9514 1404 393
Answer:
k = 3
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
__
Using these rules, we can simplify the left-side expression, then equate exponents of the same base.
[tex](3)^2(3^2)^k=3^8\\\\(3^2)(3^{2k})=3^8\\\\3^{2k+2}=3^8\\\\2k+2=8\qquad\text{equate exponents}\\\\k+1=4\qquad\text{divide by 2}\\\\\boxed{k=3}\qquad\text{subtract 1}[/tex]
Evaluate the expression.
6(3 + 5)
26.
4
HELP
Answer =1267.2
Step-by-step explanation:
6(3+5)26.4
6×8×26.4
48×26.4
1267.2 is the answer
please help in solving this math problem
9514 1404 393
Answer:
Rs 3200
Step-by-step explanation:
The actual selling price was 20% below the cost price, so was ...
sp = cp(1 -20%) = 0.80cp
Had the selling price been raised, the selling price would have been 5% above the cost price:
sp +800 = cp(1 +5%) = 1.05cp
Subtracting the first equation from the second gives ...
(sp +800) -(sp) = (1.05cp) -(0.80cp)
800 = 0.25cp . . . . . . . simplify
3200 = cp . . . . . . . . multiply by 4
The cost price was Rs 3200.
write 3.777777777 as a mixed number
m is the midpoint . LM = x+9 MN = 4x find the length of LN
Step-by-step explanation:
MN=x+16MN=x+16LN=4x+16MN=x+16LN=4x+16LM+MN=LNMN=x+16LN=4x+16LM+MN=LNLM+(x+16)=4x+16MN=x+16LN=4x+16LM+MN=LNLM+(x+16)=4x+16LM=(4x+16)-(x+16)MN=x+16LN=4x+16LM+MN=LNLM+(x+16)=4x+16LM=(4x+16)-(x+16)LM=4x+16-x-16MN=x+16LN=4x+16LM+MN=LNLM+(x+16)=4x+16LM=(4x+16)-(x+16)LM=4x+16-x-16LM=3xMN=x+16LN=4x+16LM+MN=LNLM+(x+16)=4x+16LM=(4x+16)-(x+16)LM=4x+16-x-16LM=3x MN=x+16LN=4x+16LM+MN=LNLM+(x+16)=4x+16LM=(4x+16)-(x+16)LM=4x+16-x-16LM=3x 3x=x+16 3x-x=16 2x=16 x=16/2 x=8 MN=x+16=8+16=24f(x)=x^4+3, g(x)=x-7 and h(x)=square root of x then f(g(h(x))=
Answer:
x² - 28x√x + 294x - 1372√x + 2404
Step-by-step explanation:
f(x) = [tex]x^{4}[/tex] + 3
g(x) = x - 7
h(x) = √x
f(g(h(x))) - ?
g(h(x)) = √x - 7
f(g(h(x))) = [tex](\sqrt{x} -7) ^{4}[/tex] + 3 = ( √x - 7 )² × ( √x - 7 )² + 3 =
= (x - 14√x + 49)(x - 14√x + 49) + 3 =
= x² - 14x√x + 49x - 14x√x + 196x - 686√x + 49x - 686√x + 2401 + 3 =
= x² - 28x√x + 294x - 1372√x + 2404
PLEASE HELP!!! How does the multiplicity of a zero affect the graph of the polynomial function?
9514 1404 393
Answer:
2, 4, 61crossStep-by-step explanation:
Consider a zero at x=1.
If it has multiplicity 1, the corresponding factor is (x -1). Now consider the sign of that factor for x = 1.1. The value is (1.1 -1) = 0.1, a positive number.
When the value of x is 0.9, the factor is (0.9 -1) = -0.1, a negative number.
This tells you that values to the left of a zero make the factor(s) associated with that zero be negative. For x-values to the right of the zero, the factor(s) will be positive.
If the multiplicity is even, the product of those factors is positive on either side of the zero. (A negative number to an even power is a positive number.) That is, the graph will not change sign from one side of an even-multiplicity factor to the other. At an odd-multiplicity factor, the graph changes sign.
