Answer:
(x - 5)(2x + 3)
Step-by-step explanation:
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = - 7
The factors are - 10 and + 3
Use these factors to split the x- term
2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )
= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term
= (x - 5)(2x + 3)
The factorization of the quadratic expression is presented as follows;
2·x² - 7·x - 15 is (2·x + 3)·(x - 5)
What is a quadratic expression?A quadratic expression is an expression that can be presented in the form a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
In order to factorize the quadratic expression 2·x² - 7·x - 15, it is required to find two binomials with a product equivalent to the expression is to be found
The binomial can be found from the numbers p and q such that p + q = -7 and p·q = -30 (The product of the leading coefficient and the constant term)
A possible pair of such numbers is p = -10 and q = 3. Therefore, we get;
2·x² - 7·x -15 = 2·x² + (3·x - 10·x) - 15
The first two terms and the last two terms can be grouped and each group factorized separately as follows;
2·x² + (3·x - 10·x) - 15 = (2·x² + 3·x) + (-10·x - 15)
x·(2 + 3) - 5·(2·x + 3)
The above expression can be further factorized by taking out the common factor (2·x + 3) as follows;
x·(2 + 3) - 5·(2·x + 3) = (2·x + 3)·(x - 5)
Therefore, the factored expression is; 2·x² - 7·x - 15 = (2·x + 3)·(x - 5)
Learn more on quadratic equations here: https://brainly.com/question/24628957
#SPJ6
graph this function: f(x)=x2-4x-5
find the number of distinguishable permutations of the letters ZEBRA
Step-by-step Answer:
Since there are no repetitions in the five letters of the word ZEBRA, the number of permutations is 5! = 120 = 5*4*3*2*1.
If you are going to use the ASA postulate to prove these triangles congruent what additional information do you need?
Answer:
∠C and ∠R
Step-by-step explanation:
The ASA postulate represents angle / side / angle
where the included side is the side between the vertices of the two angles.
∠H and ∠I and the sides HC and IR are the AS
The required angles would be ∠C and ∠R for ASA
Three runners competed in a race. Data were collected at each mile mark for
each runner. If the runner ran at a constant pace, the data would be linear. A
regression line was fitted to their data. Use the residual plots to decide which
data set is best fit by the regression line and then identify the runner that kept
the most consistent pace.
Based on the analysis of the residual plots, Runner B's data is best fit by the regression line. This means that Runner B kept the most consistent pace throughout the race.
Analyze the residual plots to determine the best-fit regression line and identify the runner with the most consistent pace.
Observations from the Residual Plots:
- Runner A: The residual plot shows a clear U-shaped pattern, indicating a non-linear relationship and a poor fit for the regression line.
- Runner B: The residual plot exhibits a relatively random scatter of points around zero, suggesting a better fit for the regression line compared to Runner A.
- Runner C: The residual plot displays a distinct downward trend, also indicating a non-linear relationship and a poor fit for the regression line.
Conclusion:
Based on the analysis of the residual plots, Runner B's data is best fit by the regression line. This means that Runner B kept the most consistent pace throughout the race, as their actual pace closely aligned with the predicted pace from the linear model.
Therefore, the answer is B. Runner B.
The correct option is A. A. Runner A because if Runner A’s residual plot fits the criteria of a good linear fit.
To determine which runner kept the most consistent pace based on their residual plots, you need to understand the interpretation of residual plots in the context of linear regression.
Understanding Residual Plots
1. Residuals are the differences between the observed values and the values predicted by the regression line.
2. A residual plot displays these residuals on the vertical axis and the corresponding explanatory variable on the horizontal axis.
3.Consistency in Pace: For a runner to have a consistent pace, the residuals should be randomly scattered around zero with no discernible pattern. This indicates that the linear model is a good fit.
Interpreting Residual Plots
- Runner A: If the residuals for Runner A are randomly scattered around zero with no pattern, it means Runner A's data is well-fitted by the regression line, indicating a consistent pace.
- Runner B: If Runner B's residual plot shows a pattern (e.g., residuals increase or decrease systematically), it suggests that the regression line does not fit Runner B's data well, indicating inconsistency in pace.
- Runner C: Similarly, if Runner C's residual plot shows randomness around zero with no pattern, it means Runner C's data is well-fitted by the regression line, indicating a consistent pace.
