PLEASE HELP 100 POINTS!!!!!!
A piecewise function g(x) is defined by g of x is equal to the piecewise function of x cubed minus 9 times x for x is less than 3 and negative log base 4 of the quantity x minus 2 end quantity plus 2 for x is greater than or equal to 3
Part A: Graph the piecewise function g(x) and determine the domain. (5 points)
Part B: Determine the x-intercepts of g(x). Show all necessary calculations. (5 points)
Part C: Describe the interval(s) in which the graph of g(x) is positive. (5 points)
Answers
Answer:
A) See attached for graph.
B) (-3, 0) (0, 0) (18, 0)
C) (-3, 0) ∪ [3, 18)
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}[/tex]
Therefore, the function has two definitions:
[tex]g(x)=x^3-9x \quad \textsf{when x is less than 3}[/tex][tex]g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}[/tex]Part AWhen graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies g(3)=(3)^3-9(3)=0 \implies (3,0)[/tex]
Place an open circle at point (3, 0).
Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)[/tex]
Place an closed circle at point (3, 2).
Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
Part BThe x-intercepts are where the curve crosses the x-axis, so when y = 0.
Set the first piece of the function to zero and solve for x:
[tex]\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}[/tex]
Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.
Set the second piece to zero and solve for x:
[tex]\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}[/tex]
Therefore, the x-intercept for the second piece is (18, 0).
So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).
Part CFrom the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.
Interval notation: (-3, 0) ∪ [3, 18)
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Related Questions
how to find h’(3)
base on the graph
Answers
By the quotient rule for differentiation,
[tex]\displaystyle h'(x) = \dfrac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]
According to the plots of [tex]f[/tex] and [tex]g[/tex], we have [tex]f(3)=2[/tex] and [tex]g(3)=3[/tex].
On the interval [2, 4], [tex]f[/tex] is a line through the points (2, 5) and (4, -1), and hence has slope (-1 - 5)/(4 - 2) = -3, so [tex]f'(3)=-3[/tex]. We can similarly find [tex]g'(3)=2[/tex].
Then
[tex]h'(3) = \dfrac{3\cdot(-3)-2\cdot2}{3^2} = \boxed{-\dfrac{13}9}[/tex]
can I return notebooks to target?
Answers
Answer: yes, as long as you haven't used them. :)
Step-by-step explanation:
what is 4.685 in expanded form
Answers
Answer:
4*1/1000+6*100+8*10+5*1
Step-by-step explanation:
Does this set of ordered pairs represent a function? {(–2, 3), (–1, 3), (0, 2), (1, 4), (5, 5)} A. The relation is a function. Each input value is paired with more than one output value. B. The relation is a function. Each input value is paired with one output value. C. The relation is not a function. Each input value is paired with only one output value. D. The relation is not a function. Each input value is paired with more than one output value.
Answers
The correct option regarding whether the relation is a function is:
B. The relation is a function. Each input value is paired with one output value.
When does a relation represent a function?A relation represent a function if each value of the input is paired with one value of the output.
In this problem, when the input - output mappings are given by:
{(–2, 3), (–1, 3), (0, 2), (1, 4), (5, 5)}.
Which means that yes, each input value is paired with one output value, hence the relation is a function and option B is correct.
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I need help with the question
Answers
Answer:
B
Step-by-step explanation:
Comment
√15 = 3.87
√12 = 3.46 Subtract these 2
Difference = 0.41
Pls help answer this before 8pm
Answers
Answer:
Step-by-step explanation:
16 + 12 + 5 + 3 = 36
16 prefer email, 36 total students surveyed
16:36 / 4 = 4:9
4 out of 9 students prefer email
4:9 x 680 = 302.222
302 students can be expected to prefer email.
Rhombus BCDE is shown below. Give the coordinates of C and D.
Answers
The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.
What are the properties of a rhombus?The properties of a rhombus are:
All the sides of a rhombus are congruent and equalOpposite sides are parallelOpposite angles are equalThe adjacent angles add up to 180°Diagonals perpendicularly bisect each otherDiagonals bisect opposite anglesCalculation:The given rhombus BCDE has B(n, p) and E(0, 0).
Since the diagonals of a rhombus are perpendicular bisectors,
EO = OC or BO = OD
Where O is the midpoint of EC and BD.
In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.
So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).
Thus, we have B(n, p), D(n, -p), and E(0, 0)
Consider the coordinates of C as (x, y).