__
For the problem at hand, the only even-multiplicity factor is (x -1), so the graph will not change sign at x=1. It will touch the axis (be tangent to the x-axis), but will not cross. The other zeros have odd multiplicity (1 or 3), so the graph will change sign there.
It is worthwhile to note that the higher the multiplicity, the "flatter" the graph is at the zero. You can see this in the attachment by comparing the shape of the graph at x=6 with the shape at x=2 (also an upward zero crossing).
_____
Additional comment
You may wonder why the curve is below the x-axis at x=1 when the product of the factors in that neighborhood is always positive. The reason is that there are an odd number of zeros to the right of x=1, so the product of those factors is negative.
435 divided by 15 equals what?
Cody won 64 super bouncy balls playing hoops at the county fair. At school he gave three to every student in his math class. He only has 7 remaining. How many students are in his class ?
need algebraic equation too
write in descending order . answer it as soon as possible
Step-by-step explanation:
7[3]
3[7]
I don't hv the square root key
plss mark brainliest
Sample annual salaries (in thousands of dollars) for employees at a company are listed.
41 54 61 48 27 27 41 54 61 31 48 41 47
(a) Find the sample mean and sample standard deviation.
(b) Each employee in the sample is given a 5% raise. Find the sample mean and sample standard deviation for the revised data set.
(c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set.
(d) What can you conclude from the results of (a), (b), and (c)?
Answer:
Down
Step-by-step explanation:
List from low to high
27 27 31 41 41 41 47 48 48 54 54 61 61
a. Mean = sum of sample/2
Mean = 581 / 2 = 290.5
b. Mean + 5%
290.5 + 5% = 305.025
c. 305.025 / 12 = 25.41875
d. Mean is ratio. Thus the adding and dividing with anything will affect the mean overall
Integers bigger than 3 and smaller than 10
Answer:
There are 6 integers in-between 3 & 10
Explanation:
Integers are simply whole numbers.
4,5,6,7,8,9.
Find the nth term for the following sequences, 100,96,90,82,72.(an^2+bn+c)
9514 1404 393
Answer:
t(n) = -n^2 -n +102
Step-by-step explanation:
We can use the first 3 terms to find a, b, c.
a(1)^2 +b(1) +c = 100
a(2)^2 +b(2) +c = 96
a(3)^2 +b(3) +c = 90
Subtract the first equation from the other two:
3a +b = -4 . . . . . . [eq4]
8a +2b = -10 . . . . [eq5]
[eq5] can be reduced to
4a +b = -5 . . . . . . [eq6]
Subtracting [eq4] from [eq6] gives ...
(4a +b) -(3a +b) = (-5) -(-4)
a = -1 . . . . . . . . simplify
Filling that into [eq4], we get
3(-1) +b = -4
b = -1 . . . . . . . add 3
Putting the values for 'a' and 'b' into the first equation gives ...
-1 +-1 +c = 100
c = 102
Then the n-th term t(n) of the sequence is ...
t(n) = -n^2 -n +102
_____
Additional comment
As you might guess, there is a generic solution for quadratic sequences. In terms of the first term (a1), first first difference (d1), and second difference (d2), the coefficients can be written as ...
a = d2/2b = d1 -3ac = a1 -d1 +d2This sequence has first differences of -4, -6, -8, -10, and second differences of -2. Putting the sequence values into the above formulas, we find ...
a = -2/2 = -1b = -4 -3(-1) = -1c = 100 -(-4) +(-2) = 102 . . . . . as aboveThe perimeter of a rectangle is 92 cm. If the length is 22 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation.
