Answer:
[tex]log_{a}[/tex] 12
Step-by-step explanation:
using the properties of logarithms
• nlog x ⇔ log[tex]x^{n}[/tex]
• log x + log y = log (xy)
[tex]\frac{1}{2}[/tex] [tex]log_{a}[/tex] 16 + [tex]\frac{1}{3}[/tex] [tex]log_{a}[/tex] 27
= [tex]log_{a}[/tex] [tex]16^{\frac{1}{2} }[/tex] + [tex]log_{a}[/tex] [tex]27^{\frac{1}{3} }[/tex]
= [tex]log_{a}[/tex] [tex]\sqrt{16}[/tex] + [tex]log_{a}[/tex] [tex]\sqrt[3]{27}[/tex]
= [tex]log_{a[/tex] 4 + [tex]log_{a}[/tex] 3
= [tex]log_{a}[/tex] (4 × 3)
= [tex]log_{a}[/tex] 12
Write the equation of the line in slope-intercept form that contains the points (4, -1) and (9, 9).
Answer:
y = 2x - 9
Step-by-step explanation:
y2 - y1 / x2 - x1
9 - (-1) / 9 - 4
10 / 5
= 2
y = 2x + b
-1 = 2(4) + b
-1 = 8 + b
-9 = b
What would be the explicit equation for the sequence 3, 9, 27, 81 
Answer:
times it by
Step-by-step explanation:
3×3=9, 9×3=27, 27×3=81, 81×3=243
sorry if this isn't the answer your looking for.
The x-coordinate of point P is positive, and the y-coordinate of point P is positive. In which quadrant is point P?
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
Answer:
Quadrant I
Step-by-step explanation:
b/c both are on the right side that means they are positive
What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120
Answer:
78
Step-by-step explanation:
13! / 11! · 2!
13 x 12 / 2
13 x 6 = 78
How to do elimination with 3 equations?
Elimination is a method of solving a system of equations using addition or subtraction to eliminate one of the variables.
Here we will use the elimination method to solve a system of three equations with three variables.
Let's say we have three equations with three variables x, y and z.
Equation 1: ax + by + cz = d
Equation 2: ex + fy + gz = h
Equation 3: ix + jy + kz = l
We will start by multiplying the first equation by a number that will make the coefficients of y in the two equations the same.
Let's say we choose to multiply the first equation by -f, so that we get:
-fax -fby -fcz = -fd
Now we add the two equations to eliminate y:
ax + by + cz + (-fax -fby -fcz) = d -fd
ax -fax + by -fby + cz -fcz = d -fd
(a -f)x + (b -f)y + (c -f)z = d -fd
Now we can multiply the second equation by a number that will make the coefficients of z in the two equations the same. Let's say we choose to multiply the second equation by -k, so that we get:
-kex -kfy -kgz = -kh
Now we add the two equations to eliminate z:
(a -f)x + (b -f)y + (c -f)z + (-kex -kfy -kgz) = d -fd -kh
(a -f)x + (b -f)y + (c -f)z -kex -kfy -kgz = d -fd -kh
(a -f -k)x + (b -f -k)y = d -fd -kh
We can now solve this equation for x:
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
Now we can substitute this expression for x in any of the original equations and solve for y:
Let's choose to substitute in the first equation:
ax + by + cz = d
(d -fd -kh - (b -f -k)y) / (a -f -k) + by + cz = d
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
Now we can substitute this expression for y in any of the original equations and solve for z:
Let's choose to substitute in the second equation:
ex + fy + gz = h
e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + gz = h
gz = h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
Now we have
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
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Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
The triangle in the figure can be proved by ASA, SAS, and AAS
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by ASA, SAS, and AAS to ensure that the the triangles are congruent.
Alternate angles in the figure are also equal
According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.
The Angle-Angle-Side (AAS) Congruence Theorem states that two angles and a non-included side in one triangle must be congruent with two angles and the equivalent non-included side in another triangle for the triangles to be congruent.
