Graph: y = (x + 3)2 – 4
Which values are solutions of the quadratic equation
0 = (x + 3)2 – 4? Check all that apply.
y
X
-4
WIEC
6
0 -5
-4
.
0 -3
-1
-6
-4
-2
2
4
6
02
3
-2 -4
0,5
-6
Answers
Answer:
0.534375
45328
36763
-6
-78
The values of x and y that satisfy the graphs are:
(-1, 0), and (-5, 0).
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
We can start by simplifying the quadratic equation:
y = (x + 3)² – 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
Now, we can use various methods to find values of x and y that satisfy this equation. Here are five possible values:
If we substitute x = -1, we get:
y = (-1)² + 6(-1) + 5
y = 0
So, one solution is (-1, 0).
If we substitute x = 0, we get:
y = 0² + 6(0) + 5
y = 5
So, another solution is (0, 5).
If we substitute x = -5, we get:
y = (-5)² + 6(-5) + 5
y = 0
So, another solution is (-5, 0).
To find rational solutions, we can factor in the quadratic expression:
y = x² + 6x + 5
y = (x + 1)(x + 5)
So, the solutions are x = -1 and x = -5. Substituting these values into the equation, we get:
For x = -1, y = (-1)² + 6(-1) + 5 = 0
For x = -5, y = (-5)² + 6(-5) + 5 = 0
So, the solutions are (-1, 0) and (-5, 0).
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Related Questions
Find the line integral with respect to arc length ∫C(9x+5y)ds, where C is the line segment in the xy-plane with endpoints P=(2,0) and Q=(0,7).
(a) Find a vector parametric equation r⃗ (t) for the line segment C so that points P and Q correspond to t=0 and t=1, respectively
(b) Rewrite integral using parametrization found in part a
(c) Evaluate the line integral with respect to arc length in part b
Answers
(a) You can parameterize C by the vector function
r(t) = (x(t), y(t) ) = P (1 - t ) + Q t = (2 - 2t, 7t )
where 0 ≤ t ≤ 1.
(b) From the above parameterization, we have
r'(t) = (-2, 7) ==> ||r'(t)|| = √((-2)² + 7²) = √53
Then
ds = √53 dt
and the line integral is
[tex]\displaystyle\int_C(9x(t)+5y(t))\,\mathrm ds = \boxed{\sqrt{53}\int_0^1(17t+18)\,\mathrm dt}[/tex]
(c) The remaining integral is pretty simple,
[tex]\displaystyle\sqrt{53}\int_0^1(17t+18)\,\mathrm dt = \sqrt{53}\left(\frac{17}2t^2+18t\right)\bigg|_{t=0}^{t=1} = \boxed{\frac{53^{3/2}}2}[/tex]
The ratio of men to women working for a company is 5 to 3. If there are 200 employees total, how many women work for the company?
Answers
Answer:
There are 200 employees, and the ratio is 5:3.
5+3 = 8
200/8 = 25
So, there are 5(25) = 125 men and 3(25) = 75 women.
There are 75 women who work for the company.
Let me know if this helps!
PLEASE HELP NO ONE IS ANSWERING ANY QUESTION I ASK!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answers
Answer:
sorry in dont know the ans
PLEASE HELP
-1/2m=-9
Show your work in details if you can, I have a hard time understanding this.
Answers
[tex] \begin{cases} \\ \large\bf{\green{ \implies}} \tt \: - \: \frac{1}{2} \: m \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - \frac{1 \: m}{2} \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 9 \: \times \: 2 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 18 \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{ \cancel- 18}{ \cancel - 1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{18}{1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: 18 \: \\ \end{cases}[/tex]
in a 5 liter milk jar water and milk are in the ratio 2:3. If 1 liter of milk and 1 liter of water is added. what will be the new ratio.
Give me answer with steps . and the answer is 3:4. but how I want to know
Answers
Answer:
ratio of water and milk=2:3
i.e. water=2
milk=3
now adding 1 liter of water in 2
2+1=3
and 1 liter of milk in 3
3+1=4
hence,
the new ratio is 3:4
Step-by-step explanation:
i hope this will help
plz mark as brainliest
trig..experts...help! Will give brainly!
Answers
Answer:
Step-by-step explanation:
189² = 215² + 123² - 2(215)(123)cos x°
35,721 = 46,225 + 15,129 - 52,890 cos x°
35,721 = 61,354 - 52,890 cos x°
52,890 (cos x° ) = 25,633
cos x° = 25,633 ÷ 52,890 ≈ 0.4846
x° ≈ 61.01°
Tìm thể tích của khối bao bởi mặt z=5+(x−4)^2+2y và mặt x=3,y=4 và mặt phẳng tọa độ.
Answers
Step-by-step explanation:
ccxiddidificifificici i i ivi i i i i i i i iivvii iix9difi
I need help to fine the statement that is true
Answers
Answer:
option A
Step-by-step explanation:
wx and zy making 90 angle with each other therefore they are perpendicular.
wx and ab making 0 angle with each other therefore they are parallel
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? O a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. O d) She will have a hard time focusing.