The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])
⇒ coordinates of O = (n, 0)
So,
The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])
⇒ coordinates of O = (x/2, y/2)
⇒ (n, 0) = (x/2, y/2)
∴ x = 2n and y = 0
Then, the coordinates of C are (2n, o)
Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).
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David signed up to provide snacks for his daughter and her school group's camping trip. He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days. He also wanted to buy some boxes of fruit snacks, which were $4 each. He just needed to decide how many to buy, and then figure the total cost.
Select the expression that will help him to determine the total cost.
Answers
The expression that will help him to determine the total cost is as follows:
y = 60 + 4x
How to construct an expression?He signed up to provide snacks for his daughter and her school group's camping trip.
He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.
He also wanted to buy some boxes of fruit snacks, which were $4 each.
The number to buy and the total cost can be expressed as follows:
let
y = total cost
x = number of boxes of fruit juice.
Therefore, the expression that will help him to determine the total cost is as follows:
y = 60 + 4x
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Suppose that $17,699 is invested at an interest rate of 6.6% per year, compounded continuously
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answers
[tex]s(t) = 17699(1 .066) {}^{t} [/tex]
b)[tex]s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73[/tex]
c)[tex]s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699[/tex]
[tex]17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years[/tex]
please help :,)
(geometry involving arc lengths)
Answers
Answer:
bx/a (3rd choice)
Step-by-step explanation:
The length of an arc, s, in a circle of radius r, and central angle Θ given in radians is
s = rΘ
Circle M has radius a. The central angle in radians of the sector is Θ. The length of the arc is x.
x = aΘ
Solve for Θ:
Θ = x/a Eq. 1
Circle N has radius b. The central angle in radians of the sector is Θ. The length of the arc is s.
s = bΘ
Solve for Θ:
Θ = s/b Eq. 2
Since Θ = Θ, then equate the right sides of Equations 1 and 2 above.
x/a = s/b
Multiply both sides by ab.
abx/a = abs/b
bx = as
as = bx
s = bx/a
Answer: bx/a
A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial position of the yo-yo at time t = 0 is x = 3.
Part A: Find the average value of v(t) on the interval open bracket 0 comma pi over 2 close bracket. (10 points)
Part B: What is the displacement of the yo-yo from time t = 0 to time t = π? (10 points)
Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)
Answers
Part A - The average value of v(t) over the interval (0, π/2) is 6/π
Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m
Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.
Part A: Find the average value of v(t) on the interval (0, π/2)The average value of a function f(t) over the interval (a,b) is
[tex]f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx[/tex]
So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by
[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt[/tex]
Since v(t) = 3cost, we have
[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}[/tex]
So, the average value of v(t) over the interval (0, π/2) is 6/π
Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?To find the displacement of the yo-yo, we need to find its position.
So, its position x = ∫v(t)dt
= ∫3cos(t)dt
= 3∫cos(t)dt
= 3sint + C
Given that at t = 0, x = 3. so
x = 3sint + C
3 = 3sin0 + C
3 = 0 + C
C = 3
So, x(t) = 3sint + 3
So, its displacement from time t = 0 to time t = π is
Δx = x(π) - x(0)
= 3sinπ + 3 - (3sin0 + 3)
= 3 × 0 + 3 - 0 - 3
= 0 + 3 - 3
= 0 + 0
= 0 m
So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m
Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)The total distance the yo-yo travels from time t = 0 to time t = π is given by
[tex]x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6[/tex]
So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.
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Simplify.
x to the 4 power x z to the 5 power over xz to the 6 power
Answers
The expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.
What expression represents the simplified form of the given expression?According to the task content, it follows that the given expression in the task content is; x⁴z⁵/(xz)⁶.
Hence, the expression can be simplified by means of the laws of indices as follows;
x^(4-6) z^(5-6)
= x-²z-¹
= 1/x²z.
Ultimately, the expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.
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Question 3 Now change the central angle, ∠CAB, and see how it affects the inscribed angle, ∠CDB. To do this, move point B around the circle without crossing points D and C, and do the same for point C without crossing points B and D. Record five data sets for m∠BAC and m∠BDC in the table.
ANSWER FAST!
Answers
By changing the central angle, ∠CAB, the inscribed angle, ∠CDB has the following data sets:
m∠BAC (β) m∠BDC (α)
42° 84°
40° 80°
45° 90°
35° 70°
52° 104°
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
In Geometry, a circle is considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.
What is the inscribed angle theorem?The inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle. Thus, this is given by this mathematical expression:
m∠BDC = ½ × m∠BAC.
