Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
Her mistake is in the first step, she wrote the equation incorrectly.
Solving quadratic equations:
A general quadratic equation:
ax^2 + bx + c = 0
has the solutions:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, the equation is:
y = x^2 - 8x + 7
And what Joyce writes in each step is:
Step 1:
x = (-8 ± √(8^2 - 4*1*7))/(2*1)
Then we can already see the mistake.
Notice that in the given equation, we have:
b = -8
And the general solution has:
x = (-b ± √(b^2 - 4ac))/(2a)
-b would be equal to 8, then what Joyce must have written here is:
x = (8 ± √((-8)^2 - 4*1*7))/(2*1)
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If you start with a number divide it by 4 then multiply it by two you end up with 8 squared
8 squared = 64
so
(x/4)*2 = 64
divide x/4 by 2 to get x/2=64
now multiply both sides by 2 to get x=128
x = 128
-10-2v<6 and 6v+12<-6.
need some help with this problem i keep messing a step
Are the two triangles below similar?
Yes, because there are two pairs of congruent corresponding angles
No, because there are not two pairs of congruent corresponding angles
Yes, because the corresponding sides are proportional
No, because the corresponding sides are not proportional
Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.
Explanation:-
In Δ ABC
∠A=30° , ∠C=65 °
By angle sum property of triangle
∠A + ∠B + ∠C= 180°
⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°
⇒∠B=85°
Now in ΔABC and ΔDEF
∠A=∠D=30° and ∠B=∠E=85°
⇒ there are two pairs of congruent corresponding angles.
So by AA-similarity criteria
ΔABC ≈ ΔDEF
Answer:
Yes, because there are two pairs of congruent corresponding angles.
Step-by-step explanation:
Two triangles ABC and DEF are given .
The measure of angles in triangle ABC are:
m<A=30°,m< C=65°,
m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)
In triangle DEF the measure of the angles are :
m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)
In triangles ABC and DEF,
< A=<D=30°
<B=<E=85°
<C=<F=65°
The two triangles are similar by AAA property.
Calculate each unit rate
$11.49 for 3 packages
PLEASE HELP
Probability allows a person to effectively measure the risks in selecting one alternative over others.
True
False
Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450
(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.
A coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. What statistic should he study?
The statistic that the coach should study is mean or the average score of the two teams. If the coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. After counting them, add the scores of the group that he divided and then divided it by the number of player in that group to get an average score on teams that warm up or do not warm up before the game.
Which answer correctly describes the relationship between two of the lines in the figure?
Sam scored 43 48 and 42 points on 3 test how many points should he get on the fourth test to get in average score of 50
what is the exact solutions of x2=5x+2
Answer:
The answer has a positive 5 and 33.
Step-by-step explanation:
I used a calculator.
Your Cell Phone plane cost 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan
Answer:
F( x) = 0.35 x + 55
Please help me ASAP.
David had a coupon for the grocery store. He graphed on the x-axis what his total bill would be if he didn’t use the coupon and graphed on the y-axis what his total bill would be if he used the coupon.
Based on the information in the graph, if David’s bill came to $66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?
a.$64
b. $65
c. $67
d. $68
Answer:
d. $68Step-by-step explanation:
First, let's find the equation of the line.
The slope is defined by
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where we are gonna use points (2,0) and (9,7).
[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]
Then, we use the point-slope formula to find the equation.
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].
Replacing this value in the equation, we have
[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]
Therefore, the price without coupon is $68.
C: -5/2 D: 5/2 help please
simplify 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³
a) -4m³ + 8p²
b) 8p² - 4
c) 4m³ - 13p³ + 5p
d) -4m³ + 13p³ - 5p
Final answer:
The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).
Explanation:
To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.
Like terms have the same variable raised to the same power.
In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.
Combine terms with p³: 7p³ + 6p³ = 13p³.Combine terms with m³: 2m³ - 6m³ = -4m³.Combine terms with p: 4p - 9p = -5p.Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).
A catering service offers 12 appetizers, 6 main courses, and 7 desserts. A banquet chairperson is to select 6 appetizers, 2 main courses, and 5 desserts for a banquet. In how many ways can this be done?
What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?
Christine buys 7 hamburgers and 3 sodas for $27.95. Laura buys 5 hamburgers and 4 sodas for $23.40. How much does a hamburger cost?
A. 1 .85
B. $3.20
C. $6.80
D. $6.55
E. $3.50
(15 POINTS) Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0).
An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
What is equation of ellipse?"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
What are vertices of the standard ellipse?"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "
What is focus of the standard ellipse?"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "
For given question,
The center of the ellipse is at the origin.
Using the standard form of equation of the ellipse,
[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
A vertex at (13, 0)
⇒ (a, 0) = (13, 0)
⇒ a = 13
And a focus at (12, 0).
⇒ (c, 0) = (12, 0)
⇒ c = 12
We know, [tex]c^{2}= a^{2}- b^{2}[/tex]
Now, we find the value of b i.e., minor axis
[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]
Substituting these values in the standard form of equation of ellipse with center (0, 0),
[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
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15 * 4 2/3 please help
4 2/3 = 14/3
15 = 15/1
14/3 * 15/1 = 14*15=210, 3*1 = 3
210/3 = 70
answer is 70
If x varies directly with y and x = 3.5 when y = 14, find x when y = 18.
Answer:
the value of x= 4.5
Step-by-step explanation:
If x varies directly with y and x = 3.5 when y = 14
x varies directly with y , so equation is x= ky
where k is the constant of proportionality
x = 3.5 when y = 14, use the given values and find out k
Plug in the given values in x=k y
3.5= k * 14
Divide by 14 on both sides
0.25= k
So the value of k = 0.25
Now find out x when y= 18
x= ky
x= 0.25 * 18= 4.5
What is 320 1/4 rounded to the nearest whole number?
3. what is the simplified form of x+4/7 - x+3/x+5
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
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Merlin industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar.
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Answer:
56
Step-by-step explanation:
Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places?
Answer: 2.661
Step-by-step explanation:
A P E X
A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?
A.75%
B.60
C.25%
D.40%
The solution would be like this for this specific problem:
Given:
{0, 1, 2, 3, 4}
Success = 2, 3, and 4
Solution:
Success = 3 numbers
Sample = 5
= 3 / 5
= .6
= .6 * 100%
= 60%
So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.
To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.
House is 50.0 ft long and 26 ft wide and has 8.0-ft- m high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters?
Choose the point on the terminal side of -45°. (-3, -3) (4, -4) (5, 5) (-2, 2)