Decision
Given the prompt, if you have residual plots for each runner:
1. Look for the plot with residuals randomly scattered around zero.
2. This runner’s data is best fit by the regression line and indicates the most consistent pace.
- Choose Runner A if Runner A’s residual plot shows randomly scattered residuals around zero.
- Choose Runner B if Runner B’s residual plot shows randomly scattered residuals around zero.
- Choose Runner C if Runner C’s residual plot shows randomly scattered
Since the question prompt explicitly mentions Runner A, the implication is that Runner A has the most consistent pace if their residual plot indeed shows a good fit with no pattern. Thus, based on the information given and assuming the residual plots for Runner A are the best fit, the answer would be:A. Runner A
The complete questionis:
Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line was fitted to their data. Use the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.
A. Runner A
B. Runner B
C. Runner C
3x+6+6x=42 what is x?
Answer:
x = 4
Step-by-step explanation:
Step 1: Combine like terms
9x + 6 = 42
Step 2: Isolate x by subtracting 6 on both sides
9x = 36
Step 3: Isolate x by dividing by 9 on both sides
x = 4
3x+6+6x=42
9x+6=42
9x+6-6=42-6
9x= 36
Divide by 9 for 9x and 36
9x/9=36/9
x=4
Check answer by using substitution method
3(4)+6+6(4)=42
12+6+24=42
42=42
Answer is x=4
At Jaylen’s school, students must choose a language, an elective, and a science class. Their options are listed in the table.
How many different combinations are possible?
4
12
32
64
Answer:
64
Step-by-step explanation:
To do this they have 4 options for each so to get the answer do 4*4*4
Answer: 64
Step-by-step explanation:
So you have a to choose a language, an elective and a science class, each of them has 4 options to choose.
The total combination is the product of all the options.
it is 4 languages * 4 electives * 4 science = 4*4*4 combinations = 64.
So you have 64 possible combinations.
Multiply or divide as indicated (3x)^12/ (3x)^4
answer has to start with a (3
gets brainiest***
Answer:
[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]
Step-by-step explanation:
As we are dividing by powers, we can just subtract the powers as they have the same base. As 12-4=8 the answer would be
[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]
Answer:
[tex] (3 x )^ 8 [/tex]
Step-by-step explanation:
We are given the following expression which we are to multiply or divide as indicated:
[tex] \frac { ( 3 x ) ^ { 1 2 } } { ( 3 x ) ^ 4 } [/tex]
We know that if the bases are same and they are divided, then the exponent of the denominator is subtracted from the exponent of the numerator. So we get:
[tex] ( 3 x ) ^ { 1 2 - 4 } =( 3 x )^ 8 [/tex]
WILL MARK BRAINLEST!!!
What is the difference when 5x^2 − 3x + 2 is subtracted from 4x^2 − 7x + 9?
A) x^2 − 4x + 7
B) −x^2 − 4x + 7
C) 9x^2 − 4x − 11
D) −9x^2 − 4x + 7
you answer is b) -x^2-4x+7
Answer:
B
Step-by-step explanation:
4x² - 7x + 9 - (5x² - 3x + 2) ← distribute by - 1
= 4x² - 7x + 9 - 5x² + 3x - 2 ← collect like terms
= (4x² - 5x² ) + (- 7x + 3x ) + (9 - 2)
= - x² - 4x + 7 → B
is 4, 16, 36, 64 a geometric sequence
ANSWER
No, there is no constant ratio.
EXPLANATION
We want to determine whether the sequence
4, 16, 36, 64
is geometric.
We need to find out if there is a common ratio between the consecutive terms.
[tex] \frac{16}{4} = 4[/tex]
[tex] \frac{36}{16} = \frac{9}{4} [/tex]
[tex] \frac{64}{36} = \frac{16}{9} [/tex]
Since the ratio is not the same for the consecutive terms, the sequence is not geometric.
4, 16, 36, 64 is a geometric sequence with a common ratio of 4.
Yes, 4, 16, 36, 64 is a geometric sequence.
