Expand and simplify (x+4) (x-3) (3x+2)
Determine the solution to the following system of equations.
y = -2x2 + 4x + 8
y = -4x + 16
Answer: (2, 8)
Since both equations in the system are equal to y, substitute -4x + 16 for y in the quadratic equation, and then solve for x as follows.
Next, substitute x = 2 into either of the original equations to find the y-value of the solution to the system of equations.
Therefore, the solution to the given system of equations is (2,8).
The solution of the system of equations will be;
⇒ x = 2
⇒ y = 8
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
⇒ y = - 2x² + 4x + 8
⇒ y = - 4x + 16
Now,
Since, The system of equations are,
⇒ y = - 2x² + 4x + 8 ..(i)
⇒ y = - 4x + 16 ..(ii)
Substitute the value of y from (ii) in equation (i), we get;
⇒ - 4x + 16 = - 2x² + 4x + 8
⇒ - 2x² + 4x + 8 + 4x - 16 = 0
⇒ - 2x² + 8x - 8 = 0
⇒ - x² + 4x - 4 = 0
⇒ x² - 4x + 4 = 0
⇒ x = - (-4) ± √ (-4)² - 4×1×4 / 2×1
⇒ x = 4 ± √16 - 16 / 2
⇒ x = 4 / 2
⇒ x = 2
And, y = - 4x + 16
⇒ y = - 4 × 2 + 16
⇒ y = - 8 + 16
⇒ y = 8
Thus, The solution of the system of equations will be;
⇒ x = 2
⇒ y = 8
Learn more about the mathematical expression visit:
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Which one would it be
Answer:
A or [tex]\frac{\sqrt{6} }{2}[/tex]
Step-by-step explanation:
*note- this method only works because the denominator values are being multiplied, if they were being added then there are extra steps to keep in mind but for now this is simple*
Start by dividing the root 12 in the numerator by the root 2 in the denominator
[tex]\frac{\sqrt{12} }{\sqrt{2} }=\sqrt{6}[/tex]
Then we simply substitute back in the 2 (from the denominator) that we ignored for a second to get our answer
[tex]\frac{\sqrt{6} }{2}[/tex]
*note- if you are allowed to use a calculator then you could also plug in your values to check each answer option but since this question isn't too complicated there should be no need to do so unless you forget how to solve it algebraically*
What is the y-intercept for 2x + 4y= -8
a) Write down the mathematical name of this shape?
Answer
this is a Parallelogram or a Polygon
Step-by-step explanation:
most likey the polygon
as i see it, it looks like a polygon
The company charges $45 a day for the car
as well as charging a one-time $25 fee for
the car’s navigation system (GPS). Write an
equation for the cost in dollars, C, as a
function of the number of days, d, the car
was rented.
Answer:
I personally find it easier to put my equation in words before actually writing the equation, so for this particular situation, the equation would sound like this :
→ The cost (C) is equal to 45$ a day (d) plus 25$!
Now that your equation is put into words, all that you have to do is write down the equation without the words :
→ C = (45d) + 25
If you want to make sure that your equation is correct, you can try it out, say for instance you want to rent a car for a week, so for a total of 7 days, and you want to see how much it would cost :
d = 7 (in this particular situation)
C = (45 × 7) +25
↓
C = 315 + 25
↓
C = 340
→ So it would cost 340$ to rent a car for a week!
credit goes to naomi479xx for solving this answer.
Ron drew an angle that measured 160 degrees. Then he drew a ray that divided the angle in half. What is the measure of each of the new angles formed?
is it
A. 180°
B. 160°
C. 80°
D. 60°
GIVING BRAINLIEST!!!!!
What type of triangle is shown in the image?
Acute triangle
Right triangle
Equilateral triangle
Obtuse triangle
Answer:
A. Obtuse triangle
B,C,D. Acute
Step-by-step explanation:
Kayla drew 2 numbered cards from a deck. When she added the numbers, their sum was 12. One number was twice as big as the other one. What 2 cards did she draw out?
Answer:
4 & 8
Step-by-step explanation: hope this helps :)
What’s 300(6+20)-120?
Answer: 7680
Step-by-step explanation:
Answer:
7,680
Step-by-step explanation:
Okay, so we use PEMDAS right, so we start with the parenthesis:
6 + 20 = 26
300 x 26 = 7,800
7,800 - 120 = 7,680
So 300(6+20)-120=7,680
hope this helps:)
If you get a student loan for $2,000 at 8% interest, what is the simple interest for one year?
helpppp plss:)))))))
(the answer is not c though)
Hey can you help me fast!!!
