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).
To learn more about the quadratic equation;
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Related Questions
A rectangle is drawn so the width is 6 inches longer than the height. If the rectangle's diagonal measurement is 27 inches, find the height.
Give your answer rounded to 1 decimal place.
Answers
Answer:
height = 3
Step-by-step explanation:
x(x+6) = 27
x^2 + 6x - 27 = 0
(x+9)(x-3) = 0
x = 3
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!!
Answers
Finding the line of best fit is something a Machine Learning Model would do.
This particular ML model is called "Linear Regressor" or "Linear Regression Model". Look it up and there are definitely calculators for it, as it is relatively simple.
You can also, if you know how to use ML libraries and code, use Python to determine the value of [tex]b[/tex].
Hope this helps.
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options.
Answers
Given:
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.
To find:
The 2-digit numbers.
Solution:
Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].
We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.
Now,
[tex]5500=229\times 24+4[/tex]
It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:
[tex]5496+24=5520[/tex]
[tex]5520+24=5544[/tex]
[tex]5544+24=5568[/tex]
[tex]5568+24=5592[/tex]
Therefore, the possible 2-digit numbers are 20, 44, 68, 92.
eight times the reciprocal
of a number equals 4 times
the reciprocal of 10.
Answers
Answer:
8(1/x) = 4(1/10)
Step-by-step explanation:
lets say the number is x
eight times the reciprocal of a number equals 4 times the reciprocal of 10
8 * 1//x = 4 * 1/10
8/x = 4/10 , cross multiply
4x =8*10, divide both sides by 4
x= 80/4
x= 20
Which system of equations shows a solution of (0.5, -1)?
Need answers asap plzzz
Answers
Answer:
The first graph
Step-by-step explanation:
what can you infer about angles w and z based on the information in the other triangles?
Answers
Answer:
They are supplementary and their sum is 180°
w = 45 + 60 or w = 105
z = 180 - 105 or z = 75
A(n) _____ is an expression that uses variables to state a rule.
plz help asap
Answers
Answer:
A FORMULA is an expression that uses variables to state a rule.
Express these system specifications using the propositions p “The user enters
a valid password,” q “Access is granted,” and r “The user has paid the
subscription fee” and logical connectives (including negations).
a) “The user has paid the subscription fee, but does not enter a valid
password.”
b) “Access is granted whenever the user has paid the subscription fee and
enters a valid password.”
c) “Access is denied if the user has not paid the subscription fee.”
d) “If the user has not entered a valid password but has paid the subscription
fee, then access is granted.”
Answers
Answer:
a) r ⋀~p
b)(r⋀p)⟶q
c) ~r ⟶ ~q
d) (~p ⋀r) ⟶q
Step-by-step explanation:
To solve this question we will make use of logic symbols in truth table.
We are told that;
p means "The user enters
a valid password,”
q means “Access is granted,”
r means “The user has paid the
subscription fee”
A) The user has paid the subscription fee, but does not enter a valid
password.”
Fist part of the statement is correct and so it will be "r". Second part of the statement is a negation and will be denoted by ~p. Since both statements are joined together in conjunction, we will use the conjuction symbol in between them which is "⋀" Thus, we have; r ⋀~p
B) Still using logic symbols, we have;
(r⋀p)⟶q
⟶ means q is true when r and p are true.
C) correct symbol is ~r ⟶ ~q
Since both statements are negation of the question. And also, if ~r is true then ~q is also true.
D) Similar to answer A to C above, applying similar conditions, we have (~p ⋀r) ⟶q
PLEASE BE RIGHT AND SOLVE PLEASE
Answers
Answer:
That transformation that happened was B rotation since b is rotated 180 degrees from A
Hope This Helps!!!
by what number should 2/9 be divided to obtain 8/3
Answers
Answer:
[tex] \frac{1}{12} [/tex]
Step-by-step explanation:
[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]
So, if you divide 2/9 by 1/12, you'll get 8/3
Answered by GAUTHMATH
Find each product
-4 (41)
4 (-41)
-4 (-41)
Please help me!!
Answers
-164
164
Hope this helps!
HELP WILL MARK BRAINLIESG
Write an equation that represents the line,
Use exact numbers.
Answers
Answer:
3/2 + 7
Step-by-step explanation:
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 110 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answers
Answer:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
Step-by-step explanation:
L numbers of hours assigned to Lisa
D numbers of hours assigned to David
S numbers of hours assigned to Sara
Objective Function to minimize:
z = 30*L + 25*D + 18*S
Constraints:
Total time available
L + D + S ≤ 110
Lisa experience
L ≥ 0.4 * ( L + D ) then L ≥ 0.4*L + 0.4*D
0.6*L - 0.4*D ≥ 0
To provide designing experience to Sara
S ≥ 0.15*110 then S ≥ 16.5
Time for Sara
S ≤ 0.25 * ( L + D ) S ≤ 0.25*L + 0.25*D or -0.25*L - 0.25*D + S ≤0
Availability of Lisa
L ≤ 50
The Model is:
z = 30*L + 25*D + 18*S to minimize
Subject to:
L + D + S ≤ 110
0.6*L - 0.4*D ≥ 0
S ≥ 16.5
-0.25*L - 0.25*D + S ≤0
L ≤ 50
L ≥ 0 ; D ≥ 0 , S ≥ 0
After 6 iterations optimal ( minimum ) solution is:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is z = 30L + 25D + 18S and the minimum z is 2079.