To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms. In this case, the common ratio is 4.A geometric sequence is one where each term after the first is found by multiplying the previous term by a constant, which is the common ratio.Which function represents a reflection of f(x)=5(.08)^x across the x axis
Answer:
The function f(x) = 5(0.8)x is located in the first quadrant, forming a increasing curve. Imagine the reflection of the graph of the function. It is located in the fourth quadrant, forming a decreasing curve.
The graph that shows reflection is just the negative of the function. So the answer is (x) = –5(0.8)x
Step-by-step explanation:
I need help on this question.
Answer:
The constant of proportionality is y/x so the rate us 35
Step-by-step explanation:
Which of the following is equal to √-12?
Answer:
2i√3
Step-by-step explanation: Simplify the radical by breaking the radicand up into a product of known factors.
Hope this helps! :) ~Zane
For this case we must find an expression equivalent to:
[tex]\sqrt {-12}[/tex]
Then, rewriting:
[tex]\sqrt {-1 (12)} =\\\sqrt {-1} * \sqrt {12} =[/tex]
We know that:
[tex]i = \sqrt {-1}\\12 = 4 * 3 = 2 ^ 2 * 3[/tex]
Then we have:
[tex]i * \sqrt {2 ^ 2 * 3} =\\i * 2 \sqrt {3} =[/tex]
Finally we have:
[tex]2i \sqrt {3}[/tex]
Answer:[tex]2i \sqrt {3}[/tex]
Ryan is building a tree house. It will take 85 1/4 hours to complete. He can work on the tree house 15 1/2 hours each week. To the nearest tenth, how many weeks will it take Ryan to complete the tree house
5 1/2 weeks. you divide 85 1/4 by 15 1/2 to get the answer
Ryan will take 5 weeks and 5 days to complete the tree house.
What is unitary method?'The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.'
According to the given problem,
Time taken by Ryan to complete building the tree house = 85[tex]\frac{1}{4}[/tex] hours
= [tex]\frac{341}{4}[/tex] hours
Hours he work on the tree house = 15[tex]\frac{1}{2}[/tex] hours
= [tex]\frac{31}{2}[/tex]
Weeks taken by Ryan to complete building = [tex]\frac{341}{4}[/tex] ÷ [tex]\frac{31}{2}[/tex]
= 5.5 weeks
= 5 weeks 5 days
Hence, we can conclude that Ryan is going to take 5 weeks and 5 days to complete building the tree house.
Learn more about Unitary Method here: https://brainly.com/question/24406804
#SPJ2
determine the direction that this parabola opens y=-4x^2-8x-13
Answer:
The direction that the paraboa y=-4x^2-8x-13 open is
Down
An object traveling 40 meters in one direction has a velocity defined by the function , where t is the time, in seconds. The momentum of the object can be determined by the function p(v) = mv, where m is the mass of the object and v is the velocity of the object. Which function can be used to determine the momentum the object has if it travels 40 meters in t seconds?
Answer:
p(v(t))=40m/t
Step-by-step explanation:
Answer: The answer is A
Step-by-step explanation:
Yes
Alexandra is installing edge material around her yard. She has 400 ft of edge material to surround three sides of her rectangular yard. The fourth side will be against her deck and does not need edging. What is the maximum area that can be enclosed by the edging? Enter your answer in the box.
Answer:
The maximum area is equal to [tex]20,000\ ft^{2}[/tex]
Step-by-step explanation:
Let
x ----> the length of the rectangular yard
y ----> the width of the rectangular yard
we know that
The perimeter is equal to
[tex]400=x+2y[/tex] --> remember that the fourth side will be against her deck
isolate the variable y
[tex]y=200-0.5x[/tex] -----> equation A
The area of the rectangular yard is equal to
[tex]A=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=x(200-0.5x)\\ \\A=200x-0.5x^{2}[/tex]
The quadratic function is a vertical parabola open downward
The vertex is a maximum
The x-coordinate of the vertex represent the length of the rectangular yard for an maximum area
The y-coordinate of the vertex represent the maximum area of the rectangular yard
Using a graphing tool
The vertex is the point (200,20,000)
see the attached figure
therefore
The length of the rectangular yard is 200 ft
The width of the rectangular yard is [tex]y=200-0.5(200)=100\ ft[/tex]
The maximum area is equal to [tex]20,000\ ft^{2}[/tex]
Ava wants to paint two walls in her room blue. Both walls are 9 feet tall and 12 feet long. One wall has a 3 foot by 2 foot window and the other wall has a 3 foot by 7 foot door. What is the combined area of the two walls Ava wants to paint?
