Can someone please help me with this last one. I am totally lost and don’t understand
Answers
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
Related Questions
Mrs. Clarke saved $60 by buying a dress at a 30% discount. The original price of the dress was
Answers
Answer:
$200Step-by-step explanation:
Step one:
given
let the original price of the be x
discount = 30%
30 of x is $60
Step two:
Mathematically
30/100*x=60
0.3x=60
divide both sides by 0.3
x=60/0.3
x=200
Hence the original price of the dress is $200
By the square property, if b is a real number , and a2=b, then a=
Answers
Answer:
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
Step-by-step explanation:
Given
b is a real number[tex]a^2=b[/tex]as
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
so
[tex]a^2=6[/tex]
[tex]a=\sqrt{b},\:a=-\sqrt{b}[/tex]
Therefore,
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
Answer:
lal
Step-by-step explanation:
ap3x
Given: m∠A = m∠C = 90°
AB ║ DC
Prove: ∆ABD ≅ ∆CDB
40 points
Answers
Answer:
ABD = CDB
AB is parallel to DC
Step-by-step explanation:
angle a and c are right angles so they are equal and angle b and d are equal because they have a line that touch both letters
AB and DC are parellel because they are the same looking lines just on oppisite sides
As per the ASA congruence theorem, the triangles ΔABD and ΔCDB are congruent.
What are alternate interior angles?When two parallel lines are intersected by a transversal, alternate external angles are created.
Given that, m∠A = m∠C = 90° and AB║DC.
In triangles ΔABD and ΔCDB,
m∠A = m∠C = 90°
m∠ABD = m∠BDC (Alternate interior angles)
BD = DB (Common side)
Hence, as per the ASA congruence theorem, the triangles ΔABD and ΔCDB are congruent.
Learn more about the alternate interior angles:
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Spidermans web is 100 feet long. He wants to shoot his web at a projection of 30 degrees. How tall is the building if he is trying to reach the top of the building?
Answers
Answer:
50 ft
Step-by-step explanation:
The concept to apply here is that of laws of sine of an angle where;
Sine of an angle theta = opposite length / hypotenuse
Sin 30° = height of building / length of the web
Sin 30° = h / 100
h = 100 sin 30° = 100 * 0.5 = 50 ft
The length of two sides of a triangle are 5in. And 17in. Which is a possible length for the third side?
Answers
Answer:
b= 2[tex]\sqrt{66}[/tex] or 16.248
Step-by-step explanation:
5^2 +b^2= 17^2
25 + b^2 = 289
-25 -25
b^2=264
b= 2[tex]\sqrt{66}[/tex] or 16.248
If the new iPhone was on sale for $1200, what is the percent of change if the original prices was $1500.
Answers
Answer:
its a -20%changeor a general 20%change
The cubic polynomial below has a double root at r4 and one root at x = 6 and passes Through the point (2, 36) as shown. Algebraically determine its equation in factored form. Show how you arrived at your answer.
PLEASE HELP ITS BEEN HOURS
Answers
The graph in the question is missing.
Answer:
y = [tex]\frac{-1}{4}( x^3 + 2x^2 - 32x -96)[/tex]
Step-by-step explanation:
The function is cubic
It has roots as -4, -4 , 6
this means the value of x = -4, -4 , 6 which makes the entire equation zero
so we have solutions as
x+4 = 0
x+4 = 0
x- 6 = 0
on forming a cubic equation using these
(x+4)(x+4)(x-6)
the equation passes through (2,36)
put x = 2
(2+4)(2+4)(2-6) = (6)*(6)*(-4)
which exceeds 36 so we product the equation with -1/4 to get 36
Final equation
y = [tex]\frac{-1}{4} (x+4)(x+4)(x-6)[/tex]
y = [tex]\frac{-1}{4}( x^3 + 2x^2 - 32x -96)[/tex]
Solve using ELIMINATION (with step by step explanation) Please
3x+y=-9
y=5x+7
Answers
Answer:
x = -2 (verified by algebra) ✅Step-by-step explanation:
Since we are given the value of y, we can replace it with 5x + 7.
We now have: 3x + 5x + 7 = -9
We can now simplify by adding 3x and 5x to get 8x.
8x + 7 = -9
We can subtract 7
8x = -16
And now, we divide by 8
x = -2
We can check to make sure we are correct
3(-2) + 5 (-2) + 7 = -9
-6 + -10 + 7 = -9
-9 = -9 ✅
On a road trip you drove 280 miles in 4 hours. a) What is your speed in miles per hour? b) Use your equation to determine how far you will travel after 12 hours of driving.
Answers
Answer:
a. 70 miles per hour
b. 840 miles
Step-by-step explanation:
280/4 = 70 miles per hour
70*12 = 840 miles
Answer:
a) 70 miles per hour
b)840 miles
Step-by-step explanation:
a) to find the speed, do distance/time
b) if you do 70 miles an hour, and you want to know 12 hours, just times 70x 12
Please help me out because I am a idiot
Answers
Answer:
With?
Step-by-step explanation:
Answer:
you didn't give what you need help with
Select the correct answer from the drop-down menu. Find the trinomial. (22-6) and (22+4) are the factors of
Answers
Answer:
im about to solvee
Step-by-step explanation:
Help plz:))) I’ll mark u brainliest
ASAP!!!!!
Answers
Answer:
X= 24
la neta no se
Answer:
x = 8.3
Step-by-step explanation:
Triangles always equal to 180 degrees when taking about angles.
