Answer:
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Step-by-step explanation:
The Newton's method is a numerical method by approximation that help find roots of a equation of the form [tex]f(x) = 0[/tex] with the help of the equation itself and its first derivative. The Newton's formula is:
[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]
Where:
[tex]x_{i}[/tex] - i-th approximation, dimensionless.
[tex]x_{i+1}[/tex] - (i+1)-th approximation, dimensionless.
[tex]f(x_{i})[/tex] - Function evaluated at the i-th approximation, dimensionless.
[tex]f'(x_{i})[/tex] - First derivative of the function evaluated at the i-th approximation, dimensionless.
The function and its first derivative are [tex]f(x) = x^{3}+x+8[/tex] and [tex]f'(x) = 3\cdot x^{2}+1[/tex], respectively. Now, the Newton's formula is expanded:
[tex]x_{i+1} = x_{i}-\frac{x_{i}^{3}+x_{i}+8}{3\cdot x_{i}^{2}+1}[/tex]
If [tex]x_{1} = -1[/tex], the value of [tex]x_{2}[/tex] is:
[tex]x_{2} = -1 - \frac{(-1)^{3}+(-1)+8}{3\cdot (-1)^{2}+1}[/tex]
[tex]x_{2} = -1.5000[/tex]
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Answer:
-2.5000
Step-by-step explanation:
what is the answer 2×3+4×100-50+10
Answer:
366
Step-by-step explanation:
2×3+4×100-50+10
PEMDAS says multiply and divide from left to right
6 + 400 - 50 +10
Then add and subtract
406-50+10
356+10
366
Answer:
[tex]\boxed{366}[/tex]
Step-by-step explanation:
[tex]2 \times 3+4 \times 100-50+10[/tex]
Multiplication is first.
[tex]6+400-50+10[/tex]
Add or subtract the numbers.
[tex]350+10+6[/tex]
[tex]366[/tex]
Marie is saving money for home repairs. So far, she has saved $1,558. She needs at least $2,158 for the repairs. She plans to
add $60 per week to her current savings until she can afford the repairs.
In this activity, you will algebraically model and solve an inequality based on this situation and interpret the solutions within
realistic guidelines
Part A
Question
Given the situation, which inequality models the number of additional weeks Marie needs to continue saving to afford the
home repairs?
Select the correct answer.
1,558 + 60x 22,158
60x + 1,558 5 2,158
1,558 - 60x s 2,158
2,158 - 60x 2 1,558
Answer:
Inequality: [tex]1558 + 60 x \geq 2158[/tex]
Number of Weeks: [tex]x \geq 10[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Savings = \$1558[/tex]
[tex]Amount\ Needed = \$2158[/tex]
[tex]Additional\ Savings = \$60\ weekly[/tex]
Required
Represent this using an inequality
Represent the number of weeks as x;
This implies that, She'll save $60 * x in x weeks
Her total savings after x weeks would be
[tex]Initial\ Savings + 60 * x[/tex]
From the question, we understand that she needs at least 2158;
Mathematically, this can be represented as (greater than or equal to 2158)
[tex]\geq 2158[/tex]
Bringing the two expressions together;
[tex]Initial\ Savings + 60 * x \geq 2158[/tex]
Substitute 1558 for Initial Savings
[tex]1558 + 60 * x \geq 2158[/tex]
[tex]1558 + 60 x \geq 2158[/tex]
Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]
Solving further for x (number of weeks)
[tex]1558 + 60 x \geq 2158[/tex]
Subtract 1558 from both sides
[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]
[tex]60x \geq 600[/tex]
Divide both sides by 60
[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]
[tex]x \geq 10[/tex]
This means that she needs to save $60 for at least 10 weeks
Answer:
Its the first one
Step-by-step explanation:
I just did it lol
Please answer this correctly without making mistakes I want expert genius or ace people to answer this correctly
Answer:
45.5 km
Step-by-step explanation:
18.3 km + 27.2 km = 45.5 km or 45 km and 500 m
Answer:
45.5km
Step-by-step explanation:
The distance between the locksmith and the furniture=18.3km
The distance between the furniture and the hotel=27.2km
S(locksmith)+S(furniture)=S(hotel)
18.3km+27.2km=45.5km
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
A small company that manufactures snowboards uses the relation below to model its profit. In the model,
represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.