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find the height of the two pillar with same height
Answer:
ED = AB = 25√3
Step-by-step explanation:
Let ED = AB = X
DC = 100 - BC
Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]
[tex]\sqrt{3} (100-BC) = X[/tex]
Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]
[tex]\frac{BC}{\sqrt{3} } = X[/tex]
[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]
X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]
X = 25√3
Hey guys so I NEEEEEED HELP ON THIS MATH QUESTION, so here it is please help me P.S: LIMITED TIME, P.P.S: LIKE IN 40-74 MINUTES!!! HELP
The approximate diameters of Uranus and Mars are listed below:
Uranus: 5.11×10^4
kilometers
Mars: 6.79×10^3
kilometers
How many times larger is the diameter of Uranus? Write your answer in standard notation, rounding to the nearest tenth.
The number of times the diameter of Uranus is larger than the diameter of Mars is 7.5 times
How to determine the number of times larger is the diameter of UranusFrom the question, we have the following parameters that can be used in our computation:
The diameters of Uranus and Mars
These diameters are given as
Diameter of Uranus: 5.11×10^4 kilometers
Diameter of Mars: 6.79×10^3 kilometers
Express the diameters properly
So, we have the following representation
Diameter of Uranus: 5.11 × 10⁴ kilometers
Diameter of Mars: 6.79 × 10³ kilometers
This means that
Number of times larger = Diameter of Uranus/Diameter of Mars
Substitute the known values in the above equation, so, we have the following representation
Number of times larger = 5.11 × 10⁴ kilometers/6.79 × 10³ kilometers
Evaluate the quotient
So, we have the following representation
Number of times larger = 7.5
Hence, the number of times is 7.5
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Edgar has a fountain that holds 5 quarts of water. He only wants to fill it 3/4 full. How many 1-pint containers does it take to fill the fountain? How could he fill it with pint and cup containers? Explain.
Answer:
Step-by-step explanation:
1 quart = 2 pints = 4 cups
1 pint = 2 cups
1/2 pint = 1 cup .....so.....
First question
5 quarts = 10 pints
10 * (3/4) = 7.5 pint contianers will fill it 3/4 full
7.5 pints = 7 pints + 1 cup
Tori spends $38.00 on coffee each month. About how much dose Tori spend on coffee over 9 months
Answer:
Tori spends $342.00 on coffee over 9 months
Step-by-step explanation:
38 x 9 = 342
= $342.00
Which equation represents a line that is perpendicular to the line with equation y = 2x - 8? Select all that apply.
Ay=1/2x+1
B. y=-1/2x+1
C. x + 2y = 5
D. -x + 2y = -3
E. -x-2y = 9
Step-by-step explanation:
credits are also on there
There are 84 classes in a school. Two-thirds learned about the Holocaust. The rest did not. How many classes did not learn about the Holocaust?
Answer:
28 classes
Step-by-step explanation:
84/3 = 28 classes
Answer:
28 classes didn't learn about the Holocaust
Step-by-step explanation:
If there are 84 classes and two-thirds learned about the Holocaust that means that you have to divide by three.
84 ÷ 3 = 28
Then, you can check your answer by multiplying 28 × 3 = 84
1) Iris' puppy is 2 1/5 feet long. Which
decimal represents Iris' puppy's length?
a) 2.15 feet
b) .215 feet
c) 2.2 feet
d) 2.02 feet
need an answer ASAP!
Answer:
c) 2.2 feet
Step-by-step explanation:
1) Iris' puppy is 2 1/5 feet long. Which
decimal represents Iris' puppy's length?
c) 2.2 feet
please help no links please
Answer:
x = 38
Step-by-step explanation:
180 - 68 = 112
122 + 20 + x = 180
142 + x = 180
180 - 142 = x
x = 38
Have a nice day!
I GIVE THANKS AND MARK BRAINLIEST
WHAT ARE THE CORRECT ANSWER(S)?