Answer:
W = 24cm
Step-by-step explanation:
p of a rectangle = 92
L = 22cm and W = ?
p = 2(L+W)
92 = 2(22+W)
92 = 44 + 2W
2W = 92 - 44
2W = 48
W = 48/2
W = 24cm
Which two integers is 91 squared by 3 between
Answer:
9 and 10
Step-by-step explanation:
[tex]-2b-(-7)=11[/tex]
[tex] - 2b - ( - 7) = 11 \\ \\ - 2b + 7 = 11 \\ \\ - 2b = 11 - 7 \\ \\ - 2b = 4 \\ \\ b = \frac{4}{ 2} \\ \\ b = 2[/tex]
Hope it help youAnswer:
b = -2
Step-by-step explanation:
[tex] - 2b - ( - 7) = 11[/tex]
[tex] - 2b + 7 = 11[/tex]
[tex] - 2b + 7 - 7 = 11 - 7[/tex]
[tex] - 2b = 11 - 7[/tex]
[tex] - 2b = 4[/tex]
[tex]b = 4 \div( - 2) = - 4 \div 2 [/tex]
[tex]\boxed{\green{b = - 2}}[/tex]
I need you help, help me pleaseeeee
Answer:
y=4x+2 is answer .......
23 + 3.54 ÷ 3 − 1.089
Answer:
23.089
Step-by-step explanation:
Always divide first then continue with subtraction then addition.
Hey there!
Just do PEMDAS
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
23 + 3.54 / 3 - 1.089
= 23 + 3.54 / 3 - 1.089
3.54 / 3 = 1.18
= 23 + 1.18 - 1.089
23 + 1.18 = 24.18
= 24.18 - 1.089
= 23.091
Answer: 23.091
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A hotel has a total of 7 floors if there are 35 standard rooms on each floor how many standard rooms are there
Answer:
245
Step-by-step explanation:
multiple the amount of rooms on each floor (35) by the amount of floors (7)
35x7=245 rooms
Paul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.30. After one month, Paul bought 12 passes and spent a total of $22.60.
How much did he spend on the student discount card?
Answer:
$10.24
Step-by-step explanation:
12(1.30)=12.36
22.60-12.36=10.24
Write the equation of the line that
Passes through (-9,4) and 10,-2)
Answer:
y = -6/19x - 2
Step-by-step explanation:
First we need to find the slope and we can do that by using slope-intercept form [ y2-y1/x2-x1 ].
-2-4/10-(-9)
-6/19
Second we can find the y-intercept using slope intercept form [ y = mx + b], the slope, and a given point.
y = -6/19x + b
4 = -6/19(-9) + b
4 = 54/19 + b
-2 = b
Third we will input all the data we solved for back into the formula.
y = -6/19x - 2
Best of Luck!
Help me pleaseeeesndjkdnskxndkdjd
Step-by-step explanation:
[tex]8x - 3 = 5 + 4y[/tex]
Isolate y first subtract 5 from both sides
[tex]8x - 8 = 4y[/tex]
Divide both sides by 4.
[tex] \frac{8x - 8}{4} = y[/tex]
[tex]2x - 2 = y[/tex]
y= 1
Step-by-step explanation:
Solve for y:
8x - 3 = 5 + 4y
8x = 4y + 5+3
Divide both sides by 8
x = 1÷2y + 1
plug into equation
8 (1÷2y +1) - 3 = 5 + 4y
Distribute
8÷2+ 8 - 3 = 5 + 4y
4 + 5 -5 = 4y
Combine like item
4 = 4y
divide both sides by 4
y= 1
Help ASAP pleaseeee!!!!!
Answer:
x = -2/ 9
Step-by-step explanation:
[tex] \frac{2}{5}(x - 2) = 4x \\ \frac{5}{2} \times \frac{2}{5}(x - 2) = 4x \times \frac{5}{2} \\ x - 2 = 10x \\ 9x = - 2 \\ x = \frac{ - 2}{9} [/tex]
a circle has a radius of 4m. find the circumference of the circle show your worth and strictly answering used 3.14 for pi
Answer:
25.12
Step-by-step explanation:
Circumference (C) = 2πr
Where r = radius
We want to find the circumference of a circle with a radius of 4m ( this means that r = 4 )
To do so we simply plug in the value of r into the circumference formula
Formula: C = 2πr
r = 4 ( note that it says use 3.14 for π )
plug in values
C = 2(3.14)(4)
Simplify
C = 25.12
Can someone help me (Geometry)
Answer:
sum of angles on a straight line =180 degrees
DAB=180-36-35=109 degrees
A king Palm can grow about 21 feet a year . Estimate the height of the kind palm , yard ,after 15 years
Answer:
10.5 yards after 15 years
Step-by-step explanation:
2.1 feet times 15 years, which equals to 31.5 feet, convert 31.5 feet into yards, so divide it by 0.3, and that equals to approximately 10.5 yards
hi guys all can come
qwo-jtvf-xkb
Answer
Hello
how are you
Kakuro is like a crossword puzzle with numbers.
