What are the steps to this problem (along with the answer)?
Answer:
x = 3
Step-by-step explanation:
In this piece-wise function, there are three defined sections, each for a different range of x. To find an x where y is -9, we have to set all parts of it equal to -9.
-x, x < -3
So, we can start by setting -x equal to -9 and solve for x:
-x = -9
x = 9
Our domain for this piece of the function is supposed to be x < -3. x = 9 does not fit into this range, meaning, in this range, there is no x for y = -9.
2x, -3 ≤ x ≤ -2
We can set the value 2x equal to -9 and, again, solve for x:
2x = -9
x = -4.5
The solution x = -4.5 does not fit into the defined domain of -3 ≤ x ≤ -2, therefore it is not a solution.
-x^2, x > -2
One last time, we can set -x^2 equal to -9 and solve for x:
-x^2 = -9
x^2 = 9
x = 3, x = -3
We are looking for a solution that fits into the domain, x > -2, x = -3 does not work, but x = 3 does.
In conclusion, the only solution where it fit the domain was x = 3
Answer:
x = 3
Step-by-step explanation:
x = - 3 in interval - 3 ≤ x ≤ - 2 then f(x) = 2x , so
f(- 3) = 2(- 3) = - 6 ≠ - 9
x = 9 in interval x > - 2 then f(x) = - x² , so
f(9) = - 9² = - 81 ≠ - 9
x = 3 in interval x > - 2 then f(x) = - x²
f(3) = - 3² = - 9
x = - 4.5 in the interval x < - 3 then f(x) = - x , so
f(- 4.5) = - (- 4.5) = 4.5
Thus
y = - 9 when x = 3
Can you guys help me find x for both
Answer:
x = 6 and x = 9
Step-by-step explanation:
16
MN is half the length of KL
MN = [tex]\frac{1}{2}[/tex] × 12 = 6
--------------------------------------------
17
Δ LMN and Δ LJK are similar triangles, so the ratios of corresponding sides are equal, that is
[tex]\frac{LM}{LJ}[/tex] = [tex]\frac{MN}{JK}[/tex] , substitute values
[tex]\frac{x}{x+9}[/tex] = [tex]\frac{8.5}{17}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = x + 9 ( subtract x from both sides )
x = 9
4. PLEASE HELP ME
Which of the quadratic functions has the widest graph?
A. y= -4/5x2
B. y= -4x2
C. y= 1/3x2
D. y= 0.3x2
Answer:
D. y= 0.3x2
Step-by-step explanation:
In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.
Can someone please help me out
Step-by-step explanation:
[tex] \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} [/tex]
You wait in line for hours to get the new special edition Nikes for $250, but you have to pay 5.3% in Virginia state sales tax. What is the total you will pay?
Answer:
263.25
Step-by-step explanation:
250 x .053 (5.3%) = 13.25 tax
250 + 13.25 = 263.25 price plus sales tax
Answer:
263.25
Step-by-step explanation:
If Ф ∈ (0, pi/2) and tan(pi cosФ) = cot(pi sinФ), then cos(Ф- pi/4) is equal to?\
Answer:
please see the answer in the picture.
(c+d)^2+11(c+d)+30
Factor completely.
Answer:
firstable give c+b a polynomial value like x
so its will be x^2+11x+30
after the we have to factor it
30=6×5
and 11=6+5
so its will become
(x+6)×(x+5)=x^2+11x+30
x=c+d
(c+d+6)×(c+d+5)=(c+d)^2+11(c+d)+30
have a great day
Which graphs are the graphs of even functions?
5/21 as a decimal rounded to 3 decimal places
[tex] \sf \: \frac{5}{21 } \: rounded \: to \: 3 \: decimal \: places \: is \: \boxed{ \underline{ \bf0.238}}. \\ \longrightarrow \sf \: Just \: divide \: 5 \: by \: 21 \: upto \: 3 \: decimal \: places \\ \sf \: to \: get \: the \: answer.[/tex]
Use special right triangle ratios to find the lengths of the other leg and the hypotenuse
Answer:
leg = 18
hypotenuse = 18 sqrt(2)
Step-by-step explanation:
We know that sin theta = opp side / hypotenuse
sin 45 = 18 / hyp
hyp sin 45 = 18
hyp = 18 / sin 45
hyp = 18 sqrt(2)
Since this is an isosceles triangle ( the two angles are the same measure), the two legs have to be the same length
leg = 18
the lengths of the other leg and the hypotenuse
is 18 units and 18[tex]\sqrt{2}[/tex]units respectively.
Answer:
Solution given:
Let <C=<B=45°
AB=18 units
BC=?
AC=?
again
By using
By usingspecial right triangle ratios
sin C=opposite/hypotenuse=AB/AC=18/AC
Sin 45=18/AC
AC=18/sin45
AC=hypotenuse=18[tex]\sqrt{2}[/tex]units
again
Tan A=opposite/adjacent=BC/AB=BC/18
Tan45=BC/18
BC=Tan45*18
BC=length of another leg=18 units.
Use the expression, X^2-7
What is the value of the expression above when n=5
Answer:
18
Step-by-step explanation:
X^2 - 7 =
Since we need to evaluate the expression when X = 5, we replace X with 5.
= 5^2 - 7
Now, according to the correct order of operations, we need to do the exponent first. 5^2 = 5 * 5 = 25
= 25 - 7
Finally, we subtract.
= 18
Answer: 18
ASAP HELP!! PLEASEEEE!!
Answer:
Step-by-step explanation:
5.1, please this is just a guess from using my head to calculate
write 5 lcms of 100 and 120
Answer:
The LCM of 100 and 120 is 600.
The LCM of 5 and 120 is 120.
LCM of 5 and 100 is 100.