Answers
Option C
Customers will think she is very busy
A messy desk indicates that the person is very busy.
Must click thanks and mark brainliest
Which expression is equivalent to (3 squared) Superscript negative 2?
Answers
Answer:
–81
Step-by-step explanation:
All of my friends like fruit. 9 friends like bananas, 8 friends like oranges, and 7 friends like plums. 5 friends like both bananas and oranges, 3 friends like both bananas and plums, 4 friends like both oranges and plums, and 2 friends like bananas, oranges and plums. How many friends do I have?
Answers
Answer:
you have 38 friends
Step-by-step explanation:
because you have to add I think so
Answer:
38 friends
Step-by-step explanation:
Carlos is an administrative assistant at an insurance agency. He wants to gather feedback from customers on their service. He doesn't have a lot of time, and he wants to have some data to share with his supervisor. What is the best way for Carlos to gather feedback? O a) Individual interviews O b) Survey O c) Focus group d) Phone calls
Answers
When a person does not have enough time he must should take the faster and effective route in this case carlos does not have time for individual interviews or phone calls. Focus group will not work i guess because discussion takes time so i guess it should be survey. I am not sure but it should be Survey or Focus Group
Must click thanks and mark brainliest
f(x) = - 2x
g(x) = 8x^2 - 5x + 7
Find (f • g)(x).
Answers
9514 1404 393
Answer:
(f•g)(x) = -16x^3 +10x^2 -14x
Step-by-step explanation:
(f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)
Use the distributive property:
(f•g)(x) = -16x^3 +10x^2 -14x
Solve for x.
–5(–2x – 5) – 2 – 1= -12
Answers
Answer:
x=-17/5
Step-by-step explanation:
–5(–2x – 5) – 2 – 1= -12
+10x+25-2-1=-12
10x+22=-12
10x=-12-22
10x=-34
x=-34/10
x=-17/5
Step-by-step explanation:
Open the brackets
10x +25 -2 - 1= -12
Collect the like terms
10x = -12-25+2+1
10x = -34
Divide both sides by 10
Therefore,x = -34/10 = -3.4
15 times a certain number plus 5 times the same number is 80 what is the number
Answers
x = 4
Every step shown. Once you become used to doing this you will almost be able to do the basic one's in your head without writing much down.
Explanation:
Let the unknown value be
x
Converting the words into numbers:
First part: "15 times a certain number" → 15 x
Second part: "plus 5 times the same number" → 15 x + 5 x
The last part: " is 80" -> 15x + 5 x = 80
We are counting x ' s . 15 of them plus another 5 of them gives a total of 20.
So 15 x + 5 x = 20 x = 80
Divide both sides by 20
20 x ÷ 20 = 80÷ 20
20/20x=80/20
x=4
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 15x+5x=80[/tex]
[tex]\\ \sf\longmapsto (15+5)x=80[/tex]
[tex]\\ \sf\longmapsto 20x=80[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{80}{20}[/tex]
[tex]\\ \sf\longmapsto x=4[/tex]
Please help 20 points
Answers
the line parallel to 2x – 3y = 6 and containing (2,6)
what is the equation of the line ?
Answers
First, write out the equation in slope intercept form.
-3y= -2x+6
y= 2/3x -2
The slope of the equation is 2/3, m.
Substitute the slope and coordinate into y=mx+b. Since it’s parallel, the slope remains the same.
6= 2/3(2)+b
6= 4/3+b
14/3=b
y= 2/3x + 14/3
What is the surface area of this figure in square centimeters?
A.96
B.75
C.84
D.60
Answers
9514 1404 393
Answer:
A. 96
Step-by-step explanation:
The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.
A = 2(1/2)bh + PH
where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.
A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²
A = 96 cm²
The surface area of the triangular prism is 96 square cm.
2. What is the length of AB? Round your
answer to the nearest hundredth.
Answers
Answer:
The required length of AB is 7.28 units.
$26,876 is invested, part at 9% and the rest at 5%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 5% by $720.78, how much is invested at each rate? (Round to two decimal places if necessary.)
Answers
9514 1404 393
Answer:
$14,747 at 9%$12,129 at 5%Step-by-step explanation:
Let x represent the amount invested at 9%. Then the difference in interest amounts is ...
(9%)x -(5%)(26876 -x) = 720.78 . . . . . assuming a 1-year investment
0.14x -1343.80 = 720.78 . . . . . . . . . simplify
0.14x = 2064.58 . . . . . . . . . . . . . . add 1343.80
x = 14,747 . . . . . . . . . . . . . . . . divide by 0.14
$14,747 is invested at 9%; $12,129 is invested at 5%.
The length of rectangle is double of it's breadth .if its perimeter is 48 cm then find it's length.
