Answer:
let g(x)=y
y=6(x-1)
interchange the values of x and y
x=6(y-1)
Make y the subject
x=6y-6
x+6=6y
(x+6)/6=y
This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?
Given:
The table that shows the relationship of the total number of pieces of fruit to the number of bananas.
To find:
Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].
Solution:
If a, b, c are real numbers, then
[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]
The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:
[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]
The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].
Therefore, the correct option is A.
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
Solve log2(x + 5) + log2(x − 5) = log211.
Answer:
x = 6
Step-by-step explanation:
log2(x + 5) + log2(x − 5) = log2 11.
We know that loga (b) + log a(c) = log a( bc)
log2(x + 5) (x − 5) = log2(11)
Multiply
log2(x^2 -25) = log2(11)
Raise each side to the power of 2
2^log2(x^2 -25) = 2^log2(11)
x^2 - 25 = 11
Add 25
x^2 -25 +25 = 25+11
x^2 = 36
Taking the square root of each side
x = ±6
But x cannot be negative because then the log would be negative in log2(x-5) and that is not allowed
x = 6
Answer:
x = 6
Step-by-step explanation:
[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] 11
Determined the define range.
[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] (11), x ∈ ( 5, + ∞ )
We know that [tex] log_a ( b ) + log_a ( b ) [/tex] = [tex] log_a( bc) [/tex]
[tex] log_2[/tex] ( x + 5 ) ( x - 5 ) = [tex] log_2[/tex] ( 11).
[tex] log_2[/tex] ( ( x + 5 ) × ( x - 5 ) ) = [tex] log_2[/tex] ( 11).
Use indentity :- ( a + b ) ( a - b ) = a² - b².
[tex] log_2[/tex] ( x² + 25) = [tex] log_2[/tex] ( 11).
Since , the base of the logarithm are the same. set the arguments equal.
x² - 25 = 11.
Move constant to the right-hand side and change their sign.
x² = 11 + 25
x² = 36.
Take square root of each side.
√x² = √36
x = ± 6
x = 6
x = -6, x ∈ ( 5, + ∞ )
Check if the solutions is in determine range.
x = 6
Banks and other financial institutions offer incentives for people to keep their money in a savings account.
True or False?
it's true because it gives interset or compensation amount to the individuals or organizations which motivates people to save their money in a saving account
PLS ANSWER YA'LL!
A house owner wishes to cover their roof with solar panels. Each solar panel is of the following size.
->The roof section is rectangular 7.2 m by 4.4 m.
->Each solar panel measures 1400 mm by 850 mm.
There needs to be at least a 30 cm gap left at each edge of the roof section. The house owner thinks he can have at least 15 solar panels fitted to the roof section.
Can u agree? If yes, show the working. (Hint: He can rotate the solar panel)
Answer:
Yes
Step-by-step explanation:
The roof is Rectangular :
Dimension of roof section : 7.2 m by 4.4 m
Area of roof = length * width
Area of roof = 7.2 * 4.4 = 31.68 m²
Dimension of solar panels = 1400 mm by 850 mm
Converting to m:
1000mm = 1 m
1400/1000 by 850/1000 = 1.4 m by 0.85 m
Area each solar panel = 1.4 * 0.85 = 1.19 m²
Gap left at each edge :
30cm gap about the 4 edges gives a square with side length 30cm:
30cm = 30/100 = 0.3m
Area of gap left = 0.3² = 0.09 m²
Total area that can be covered = (31.68 - 0.09) m² = 31.59 m²
Maximum number of panels that can be placed on roof section :
Total area that can be covered / area of panel
31.59 m² / 1.19 m²
= 26.54 panels
Find sin 0
A. 16/20
B. 12/16
C. 12/20
D. 16/12
Answer:
16/20
Step-by-step explanation:
Since this is a right triangle
sin theta = opp side / hypotenuse
sin theta = 16/20
Answer:
A.
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]
A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.
