what values of a are the following expressions true?
Expression :-|a-5| =5-a
Answer:-Try putting values of ( a )
Greater than 5 Less than 5 Equal to 5First attempt :- Greater than 5picking random number :-
Putting a = 6 :-
[tex] |a-5| =5-a \\ |6-5| =5-6 \\ | 1| = -1 \\ 1 \cancel = ( - 1) [/tex]
so a is not equal to 6
Putting a = 8
[tex]|a-5| =5-a \\ |8 - 5| =5-8 \\ |3| = - 3 \\ 3 \cancel = - 3[/tex]
a is also not equal to 8
so above values we can find a common result that a not equal to value bigger than 5
Second attempt :- Less than 5picking random number
Putting a equal to 1
[tex]|a-5| =5-a \\|1-5| =5-1 \\ | - 4| =4 \\ 4 = 4[/tex]
a can be equal to 1
Putting a equal to -3
[tex]|a-5| =5-a \\| - 3-5| =5-( - 3) \\ | - 8| = 8\\ 8 = 8[/tex]
a can be equal to -3
So we can have a common result that a can be equal to values less than 5
Third attempt :- a equal to 5putting a equal to 5
[tex]|a-5| =5-a \\ |5 - 5| =5-5 \\ |0| =0 \\ 0 = 0[/tex]
So we can say a can be equal to 5
Result :- (a) can be equal to or less than 5Match graph with choices below!
Answer:
○ [tex]\displaystyle None\:of\:these[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = 2cos\:(2x - \frac{\pi}{2})} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle \boxed{y = 2sin\:2x} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:2x,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(2x - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-2\frac{1}{4}\pi, -2],[/tex]from there to [tex]\displaystyle [-1\frac{1}{4}\pi, -2],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
(3)m+2= (-3)4 . 9 solve for m
Answer:
m = - 6.9
Step-by-step explanation:
3 × (m + 2) = - 3 × 4.9
3m + 6 = - 14.7
3m = - 20.7
m = - 6.9
I am Confused will give brainleist
Answer:
steps 4 and 5
Step-by-step explanation:
i think
Answer:
idrk
Step-by-step explanation:
Dr. David Smith lived 1/13 of his life as a child. He spent 4/39 of his life preparing for an outstanding
medical career. For 1/ 2 of his life, he was a successful surgeon in a famous children's hospital. Since his
retirement, he has lived 13 years on a comfortable pension. How old is he? (unrealistic answer))
Answer:
40 14/25 years
Step-by-step explanation:
Well, this certainly is fun.
First, to find the fraction of the doctor's life which 13 years represents, subtract the fractions from 1 (and in this case l stands for lifetime):
[tex]13 = (1 - (\frac{1}{13} + \frac{4}{39} + \frac{1}{2}))(l)[/tex]
[tex]13 = (\frac{25}{78})(l)[/tex]
So, multiply this equation by the reciprocal of 25/78 to isolate one of l:
[tex]13(\frac{78}{25}) = l[/tex]
[tex]l = 40\frac{14}{25}[/tex] years
please get this right pleaseee
Answer:
22 is the median
the minimum is 16
idrk for number 3 or 5
the maximum is 28
idrk for 6 or 7
Step-by-step explanation:
i wrote some of the answers, all you have to do is use the box plot
a box is 60 cm long. which of these is closest to the length of this box in feet?
1 inch = 2.54 cm
a. 1.84 feet
b. 1.97
c. 2.54
d. 2.82
Answer:
b. 1.97
Step-by-step explanation:
1cm≈0.032feet
60/0.032≈1.97feet
The ratio of dogs to cats in a zoo choir is 4 : 3. There are 6 more dogs than cats. If another 2 cats join the choir, what will be the new ratio of dogs to cats?
Answer:
6:5
Step-by-step explanation:
c = number of cats
d = number of dogs
d = c+6
Set up a ratio:
4/3 = d/c
Then replace d with c+6, so your equation only has one variable.
[tex]\frac{4}{3} = \frac{c+6}{c}[/tex]
Cross multiply
4c = 3(c+6)
Multiply everything in the parentheses by 3.
4c = 3c + 18
Subtract 3c from both sides
4c - 3c = 18
c = 18
d = c + 6 = 18 + 6 = 24
If 2 more cats join, then you will have 20 cats and 24 dogs, so the ratio of dogs to cats will now be 24:20. Divide each side by 4 for a ratio of 6:5.
Circle the irrational number in the list below. 7.27, 5, 9215, 2196
Answer:
7.27 is the irrational number
Step-by-step explanation:
7.27 can not turn into a fraction because it keeps on repeating
There are no Irrational numbers in the list.
We have a set of numbers - 7.27, 5, 9215, 2196.
We have to circle out the Irrational ones.
