Ignore the negative sign, since that only affects the sign of the final product
3415₇ × 432₇
You can compute the product by considering the digit expansion, by which I mean first expanding each number as sums of powers of 7:
3415₇ = 3000₇ + 400₇ + 10₇ + 5₇
(It's the same thing as writing, for example, the decimal 3415 as 3000 + 400 + 10 + 5, just in a different base.)
Similarly,
432₇ = 400₇ + 30₇ + 2₇
Then apply the distributive property:
= (3000₇ + 400₇ + 10₇ + 5₇) × (400₇ + 30₇ + 2₇)
= 3000₇ × (400₇ + 30₇ + 2₇)
… + 400₇ × (400₇ + 30₇ + 2₇)
… + 10₇ × (400₇ + 30₇ + 2₇)
… + 5₇ × (400₇ + 30₇ + 2₇)
= {12}00000₇ + {9}0000₇ + 6000₇
… + {16}0000₇ + {12}000₇ + {8}00₇
… + 4000₇ + 300₇ + 20₇
… + {20}00₇ + {15}0₇ + {10}₇
where I use the curly braces to indicate products (written in base 10) of digits that exceed 6. Anything in these braces needs to be properly converted to base 7. For example,
{12}₇ = 7 + 5 = 15₇
So you would have
= 1500000₇ + 120000₇ + 6000₇
… + 220000₇ + 15000₇ + 1100₇
… + 4000₇ + 300₇ + 20₇
… + 2600₇ + 210₇ + 13₇
Add everything up:
• In the 7⁰ place,
3₇
• In the 7¹ place,
1₇ + 1₇ + 2₇ = 4₇
• In the 7² place,
2₇ + 6₇ + 3₇ + 1₇ = {12}₇ = 15₇
• Carry the 1 (underlined). In the 7³ place,
2₇ + 4₇ + 1₇ + 5₇ + 6₇ + 1₇ = {19}₇ = 25₇
• Carry the 2. In the 7⁴ place,
1₇ + 2₇ + 2₇ + 2₇ = {7}₇ = 10₇
• Carry the 1. In the 7⁵ place,
2₇ + 1₇ + 5₇ + 1₇ = {9}₇ = 12₇
• Carry the 1. In the 7⁶ place,
1₇ + 1₇ = 2₇
So, we end up with
3415₇ × 432₇ = 22045543₇
and thus
3415₇ × (-432₇) = -22045543₇
What is the slope of the line that passes through the points (-4, 0)and (-4, -10) ?
Write your answer in simplest form.
Answer:
Slope is undefined or infinity.
Step-by-step explanation:
Which of the following equations could be used to predict the value, V(t), after t years, of a $1000 investment expected to appreciate by 5% each year?
A
V(t)=1000(0.5)t
B
V(t)=1000(1+0.5)t
C
V(t)=1000(0.05)t
D
V(t)=1000(1+0.05)t
Answer:
D
Step-by-step explanation:
The equations could be used to predict the value is
V(t) = 1000 (1+ 5/100[tex])^t[/tex]
What is Future Value?A financial concept known as future value (FV) assigns a value to an asset based on anticipated factors like future interest rates or cashflows. Knowing how much their investment would be in five years, given a projected rate of return, may be valuable for an investor.
We have,
P= $1000
R= 5%
T= time in years
We know that amount
A(t) = P(1 + R/100[tex])^t[/tex]
So, V(t) = 1000 (1+ 5/100[tex])^t[/tex]
Thus, the required function is V(t) = 1000 (1+ 0.05[tex])^t[/tex]
Learn more about Future Value here:
https://brainly.com/question/14860893
#SPJ3
Can someone please help
Answers:
Lateral Area = No lateral area (choice D)Surface Area = 25.97 square inches (choice E)Volume = 12.44 cubic inches (choice A)============================================
Explanation:
Lateral area only applies to prisms and cylinders. Spheres do not have lateral sides, so there is no lateral area.
-----------------------
The radius is 1 & 7/16
Let's convert this to decimal form
1 & 7/16 = 1 + (7/16)
1 & 7/16 = 1 + 0.4375
1 & 7/16 = 1.4375
The radius is r = 1.4375 inches.
-----------------------
SA = Surface area the sphere
SA = 4*pi*r^2
SA = 4*pi*(1.4375)^2
SA = 25.9672267773281
SA = 25.97 square inches (choice E)
-----------------------
V = Volume of the sphere
V = (4/3)*pi*r^3
V = (4/3)*pi*(1.4375)^3
V = 12.4426294974698
V = 12.44 cubic inches (choice A)
Which is the correct answer?
(explain how you got your answer)
Answer:
Option B. f¯¹(x) = ³√(– x – 9)
Step-by-step explanation:
From the question given above:
f(x) = – x³ – 9
f¯¹(x) =?