What is the maximum profit the company can earn? How many snowboards must it produce to earn this
maximum profit?
a. Factor P =
4x2 + 32x + 336 to find the roots.
b. Find the axis of symmetry then use it to find the vertex.
c. Therefore, we need to see snowboards to make a maximum profit of
Answer:
a) x₁ = 14
x₂ = - 6
b) x = 4
c) P(max ) = 4000000 $
Step-by-step explanation:
To find the axis of symmetry we solve the equation
a) -4x² + 32x + 336 = 0
4x² - 32x - 336 = 0 or x² - 8x - 84 = 0
x₁,₂ = [ -b ± √b² -4ac ]/2a
x₁,₂ = [ 8 ±√(64) + 336 ]/2
x₁,₂ = [ 8 ± √400 ]/2
x₁,₂ =( 8 ± 20 )/2
x₁ = 14
x₂ = -6
a) Axis of symmetry must go through the middle point between the roots
x = 4 is the axis of symmetry
c) P = -4x² + 32x + 336
Taking derivatives on both sides of the equation we get
P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32
x = 32/8
x = 4 Company has to sell 4 ( 4000 snowboard)
to get a profit :
P = - 4*(4)² + 32*(4) + 336
P(max) = -64 + 128 + 336
P(max) = 400 or 400* 10000 = 4000000
f(n)=4n-3 find the 15th term of the sequence defined by the explicit rule
Answer:
57
Step-by-step explanation:
f(15)=4(15)-3
f(15)=60-3
f(15)=57
Hope that helps, tell me if you need more help
Answer:
57
Step-by-step explanation:
If you plug 15 into the equation, you get f(15)=4(15)-3
60-3
57
:)
Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 –3x + 5y = 10
Answer:
(0,2)
Step-by-step explanation:
solve by addition/elimination
2x + 3y= 6
–3x + 5y = 10
multiply first equation by 3 and second one by 2 to eliminate x)
6x+9y=18
-6x+10y=20 (add the two equations)
6x+9y-6x+10y=38
19y=38
y=38/19=2
2x+3y=6
2x=6-6
x=0
Answer:
a
Step-by-step explanation:
Jamie's dog eats 3/4 pound of dog food each day. How many pounds of dog
food does Jamie's dog eat in 4 days?
Answer:
The dog will eat 3 lbs
Step-by-step explanation:
Take the amount eaten per day and multiply by the number of days
3/4 * 4 = 3
The dog will eat 3 lbs
Answer:
3 pounds
Step-by-step explanation:
Multiply the amount of dog food per day with the number of days.
[tex]\frac{3}{4} \times 4[/tex]
[tex]\frac{12}{4} =3[/tex]
In 4 days, Jamie's dog will eat 3 pounds of dog food.
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
What is the total amount of 2/5+5/3+9/3 and the lowest common denominator?
The lowest common denominator is lcm(5, 3), which is 15.
The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].
help!! I have problem to solve this question
Answer:
Step-by-step explanation:
[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]
[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]
now you find the point of intersection.
then calculate the angle.
16. Find the equation of a parabola with a focus at (3,1) and a directrix at y = 3.
A) y = 1∕4(x – 3)^2 + 3
B) y = –1∕4 (x – 3)^2 + 3
C) y = –1∕4 (x – 3)^2 + 2
D) y = 1∕4(x – 3)^2 + 2
Answer:
C
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-3)^2+(y-1)^2}[/tex] = | y - 3 | ← square both sides
(x - 3)² + (y - 1)² = (y - 3)² ← expand the y- factors
(x - 3)² + y² - 2y + 1 = y² - 6y + 9 ← subtract y² - 2y + 1 from both sides
(x - 3)² = - 4y + 8 ( subtract 8 from both sides )
(x - 3)² - 8 = - 4y ( divide both sides by - 4 )
- [tex]\frac{1}{4}[/tex] (x - 3)² + 2 = y, that is
y = - [tex]\frac{1}{4}[/tex] (x - 3)² + 2 → C
Answer:
Step-by-step explanation:
C) y = –1∕4 (x – 3)^2 + 2
Which algebraic expression represents the phrase "six less than a number"?
SERE
6x - X
X-6
6- X
X - 6x
Answer:
The answer is option B.
Step-by-step explanation:
six less than a number is written as
x - 6
Hope this helps you
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years. Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100? Assuming the life expectancy between 2000 and 2100 will increase by the same percentage as it did between 1900 and 2000, the life expectancy for women will be —— years
Answer:
49145 years
Step-by-step explanation:
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.
Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?
In 10 years, the expectancy increased by 85/45 = 17/9
between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is [tex]85*(\frac{85}{45})^{10} = 49145[/tex] years
The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.
Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would expectancy for women in 2100
Over a ten-year period, life expectancy rose by 85/45 = 17/9.
It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be
⇒ 85×(85/45)¹⁰
⇒ 85×(1.88)¹⁰
⇒ 49145 years
Hence, the life expectancy for women will be 49145 years
Learn more about exponential function here:
brainly.com/question/11487261
#SPJ2
What is the lateral surface area of the cone? A cone with diameter 18 centimeters, height of 12 centimeters, and slant height of 15 centimeters. L A = pi r l 108 pi centimeters squared 135 pi centimeters squared 180 pi centimeters squared 270 pi centimeters squared
Answer:
3051.08 cm squared
Step-by-step explanation:
The equation to find lateral surface area of a cone:
SA = pi r sqrt(h^2 * r^2)
Plug your values in.
SA = 3.14 * 9 * sqrt(144*81)
SA = 3.14 * 9 * 108
SA = 3051.08
The lateral surface area is 3051.08 cm squared.
Answer:
424.12cm^2
Step-by-step explanation:
make sure you have the radius, half of the diameter!
remember to use this formula! Lateral surface area = πrs = πr√(r2 + h2)
hope this helped!
r=radius
h=hight
s=slant
For the functions f(x)=4x+5 and g(x)=6x+4,find (f•g)(0)and (g•f)(0)
Answer:
Step-by-step explanation:
f(x)=4x+5
g(x)=6x+4,
first: (f*g)=(4x+5) (6x+4)=24x²+46x+20
next:(f*g)(0)=((g*f)=24x²+46x+20=20
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 4 (g (x)) +5
4 (6x+4) +5 = 24x+16+5 = 24x+21
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
How much meat would seven Siberian tigers need for the month of April?
Select one:
a. 750 pounds
b. 175 pounds
c. 5425 pounds
d. 5250 pounds
Answer:
d. 5250 pounds
Step-by-step explanation:
25 lbs per day
There are 30 days in april
25 lbs/ day * 30 days
1 tiger would eat 750 lbs
There are 7 tigers
7 * 750 =5250 lbs
Answer:
D. 5250 pounds
Step-by-step explanation:
What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.
25 x 30 = 750
Then multiply that amount by seven because there are 7 tigers.
750 x 7 = 5250
What is the correlation coefficient for the data in the table?
–0.57
–0.28
0.28
0.57
Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!
Step-by-step explanation:
Answer:
c- 0.28
Step-by-step explanation:
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
Learn more about radioactive materials here:
https://brainly.com/question/24339152?referrer=searchResults
the product of two consequtive integers is 72 the equation x(x+1)=72 represents the situation, where x represents the smaller integer, which equation can be factor and solve for the smaller integer?
Answer:
x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.
Step-by-step explanation:
Step 1: Distribute x
x² + x = 72
Step 2: Move 72 over
x² + x - 72 = 0
Step 3: Factor
(x - 8)(x + 9) = 0
Step 4: Find roots
x - 8 = 0
x = 8
x + 9 = 0
x = -9
Answer:
x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0
Step-by-step explanation:
Let the first consecutive integer be x.
Let the second consecutive integer be x+1.
The product of the two consecutive integers is 72.
x(x + 1) = 72
x² + x = 72
Subtracting 72 from both sides.
x² + x - 72 = 0
Factor left side of the equation.
(x - 8)(x + 9) = 0
Set factors equal to 0.
x - 8 = 0
x = 8
x + 9 = 0
x = -9
8 and -9 are not consecutive integers.
Try 8 and 9 to check.
x = 8
x + 1 = 9
x(x+1) = 72
8(9) = 72
72 = 72
True!
The two consecutive integers are 8 and 9.
Find the midpoint of AC.
B (0, a)
C (a, a)
A(0, 0) D (a,0)
Answer:
[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]
Step-by-step explanation:
The formula of a midpoint:
[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]
We have the points
[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]
Substitute:
[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]
Answer:
The answer is (a/2,a/2)
Step-by-step explanation:
Fill in 2 then a
In conclusion (a/2,a/2)
Which graph best models the inequality y<_ -2/5x+2
Answer:
Step-by-step explanation:
Simplify each term.
y ≤ −2x/5 + 2
Find the slope and the y-intercept for the boundary line.