What are Irrational Numbers?Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction - p/q where p and q are integers.
According to the question, we have -
7.27, 5, 9215, 2196
Now -
7.27 = [tex]$\frac{727}{100}[/tex] → It is Rational.
5 = [tex]$\frac{5}{1}[/tex] → It is Rational.
9215 = [tex]$\frac{9215}{1}[/tex] → It is Rational.
9215 = [tex]$\frac{2196}{1}[/tex] → It is Rational.
All the numbers are Rational as they can be expressed in the form of p/q.
Hence, there are no Irrational numbers in the list.
To solve more questions on Rational and Irrational numbers, visit the link below-
https://brainly.com/question/20400557
#SPJ2
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
C. -16.25 inches
Step-by-step explanation:
First, we need to find out the total rainfall in the three days
0.75 + 0.75 + 0.75 = 2.25
Now, we need to subtract this number from 18.5
18.5 - 2.25 is 16.25
So, your answer is -16.25
I really hope this is right and I really hope this helps!
All real number less than 38
help please do quickly
Answer:
1.79m^2
Step-by-step explanation:
(0.1×1)+2(0.5×0.8×0.1)+(1×0.8)+(1×0.81)
=1.79
Answer:
17.5m
Step-by-step explanation:
You gotta do this:
0.81 x 1 = Top area
((0.8 x 0.1) ÷ 2) x 2 = left side and right side area
1 x 0.1 + Back Area
0.8 x 1 = Bottom
Add them all together and remember that the final answer has to be in metres, you get - 17.5m
Solve for x and y
Y=2/3x-2 y=-x+3
Answer:
[tex]y=0,\:x=3[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}y=\frac{2}{3}x-2\\ y=-x+3\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=-x+3[/tex]
[tex]\begin{bmatrix}-x+3=\frac{2}{3}x-2\end{bmatrix}[/tex]
Isolate x for -x+3=2/3x-2: x=3
[tex]\mathrm{For\:}y=-x+3[/tex]
[tex]\mathrm{Substitute\:}x=3[/tex]
[tex]y=-3+3[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]y=0[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=0,\:x=3[/tex]
Using figure at the right, find:
1. BS
2. RS
3. ST
Answer:
1. BS = 4
2. RS = 2√5
3. ST = 4√5
Step-by-step explanation:
Use the right triangle altitude theorem.
Then use the Pythagorean Theorem.
1.
BT/BS = BS/BR
8/BS = BS/2
(BS)² = 16
BS = 4
2.
2² + 4² = (RS)²
RS = √(20)
RS = 2√5
3.
4² + 8² = (ST)²
ST = √(80)
ST = 4√5
Which expression is equivalent to log subscript 12 baseline startfraction x superscript 4 baseline startroot x cubed minus 2 endroot over (x 1) superscript 5 baseline endfraction? 4 log subscript 12 baseline x one-half log subscript 12 baseline (x cubed minus 2) minus 5 log subscript 12 baseline (x times 1) 4 log subscript 12 baseline x one-half log subscript 12 baseline startfraction x cubed over 2 endfraction minus 5 log subscript 12 baseline 1 log subscript 12 baseline 4 x one-half log subscript 12 baseline (x cubed minus 2) minus 5 log subscript 12 baseline (x) 1 4 log subscript 12 baseline x one-half log subscript 12 baseline (x cubed minus 2) minus 5 log subscript 12 baseline (x 1)
There are four basic properties of logarithms. The solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex].
What are the Properties of logarithms?There are four basic properties of logarithms:
[tex]\rm log_aU+ log_aV = log_a(UV)\\\\\rm log_aU - log_aV = log_a(\dfrac{U}{V})\\\\\rm log_aU^n = n\ log_aU\\\\\rm log_ab = \dfrac{log_xb}{log_xa}[/tex]
The given logarithmic problem can be solved in the following manner,
[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex]
By using the division law of logarithm, [tex]\rm log_a(\dfrac{x}{y}) = log_ax - log_ay[/tex]
[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5} = log_{12}\ {x^4\sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]
By addition law of Logarithm, [tex]\rm log_a(xy)= log_ax+ log_ay[/tex]
[tex]\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]
Using the logarithmic Property, [tex]\rm log\ a^m =mlog\ a[/tex]
[tex]=\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}\\\\=log_{12}\ x^4+ log_{12} (x^3-2)^{\frac12}-log_{12}{(x+1)^5\\\\[/tex]
[tex]=4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]
Hence, the solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]
Learn more about Logarithms:
https://brainly.com/question/7302008
find a9 of an= 3n-7.
Answer:
a9=20
Step-by-step explanation:
an=3n-7
a1=3(1)-7
=3-7
=-4
a2=3(2)-7
=6-7
=-1
a3=3(3)-7
=9-7
=2
a=-4....a2=-1....a3=2
d=a2-a1
=3
a9=a+(n-1)d
=-4+(9-1)3
=-4+8(3)
=-4+24
=20..