We can obtain the inverse f¯¹(x) of the above equation by doing the following:
f(x) = – x³ – 9
Replace f(x) with y
y = – x³ – 9
Interchange x and y
x = – y³ – 9
Make y the subject . This is illustrated below:
x = – y³ – 9
Rearrange
x + 9 = – y³
Multiply through by –1
–(x + 9) = y³
y³ = – x – 9
Take the cube root of both side
y = ³√(– x – 9)
Replace y with f¯¹(x)
f¯¹(x) = ³√(– x – 9)
Thus, the inverse of the function
f(x) = – x³ – 9
is
f¯¹(x) = ³√(– x – 9)
Noah picked 3 kilograms of cherries. Mai picked half as many cherries as Noah. How many total kilograms of cherries die Mia and Noah pick together? Group of answer choices LaTeX: 3+\frac{1}{2}3 + 1 2 LaTeX: 3-\frac{1}{2}3 − 1 2 LaTeX: \left(1+\frac{1}{2}\right)\cdot3( 1 + 1 2 ) ⋅ 3 LaTeX: 1+\frac{1}{2}\cdot3
it would be 4.5 total
Answer:
4.5 or 4 1/2. Based on the given conditions, formulate: 3 + 3 / 2 Find common denominator and write the numerators
Step-by-step explanation:
MARK A BRAIN LESS
CARRY ON LEARNING
BRAIN LY FAST
Is -27 greater than -28
Roxanne started making sugar cookies for her friends at 11:35 A.M. It took her 50 minutes to make the dough and 50 minutes to bake all of the cookies. Then, Roxanne spent 40 minutes decorating the cookies with icing and sprinkles. What time was it when Roxanne finished making the cookies?
Include A.M. or P.M. in your answer .Please help me fast !!!
Answer: 1:55Pm
Step-by-step explanation:
Answer:
1:55 P.M
Step-by-step explanation:
You would add 50 and 50 together it 100 add 40 equal 140.2 hours and 20 mins. 11:35 P.M add 2 hours is 1:35 add 20 mins equal 1:55 P.M
PLEASE HELP, BEEN STUCK FOR AN HOUR
How will you graph the function g(x) = (x – 4)+ 12 using the parent quadratic function, f (x) = x2?
9514 1404 393
Answer:
see below
Step-by-step explanation:
We assume your functions are ...
f(x) = x²
g(x) = (x -4)² +12
_____
You need to be able to recognize that g(x) matches a pattern:
g(x) = f(x-h) +k
where h = 4, and k = 12.
In this pattern, the value of h is the number of units the graph is translated to the right. The value of k is the number of units the graph is translated up.
So, g(x) is the same as the graph of f(x), but translated 4 units right and 12 units up.
correct solution to the inequality x+1>5?
Help please tell me
Answer:
x and y are not in a proportional relationship
Step-by-step explanation:
x and y can be said to be in a proportional relationship, if the ratio of each given pair of values (y/x) on the table are equal. The ratio would represent the constant of proportionality.
Let's find out:
(3, 7) = y/x = 7/3 = 2.33
(6, 13) = y/x = 13/6 = 2.17
(9, 19) = y/x = 19/9 = 2.11
(12, 25) = y/x = 25/12 = 2.08
The ratio of each given pair of values are not the same. Therefore, x and y are not in a proportional relationship.
The diagram shows two Parallel lines cut by a transversal. PLEASE HELP!
Answer:
you are right it is option a
Step-by-step explanation:
cause
Write an integer for loss of 18 pounds
PLEASE HELP
So a loss is negative it will be -18 on the number line.
UwU hope this helps
The hose on a power washer is 42-ft. long. If the compressor to which the house is attached is located at the corner of a 28-ft wide house, how can the hose reach up the far corner without moving the compressor?
a. What is the exact height that the hose can reach up?
b. What is the approximate height that the hose can reach up?
9514 1404 393
Answer:
a) 14√5 feet
b) about 31.3 feet
Step-by-step explanation:
a) The 42-ft hose is the hypotenuse of a right triangle with one leg 28 ft. We are asked to find the other leg. The Pythagorean theorem is useful.
h² +(28 ft)² = (42 ft)²
h² = (1764 -784) ft² = 980 ft²
h = √(196·5) ft
h = 14√5 ft
__
b) The approximate height is ...
14√5 ≈ 31.305, about 31.3 feet
what is the percent of change from 800 to 40?
Answer:
95%
Step-by-step explanation:
%Change from 800 to 40 = %Decrease
%Decrease = Old Value - New Value/Old Value × 100%
%Decrease = 800-40/800 × 100%
%Decrease = 760/800 × 100%
% Decrease = 95%(Answer)
Which of the best following statements BEST described the location of -(-6) on a number line?
A. It is 6 units to the left of 0
B. It is 6 units to the right 6
C. It is 6 units to the right of the 0
D. It is 6 units to the left of 6
Answer:
A
Step-by-step explanation:
because it is a
NEED ANSWER ASAP- FOR FINALS
A rectangular swimming pool is 6 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2940 cubic feet. Find the dimensions of the pool.
The smaller dimension of the pool is __ ft.
The larger dimension of the pool is __ ft.
Answer:
The smaller dimension of the pool is 14 ft.
The larger dimension of the pool is 35 ft.
Step-by-step explanation:
We are told that:
The rectangular swimming pool is 6 ft deep. Thus, depth: h = 6 ft
One side of the pool is 2.5 times longer than the other.
