[tex]3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10[/tex]
Complete the square on the left side:
[tex]3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196[/tex]
Then the equation becomes
[tex]\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}[/tex]
Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:
[tex]\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)[/tex]
Then in increasing order, the solutions are
c = log₃(14 - √186), c = log₃(14 + √186)
Pls Say
hard question
Answer:
Range is 19.54
Step-by-step explanation:
I. If R = H - L
when R is Range, H is highest value and L is lowest value
R = 25.6 - 6.06
R = 19.54
ANSWER FAST 50 POINTS PLEASE !!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-
[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
Complete the following problem "by hand", using pencil and paper. Start with a general equation, and simplify one step at a time. Or, use the shortcut method shown in class (circling the appropriate values). You must show more than just the answer. Use correct math notation and complete math sentences. The goal is not merely to get the right answer, but to show me that you understand the correct process to arrive at the right answer.
The probability that a randomly selected student is female or left-handed is 107/137.
Probability = required outcome / Total possible outcomes
Probability that student is female or left-handed = [(probability that student is female + probability that female is left-handed)]
Therefore,
Probability that student is female :
P(Female student) = number of female / total number of student
Number of female student = 81
Total number of student = 137
P(Female student) = 81 / 137
P(Left handed student) = number of lefthanded student / total number of student
Number of left handed student = 26
Total number of student = 137= 26 / 137
P(student is female or left-handed) :
P(student is female or left-handed) :[(81/137) + (26/137)] = 107/137
Probability that student is female or left-handed is 107/137
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Follow the instructions to find out what number you end up with.
=========================================================
Explanation:
"Decrease the number by 4 tenths" means we're subtracting off 0.4"Increase the number by 8 thousandths" means we're adding 0.008"Increase the number by 2 tens" is the same as adding on 2*10 = 20The changes of this number are
-0.4+0.008+20The overall net change is -0.4+0.008+20 = 19.608
We'll be adding this net change to the original number
143.351 + 19.608 = 162.959
This value is exact and hasn't been rounded.
test the validity of the following whenever he participates in a race, he is the winner. either he participates in the race or he is sick he is not the winner. therefore he is sick
To test the validity of a given argument, we need to see if we can find a counter-example that makes one of the statements non-valid. If after analyzing the statements we can't find a counterargument, then we can conclude that the argument is valid.
Here we will find that the argument is valid.
We can write this as:
If he participates in a race then he is the winner.
Either he participates in the race, or he is sick.
He is not the winner, then, he is sick.
Now, from the first statement, we know that always that this person participates in a race, he wins.
From the second statement we know that he only participates if he is not sick, we can rewrite that one as:
"If he is sick, then he does not participate in the race".
Finally, from the third one, if he does not win, then he is sick.
This makes sense, he only does not participate when he is sick, then the only races where he is not the winner, are these races where he does not participate, and he does not participate only if he is sick, then this is a valid argument.
Concluding, the 3 statements are valid, as we can't find any counterargument to any of these 3.
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Use the Distributive Property to multiply. 2(b – 7)
Answer:
2b - 14
Step-by-step explanation:
2(b – 7)
2b - 14
Answer:
[tex]2b-14[/tex]
Step-by-step explanation:
Using the distributive property, [tex]2(b-7)[/tex] can be written as [tex](2\cdot b)-(2\cdot7)[/tex] which solved/simplified is [tex]2b-14[/tex]
Man, it's late! Well, hope this helped you out and answered your question!
Can someone help me with this question? please
Answer:
6 cm3
Step-by-step explanation:
3 x 2 x 1 = 6
( 27 thousands 3 hundreds 5 ones) x 10=
Answer:
273,050
Step-by-step explanation:
(27000+300+5)×10
=27305×10
=273050
Mitchell can grow 2 flowers with every seed packet. How many seed packets does Mitchell need to have a total of 4 flowers in his garden?
Answer:
2 seed packets
Step-by-step explanation:
Since Mitchell can grow 2 flowers per seed packet, you can divide the number of flowers he wants with the number of flowers each seed packet can grow. Since he wants 4 flowers, 4 divided by 2 is equal to 2, meaning he needs 2 seed packets to grow 4 flowers.