Given :
The company estimates that 110 hours will be required to complete the project.Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers.To provide a label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time.The number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers.Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is given by:
z = 30L + 25D + 18S
The constraints are given by:
1) L + D + S [tex]\leq[/tex] 110
2) L [tex]\geq[/tex] 0.4(L + D)
L [tex]\geq[/tex] 0.4L + 0.4D
0.6L - 0.4D [tex]\geq[/tex] 0
3) S [tex]\geq[/tex] 0.15(110)
S [tex]\geq[/tex] 16.5
Now, to minimize 'z' then use:
[tex]\rm -0.25L-0.25D+S\leq 0[/tex]
L [tex]\leq[/tex] 50
L [tex]\geq[/tex] 0, D [tex]\geq[/tex] 0, S [tex]\geq[/tex] 0
Now, the minimum z is given by:
z = 2079
L = 26, D = 39.6, S = 16.5
For more information, refer to the link given below:
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what is the value of -3^2+(4+7)(2)?
Answers
Answer:
[tex] { - 3}^{2} + (4 + 7)(2) \\ = - 9 + 22 \\ = 13[/tex]
In the diagram, the measure of angle 3 is 76°. A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8. What is the measure of angle 4?
Answers
Answer:
104
Step-by-step explanation:
180-76=104
Answer:
104
Step-by-step explanation:
heres my proof. have a nice day :)
Tell whether ADEF and AGHI can be proven
congruent.
A.No, ADEF and AGHI aren't congruent
because they don't share a side.
B.Yes, ADEF and AGHI can be proven
congruent by HL.
C.No, there isn't enough information
because the triangles aren't right
triangles.
D.Yes, ADEF and AGHI can be proven
congruent by SSS.
Answers
Answer:
A. No, ADEF, and AGHI aren't congruent because they don't share a side.
----------------------------
hope it helps...
have a great day!!
Can someone help me solve this? Thanks!
Answers
9514 1404 393
Answer:
p(x) = x³ -3x²+4x -2
Step-by-step explanation:
When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.
Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...
p(x) = (x -1)(x -(1+i))(x -(1-i))
The last two factors can be recognized as the factors of the difference of squares:
((x -1) +i)((x -1) -i) = (x -1)² -i²
= (x² -2x +1) -(-1) = x² -2x +2
Now the whole polynomial can be seen to be ...
p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)
p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses
p(x) = x³ -3x²+4x -2
I need at least two more sentences in regards with this assignment. Note the included photo. Please come up with two proper sentences following the assignments instructions. Ps. Don’t try to steal points from this or you will be reported
Answers
Answer:
A={x: x is a cat}
B={x: x likes climbing on trees}
My little cat Louis likes climbing on trees (Louis is in the intersection of the two sets)
A={x: x is a town in the USA}
B={x: x is a town in the UK}
To improve my English I'd like to go on holiday to a town in the USA, but a town in the UK would work too (the town shall be in the union of the two sets)
Olivia rides her scooter 3/4 mile in
1/3 hour. How fast, in miles per hour,
does she ride her scooter?
Answers
Answer:
2.25 miles per hr
Answer:
2.25 miles per hour
Step-by-step explanation:
speed = distance / time
speed = [tex]\frac{3}{4} / \frac{1}{3}[/tex] (take the reciprocal of [tex]\frac{1}{3}[/tex])
= [tex]\frac{3}{4} * 3[/tex]
= [tex]\frac{9}{4}[/tex] = 2.25 miles per hour
1+1/2+1/4+1/8+1/16+1/32+1/64
if you continue adding on fractions according to this pattern, when will you reach a sum of 2?
Answers
Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.
============================================================
Explanation:
We have this sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
which is geometric with the following properties
a = first term = 1r = common ratio = 1/2 = 0.5Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.
Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.
That infinite sum is
S = a/(1-r)
S = 1/(1-0.5)
S = 1/0.5
S = 2
So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.
In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.
Here's a list of partial sums
1+1/2 = 1.51+1/2+1/4 = 1.751+1/2+1/4+1/8 = 1.8751+1/2+1/4+1/8+1/16 = 1.93751+1/2+1/4+1/8+1/16+1/32 = 1.968751+1/2+1/4+1/8+1/16+1/32+1/64 = 1.9843751+1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 1.99218751+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 = 1.99609375We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.
Donald and Sara are surveying their neighbors about the community playground. Their questions, written on the survey, are below:
Donald: How many times do you visit the playground in a month?
Sara: Did you visit the playground this month?
