/3
Step-by-step explanation:
GH =√90²-72²=
√8100-5184=
√2916= 54
so, tan (H) = 72/54 = 4/3
⁴/3 is a required answer.
Answer:
Solution given:
FG=72
FH=90
By using Pythagoras law
GH=[tex]\sqrt{90²-72²}=54[/tex]
Step-by-step explanation:
we have
Tan H=[tex] \frac{opposite}{adjacent}[/tex]
[tex]TanH=\frac{GF}{GH}=\frac{72}{54}=\frac{4}{3}[/tex]
what is the mean to this
Sample #2
21 14 0 3 6
7 10 11 7 9
14 0 15 5 12
20 0 12 11 6
0 21 14 0 6
Answer:
44.8
Step-by-step explanation:
Please help!!!!!!!!!1
what is the volume of a cylindrical can of radius 2 inches and height of 6 inches.
Volume of a cylinder = pi x r^2 x h
R is the radius which is given as 2 inches.H is the height given as 6 inches.
Using 3.14 for pi:
Volume = 3.14 x 2^2 x 6
Volume = 75.36 cubic inches
Answer:
[tex]\large \sf {\underline{\underline{ \fcolorbox{green}{g}{vσlumє \: σf \: cчlíndєr \: ís \: 75.36 \: cuвíc \: ínchєs}}}}[/tex]
Step-by-step explanation:
◇ Gívєn ◇➟ Rαdíus σf cчlíndrícαl cαn ís 2 ínchєs.
➟ Hєíght f cчlíndrícαl cαn ís 6 ínchєs.
◇ Fínd ◇➟ Vσlumє σf cчlíndrícαl cαn.
◇ Fσrmulα Usєd ◇➟ vσlumє σf cчlíndєr = π × r ² × hєíght
◇ Sσlutíσn ◇wє usєd fσrmulα
vσlumє σf cчlíndєr = π × r ² × hєíght
vσlumє σf cчlíndєr = 3.14 × (2 ínchєs) ² × 6 ínchєs
vσlumє σf cчlíndєr = 3.14 × 4 squαrє ínchєs × 6 ínchєs
vσlumє σf cчlíndєr = 3.14 × 24 cuвíc ínchєs
vσlumє σf cчlíndєr = 75.36 cuвíc ínchєs
–––––––––☆–––––––––The subject is: Solving Quadratic Formula, if you know the answer and it’s correct please let me know, if not, do not comment.
Answer:
The equation needs to be in standard form
Step-by-step explanation:
The equation needs to be in standard form
so the the coefficients a, b and c can be determined
for use in the quadratic formula
A stove can be bought on hire purchase by making a deposit of $650 and 12 monthly instalments of $195 each. Calculate the hire purchase price of the stove.
Answer:
$2,990?
Step-by-step explanation:
Classify the triangle by its side lengths.
Answer:
isosceles triangle
Step-by-step explanation:
isosceles triangles have two equal sides
What is an equation of the line that passes through the points (-3,-1) and (6,2)?
Answer:
[tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points the line passes through are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-3,-1) and (6,2)
[tex]=\frac{2-(-1)}{6-(-3)}\\=\frac{2+1}{6+3}\\=\frac{3}{9}\\=\frac{1}{3}[/tex]
Therefore, the slope of the line is [tex]\frac{1}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{3}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{3}x+b[/tex]
Plug in one of the given points and solve for b
[tex]2=\frac{1}{3}(6)+b\\2=2+b[/tex]
Subtract 2 from both sides to isolate b
[tex]2-2=2+b-2\\0=b[/tex]
Therefore, the y-intercept is equal to 0. Plug this back into [tex]y=\frac{1}{3}x+b[/tex]:
[tex]y=\frac{1}{3}x+0\\y=\frac{1}{3}x[/tex]
I hope this helps!
Choose the inequality that represents the following graph.
the answer is C since it needs to be lees than or -2
how many equal parts are in each whole? iready
Write the equation of the line in fully simplified slope-intercept form.
The lengths of the sides of a triangle or an extended ratio 7 8 and 9 the perimeter of the triangle is 48 cm what are the lengths of the sides
Answer:
14cm, 16 cm, 18 cm
Step-by-step explanation:
Note that
= a:b: c = 7:8:9
We have to find the sum of the proportion
Sum of proportion = 7 + 8 + 9
= 24
Length of side a
7/24 × 48 = 14 cm
Length of side b
8 /24 × 48 = 16cm
Length of side a
9/24 × 48 = 18 cm
What are the lengths of the sides?