Answer:
b and d
Step-by-step explanation:
slope is -0.632 which is quite literally what d is saying, (on terms of graphs) for every 1 square over it goes -0.63 squares down
After Charlie ate 2/3 of the remaining cake, he divided the rest equally among his 3 friends. What fraction of the pan of cake did each friend get? Write an expression and show all of your work.
Answer: 1/9 of the cake
Step-by-step explanation:
Charlie ate 2/3 of the cake which means that what is left to give the friends is:
= 1 - 2/3
= 1/3 of the cake
This was divided equally amongst three friends so the expression would be:
= 1/3 ÷ 3
This can also be written as:
= 1/3 * 1/3
= 1/9
Each friend got 1/9 of the cake.
Answer:
1/9 of the cake
Step-by-step explanation:
1 - 2/3 = 1/3 left
(1/3) / 3 = 1/9 = what each friend got
In one fell swoop we have ( 1 - 2/3) / 3 = 1/9
Jai is 1. 45 meters tall. At 11 a. M. , he measures the length of a tree's shadow to be 39. 55 meters. He stands 34. 1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter
The height of the tree to the nearest hundredth of a meter is 10.5 meters.
The length of Jai's shadow = length of tree's shadow - distance of standing of Jai
Length of Jai's shadow = 39.55 - 34.1
Performing subtraction on Right Hand Side of the equation
Length of Jai's shadow = 5.45 meters
Tan theta = height of tree/length of shadow = height of Jai/length of his shadow
height of tree/39.55 = 1.45/5.45
Keep the values in formula
Height of tree = 39.55×1.45/5.45
Performing multiplication
Height of tree = 57.35/5.45
Performing division
Height of tree = 10.5 meters
Thus, the height of tree is 10.5 meters.
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Anyone know how to solve this?
Given the point (4,2), what is the image point if it is reflected over the x-axis?
Answer:
(4,-2)
Step-by-step explanation:
Erin is picking out some movies to rent, and he has narrowed down his selections to 5 documentaries, 5 mysteries, 5 dramas, and 7 action movies. How many different combinations of 9 movies can he rent if he wants all 5 mysteries
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
How are the various combinations determined?The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .
She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).
Five documentaries make up the total.
7 comedies total are available.
Four mysteries are present.
5 horror movies are there.
A total of 14 films, excluding comedies, are available.
If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.
1 * (14*13)/2 = 91
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
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A loan worth $1000 collects simple interest each year for 6 years. At the end of that time, a total of $1270 is paid back. Determine the percentage rate for this loan?
Answer:
The percentage rate is 4.5%
Step-by-step explanation:
The simple interest earned in this situation is $1270 - $1000, or $270.
the simple interest formula is i =prt.
Here, i = $270 = ($1000)(r)(6 yr).
$270
Then r = ------------------- = 0.045
$1000(6 yr)
The percentage rate is 4.5%
HELP PLEASE!!
a swimmer takes a running jump off a pier. The path of the swimmer can be modeled by the equation h=-0.1d^2+0.1d+3, where H is the height in feet and d is the horizontal distance in feet. How far from the pier does the swimmer enters the water?
Answer: 5 ft
Step-by-step explanation:
Given
The path of the swimmer is given by
[tex]h=-0.1d^2+0.1d+3[/tex]
The swimmer can go horizontally depends upon the depth
So, find the maximum depth by taking derivative w.r.t height
[tex]h'=-0.2d+0.1[/tex]
Put derivative equal to 0
[tex]\Rightarrow -0.2d+1=0\\\\\Rightarrow d=\dfrac{1}{0.2}\\\\\Rightarrow d=5\ ft[/tex]
thus, the swimmer can go up to a distance of 5 ft.
PLEASE HELP ASAP!!!!!