189 ft2
210 ft2
216 ft2
243 ft2
Answer:
a
Step-by-step explanation:
it is 189ft² just trust me
Answer:
a
Step-by-step explanation:
A pyramid and a cone are both 10 centimeters tall and have the same volume. What state must be true about the two solids
Answer:
The horizontal cross-sections of the pyramid and the cone at the same height must have the same area.
Step-by-step explanation:
We are given that a pyramid and a cone are both 10 centimeters tall and have the same volume and we are to determine a statement which must be true for both the solids.
The horizontal cross-sections of the pyramid and cone at the same height must have the same area.
This is because
Answer:
Tbase area is same for both pyramid and cone
And cross section at same height the cross sectional area is same
Step-by-step explanation:
Points to remember
Volume of pyramid = (a²h)/3
Where a - side of base
h - height of pyramid
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the correct answer
We have height of pyramid and cone is 10 cm
(a²h)/3 = (πr²h)/3
(a² * 10)/3 = (πr² * 10)/3
10a² = 10πr²
From this we get base area is same for both pyramid and cone
And cross section at same height the cross sectional area is same
Determine which relation is a function.
{(-4, 3), (-2,3), (-1, 2), (2,5), (3, 2)}
{(-4,1), (-2, 3), (-2, 1), (-1, 5), (3, 2)}
{(-4,1), (-2, 3), (-1, 2), (3,5), (3, 2)}
{(-4, 1), (-2, 3), (-1, 1), (-1, 5), (3, 2)}
Hello! :)
Since there is one value of y for every value of x in ( − 4 , 3 ) , ( − 2 , 3 ) , ( − 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) ( - 4 , 3 ) , ( - 2 , 3 ) , ( - 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) , this relation is a function. The relation is a function.
Hope I helped and wasn’t too late in answering!
Have fun and good luck!
~ Destiny ^_^
the correct answer is a) Function 1 only.
To determine which relations are functions from the given sets, we need to check if each element of the domain (the first number in each ordered pair) is mapped to only one element in the range (the second number in each ordered pair).
Set 1: {(-4, 3), (-2, 3), (-1, 2), (2, 5), (3, 2)}
Set 2: {(-4, 1), (-2, 3), (-2, 1), (-1, 5), (3, 2)}
Set 3: {(-4, 1), (-2, 3), (-1, 2), (3, 5), (3, 2)}
Set 4: {(-4, 1), (-2, 3), (-1, 1), (-1, 5), (3, 2)}
Analyzing each set:
Set 1 is a function because each domain value is unique and pairs with only one range value.
Set 2 is not a function because the domain value -2 is mapped to two different range values (3 and 1).
Set 3 is also not a function because the domain value 3 is mapped to two different range values (5 and 2).
Set 4 is not a function because the domain value -1 is mapped to two different range values (1 and 5).
Therefore, the correct answer is a) Function 1 only.
HELP!!! Use the factor Theorem to determine whether the binomial x+1 is a factor of the polynomial function f(x) =2x^3-9x^2+13x-6
A. No because f(c)=-30
B. No because f(c)=-4
C. Yes
D. No because f(c) =14
ANSWER
A. No because f(c)=-30
EXPLANATION
The given polynomial is
[tex]f(x) =2x^3-9x^2+13x-6[/tex]
If x+1 is a factor , then f(-1) must evaluate to zero.
[tex]f( - 1) =2( - 1)^3-9( - 1)^2+13( - 1)-6[/tex]
[tex]f( - 1) =2( - 1)-9( 1)+13( - 1)-6[/tex]
[tex]f( - 1) = - 2-9 - 13-6[/tex]
[tex]f( - 1) = -11 - 19[/tex]
[tex]f( - 1) = - 30[/tex]
Since f(-1) is not equal to zero, x+1 is not a factor of
[tex]f(x) =2x^3-9x^2+13x-6[/tex]
6. Describe the end behavior and determine
whether the graph represents an
odd-degree or an even-degree polynomial function. Then state the number of real 0s
7. GEOMETRY Recall the formula for finding the area of a rectangle Define a
variable for the width and set up an equation to find the dimensions of a rectangle with an area of 144 square inches given the length is 10 inches longer than the width
Answer:
6. an odd-degree polynomial function.
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
7. Length =x+10=8+10=18 inches
Width=x=8 inches
Step by step explanation;
6. The graph represent an odd-degree polynomial function.
The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
7.
The area of a rectangle is given by l×w, where l is length and w is the width
Let=w=x , l=x+10 and A=144 in² then;
l×w=144
(x+10) × x = 144
x²+10x =144......................complete squares on both sides
x²+10x+25=144+25
x²+10x+25=144+25................factorize
(x+5)²=169.......................square root the right-hand side
x+5= ±√169
x+5=±13.
x+5=13⇒⇒⇒x=8
x+5=-13⇒⇒⇒x= --18
x=8 inches....................value of width should be positive
Length =x+10=8+10=18 inches
Width=x=8 inches
Answer:
6. Since, by given graph,
The end behavior of the function f(x),
[tex]f(x)\rightarrow -\infty\text{ if }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ if }x\rightarrow +\infty[/tex]
Thus, the function f(x) must has odd number of roots ( where the graph of a function intersects the x-axis )
⇒ The function must has odd number of solutions,
Again by the graph,
Graph of the function intersects the x-axis 5 times ( it touches the origin so it have the repeated root of x = 0 ),
Hence, the total number of real solution of f(x) is 5.
7. Let x represents the width of the rectangle( in inches ),
Given,
The length is 10 inches longer than the width,
⇒ Length of the rectangle = ( x + 10 ) inches
Thus, the area of the rectangle,
A = length × width = x(x+10)
According to the question,
A = 144 in²
⇒ x(x+ 10) = 144
[tex]x^2+10x=144[/tex]
[tex]x^2+10x-144=0[/tex]
[tex]x^2+18x-8x-144=0[/tex] ( Middle term splitting )
[tex]x(x+18)-8(x+18)=0[/tex]
[tex](x+18)(x-8)=0[/tex]
⇒ x = -18 or x = 8 ( By zero test property )
The width can not be negative,
Hence, the width of the rectangle would be 8 inches.
One evening 1600 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $25 for covered pavilion seats and $20 for lawn seats. Total recipts $36,000. How many tickets of each type were sold?How many pavilion seats were? sold?How many lawn seats were? sold?
Answer:
• 800 pavilion seats
• 800 lawn seats
Step-by-step explanation:
Let p represent the number of pavilion seats sold. Then 1600-p is the number of lawn seats sold. Total revenue is ...
25p +20(1600 -p) = 36000
5p + 32000 = 36000
5p = 4000
p = 800 . . . . . . . . . . number of pavilion seats sold
1600-p = 800 . . . . . number of lawn seats sold
_____
You can work these problems in your head. Consider that all seats were sold at the lower price. Then revenue would be 1600·20 = 32000. It was 36000 -32000 = 4000 more than that. The difference in ticket price is 25 -20 = 5 dollars, so there must have been 4000/5 = 800 higher-priced tickets sold. (Compare this working to the math above. You will find it substantially similar.)
Find the zeros of f(x) = x^2+5x-6.
A. {-2,3}
B. {-6,1}
c. {-2,-3}
D. {-6,-1}
Answer:
x^2+5x-6
a = 1 b = 5 and c = -6
Using the quadratic formula:
x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1
x = [-5 +- sq root (49)] / 2
x = [-5 +- 7] / 2
x1 = 1
x2 = -6
Step-by-step explanation:
Which of the following is a business application that would utilize the slope....
Answer: fixed costs of production
The business application that would utilize the slope-intercept form of a linear equation is 1."break-even analysis." therefore, option 1.break-even analysis is correct.
In break-even analysis, you are trying to find the point at which your total revenue equals your total costs, resulting in zero profit (break-even point). This analysis often involves linear equations, and the slope-intercept form (y = mx + b) is commonly used to represent cost and revenue functions. The slope (m) represents the variable cost per unit, and the y-intercept (b) represents the fixed costs.