9514 1404 393
Answer:
[[. . 3 6 .][1 3 4 9 .][9 2 . 7 1][. 1 2 8 3][. 4 9 . . ]]
Step-by-step explanation:
It is helpful to remember that the first four digits {1, 2, 3, 4} total 10, and the last four digits {6, 7, 8, 9} total 30. It is also worthwhile to note that the smallest sum of two digits is 3 = 1+2, and the largest sum of 2 digits is 17 = 8+9. Some sums can only be made one way: 4 = 1+3, 16 = 7+9.
Here, we will refer to rows 1-5 from the top down, and columns 1-5 from the left to right.
__
Based on the above, column 5 can only be made one way: 1+3. Column 4 can only be made one way: 9+8+7+6. Then the choices for row 3B will be 1+7 or 5+3. We know it can't be 5+3 because 5 is not part of column 4. This makes our first fill-in (row, column) be (3,4)=7, (3,5)=1, (4,5)=3.
The sum of the remaining cells in row 4 must be 14-3 = 11, and cell (4,4) must be 6, 8, or 9. It cannot be 9, because that would require the remaining two cells to have a sum of 2, which they cannot. So, cell (4,4) is 6 or 8.
Cell (1,4) cannot be 9, either, because we cannot use 0 in cell (1,3). Then the only place for 9 in column 4 is in cell (2,4)=9.
With cell (1,4) being restricted to 6 or 8 (the two remaining numbers in column 4, cell (1,3) must be 3 or 1, and cell (2,3) must be 4 or 6. It cannot be 6 because that would require a sum of 2 in the first two cells of row 2, so (2,3)=4, (1,3)=3, and (1,4)=6. This makes (4,4)=8 and the remaining two cells of row 4 must be 1 and 2. 1 cannot go in (4,3), so we must have (4,3)=2 and (5,3)=9, (5,2)=4, (4,2)=1. That leaves 2 and 3 for rows 2 and 3 of column 2. The first two cells of row 2 must total 4, so must be 1 and 3. Cell (2,2) cannot be 1, so must be 3, leaving (2,1)=1, (3,1)=9, (3,2)=2 and that completes it.
The fill-ins are ...
[. . 3 6 .]
[1 3 4 9 .]
[9 2 . 7 1]
[. 1 2 8 3]
[. 4 9 . . ]
Which of the following is an arithmetic sequence?
Answer:
please mark me brainliest pleaseMatch the expression to its value.
104
1
= 0.01
102
104
102
10,000
10-4. 102
1
= 0.000001
109
10-4
1
= 0.0001
10-
Answer:
Ans; 10⁴ —> 10, 000
Ans; 10-⁴ / 10² —> 1/ 10⁶ = 0. 000 001
Ans; 10-⁴ × 10² —> 1/ 10² = 0.01
Ans; 10-⁴ —> 1/ 10⁴ = 0. 000 1
I hope I helped you^_^
Answer:
A=a
B=d
C=c
D=b
Step-by-step explanation:
Express (16^3)^1/2
in simplest radical form.
Answer:
I assume you mean 16^(1/3) i.e. the cube root of 16
I am also assuming you mean the real cube root because, as you may know, every non-zero real number has three cube root - one real and two complex conjugates.
Since 16 = 8 x 2 and 8 = 2³ then (2³ x 2)^1/3 = (2³)^1/3 x 2^1/3 = 2 x 2^1/3
You might check that the cube root of 16 is about 2.52 which is twice the cube root of 2
Step-by-step explanation: