Task 1
Nonlinear Systems of Equations
Create a system of equations that includes one linear equation and one quadratic equation.
Part 1. Show all work in solving your system of equations algebraically.
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
Task 2
Polynomial Identities
Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
Answer:
part 1 : y = x^2 + 3x + 5
y = x + 13
solution:
x^2 + 3x + 5 = x + 13
x^2 + 2x -8 = 0
(x+4)(x-2) = 0
x = -4 or x = 2
if x = -4, y = 9
if x = 2 , y = 15
part 2 : x^2 + 2x + 1 = 0
(x + 1)^2 = 0
x = -1
y = 1
task 2
part 1 : Let our two digit number be 26
Next, we rewrite it as a difference of two numbers
26=32-6
We want to square 26 using the identity:
In this case,
x=32
y=6
Substituting into the identity
plz make me brainliest
what is the solution set of the equation (x -2) (x-a) = 0 ?
Answer:
x=2, x=a
Step-by-step explanation:
(x -2) (x-a) = 0
(x-2)(x-a) = 0
x-2=0
x-2+2=0+2
x=2
x-a=0
x-a+a=0+a
x=a
simplify the variable expression: g-16/4
Answer:
im not sure if this is what ur looking for but id k hopefully yes
Step-by-step explanation:
-16/4=-4
g-4
The solution after simplifying the variable expression by evaluating its numerical part is (g - 4).
Given that,
The expression is,
[tex]g - \dfrac{16}{4}[/tex]
Used the concept of expression by combining the like terms.
Now, simplify each term as,
[tex]g - \dfrac{16}{4}[/tex]
Here, [tex]\dfrac{16}{4} = 4[/tex]
So, we get;
[tex]= g - 4[/tex]
Therefore, the solution is (g - 4).
To learn more about the equation visit:
brainly.com/question/28871326
#SPJ6
Compute the exact value of the function for the given x-value without using a calculator. (2 points) f(x) = 5x for x = -1
Answer:
The exact value of the function for the given x-value is of -5.
Step-by-step explanation:
In this question, we compute the numeric value of the function f(x) for x = -1, that is, we replace every instance of x in the function by -1.
f(x) = 5x for x = -1
[tex]f(-1) = 5(-1) = -5[/tex]
The exact value of the function for the given x-value is of -5.
PLS HELP!!!!
7x=28
x/9=3
5x=125
14=x÷2
8x=40
Answer:
7x=28
x = 4
x/9=3
x = 27
5x=125
x = 25
14=x÷2
x = 28
8x=40
x = 5
hi could anyone please help me with this
Just need the answer
Answer:
It seems no one can eat just one potato ship
Step-by-step explanation:
A square flag includes three colors: yellow, black, and green. The colors of the flag appear in the proportion 3:2:1, with yellow accounting for the greatest area and green accounting for the least. If a total of 48 square inches of the flag is black, what are the dimensions of the flag?
Answer:
423
Step-by-step explanation:
2313
Given g(x) = -2x – 4, find g(6).
Answer:
x= -16
Step-by-step explanation:
g(x) =-2x-4
g(6)=-2(6)-4
g(6) = -12-4
g(6)=-16
The value of g(6) for the given function g(x) = -2x – 4 will be -16.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
Given the function,
g(x) = -2x – 4
Now,
g(6) means value of g(x) at x = 6
So,
g(6) = -2(6) - 4
g(6) = -12 - 4 = -16
Hence "The value of g(6) for the given function g(x) = -2x – 4 will be -16".
For more about the linear function,
brainly.com/question/21107621
#SPJ2
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator
0.30 cm to 0.42 cm
Answer:
[tex]\dfrac{5}{7}[/tex]
Step-by-step explanation:
Given numbers are :
0.30 cm and 0.42 cm
We need to find the ratio of the above whole numbers.
Taking 0.3 cm on the numerator and 0.42 cm on the denominator. So,
[tex]\dfrac{0.3}{0.42}=\dfrac{\dfrac{3}{10}}{\dfrac{42}{100}}\\\\=\dfrac{3}{10}\times \dfrac{100}{42}\\\\=\dfrac{10\times 3}{42}\\\\=\dfrac{10}{14}\\\\=\dfrac{5}{7}[/tex]
So, the required fraction is equal to [tex]\dfrac{5}{7}[/tex].
How many miles are in 506,880 inches
Answer:
8 miles
Step-by-step explanation:
Answer:
8 miles
Step-by-step explanation:
1 mile:63360 inches
506880 divided by 63360 = 8
michelle has four credit cards with the balances and interest rates listed below. She wants to pay off her credit cards one at a time, based on the interest rate. In which order should Michelle pay off her credit cards
Answer:
3,2,1,4
Step-by-step explanation:
PLEASE HELP REALLY URGENT
Step-by-step explanation:
[tex]2 + \sqrt{2} [/tex]
I don’t know it help me pls
Answer:
its the yellow one hope this helps
Step-by-step explanation:
i did the math and checked !!!
Round 5,278 to the nearest thousand.
Hi im sorry to ask for help but im really stressed about this IN OWN WORDS PLEASE. and sorry to add more but please no scam<3
Answer:
1008
Step-by-step explanation:
volume formula: l×w×h
18×8×7=1008
Answer:
Volume = 1008 ft.
Step-by-step explanation:
The process to solving volume is L x W x H (length times width times hight). 18 ft. x 8 ft. x 7 ft. = 1008 ft. total.
A young couple just purchased a home for $180,000 in a nice area. The realtor suggested they can expect the value of their home to
Increase by 6% each year.
A function model that describes the value of the house is:
h(x) = 180000(1.06)*
where x is the number of years they have owned their home.
Using the model, how much should the house be worth after they have owned it for 5 years? (round to the nearest dollar)
A $954,000
B. $240,881
C. $190,800
D. $234,000
ILL GIVE BRAINLYIEST
Answer:
D. $234,000
Step-by-step explanation:
6% of $180,000 is $10,800
Multiply that times 5 years
$10,800x5=$54,000
add that value to the base price
$180,000+$54,000=$234,000
Suppose a caravan (5 cars) travels 100 km, beginning in front of one tollbooth, passing through a second tollbooth, and nishing just after a third tollbooth. The distance between two tollbooths is 50 km. Each car takes 12 sec to serve. The tollbooth starts to serve the caravan when the entire caravan is lined up. The caravan can only dispatch a tollbooth after all cars in the caravan are served. What is the end-to-end delay (from when the caravan is lined up before 1st tollbooth till the caravan is served by the 3rd tollbooth)
Answer:
1 hr 2 min 30 secs
Step-by-step explanation:
Assume Propagation speed = 100 km/hr
number of cars = 5
distance between booths = 50 km
Total distance = 100 km
take taken to serve each car = 12 secs
Determine the end to end delay
first calculate the propagation delay = Total distance / propagation speed
= 100 / 100 = 1 hr
next calculate : Time taken to serve 5 cars in each Tollbooth
= 5 * 12 secs = 60 secs
Next calculate : transmission delay ( time taken by three tollbooth to reach 5 cars )
= 60 secs * 3 = 180 secs = 2 min 30 secs
therefore end-end delay
= propagation delay + transmission delay
= 1 hr 2 min 30 secs
Find the domain of the following function: f(t) = √(t + 9)(t - 5)
Please help ASAP!! Thank you!!
Answer:
{ t | t ≥ − 9 }
Step-by-step explanation:
plz help me ill give brainly
Answer:
3.6 divided by 3 = 1.2 so 1.2 yards of material can be used on each skirt.
Step-by-step explanation:
solve 3 - x/2 ≥ 15.
A. x ≤ - 24
B. x ≥ - 6
C. x ≥ - 24
D. x ≤ 6
Answer:
A
Step-by-step explanation:
subract the three on both sides to get 12. then multiple by -2. when multiplying or dividing by negatives you want to flip the sign
Answer:
A. X ≤ -24
Step-by-step explanation:
(3 - X/2 ≥ 15)2
6 - X ≥ 30
-X ≥ 30-6
-X ≥ 24
-X/-1 ≤ 24/-1
X ≤ -24
One hundred tomato plants were randomly selected from a large garden, and a 90% confidence interval was computed to determine the true proportion of plants that produce useable tomatoes. The interval is 0.86 to 0.92. What would happen to the width of the confidence interval if the sample size was quadrupled
Answer:
D. the interval would be half the original width.
Step-by-step explanation:
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x^2-8x-3
Answer:
x = 1 and vertex = (1, - 7 )
Step-by-step explanation:
Given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
The the equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 4x² - 8x - 3 ← is in standard form
with a = 4, b = - 8 , then
x = - [tex]\frac{-8}{8}[/tex] = 1
That is equation of axis of symmetry is x = 1
Substitute x = 1 into the function for y- coordinate of vertex
y = 4(1)² - 8(1) - 3 = 4 - 8 - 3 = - 7
vertex = (1, - 7 )
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answer:
300 inches cubed
Step-by-step explanation:
Attached is an image of the explanation. Sorry about the handwriting I was trying to write fast.
If each edge of a cube is 5 cm, what is the volume of the cube?
Answer:
Volume =[tex]5^{3}[/tex] = [tex]125 cm^{3}[/tex]
A Ferris wheel has a radius
of 72 feet. What is the
distance a passenger will
travel one time around the
Ferris wheel?
Answer:
144
Step-by-step explanation:
radius is half of a diameter so that means you need to multiply 72 times 2
b)Given 0º < x < 360° , solve for x in:
2 sin (2x - 30°) = √3.
Answer:
180°
because x is the mid pf 0° and 360°
A restaurant bill is $21. You leave a 15% tip. Which of the following represents the amount a customer pays including the tip of 15% if the bill was dollars?
a. 0.15b
b. 15b
c. b + 0.15b
d. 1.15b
e. 1.015b
f. b + 15/100b
g. b + 0.15
which of the following shows the correct solution steps and solution to
3x - 2 = -11
Can someone help me pls
Answer:
x = 10 units
Step-by-step explanation:
By theorem,
Perpendicular drawn from the center to the chord of a circle, bisects the chord.
AB = BC = 6
In right triangle ΔCBD,
By applying Pythagoras theorem,
CD² = BC² + BD²
= 6² + 8²
CD = [tex]\sqrt{36+64}[/tex]
= 10
Since, CD and the side measuring x are the radii of the circle D.
x = CD = 10 units