For this exercise, we would change the central angle, ∠CAB, so that the inscribed angle, ∠CDB can have the following data sets:
m∠BAC (β) m∠BDC (α)
42° 84°
40° 80°
45° 90°
35° 70°
52° 104°
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Answer:
plato
Step-by-step explanation:
m∠BAC m∠BDC
50° 25°
70° 35°
90° 45°
125° 62.5°
150° 75°
5. Compound Interest - Single Payment: $5000 was invested at 5.2%, compounded semi-annually, for 3 years. What was the investment worth at its maturity? (3)
Answers
Answer:
78000
Step-by-step explanation:
5000/1 times 52/10 times 3)1
PLEASE HELP!!!!! ASAP
Answers
The absolute value equation that satisfies the solution set shown on the number line is given by:
|x| = 1/2
What is the absolute value function?The absolute value function is defined by:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
It measures the distance from a point x to the origin at x = 0. In this problem, the solution set has a distance to the origin of [tex]\frac{1}{2}[/tex], as |-0.5 - 0| = |0.5 - 0| = 0.5, hence the equation is:
|x| = 1/2
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please help!!!
Using long division, what is the quotient of this expression?
3x42x³-x-4
x²+2
OA. 3x²
3x - 4
OB. 3x² + 2x + x² + 2
O C.
3x² 2x
O D.
-
2x
3x² + 2x
- 6 +
-
- 5+
-
3x + 8
x² + 2
-
3x+6
x²+2
5x8
x² + 2
Rese
Answers
Check the picture below.
notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.
Here is the solution process:
3 x² - 2 x - 6
x² + 0x + 2 | 3 x⁴ - 2 x³ + 0 x² - x - 4
3 x⁴ + 0 x³ + 6 x²
- 2 x³ - 6 x² - x - 4
- 2 x³ + 0 x² - 4 x
- 6 x² + 3 x - 4
- 6 x² + 0 x - 12
3 x + 8
Long division:
Standard: [tex]\sf{3x^{2} -2x-6+\dfrac{3x+8}{x^{2} +2} \ \ \to \ \ \ Option \ "A" }[/tex]Quotient: 3x² - 2x - 6Rest: 8 + 3xTherefore, the correct option is "A".
Which pair of angles are vertical angles? AngleWRU and AngleSRT AngleWRS and AngleVRT AngleVRU and AngleTRS AngleVRT and AngleSRT
Answers
Step-by-step explanation:
important of festival in nepali languages for class seven
Answer:
b
Step-by-step explanation:
A machinist needs 98 pieces of steel rod. The rods come in bundles of 8 pieces. How many bundles of steel rod does the machinist require?
Answers
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
How many bundles of steel rod does the machinist require?Given the data in the question;
Machinist needs 98 pieces of steel rodThe rods come in bundles of 8 piecesNumber of bundles of steel rods required by the mechanist = ?To determine the bundle of steel required, let y represent the bundle.
Since;
1 bundle = 8 piece
y bundle = 98 piece
We cross multiply
y bundle × 8 piece = 1 bundle × 98 piece
y = ( 1 bundle × 98 piece ) / ( bundle × 8 piece )
y = 98 pieces / 8 piece
y = 12.25 ≈ 13
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
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if 6m of a uniform iron rod weighs 21 kg what will be the weight of 16 m of the same rod?
Answers
Answer:
56kg
Step-by-step explanation:
If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg
16*3.5 = 56 kg
f(x) = x². What is g(x)?
5
g(x)
A. g(x)=x²-4
OB. g(x)=x2-4
C. g(x)=-4x2²
OD. g(x)=x²+4
+
f(x)=x²
Answers
The function f(x) = x² then the required function exists g(x) = -x²- 4.
What is a function?The function exists described as y = f(x).
In mathematics, a function from a set X to a set Y allocates to each element of X exactly one element of Y. The set X exists named the domain of the function and the set Y exists named the codomain of the function. Functions stood originally for the idealization of how a variable quantity relies on another quantity.
For every x there exists a certain value of y.
From the graph g(x) exists reflection of f(x) at y = -4.
So g(x) = -f(x) - 4, the negative sign for reflection.
g(x) = -x² - 4
The required function exists g(x) = -x² - 4.
Therefore, the correct answer is option D. g(x) = -x² - 4.
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The complete question is:
F(x) = x². What is g(x)?