Thus, length = 2.5(width)
l = 2.5w and width = w
Volume; V = lwh = (2.5w × w × 6) = 15w²
The amount of water needed to fill the swimming pool is 2940 cubic feet.
Thus;
15w² = 2940
w² = 2940/15
w² = 196
w = √196
w = 14 ft
Length: L = 2.5w = 2.5 × 14 = 35 ft
Csctheta x tantheta= sectheta
Answer:
TRUE
Step-by-step explanation:
That is true, you get 1/cos(Θ) which is sec(Θ)
please give thanks and hit that heart button :)
Im having difficulty with these problems. Can someone please help me out?
1) Solve 2cos x=1
2) Solve: tan x -2sin x tan x=0
3) Solve: cos (2x)= -3^(1/2)/2
Answer:
x=60° or 300°
Step-by-step explanation:
2cosx=1
cosx=1/2
cosx=cos60°,cos(360-60)°
cosx=cos60,cos300
either,
cosx=cos60
x=60
or,
cosx=cos300
x=300
From the definition of absolute value
3|x| = when x≥0
and
3|x| = when x<0.
Answer:
To answer your question use the code ICE on here to get your answer works every time for me hope this helps
need answers before 12:13
Answer/Step-by-step explanation:
17. Slope = rise/run
rise = 5
run = 7
Slope = -⁵/7
18. Slope = rise/run
rise = 4
run = 4
Slope = -⁴/4 = -1
19. Slope = rise/run
rise = 3
run = 5
Slope = -⅗
20. Slope = rise/run
rise = 4
run = 1
Slope = -⁴/1 = -4
I need help please I have to finish this
Answer:
Look at the Screenshot below for the answer
Step-by-step explanation:
Answer:
-5/2
Step-by-step explanation:
According to an accepted chemistry reference, the
heat of vaporization of water is 540 calories per
gram. A student determined in the laboratory that
the heat of vaporization of water was 620 calories
per gram. The student's results had a percent error
of
Answer:
14.8%
Step-by-step explanation:
Step 1: Given data
True value for the heat of vaporization of water (ΔH°vap(T)): 540 cal/g
Experimental value for the heat of vaporization of water (ΔH°vap(E)): 620 cal/g
Step 2: Calculate the experimental percent error
To determine the experimental percent error we will use the following expression.
%E = |ΔH°vap(T) - ΔH°vap(E)|/ΔH°vap(T) × 100%
%E = |540 cal/g - 620 cal/g|/540 cal/g × 100%
%E = 14.8%
The probability of a coin landing on heads when it is flipped is
0.5.
What is this probability written as a percent?
Answer:
50%
Step-by-step explanation:Since there is a 0.5 chance of the coin landing on heads add a zero and take off the .0 and you get 50%.
Answer:
50%
Step-by-step explanation:
The theoretical probability to get either heads or tails is 0.5 (or 50 percent). The probabilities of all possible outcomes should add up to 1 (or 100 percent), which it does.
Let v be a vector with initial point (–5, –11) and terminal point (6, 2). What is Norm of vector v?
StartRoot 24 EndRoot
StartRoot 290 EndRoot
24
290
Answer:
B. [tex]\sqrt{290}[/tex]
Step-by-step explanation:
On Edge, just finished the test.
The correct answer is option B which is the norm of the vector v is √290.
What is a vector?The quantity that needs both the direction and the magnitude for their representation is called a vector.
The norm of vector v will be calculated as:-
Let v be a vector with an initial point (–5, –11) and terminal point (6, 2).
Norm = [tex]\sqrt{(6-(-5))^2+( 2-(-11))^2[/tex]
Norm = [tex]\sqrt{121 + 169\\[/tex]
Norm = [tex]\sqrt { 290[/tex]
Therefore the correct answer is option B which is the norm of the vector v is √290.
To know more about vectors follow
https://brainly.com/question/25705666
#SPJ2
Ms. Kork sold her car for $8700. This was $100 more than two fifths of what she had paid for the car originally. How much mad Ms. Kork paid for the car?
Answer:
8600 is 100 less
3440?
Step-by-step explanation:
what is5+10=
and 20+5=
help
Answer:5+10=15 and 20+5=25 is tht wht u need help on?
Step-by-step explanation:have a wonderful Christmas
Which of the following questions describes the equation = -20? What number, when multiplied by four, is equal to negative twenty? What number, when divided by four, is equal to negative twenty? What number, when multiplied by negative twenty, is equal to four? What number, when divided by negative four, is equal to twenty?
Answer:
An equation contains an equal sign so -20 is not an equation, I think it's a typing error
The lowest common denominator of 1/2 ,1/4 , and 1/4 is:
Answer:
LCD = 24
Step-by-step explanation:
Equivalent Fractions with the LCD
1 1/2 = 36/24
3/8 = 9/24
5/6 = 20/24
3 = 72/24
Hope this Helped! :}
f) -7x + 8x =
simplify
Answer:
The answer is: X
Step-by-step explanation:
-7x+8x = 1x
this means the answer is X
You have 3/8 of a cake. You divide the remaining cake into 6 equal pieces. What fraction of the original cake is each piece? *