I’m so confused help
Distribute: 7(t+4)
Explanation:
Multiply the outer term 7 by each term inside the parenthesis.
7 times t = 7*t = 7t7 times 4 = 7*4 = 28We then add up those results, combining like terms if possible.
That's how we get to 7t + 28
Answer:
7t+28
Step-by-step explanation:
multiply each term in the parentheses by 7
7t+7×4
multiply the numbers
7t+28
565, 961, 867, 517, 627, 714, 517, 728
What is the range of these areas in square feet?
Answer:
No Clue
Step-by-step explanation:
A store pays $8 for a pool noodle. The markup is 20%. What is the selling price?
Answers: he markup price is $9.6
You will be paying 120% which is 1.20 as a decimal
So you multiply. 8(1.20) which gives you $9.6
Step-by-step explanation: thank you for letting me answer this question hope it's helpful
Ryan walked 2 1/2 miles in 3/4 hours find unit
Answer:
2/3
Step-by-step explanation:
Divide 1/2 by 3/4 to get 1/2 x 4/3 = 2/3 mph
which statements are true when solving x^2=81
Answer: x
2
=
81
can be written as
x
2
−
81
=
0
by property ,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
The expression becomes
x
2
−
(
9
)
2
=
0
(
x
−
9
)
(
x
+
9
)
=
0
equating each of the terms with zero we obtain the solution
x
−
9
=
0
and
x
+
9
=
0
the solutions are
x
=
9
or
x
=
−
9
Step-by-step explanation:
Answer:
A) Take the square root of both sides to solve
E) x = ±9
Step-by-step explanation:
The cost of renting a car for one day is $39 plus 15 cents per mile driven. In a graph of the situation, what does the cost per mile driven represent?
Answer:
It will represent the slope of the graph
Step-by-step explanation:
Here, we are interested in getting what the cost per mile driven represent
From the information, we can represent the cost as;
C = 15d + 39
In this case we have a representation of the cost using the fixed daily cost(y-intercept) and the cost depending on the number of miles driven which will change based on the number of miles.
Since it is changing, it represents the slope of the function for cost
Among all pairs of numbers with a sum of 39, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms
Answer:
39/2, 39/2 give a maximum product.
Step-by-step explanation:
Let 1 number be x then the other is 39-x.
Product P = x(39 - x)
= 39x - x^2.
Finding the derivative:
dP/dx = 39 - 2x
When P is a maximum or minimum dP/dx = 0, so
39 - 2x = 0
x = 39/2.
The 2 numbers are both 39/2.
10 points
4. An expression is shown. Which is equivalent to this expression? *
4x^4- 16x^2
A. 0 (4x - 2)(x + 2)
B. 4x2(x - 2)(x + 2)
C. x2(x - 4)(x + 4)
D. 4(x2 - 2)(x2 + 2)
Find a4 in the sequence given by {a1=-3 and an=an-1+7
Answer:
a4 = -12
Step-by-step explanation:
Activity 1 Lesson 1 Patterns, Sequences, and Rules
AB, CD, and EF intersect at O. If CD is perpendicular to EF and m
Answer:
m(∠AOF) = 148°
Step-by-step explanation:
From the figure attached,
CD intersects line EF at a point O.
Line CD is perpendicular to the line EF.
m(∠AOE) = 32°
m(∠COE) = 90°
Since m(∠COE) = m(∠AOE) + m(∠AOC) = 90°
32° + m(∠AOC) = 90°
m(∠AOC) = 90° - 32° = 58°
m(∠AOF) = m(∠AOC) + m(∠COF)
= 58° + 90°
= 148°
Therefore, m(∠AOF) = 148° will be the answer.
what are the solutions of the quadratic equation 4x^2-8x-12=0
Answer:
x₁ = -1, x₂ = 3Step-by-step explanation:
[tex]4x^2-8x-12=0\\{}\qquad\qquad^{\div4\qquad\div4}\\x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\\\\x+1=0\quad\vee\quad x-3=0\\\\x=-1\quad\vee\quad x=3[/tex]
Can someone please help me asap?!?! I’ll mark brainlist !
Answer: $36.80 and the difference is $9.20
Step-by-step explanation:
Solve for x
Show work please
Answer:
[tex]\tt x=5[/tex]
Step-by-step explanation:
[tex]\tt 18x-5=13x+4x+1-11[/tex]
[tex]\tt 18x-17x=15-10[/tex]
[tex]\tt x=5[/tex]
~
HELP WILL GIVE BRAINLIEST!!!!
Answer:
2 x 20^2
Step-by-step explanation:
I did it on paper and looked it up to make sure