Answers
Step-by-step explanation:
Let breadth be x,
then length is 2x cm,
perimeter of rectangle=2(l+b),
48=2(2x+x),
48÷2=3x
24=3x
24÷3=x
8cm =x,
B=8cm
L=2×8=16cm
Answer:
length =2x
breadth= let x be breadth
Perimeter = 48cm
now
Perimeter = 2 (l+b)
or, 48 cm = 2 (2x+x)
or, 48cm= 4x + 2x
or, 48 cm = 6x
or, 48cm÷6 =x
x = 8 cm
breadth= 8cm
length = 8 ×2 =16cm
How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155
Answers
9514 1404 393
Answer:
10
Step-by-step explanation:
The sum of terms of an arithmetic series is ...
Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2
For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...
155 = (3n^2 +n(2·2 -3))/2
Multiplying by 2, we have ...
3n^2 +n -310 = 0 . . . . . arranged in standard form
Using the quadratic formula, the positive solution is ...
n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10
10 terms of the series will have a sum of 155.
Step-by-step explanation:
[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]
Factor the polynomial expression 3x4 + 24x.
Answers
Answer:
3x ( x+2)(x^2−2x+4)
Step-by-step explanation:
3x^4 + 24x.
Factor out the greatest common factor
3x*x^3 + 3x*8
3x(x^3+8)
Then factor the cubic term
The sum of cubes is a^3+b^3=(a+b)(a^2−ab+b^2)
3x ( x+2)(x^2−2x+4)
Find the measure of TU
A. 8
B. 12
C. 14
D. 11
Answers
Answer:
D. 11
Step-by-step explanation:
First apply the secant-secant theorem to find the value of x.
Thus,
VU(TU + VU) = VW(BW + VW) (secant-secant theorem)
Substitute
(7)(x + 4 + 7) = (9)(-2 + x + 9)
7(x + 11) = 9(7 + x)
7x + 77 = 63 + 9x
Collect like terms
7x - 9x = 63 - 77
-2x = -14
Divide both sides by -2
x = 7
✔️Find TU
TU = x + 4
Substitute get value of x
TU = 7 + 4 = 11
Answer:
11
Step-by-step explanation:
ASAP ITS TIMED
What is the following sum? Assume x20 and 20.
W x ² + 2 / x 374 + xy ſy
0 x ²7² ſy- 2xy?
0 2xy ſy + 2xy ² x
0 4xy dx
o 2xyxy
وی در مورد
Answers
Answer:
The right answer is the 2nd one
hope it will help :)
The given sum is option B. 2xy√y + 2xy²√x.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression of sum is,
√(x²y³) + 2√(x³y⁴) + xy √y
We have to find the sum.
√(x²y³) = √x² √y³ = x√y³ = x√(y²)√y = xy√y
Now,
2√(x³y⁴) = 2[√x² √x √(y²)²] = 2x√x y² = 2xy²√x
Substituting these,
√(x²y³) + 2√(x³y⁴) + xy √y = xy√y + 2xy²√x + xy √y
= 2xy√y + 2xy²√x
Hence the equivalent sum is 2xy√y + 2xy²√x.
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Which equation is represented by the graph?
Answers
Answer:
I don't knowledge bro sorry
[tex]log(x) * log(2)[/tex]
Why can't this problem be solved?
Answers
Answer:
Because it is not an equation.
Step-by-step explanation:
[tex] log(x) \times log(2) \\ = log(x + 2) [/tex]
The following are on a parabola defining the edge of a ski
(-4, 1), (-2, 0.94), (0.1)
The general form for the equation of a parabola is:
Ax^2+ Bx +C= y
Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Repeat this process with 1 of the other to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.
Answers
9514 1404 393
Answer:
a) 16A -4B +C = 1
b) 4A -2B +C = 0.94
c) C = 1
Step-by-step explanation:
Substitute the x- and y-values into the general form equation.
a. A(-4)² +B(-4) +C = 1
16A -4B +C = 1
__
b. A(-2)² +B(-2) +C = 0.94
4A -2B +C = 0.94
__
c. A(0)² +B(0) +C = 1
C = 1
_____
Additional comment
Solving these equations gives A=0.015, B=0.06, C=1. The quadratic is ...
0.015x² +0.06x +1 = y
For f(x) = 4x2 + 13x + 10, find all values of a for which f(a) = 7.
the solution set is ???
Answers
Answer:
f(7)=109
Step-by-step explanation:
Since f(a)=7 then you just imput 7 on each x like this f(7)=8+13(7)+10= 109
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answers
9514 1404 393
Answer:
10·2^-8 grams
Step-by-step explanation:
The each day, the initial amount for that day is multiplied by 1/2. After 8 days, the initial amount has been multiplied by (1/2)^8, where the exponent of 8 signifies that (1/2) is a factor 8 times in the product.
After n days, the quantity remaining is ...
q(n) = 10·(1/2)^n = 10·2^(-n)
after 8 days the remaining amount is ...
q(8) = 10·2^-8 . . . grams