The other options, "fixed cost of production," "scheduling employee vacation," and "scheduling of employee," may involve mathematical modeling and equations, but they do not typically use the slope-intercept form of a linear equation for the primary analysis. Instead, these applications may involve other types of equations or mathematical models.
for such more question on break-even analysis
https://brainly.com/question/31319621
#SPJ2
A triangle has sides that are 12, 14,
and 19. Is it acute, right, or obtuse?
Answer:
acute
Step-by-step explanation:
For which equation would n = 0 not be a solution?
n + 4 = 5
7 + n = 7
n + 12 = 12
125 + n = 125
A. n+4=5
Hope this helps
What is the solution to -1-7?
Answer:
-8
Step-by-step explanation:
-1-7 = -8
-8.
-1 - 7 would be adding because when subtracting negatives you always change the sign and a trick i know is that negatives are referred to as “hate” and positives are referred to as “love”. therefore if you do a negative minus a positive you will get a negative. so the answer here is -8.
the plane that contains points C and T can also be named plane
Answer:
graph?
Step-by-step explanation:
Answer:CUB
Step-by-step explanation:
The expression on the left side of an equation is shown below. If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
The answer is D. -2x+5.
If we simplify the left side of the equation first given, we come to the expression -2x-10.
If we solve for D., we get the same results. Thus, because an equation with all the same variable terms and constants have infinite solutions, the answer is D.
Hope this helps!
Answer:
The correct option is D) -2(x+5)
Step-by-step explanation:
Consider the provided equation.
-5(x+2)+3x=
The above equation is linear equation having one variable.
For an linear equation ax=b
a=0, b=0 in that situation the equation is in the form of 0x=0 for all value of x. Then there are infinitely many solutions.
Now solve the expression on the left side
-5(x+2)+3x
-5x-10+3x
-2x-10
-2(x+5)
Now for 0x=0 form the expression on the right side must be same as the expression on the left side for the provided equation.
Consider the options.
Option A) -5(x-3)+2x
Solve the above expression.
-5x-15+2x
-3x-15
-2(x+5)≠-3x-15
Thus the option is not correct.
Option B) -5x-10
Solve the above expression.
-5x-10
-5(x+2)
-2(x+5)≠-5(x+2)
Thus the option is not correct.
Option C) x-2x+2+3x
Solve the above expression.
x-2x+2+3x
2x+2
2(x+1)
-2(x+5)≠2(x+1)
Thus the option is not correct.
Option D) -2(x+5)
-2(x+5)=-2(x+5)
Hence, the correct option is D) -2(x+5)
Use the quadratic formula to solve 4y^2+ 8y +7 =4
Answer:
[tex]y_1=-\frac{1}{2}\\\\y_2=-\frac{3}{2}[/tex]
Step-by-step explanation:
The Quadratic formula is:
[tex]y=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
Given the equation [tex]4y^2+ 8y +7 =4[/tex], you need to subtract 4 from both sides:
[tex]4y^2+ 8y +7 -4=4-4[/tex]
[tex]4y^2+ 8y +3 =0[/tex]
Now you can identify that:
[tex]a=4\\b=8\\c=3[/tex]
Then you can substitute these values into the Quadratic formula. Therefore, you get these solutions:
[tex]y=\frac{-8\±\sqrt{8^2-4(4)(3)} }{2(4)}[/tex]
[tex]y_1=-\frac{1}{2}\\\\y_2=-\frac{3}{2}[/tex]
Answer:
The solutions are y=-1/2 and y=-3/2
Step-by-step explanation:
Ok, for this problem we need to use the quadratic formula:
For [tex]ax^{2} +bx+c=0[/tex]
The values of x which are the solutions of the equation:
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex]
In this case your variable is y, so:
[tex]ay^{2} +by+c=0[/tex]
[tex]y=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex]
So, a=4, b=8 and c=3
[tex]y=\frac{-(8)+-\sqrt{(8)^{2}-4(4)(3) } }{2(4)}[/tex]
[tex]y=\frac{-(8)+-\sqrt{(16)}}{8}[/tex]
[tex]y=\frac{-8+4}{8}[/tex] and [tex]y=\frac{-8-4}{8}[/tex]
The solutions are
[tex]y=\frac{-1}{2}[/tex] and [tex]y=\frac{-3}{2}[/tex]