A. g(x) = x² - 4
B. g(x) = x² + 4
C. g(x) = -4x²
D. g(x) = -x² - 4
cos 90 - 2sin45 + 2tan180
Answers
Answer:
- [tex]\sqrt{2}[/tex]
Step-by-step explanation:
cos90° - 2sin45° + 2tan180°
= 0 - ( 2 × [tex]\frac{\sqrt{2} }{2}[/tex] ) + 2(0)
= 0 - [tex]\sqrt{2}[/tex] + 0
= - [tex]\sqrt{2}[/tex]
Solve for x. Enter the solutions from least to greatest.
Round to two decimal places.
(x+3)²-3=0
lesser x =
greater x =
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Show Calculator
pls helpp!
Answers
Answer: -4.73, -1.27
Step-by-step explanation:
[tex](x+3)^2 =3\\\\x+3=\pm \sqrt3\\\\\\x=-3 \pm \sqrt3\\\\x \approx -4.73, -1.27[/tex]
2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?
Answers
Answer:
no solution
Step-by-step explanation:
16x - 32y = 27 → (1)
8x - 16 = 16y ( subtract 16y from both sides )
8x - 16 - 16y = 0 ( add 16 to both sides )
8x - 16y = 16 → (2)
multiply (2) by - 2 and add to (1)
- 16x + 32y = - 32 → (3)
add (1) and (3) term by term
0 + 0 = - 5
0 = - 5 ← not possible
this indicates the system has no solution
(b)
the solution to a system is the point of intersection of the 2 lines
since there is no solution, no point of intersection, then
this indicates the lines are parallel and never intersect
Answer:
a) no solution
b) the two lines never intersect
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]
Part (a)To solve by linear combination (elimination):
Step 1
Write both equations in standard form: Ax + By = C
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 8x-16y=16[/tex]
Step 2
Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]
Step 3
Subtract one of the equations from the other to eliminate one of the variables:
[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]
Therefore, as 0 ≠ 5, there is no solution to this system of equations.
Part (b)
The solution to a system of equations is the point(s) of intersection.
As there is no solution to the given system of equations, this tells us that the two lines never intersect.
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Assume that a sample is used to estimate a population proportion p. Find the 95% confidence for a sample of size 246 with 52% successes. Enter your answer as an open -interval using decimals
Answers
Using the z-distribution, the 95% confidence interval for the proportion is given as follows:
(0.4576, 0.5824).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The other parameters for the interval are given as follows:
[tex]n = 246, \pi = 0.52[/tex].
The lower and upper bound of the interval, respectively, are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]
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216 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answers
Answer:
The no. of student failed is 36.
Step-by-step explanation:
Given, the number of student enrolled= 216
Let us suppose number of student failed = x
Given,
no. of student passed is 5 times no. of student failed.
Then, no. of student passed = 5x
x +5x = 216
6x = 216
x = 216/6
x = 36
Thus, the no. of student failed is 36.
Find the value of x
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 35°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:4x + 1 + x + 4 = 180[/tex]
[ by linear pair ]
[tex]\qquad❖ \: \sf \:5x + 5 = 180[/tex]
[tex]\qquad❖ \: \sf \:5(x + 1) = 180[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 180 \div 5[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 36[/tex]
[tex]\qquad❖ \: \sf \:x = 36 - 1[/tex]
[tex]\qquad❖ \: \sf \:x = 35[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 35°Because of stormy weather a pilot flying at 35,000 ft descends 8,000 ft.
What is his new altitude
Answers
Answer:
35,000 - 8000=27,000 altitude
If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,
then find f ( x ) + g ( x ).
Answers
Answer:
[tex]5x^{2} -4x-9[/tex]
Step-by-step explanation:
f(x)+g(x)
[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]
The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9
Given that:
Functions, f ( x ) = 3x² - 6x + 2
And g ( x ) = 2x² + 2x - 11.
Then find f ( x ) + g ( x ).
To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.
To find f(x) + g(x), add the coefficients of the corresponding terms:
f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)
Now, combine like terms:
f(x) + g(x) = 5x² - 4x - 9
So, the sum of the two functions is:
f(x) + g(x) = 5x² - 4x - 9
Learn more about Addition here:
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Fill in the blank with the correct response.
Twenty-one is 20% of
Answers
Answer: 105
Step-by-step explanation:
105 * .2 = 21 :)
Zachary's weight is 130% of Noah's weight. If Noah weighs 75 pounds, what does Zachary weigh?
Answers
Answer:
Zachary weights 95.7 pounds