The equation would be:
30+(11x+5)+(-5+7x)= 180
add like variables:
30+5-5 = 30
11x+7x = 18x
put them into an equation:
18x +30= 180
cancel out:
18x+30=180
-30 -30
18x = 150
Divide:
18x = 150
÷ 18 ÷18
x = 8.3
This is an estimate as the answer in the calculator would be very long.
Ella is putting her savings into a retirement fund that will compound her $7000 semiannually at 7% interest. How much will her retirement fund be worth after 10 years? *
Answers
Answer:
8099
Step-by-step explanation:
PLEASE HELP!!! A plumber charges $14 per hour and a $20 flat fee for service. If Ashley's total comes to $111, how many hours did the plumber work? Write an equation to show how you would solve.
Answers
Answer:
The plumber worked for 6.5 hours.
Step-by-step explanation:
$111 - $20 = 91
91 / 14 = 6.5
Answer:
6.5 hours
Step-by-step explanation:
111 - 20 = 91, 91 divided by 14 = 6.5, he worked 6.5 hours. Hope this helps!
What is a common tip percentage amount that people receive?
Answers
Answer:
15-20%
Step-by-step explanation:
can u make me brainiest thanks
Can somebody tell me if I did the primes right?
Answers
Answer:
You did! well done
Step-by-step explanation:
The elevation at ground level is 0 feet. An elevator starts at 29 feet below ground
level. After traveling 70 seconds, the elevator is 52 feet above ground level. What
distance does the elevator travel in those 70 seconds?
Answers
Answer:
81
Step-by-step explanation:
I just added the 52 and 29 together.
find the pattern what comes next 63,57,51,45
Answers
Answer:
counting by 6's
so it would be 69 next if your talking about the left side
or 39 if your talking abt the right side
Hope this helps!
Three friends met for a book club at a coffee shop. Each friend ordered a cup of coffee and two donuts. The total of the order was $21.75. A. If a cup of coffee costs $3.25, then use the diagram to write an equation to solve for c, the cost of the donut.
Answers
the cost of a donut is $2 and the equation that represents the given scenario will be:
3d + 6c = 21.75d = 3.25What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Three friends met for a book club at a coffee shop. Each friend ordered a cup of coffee and two donuts. The total of the order was $21.75.
Let " d" be the cost of a cup of coffee
and "c" be the cost of the donut
Since Each friend ordered a coffee and a donut
And there are 3 friends
Thus,
3(d + 2c) = 21.75
3d + 6c = 21.75
Also given, a cup of coffee costs $3.25
d = 3.25
Substituting the values in equation 1
9. 75 + 6c = 21.75
6c = 12
c = 2
therefore, the cost of a donut is $2.
Learn more about Linear equations here:
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Some one help ASAP PLEASE
Which expression represents 7 times the diffrence between 300 and 28?
Answers
Answer:
Answer
Step-by-step explanation:
300-28= g x 7
write the rational number as a decimal - 3/11
Answers
Answer
0.27
Step-by-step explanation:
3 divided by 11
= 0.27
this is it I believe
solve the literal equation 3xy+2xz for x I never learned this.help me plz!!!!
Answers
x(3y + 2z)
Step-by-step explanation:
12a[tex]12a^{2} -20a+16a^{3}[/tex]
Answers
Answer:
Step-by-step explanation:
4a(3a-5+4a^2)
What was the name of the physical barrier in ancient India?
Answers
Answer: Some natural barriers are the Himalayas isolating the Indian subcontinent from the rest of Asia, the Grand Canyon, the Dead sea, and the Mississippi river.
Given that [tex](ax+4)(2x+b)=2x^2+5x-12[/tex], what are the values of a and b?
Answers
Answer:
a = 1, b = - 3
Step-by-step explanation:
Expand the factors on the left side, then compare the coefficients of like terms on both sides.
left side
(ax + 4)(2x + b) ← expand using FOIL
= 2ax² + abx +8x + 4b
= 2ax² + x(ab + 8) + 4b
Compare coefficients of like terms with those on right side.
coefficients of x² terms
2a = 2 ( divide both sides by 2 )
a = 1
comparing constant terms
4b = - 12 ( divide both sides by 4 )
b = - 3
a woman buys a cooler for rs 800 and pays rs 60 as per transportation charges if she sells the cooler for rs 1200 find her profit percent
Answers
800+60=860
1200-860
A nurse tells Andrew he is six feet tall. What is the equivalent of Andrew's
height in yards?
A. Three yards
B. Six yards
C. Twelve yards
D. Two yards
Answers
Answer:
Option D
Step-by-step explanation:
The answer is option D or "two yards." You can find the answer by knowing that a yard equals to three feet in length and because Andrew is six feet you can add three and three together giving you a total amount of two yards.
[tex]1y=3ft[/tex]
[tex]3+3=6[/tex]
[tex]1+1=2[/tex]
[tex]=2y[/tex]
Hope this helps.
Use the figure to find the measures of
<1 and <2
Answers
angle 2 = 46
explanation:
angle 1 is a supplementary with 46
angle 2 is alternate interior with 46
PLEASE I NEED IMMEDIATE HELP I will give brainliest
BD=16 and ÁT is the
perpendicular bisector of BD
BC=
Answers
Answer:
8
Step-by-step explanation:
16/2=8
Answer:
8
Step-by-step explanation:
A bisector bisects a line in HALF. Thus, by dividing 16 in half you will get BC=8.
Suppose a relief program dropped food and medicine to a disaster area with a paper parachute. If the parachute fell 250 meters, how many feet did the parachute fall?
Answers
Answer:
About 820 feet
8.21 exact
Step-by-step explanation:
Multiply length by 3.281
250m * 3.281 = 820.21ft