Answer:
350.85
Step-by-step explanation:
90.6*2 = 181.2
27*2 = 54 (diameter)
54*pi = 169.646003294
169.646003294 + 181.2 = 350.846003294
350.846003294 = 350.85
What is the area of polygon
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
What could be the coefficient of x once the variable term is isolated on one side of the equation? Check all that apply.
3x - 6(5x + 3) = 9x + 6
1. Distribute: 3x - 30x - 18 = 9x + 6
2. Combine like terms: -27x - 18 = 9x + 6
–36
–27
–24
24
27
36
Answer:
-36,36
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6
Distribute:
3x - 30x - 18 = 9x + 6
Combine like terms:
-27x - 18 = 9x + 6
There are two possible ways to isolate x
On the left
Subtract 9x from each side
-27x - 18 -9x = 9x-9x + 6
-36x -18 = 6
On the right
Add 27x from each side
-27x - 18 +27x = 9x+27x + 6
-18 =36x+ 6
need help with this!!
Answer:
{ 1,3,4,6,7}
Step-by-step explanation:
Do B∩C first
This is B intersect C which means what they have in common
B∩C = {3,6,7}
Then A∪(B∩C)
A union {3,6,7} which means join together ( combine with no duplicates) the two sets
{ 1,3,4,6,7}
asap answer pls ----------------
Answer:
C
Step-by-step explanation:
Evaluate:
18 (5n - 4) = [?]
Answer:
90n-72=0
Step-by-step explanation:
18×5n-18×4=0
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest
form.
Answer:
x = 40
y= 20
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 20 sqrt(3)/ x
x sin 60 = 20 sqrt(3)
x = 20 sqrt(3)/ sin 60
x = 20 sqrt(3)/ sqrt(3)/2
x = 20 *2
x = 40
tan theta = opp /adj
tan 60 = 20 sqrt(3)/y
y = 20 sqrt(3)/ tan 60
y = 20 sqrt(3) / sqrt(3)
y = 20
Graph the inequality.
1
Answer:
hope it helps
Step-by-step explanation:
The median house price in Waterloo Region increased by 3.6% from Jan 1, 2018 to Jan 1, 2019. A home
was purchased in Waterloo Region on April 1, 2019 for $600,000.
(a) Assume this trend continues, write an exponential equation that models the Resale Value of this
home over time.
(b) At this rate, determine the date of the resale price of the home would reach $1 million (Show your
work to accurate to the nearest month)
(c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.
Answer:
The right answer is:
(a) [tex]P(t) = P_o \ e^{0.03536t}[/tex]
(b) [tex]t = 14 \ years \ 6 \ months[/tex]
(c) [tex]P(t) = =621,595.6[/tex] ($)
Step-by-step explanation:
Given:
House price increment rate,
= 3.6% annually
(a)
Let the exponential equation will be:
⇒ [tex]P(t) = P_o e^{Kt}[/tex]
here,
t = 0
P = P₀
t = 1 yr
then,
[tex]P(1) = P_o +3.6 \ persent \ P_o[/tex]
[tex]=1.036 \ P_o[/tex]
now,
⇒ [tex]1.036 P_o = P_o \ e^{K.1}[/tex]
[tex]ln(1.036) = K[/tex]
[tex]K = 0.03536[/tex]
Thus, the exponential equation will be "[tex]P(t) = P_o \ e^{0.03536t}[/tex]".
(b)
We know,
[tex]P_o = 600,000[/tex] ($)
[tex]P(t) = 10,00,000[/tex] ($)
∵ [tex]P(t) = P_o \ e^{0.03536t}[/tex]
[tex]1000000=600000 \ e^{0.03536 t}[/tex]
[tex]\frac{5}{3}= e^{0.03536 t}[/tex]
[tex]ln(\frac{5}{3} )=0.03536 t[/tex]
[tex]\frac{\frac{0.5}{0825} }{0.03536} =t[/tex]
[tex]t = 14.45 \ years[/tex]
or,
[tex]t = 14 \ years \ 6 \ months[/tex]
(c)
[tex]P_o=600,000[/tex] ($)
[tex]t = 1 year[/tex]
Now,
⇒ [tex]P(t) = P_o \ e^{0.03536 t}[/tex]
[tex]=600000 \ e^{ 0.03536\times 1}[/tex]
[tex]=621,595.6[/tex] ($)
Does (x, y) satisfy an equation?