Slope: -2/5
Y-intercept: 2
Graph a solid line, then shade the area below the boundary line since
y is less than -2x/5 + 2
y ≤ −2x/5 + 2
Hope this can help
prove that 1/3 root2 is irrational
Step-by-step explanation:
Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .
A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?
Answer: Null Hypothesis [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis [tex]H_{a}[/tex]: p < 0.18
Step-by-step explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis
Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol [tex]H_{0}[/tex].
For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol [tex]H_{a}[/tex].
For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis: [tex]H_{a}[/tex]: p < 0.18
The Orchard Cafe has found that about 15% of the diners who make reservations don't show up. If 77 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution
Answer:
65 dinners are expected to show up
The standard deviation of the distribution is 3.13
Step-by-step explanation:
Given
Proportion = 15%
Population = 77
Required
Expected Number that'll show up
Standard Deviation
If 15% won't show up; then
100% - 15% = 85% will show up
Expected Number, E(x) of Dinner is calculated as thus;
[tex]E(x) = np[/tex]
Where [tex]p = 85\%[/tex] (calculated above)
and [tex]n = 77[/tex]
Convert p to decimal
[tex]p = 0.85[/tex]
So;
[tex]E(x) = 0.85 * 77[/tex]
[tex]E(x) = 65.45[/tex]
[tex]E(x) = 65[/tex]
65 dinners are expected to show up
Calculating Standard Deviation, SD
Standard Deviation is calculated as;
[tex]SD = \sqrt{np(1-p)}[/tex]
Substitute 0.85 for p and 77 for n
[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]
[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]
[tex]SD = \sqrt{9.8175}[/tex]
[tex]SD = 3.13328900678[/tex]
[tex]SD = 3.13[/tex] (Approximated)
The standard deviation of the distribution is 3.13
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4178 miles, with a variance of 124,609. If he is correct, what is the probability that the mean of a sample of 40 cars would be less than 4265 miles? Round your answer to four decimal places.
Answer:
P(X' < 4265) = 0.9418
Step-by-step explanation:
Due to the fact that the population is normal, the distribution of the sample mean of 40 cars is;
X' = (x1 + x2 + x3....... + x40)/40
We are given;
Normal mean;μ = 4178 miles
Variance = 124,609
Standard deviation; σ = √variance = √124609 = 353
Formula for standard error of mean = σ/√n = 353/√40 = 55.814
So from the formula;
z = (x - μ)/(σ/√n)
So for P(X' < 4265) we have;
z-value of P(X' < 4265) = (4265 - 4178)/55.814 ≈ 1.56
From the z-table attached, we have for P(z < 1.56) = 0.94179
Approximating to 4 decimal places gives 0.9418
2. Write as a complex number.
Answer:
Your answer is correct ✔️
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
2√3 + 3i is the answer
Step-by-step explanation:
what is the answer. plz heelp 5h+2(11-h)= -5
Answer:
h = -9
Step-by-step explanation:
5h+2(11-h)= -5
Distribute
5h +22 -2h = -5
Combine like terms
3h +22 = -5
Subtract 22 from each side
3h +22-22 = -5-22
3h = -27
Divide by 3
3h/3 = -27/3
h = -9
The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).
Answer:
g ( x ) = 4x^2 + 10
Step-by-step explanation:
Solution:-
The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:
Translation guidelines
Horizontal shifts
Right : f ( x ) -> f ( x - a )Left : f ( x ) - > f ( x + a )
Vertical shifts
Up : f ( x ) -> f ( x ) + bDown : f ( x ) - > f ( x ) - bGeneral shift ( Horizontal and Vertical shift )
f ( x ) - > f ( x ± a ) ± b
We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.
f ( x ) = 4x^2 + 6
f ( x ) - > f ( x ) + b
g ( x ) = f ( x ) + 4
g ( x ) = 4x^2 + 6 + 4
g ( x ) = 4x^2 + 10 ... Answer
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
Find the points of intersection of the following function graphs: y=20x−70 and y=70x+30
Answer:
(-2,-110)
Step-by-step explanation:
First solve for x
20x−70=70x+30
x= -2
Now substitute x for -2
y=20x−70
y=20(-2)-70
y = -110