Christine made $20,000 in taxable income last year. Suppose the income tax rate is 15% for the first $8000 plus 19% for the amount over $8000. How much must Christine pay in income tax for last year?
Answer:
$3480
Step-by-step explanation:
We know that the tax rate for the first $8000 is 15% and after $8000 the tax is 19%.
This means the total amount of money that Christine have to pay is equal to $8000 × 15% + ($20000 (the total) - $8000 (the amount that she already paid for the first $8000)) × 19%
This is equal to $1200 + $12000 × 19%
= $1200 + $2280
= $3480
Therefore, Christine must pay $3480 in income tax.
What is the product of. I really need the now
Answer:
try photo math
Step-by-step explanation:
it may work for this problem
The product of two whole numbers is 891 and their sum is 60 , what is the two numbers
Answer:
33 & 27
I am positive !!!!!!!!!!!!
The product of 2 and a number k, subtracted from 17
A. 2+k+17
B. 2k+17
c. 17-2k
D. 2k-17
hi <3
product means multiplication, therefore we know there has to be a '2k' and we can eliminate option A
also, there is a mention of subtraction, so we can also eliminate option B
now we are left with C and D
it is stated that it is being subtracted FROM 17, therefore the 17 would have to come first
in short, your answer is option C
hope this helps :)
The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
given that,
The product of 2 and a number k, subtracted from 17
we have to find the expression for given statement.
let the number be x
now, we have,
The product of 2 and a number k,
i.e. 2*k = 2k
then, subtracted from 17
i.e. 17 - 2k
so, we get,
x = 17 - 2k
Hence, The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.
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Need help thanks in advance
Answer:
Exact Form: 391 /12
Decimal Form: 32.58 3 (3 is continued)
Mixed Number Form: 32 7/12
Step-by-step explanation: You evaluate and multiply the equation.
Pls pls pls helpp , im begging you , will mark the brainliest
Answer:
angle f=147 degrees (alternate angles)
angle e= 33 degrees
Step-by-step explanation:
angle d =147 degrees
angle f=147 degrees (alternate angles)
angle e +angle d=180 (allied angles)
e+ 147 =180
e =180-147
e = 33 degrees
14. The cost of 10 dozen of caps is Rs.800. How many caps can bebought for Rs.200.
Answer:
123 456lcm divison method
The table below shows the number of miles Trish drives over time in hours. According to the table, at what speed does Trish drive? Trish Time (h) Miles driven 1.5 69 3.5 161 6 276 7.5 345
Answer:
this answer could help you...
Step-by-step explanation:
make me brainiest
The speed where Trish is driving is 46 miles per hour.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
Given the table where a number of hours and miles are shown,
The unit rate of first data = 69/1.5 = 46
the unit rate of second data = 161/3.5 = 46
And so on
So, 46 will be constant of the function
It means the function will be y = 46x and the rate of the function will be y/x = 46.
Hence "The speed where Trish is driving is 46 miles per hour".
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Three million, six hundred twenty nine in numbers
Answer:
3,000,629
Step-by-step explanation:
Start with three million as shown below.
Three million, six hundred twenty nine in numbers
3,000,000
"six hundred twenty nine" is simply
629
The number you want is 629 more than 3 million.
Now add the 639 to the 3 million.
Three million, six hundred twenty nine
3,000,629
HELP PLEASE I DONT HAVE MUCH TIME!!!
Answer:
B
Step-by-step explanation:
The other answers don't divide into rational numbers
How is 1.2 x 10 written is standard decimal notation?
Answer:
12
Step-by-step explanation:
1.2*10 = 1.2
Answer:
12
Step-by-step explanation:
the "normal form" to write numbers : just the digits and a decimal point when needed.
so, 1.2 × 10 = 12
12 is the normal, standard decimal notation.
in some cases it can be also 12.0 or 12.00 (especially with money).
the other form is the scientific notation, where a number is written with its leading digits and the power of 10 as the total value "weight". like in this example 1.2 × 10¹
What is the measure of central angle AOB to the nearest tenth of a degree?
Answer:
Lob is the answer the the 2
The measure of central angle AOB is 2.