The lengths of the sides of the triangle in cm are
14cm, 16 cm, 18 cm
Solve the equation plz!
8(3x−2)/9 = 13/7
Step-by-step explanation:
(3x-2) =13/7x9/8
3x =117/56+2
3x = 117+112/56
x =229/56x3
x= 229/168
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
Answer:
x=229/168
Step-by-step explanation:
[tex]\frac{8(3x-2)}{9} =\frac{13}{7}\\or, 56(3x-2) =117\\Or,168x-112=117\\Or, 168x=229\\Or, x=\frac{229}{168} \\[/tex]
Lines lll, mmm, and nnn are parallel to each other and ppp is a transversal. parallel lines Also, \dfrac{\angle{x}}{\angle{y}}=\dfrac{3}{7} ∠y ∠x = 7 3 start fraction, angle, x, divided by, angle, y, end fraction, equals, start fraction, 3, divided by, 7, end fraction. Find \angle{z}∠zangle, z.
Answer:
The answer is 5 degrees
Step-by-step explanation:
Find the height of the cylinder given the surface area and one
other dimension:r = 5 in SA
659,4 in?
Answer:
C 16 inches
Step-by-step explanation:
a cylinder is 2 circles (1 on top, 1 at the bottom) and a round "mantle" connecting the two circles.
so, the surface area is the sum of the areas of both circles and the "mantle".
this "mantle" can be cut open and cut off the circles, and then be placed flat on the table. then it is simply a rectangle with the side lengths cylinder height (h) and circle circumference.
circle area : pi × r²
circle circumference : 2 × pi × r
rectangle area :
length × width = circle circumference × h
SA = 659.4 inches² = 2×(pi × r²) + (2×pi×r)×h =
= 2×pi×25 + 2×pi×5×h = 50×pi + 10×pi×h
=> 659.4 - 50×pi = 10×pi×h
=> (659.4 - 50×pi) / (10×pi) = h = 16 inches
Hugo has a brother and sister. Hugo is x years old. •
His sister Jasmine is 3 years older than Hugo •
His brother Manny is 2 years older than Jasmine.
Which expression represents the sum of the ages of Hugo and his two siblings?
x + 5
X + 8
3r + 5
3x + 8
pls help due soon
Answ
3xmas8
-------------------------------
listo
love how everyone hw on here is geometry and im just here like.... help...
Answer:
nope it isn't a linear function
Step-by-step explanation:
if you put it in a graph it isn't a straight line
Graph the system of linear inequalities
Consider a radioactive substance with original weight 20grams given by W(x)= 20 x (0.95)^x, where W(x) is with weight after x years. In about how many years is the radioactive substance half of its original weight? Type answer to one decimal place.
Answer:
13.5 years
Step-by-step explanation:
We are given the expression:
W(x)= 20 x (0.95)^x
Where W(x) = 20grams/2
= 10 grams
Hence:
10 = 20 x (0.95)^x
Divide both sides by 20
10/20 = 20 x (0.95)^x/20
0.5 = (0.95)^x
Take the log of both sides
log 0.5 = log (0.95)^x
log 0.5 = x log (0.95)
Divide both sides by log 0.95
x = log 0.5 / log 0.95
x = 13.513407334 years
Approximately to 1 decimal place =✓13.5 years
Therefore, it will take 13.5 years for the radioactive substance to be half of its original weight.
A three-course meal includes an appetizer, a main course, and a dessert. A restaurant offers two kinds of appetizers, four kinds of main courses, and five kinds of dessert.How many different three-course meals can be made
Answer:
2*4*5 = 40
Step-by-step explanation:
Which of the following figures has an area that can be found using the
formula A = 8r2?
A. Circle
B. Pentagon
C. Square
D. Rhombus
HELP PLSS
BAnswer:
Step-by-step explanation:
Answer: circle
Step-by-step explanation:
I need answer immediately!!!!!!!
Answer:
13 inches
Step-by-step explanation:
Look at the start of where the graph becomes smooth.
Answer:
The guy above me is correct. The rise in the graph means it is snowing, the fllat line shows when it stops, then 2nd rise is the snow continuing at a different rate compared to the first. When the snow stopped the first time, look at where the flat line is on the y-axis. It lands on 13, which is 13 inches
A parabola has x-intercepts at -3 and 4. Write 2 possible equations of parabolas in
standard form that could satisfy the requirements.
x=-3
x=4
hope helps you
have a nice day