Who wrote a statistical question and why?
Sara, because there will be variability in the responses collected
Donald, because every neighbor can give a different answer
Sara, because there can be only one answer to the question
Donald, because every neighbor will give the same answer
Answers
Answer:
B
Step-by-step explanation: Because Donald asks a more broad and open question which people could give different answers too
1. You measure 24 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 3.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
2. You measure 37 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 10.1 ounces. Based on this, construct a 95% confidence interval for the true population mean backpack weight.
3. You measure 30 watermelons' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
4. A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 16. Which of the following is a correct interpretation of the interval 11.8 < μ < 20.4?
A. There is a 99% chance that the mean of a sample of 16 widgets will be between 11.8 and 20.4.
B. The mean width of all widgets is between 11.8 and 20.4, 99% of the time. We know this is true because the mean of our sample is between 11.8 and 20.4.
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 11.8 and 20.4.
E. There is a 99% chance that the mean of the population is between 11.8 and 20.4.
5. For a confidence level of 90% with a sample size of 23, find the critical t value.
Answers
Answer:
(73.845 ; 76.155) ;
(41.633 ; 48.367) ;
1.273 ;
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;
1.717
Step-by-step explanation:
1.)
Given :
Mean, xbar = 75
Sample size, n = 24
Sample standard deviation, s = 3.3
α = 90%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 24 - 1 = 23
Tcritical = 1.714
Margin of Error = 1.714 * 3.3/√24 = 1.155
Confidence interval = 75 ± 1.155
Confidence interval = (73.845 ; 76.155)
2.)
Given :
Mean, xbar = 45
Sample size, n = 37
Sample standard deviation, s = 10.1
α = 95%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 37 - 1 = 36
Tcritical = 2.028
Margin of Error = 2.028 * 10.1/√37 = 3.367
Confidence interval = 45 ± 3.367
Confidence interval = (41.633 ; 48.367)
3.)
Given :
Mean, xbar = 37
Sample size, n = 30
Sample standard deviation, s = 4.1
α = 90%
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 30 - 1 = 29
Tcritical = 1.700
Margin of Error = 1.700 * 4.1/√30 = 1.273
5.)
Sample size, n = 23
Confidence level, = 90%
df = n - 1 ; 23 - 1 = 22
Tcritical(0.05, 22) = 1.717
circle A has a center of (2,3) and a radius of 5 and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B
Answers
Answer:
12
Step-by-step explanation:
Find the slope of the line y= -3x+7
Answers
Answer:
If you had a line of x = 7, (or any time you have an equation where x equals a number) then you would have a vertical line. In every vertical line, the slope is undefined. In equations of lines that are in the format of y = mx + b, the slope is represented by the "m".Answer:
-3
Explanation:
The given equation is in slope-intercept form. The format of slope-intercept is y = mx + b, where m is the slope and b is the y-intercept.
The slope is the coefficient of x.
In the equation y = -3x + 7, the slope is -3, because -3 is the coefficient of x.
Hence, the slope is -3.Question 23 (5 points)
A triangle has two interior angles with the measurement of 68° and 54º. What's the
measurement of the third interior angle?
55°
620
58°
65°
Answers
Answer:
58°
Step-by-step explanation:
Given that,
The measure of two interior angles are 68° and 54º.
We need to find the measurement of the third interior angle.
We know that, the sum of angles of a triangle is equal to 180°. Let the angle is x. So,
x+68+54 = 180
x+122 = 180
x = 180-122
x = 58°
So, the measure of the third interior angle is equal to 58°.
find the sum and difference between the place value and face value of 5 in the number 3508 6941
Answers
Answer:
Sum= 5000005
Difference= 4999995
Step-by-step explanation:
The place value of 5 in the number 35086941 is 5000000
The face value is 5
The sum between the face value and place value can be calculated as follows
°= 5000000+5
= 5000005
The difference can be calculated as follows
= 5000000-5
= 4999995
What is the sum?
8+(-12)
-20
4
ОО
20
Answers
Which of these is an example of technology?
an idea for a story
the first wheel ever built
an engineer
Answers
Answer:
the first wheel ever built
Answer:
The first wheel ever built
Step-by-step explanation
(*) Sorry for my late answer but I hope this helps others that are looking for this.
100% in the test :)
What is the expression (x+1)(x2+3x+2) as a polynomial in standard form?
Answers
Step-by-step explanation:
hope u like it.......
She decides that ordering that many cars would not be economically feasible at this time and asks her sales manager to randomly choose one of the models for the sales lot. What is the probability that he chooses the 4-door, special edition model, with four-wheel drive?
The probability that he chooses the 4-door, special edition, four-wheel drive model is (44)=
P(4S4)=
Answers
Answer:
The probability that he chooses the 4-door, special edition, four-wheel drive model is P( 454) = 1 (Enter your answer as reduced fraction.) ...Step-by-step explanation:
The probability that he chooses the 4-door, special edition, four-wheel drive model is (44)=P(4S4)=