What is measure of central angle?The measure of the central angle stands twice the measure of the inscribed angle subtended by the identical arc. (An inscribed angle exists an angle whose vertex fibs on the circumference of the circle.) The sum of the measurements of the central angles of a circle with no common points stands 360°.
Central angles exist subtended by an arc between those two points, and the arc length stands the central angle of a circle of radius one.
The measure of central angle AOB is 2.
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Need help!!
What is the equation of the quadratic functions shown in the graph?
Answer:
F(x)= (x+1)(X-3)
Step-by-step explanation:
Plug in the Zeros of the equation
How many of hours of work is normal for a shift?
Answer: 7-9
Step-by-step explanation: normal job hours
Like an 8, a 9-5 is what most people have so over 40 hours is overtime
if k=(a,b,c) and B=(10,5) find b×k
Answer:
nose eee e e e e e e e e
Step-by-step explanation:
qhhabbejeheh0
Answer:
IS BIGGNER
Step-by-step explanation:
ABC WINNER ZILONG
ANSWERRR BY✏
SUGIONO REALL☠
You bought a total of 6 pens and pencils for $4. If each
pen costs $1 and each pencil costs $.50, how many
pens and pencils did you buy?
Answer: 2 pens and 4 pencils.
Step-by-step explanation:
If you buy 2 pens it is equal to $2.
If you buy 4 pencils it is also equal to $2.
2+2=4
and 2 pens and 4 pencils is equal to 6 in total.
Answer
[tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex] such that [tex]6[/tex] pens and pencils are bought for [tex]\$4[/tex] and each pen costs [tex]\$1[/tex] and each pencil costs [tex]\$0.50[/tex].
Linear EquationThe equation whose variables' highest power is one is known as linear equation.
To find the unknown quantities, always assume it to be a variable and then form the equation based on the conditions given in the question.
How to solve the linear equations?Let the number of pens bought be [tex]x[/tex].
and the number of pencils bought be [tex]y[/tex].
The total number of pens and pencils [tex]=6[/tex].
So, the first equation is,
[tex]x+y=6[/tex]
[tex]x=6-y[/tex] ... (i)
And the costs per pen and pencil is [tex]\$1[/tex] and [tex]\$0.50[/tex] respectively.
So, the second equation is,
[tex]x+0.5y=4[/tex] ... (ii)
Now, solve the pair of linear equations.
Put the value of [tex]x[/tex] in the equation (ii),
[tex]6-y+0.5y=4\\-0.5y=-2\\y=4[/tex]
So,
[tex]x=6-4\\x=2[/tex]
Thus, [tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex].
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What is the answer to -(2-k)
Answer:
Step-by-step explanation:
k-2
Answer:
k-2
Step-by-step explanation:
-(2-k) - Expand the brackets
-2+k - Reorder the equation
k-2
Is (7,-2) a solution to the equation x - 4y = 15?
Please show work to help me understand.
Answer:
yes
Step-by-step explanation:
x - 4y = 15
Substitute the point into the equation and see if the equation is true
7 -4(-2) = 15
7+8 = 15
15 =15
This is true so the point is a solution to the equation
help me out with this!
Answer:
k = 70
Step-by-step explanation:
Since we have been given the value of x to be -ve5 (-5),
we multiply 6 and -5( value of x). Which gives;
-30.
Then add the answer (-30) to 100.
-
K = -30 + 100
= 100 - 30
=70
Note;
(+ * + = +)
( + * - = -)
(- * - = +)
I hope this helps you.
Answer:
[tex]k=70[/tex]
Step-by-step explanation:
[tex]k=6x+100[/tex]
[tex]x=-5[/tex]
[tex]k=6(-5)+100[/tex]
Remove parentheses:- [tex]\left(-a\right)=-a[/tex]
[tex]k=-6\times 5+100[/tex]
Multiply [tex]6\times5= 30[/tex]
[tex]k=-30+100[/tex]
Add [tex]-30+100=70[/tex]
[tex]k=70[/tex]
OAmalOHopeO
When subtracting a negative number from a positive number, move to the left on the number
line.
A.True
B.False
3.0040916 to the nearest hundred thousandth
Answer:
3.004
Step-by-step explanation:
If you were to round it like this: 3.0041, the thousands place would still be 4, so it would come out to be 3.004. Hope that helps!!