Answer:
Yeah
Step-by-step explanation:
You are riding your bike. At 8:00am you have ridden your bike 23 miles. By 9:00pm you have ridden 179 miles. Find the rate of change in miles per hour. If needed, round your answer to the nearest whole number.
Answer:
12 miles/hour
Step-by-step explanation:
8am to 9pm = 13 hours
in that time we were driving 179-23 = 156 miles.
so, our speed was 156 miles / 13 hours.
now simplify it to our standard miles/hour format :
156/13 = 12
therefore, or standardized speed was
12 miles/hour
Which of the following is a characteristic of science?
Answer:d
Step-by-step explanation:
Answer:
D
explanation:
i got it right on the test
For what value of k are the roots of the quadratic
equation kx²+ 4x+ 1=0 equals and reals."
Answer:
k ≥ 4
Step-by-step explanation:
A Quadratic equation is given to us and we need to find out the value of k for which the equation has real roots. The given equation is ,
[tex]\rm\implies kx^2 +4x +1=0[/tex]
With respect to Standard form of Quadratic equation :-
[tex]\rm\implies ax^+bx+c=0[/tex]
For real roots ,
[tex]\rm\implies Discriminant = b^2-4ac\geq 0[/tex]
Substitute the respective values ,
[tex]\rm\implies b^2-4ac \geq 0\\[/tex]
[tex]\rm\implies 4^2 - 4(k)(1) \geq 0 \\[/tex]
Simplify the LHS ,
[tex]\rm\implies 16 - 4k \geq 0 \\[/tex]
Add 4k both sides ,
[tex]\rm\implies 4k\geq 16 [/tex]
Divide both sides by 4 ,
[tex]\rm\implies \boxed{\blue{\rm k \geq 4}}[/tex]
“The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct?
Answer:
b is the answer
Step-by-step explanation:
An acute angle of a right triangle measures 30°, and the length of the triangle's hypotenuse is 10 ft. Find the missing angle measure and side lengths.
Answer:
missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we understand from the given information that the triangle in question is a special right triangle
and since this is a special triangle the side lengths follows :
the side length that sees <90 is represented by 2x
the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]
and the side length that sees <30 is represented by x
2x = 10 so x = 5 and x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]
What action represents the "!" symbol on a TI 84 plus CE calculator for a Statistics problem??
Answer:
The "!" represents a factorial
Step-by-step explanation:
In math, a factorial when there is an ! followed by a number.
For example, 5! = 5 factorial.
To solve factorials, multiply every integer below the number before the factorial, including the number.
5! = 5 x 4 x 3 x 2 x 1 = 120.
Which of the following is the best definition of the sample space of a
probability event?
A. The number of successful outcomes
B. The measure of how likely an event is to occur
O O O O
C. The set of all possible outcomes
D. The most likely outcome
Answer:
C:The set of all possible outcomes
please explain this to me.
Answer:
Equation of line:- y=2x-7
slope(m)=2
slope of parallel line (m)=2
∴ Equation of parallel line:- y=2x+b
it passes through the point (-3,6)
6=2(-3)+b 6+6=b
b=12
∴ y=2x+12
OAmalOHopeO
A researcher decides to find out whether giving students positive
reinforcement improves or impairs their grades. The researcher's sample
group consists of the following 8 students:
0 Jack
1 Tucker
2 Susie
3 Jill
4 Charianna
5 Trey
6 Ashton
7 Jordan
52197 66082 97867 49397 47924 78900 59414 64755 48733
Which of the following represents a 5-person group selected for the
treatment group using the first number in the line from a table of random
numbers above?