Step-by-step explanation:
I think this is the answer . If it is not sorry .
The volumes of two similar solids are 512cm3 and 2197cm3. If the smaller solid has a surface are of 960cm2, find the surface area of the larger solid. Part 1: find the similarity ratio by taking the cube root of each volume. Show your work. Part 2: use your answer from part 1 to find the ratio of the surface areas. Show your work. Part 3: set up a proportion and solve to find the surface area of the larger solid.
Answer:
see below
Step-by-step explanation:
Part 1:
(512) ^ 1/3
-------------------
(2197) ^ 1/3
8
-----
13
The scale factor is 8:13
Part 2
The ratios of the areas is related by scale factor squared
8^2
-----
13^2
64
------
169
Part 3
64 960
------ = ----------------
169 SA larger
Using cross products
64 * SA = 169 * 960
64 SA = 162240
Divide each side by 64
64 SA/ 64 = 162240 / 64
SA = 2535
2535 cm^2
Find the missing segment in the image below
Answer:
8? not sure tho....
Step-by-step explanation:
HELP ME WITH THIS PLEASE PLEASE SHOW ME THE FORMULA FOR LETTER C
Answer:
Which subject is this . please tell
Answer:
see explanation
Step-by-step explanation:
1
(a)
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ = (8, 3) and (x₂, y₂ ) = (10, 7)
m = [tex]\frac{7-3}{10-8}[/tex] = [tex]\frac{4}{2}[/tex] = 2
(b)
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
(c)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (8, 3) into the partial equation
3 = - 4 + c ⇒ c = 3 + 4 = 7
y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of perpendicular line
--------------------------------------------------------------------------
2
(a)
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (4, 4)
m = [tex]\frac{4-5}{4-3}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1
(b)
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1
(c)
y = x + c ← is the partial equation
To find c substitute (3, 5) into the partial equation
5 = 3 + c ⇒ c = 5 - 3 = 2
y = x + 2 ← equation of perpendicular line
What is the area of this triangle
Answer:
14
Step-by-step explanation:
7*4*1/2=14
Select the true statement about triangle ABC.
A. cos A = cos C
B. cos A = sin C
C. cos A = sin B
D. cos A = tan C
Answer:
B
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{13}[/tex]
sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{5}[/tex]
Then
cosA = sinC → B
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
What is 1/4 0.75 1/3 0.5 greatest to least
Answer:
1/4 = 1 ÷ 4 = 0.251/3 = 1 ÷ 3 ≈ 0.330.750.50.75 → 0.5 → 1/3(0.33) → 1/4(0.25)
Need help please need it quick
Answer:
Choice A
Step-by-step explanation:
An arithmetic sequence is one which has an incremental change.
for our answer, our change is +5
3. A rectangle has a length of 2x – 9 and a width of x2 + 3x – 4. What is the polynomial that models the area
of the rectangle?
Answer:
(C) 2x^3 - 3x^2 - 35x + 36
Step-by-step explanation:
First multiply 2x by x^2 + 3x - 4:
(2x)(x^2 + 3x - 4)
2x^3 + 6x^2 - 8x
Next multiply -9 by x^2 + 3x - 4:
(-9)(x^2 + 3x - 4)
-9x^2 - 27x +36
Now add the two polynomials by adding like terms:
(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)
2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36
2x^3 - 3x^2 - 35x + 36
Hope this helps (●'◡'●)
Help me to prove it
Answer:
see explanation
Step-by-step explanation:
Using the identities
cotA = [tex]\frac{1}{tanA}[/tex]
cot²A = cosec²A - 1
tan²A = sec²A - 1
Consider the left side
(cotA + tanA)² ← expand using FOIL
= cot²A + 2cotAtanA + tan²A
= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1
= cosec²A - 1 + 2 + sec²A - 1
= sec²A + cosec²A - 2 + 2
= sec²A + cosec²A
= right side, thus proven
Options:
Rotation
Reflection
Translation
Answer: Reflection
Step-by-step explanation: Please mark brainliest
if a=(p+q),b=(p-q)and c=qsquare -psquare, show that ab+c=0
Answer:
I think this is the ans
Step-by-step explanation:
ab+c=0
(p+q)(p-q)=0
p Square-q Square =0
0=p Square-q Square
Question 5.
Given that cos(O) = 4/5, find:
a) sin(0)
b) tan (0)
Step-by-step explanation:
here's the answer to your question
Plz help me asap !!!
Answer:
all I know is sin square A +cos square A =1
According to the synthetic division below, which of the following statements are true?
Answer:
Step-by-step explanation:
That 3 sitting outside there in that little "box" thing is a root/solution/zero of the polynomial. The numbers underneath the line are the coefficients of the depressed polynomial, which means that the polynomial is 1 degree lower than the degree with which we started. If we started with an x-squared, this degree is a single x, better known as linear (a line). Anyway, (x - 3) is a zero of the polynomial, which also means that it's a factor. So A applies. x = 3 is a root, so C applies. And F also because the depressed polynomial, the remainder, is 2x + 4.
Which of the following lines is parallel to the line
y = 1/2x -6
Select one:
a) y=-1/2x-6
b) y=2x+1
c) y=-1/2x+5
d) y=1/2x-3
Answer:
y = 1/2x - 3 (option - d)
Step-by-step explanation:
The lines are parallel if they have the same slope/gradient. So by comparing with y = mx + c (where 'm' is the slope and 'c' is the y-intercept).
Line y = 1/2 x - 6 has the slope m = 1/2
and the line in option 'd'
y = 1/2 x -3 has the slope m = 1/2
Slopes are equal and lines are parallel.
Thank-you.
#Muhib
Two boys together have $12. One of them has $10 more than the other. How much money does each of them have