Answer:
40 square feet
Step-by-step explanation:
I gotcha bro
4 x 12 = 48
48 - 3 x 2 - 1 x 2 = 48 - 6 - 2 = 40
Please answer correctly and no links pls
Answer: 13.) 49, 14.) 64
Step-by-step explanation:
7x7=49, 8x8=64
if renting a bike cost $5 plus $2.50 per hour how much will i costs for 6 hours
Answer:
15per 6 hours
Step-by-step explanation:
2.5x2=5x3=15
What is the variable in the expression 12 + 5y + 4
A number of dimes and quarters are worth $2.55. If the number od dimes and quarters were interchanged the resulting new amount would be $2.70. How many of each kind of coin were there before the interchange?
Answer:
8 dimes
7 quarters
Step-by-step explanation:
Let number of
Dimes = x ; quarters = y
10x + 25y = 255 ___(1)
25x + 10y = 270 ___(2)
From (1)
10x = 255 - 25y
x = (255 - 25y) / 10
x = 25.5 - 2.5y
Put x = 25.5 - 2.5y in (2)
25(25.5 - 2.5y) + 10y = 270
637.5 - 62.5y + 10y = 270
-52.5y = - 367.5
y = 367.5 / 52.5
y = 7
x = 25.5 - 2.5(7)
x = 25.5 - 17.5
x = 8
convert five whole five over eight from fraction to decimals
Answer:
5.625 is the correct answer to convert five whole five over eight from fraction to decimals.
Step-by-step explanation:
=5/8+5
=0.625+5
=5.625#
please simplify (4x^2) ^3
Answer:
64x^6
Step-by-step explanation:
4x^2 x 4x^2 x 4x^2
16x^4 x 4x^2
64x^6
I need help fast!!!!!!
Answer:
Z= 180 X = 95 y= 147
Step-by-step explanation:
Z=180 because it is a line and when it is a line it = 180 degrees
for X you want to first find the angle of the other triangle and when you do you subtract that # from 180 because those 2 angles make a line
to find that angle next to X is...
180- (the other 2 angles in the triangle)
180- 45- 50
180-95
85 degrees
now do
180-85
95 degrees -- this is what X =
now you want to find the angle that is left in one triangle
so do
180- 95- 52
180- 147
33 degrees -- the angle that was missing
to find Y do...
180- 33
147 degrees -- this is what Y =
Fantasy 5 lottery game is picking 5 numbers from 1-41. If you match them all you win the jackpot. What is the probability you win the jackpot?
Answer:
1 / 89927760
Step-by-step explanation:
Recall :
Probability = required outcome / Total possible outcomes
To pick five number for a lottery from the range (1 - 41) ;
For this scenario, selection will be done without replacement
To win lottery , all 5 selections must be matched
P(1st pick) = 1 / 41
P(2nd pick) = 1 /40
P(3rd pick) = 1/39
P(4th pick) = 1/38
P(5th pick) = 1/37
(1/41 * 1/40 * 1/39 * 1/38 * 1/37) = 1 / 89927760
Hence, Probability of winning lottery = 1 / 89927760
During a school assembly, 15 out of 60 students wore orange shirts to show school spirit. what percent of the students did NOT wear orange shirts?
Answer: 75%
15/60 wore orange shirts
45/60 didn’t
45/60 = 0.75 = 75%
Can someone help me with this geometry volume question ty
Please please ASAP ASAP please ASAP thank you so much please
No links or files please
Answer:
(0, 3)
Step-by-step explanation:
Y axis changes and x axis stays the same
you deposit $1050 into an account that pays 7.25% interest per year. find the amount after six year given the following: a) compounded semiannually b) compounded monthly
Answer:
semiannually = $1609.77
monthly = $1128.71
Step-by-step explanation:
What is the slope of (10,3) and (2,3)
Answer:
m=0
Step-by-step explanation:
the formula given for slope (m) calculated from two points is given as (y2-y1)/(x2-x1)
we are given the points (10,3) and (2,3)
label the values of the points to use for the formula:
x1=10
y1=3
x2=2
y2=3
plug into the formula
m=(3-3)/(2-10)
subtract
m=0/-8
divide
m=0
therefore, the slope is 0
Hope this helps! :D
0/-8
i’m not very good at explaining but that is the answer ^^
Find the length of the missing side of the triangle
Answer:
65ft
Step-by-step explanation:
Pythagoreom therom
determine equation for line that is perpendicular to x=-2 and passes through the point (6,1)
Answer:
y = 1
Step-by-step explanation:
How to solve X²-X-42uing
using Fertoning Polynomials
Answer:
x = - 6, x = 7
Step-by-step explanation:
Begin by equating to zero
x² - x - 42 = 0
Consider the factors of the constant term (- 42) which sum to give the coefficient of the x- term (- 1)
The factors are - 7 and + 6 , since
- 7 × + 6 = - 42 and - 7 + 6 = - 1 , then
(x - 7)(x + 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 7 = 0 ⇒ x = 7
Simplify each expression using the properties of exponents and match it to the correct answer