A. Charianna, Tucker, Jack, nobody, Ashton
B. Tucker, Susie, Trey, Ashton, Jordan
C. Trey, Susie, Tucker, Jordan, Ashton
D. Charianna, Tucker, Jack, Ashton, Trey
Answer: C. Trey, Susie, Tucker, Jordan, Ashton
========================================================
Explanation:
The random sub-sequence 52197 66082 helps directly determine who we pick.
The digit 5 is first of that sequence, so we pick Trey first (as he's the 5th student). Then we pick student #2 next, who is Susie.
Up next is student #1, and that would be Tucker
Up next is student #9, but the list only goes high as 7. So we skip over 9
Jordan is next up since 7 is the next digit
Finally, the last selection is Ashton because 6 follows after.
--------------
In other words, the sequence 52197 6 will lead to these selections in the order provided.
5 = Trey2 = Susie1 = Tucker9 = skip, since it's not on the list7 = Jordan6 = AshtonSide note: if we wanted a 6th student, then we'd have to skip over the next 6 since we cannot pick Ashton twice. The 6th selection would be Jack since he's student #0
please answer all the questions above.
Answer:
hope it was helpful!! You are welcome to ask any question
Answer:
Step-by-step explanation:
1) 7 - ( 3+4) = 7 + [- (3+ 4)] = 7 + (-3) + (-4)
(-) is distributed to 3 and 4
A
2) C
I (-3) - 4 I
3) 5 + 3 = 8 miles
B
Find the equation of the line that passes through (1,6) and (3,10).
y=2x+4
y=-2x+4
y=-24-4
Oy-23-4
Answer:
m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2 slope of line
y = m x + b standard form of straight line
y = 2 x + b where b is the intercept at x = 0
b = y - 2 x
b = 6 - 2 = 4 from our first equation
Also, b = 10 - 6 = 4 check from second equation
y = 2 x + 4 is our equation
Check if y = 6 and x = 1 then
y = 2 * 1 + 4 = 6 verifying the first point given
Which expressions are equivalent to the given expression?
Answer:
The answers are option B and E.
Two exponential functions are shown in the table.
Which conclusion about f(x) and g(x) can be drawn from
the table?
X
Х
f(x)=2*
g(x) =
2
4
1
4
1
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
The function f(x) has a greater initial value than g(x).
1
2
1
0
-1
1
2
A-NI-
-2
4
Save and Exit
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Submit
Given:
The two exponential functions are shown in the given table.
To find:
The correct conclusion about the functions f(x) and g(x).
Solution:
The given functions are:
[tex]f(x)=2^x[/tex]
[tex]g(x)=\left(\dfrac{1}{2}\right)^x[/tex]
The function g(x) can be written as:
[tex]g(x)=\dfrac{1}{2^x}[/tex]
[tex]g(x)=2^{-x}[/tex]
[tex]g(x)=f(-x)[/tex]
It means the graphs of f(x) and g(x) are reflections over the y-axis. So, option B is correct.
Since [tex]g(x)\neq -f(x)[/tex], therefore the functions f(x) and g(x) are not the reflections over the x-axis. So, option A is incorrect.
The function f(x) is an increasing function because the base of the exponent is [tex]2>1[/tex]. The function g(x) is a decreasing function because the base of the exponent is [tex]\dfrac{1}{2}<1[/tex]. So, option C is incorrect.
At x=0 the value of f(x) is 1 and the value of g(x) is also 1. It means the functions has same initial values. So, option D is incorrect.
Therefore, the correct option is B.
We can conclude that g(x) is a reflection over the y-axis of f(x).
How to find the transformation that relates the two functions?
The two functions are:
f(x) = 2^xg(x) = (1/2)^xYou can see the graph of these functions at the end of the answer.
You can also notice that g(x) can be written as:
g(x) = (1/2)^x = 2^(-x) = f(-x)
Then this is a reflection over the y-axis, thing that you can also see in the graph below.
So the correct option is:
"The functions f(x) and g(x) are reflections over the y-axis."
If you want to learn more about reflections, you can read:
https://brainly.com/question/4289712