Answer:
Left triangle: 12.5 cm
Right triangle: 21 cm
Trapezoid: 50 cm
Total: 83.5
Step-by-step explanation:
Left triangle: The formula to find the area of a triangle is 1/2bh, in which b=base and h=height. The base of the left triangle is 5 cm and the height is 5 cm. 5*5=25. 25/2=12.5 cm.
Right triangle: Once again, use the area formula for a triangle. The base of the right triangle is 6 cm and the height is 5+2=7. 6*7=42. 42/2=21 cm.
Trapezoid: The formula to find the area of a trapezoid is a+b/2(h) in which a and b are the top and bottom of the trapezoid and h=height. In this case, a=9 cm and b=5+6=11 cm. The height is 5 cm. 9+11=20. 20/2=10. 10*5=50 cm.
Add all of the areas. 12.5+21+50=83.5. So, the total area is 83.5 cm.
If G-H-I, and if GH = 2x - 9 , HI = 14 , and GT = 3x - 8 , then find GI.
The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.
What is the value of the variable?An algebraic equation is formed by comparing two algebraic expressions to one another.
In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8
If G-H-I is a line and GH, HI and GT lies between G to I
To find G to I ⇒ GI = GH + HI = GT
GI = 2x - 9 + 14 = 3x - 8
2x + 5 = 3x - 8
2x - 3x = -8 - 5
-x = -13
x = 13
Substituting x in GT = 3x - 8; GI = GT
GI = 3(13) - 8
GI = 39 - 8
GI = 31
Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31
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Yesenia buys water to make tea for all her friends. She buys 1 qurt of water and 1/2 gallon of water. How many cups of water does she buy
Answer:
12 cups of water
Step-by-step explanation:
This question has to do with conversion
We are told that she buy 1 quart and 1/2 gallon of water.
Hence,
1 quart of water = 4 cups of water
1 gallon of water = 16 cups of water
1/2 gallon of water = x
Cross Multiple
x = 1/2 × 16 cups of water
x = 8 cups of water.
Therefore, the total cups of water that she bought = 4 cups of water + 8 cups of water = 12 cups of water
Julien's parents want $64,000 at the end of 3 years. They put their money in an account that yields 10% per year compounded monthly. Julien's parents should deposit $______. Round your answer to the nearest dollar.
Answer: [tex]\$47,471[/tex]
Step-by-step explanation:
Given
Julien's parents want $64,000 at the end of 3 years
The rate of interest is 10% annually
Suppose they invested P amount initially
So, compound interest, compounded monthly is
[tex]\Rightarrow A=P\left( 1+\frac{r}{n}\right)^{nt}\quad [\text{n=Numner of compounding periods}]\\\\\text{Insert the values}\\\Rightarrow 64,000=P\left( 1+\frac{0.10}{12}\right)^{12\times 3}\\\\\Rightarrow 64,000=P\left( 1+\frac{10}{12}\right)^{36}\\\\\Rightarrow P=\dfrac{64000}{1.3481}\\\\\Rightarrow P=\$\ 47,471.37\approx \$ 47,471[/tex]
What is the volume of the following rectangular prism?
Answer:
Length * Height * Width, or V = L * H * W. Ex: V = 5 in.
Answer:
28
Step-by-step explanation:
We are given the area of a base and the width of the prism.
Volume = area of base * width
Volume = 8/3 * 21/2 = 28
Help! NO LINKS!!!
I need an answer so if anyone can help,please do!
Necesito esta actividad hecha para mañana y no ne dieron explicación previa
Answer:
uhhugvtrctreex
Step-by-step explanation:
The number of pages in an Algebra 1 book is 99 less than the number of pages in a geometry book. Write and solve an equation to find the number n of pages in the geometry book. (big ideas)
On solving the provided question we can say that *629 = n - 99 is an equation. The textbook contains 728 pages*.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
In other words, the geometry book is 99 pages LONGER than the algebra book, which is 99 pages SHORTER. The solution can be obtained using this equation. I'm sorry, but 530 is not the solution.
629 = n - 99 is an equation. The textbook contains 728 pages*.
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