Answers
Answer:
I) The roots are:
First Case:
[tex]x=-2\text{ or } x=-6[/tex]
Second Case:
[tex]x=2\text{ or } x=6[/tex]
II) Possible values of p are:
First Case:
[tex]p=-12[/tex]
Second Case:
[tex]p=4[/tex]
Step-by-step explanation:
We have the equation:
[tex]x^2-(4+p)x+12=0[/tex]
We know that one of the roots is three times the other.
And we want to find the roots of the equation and the possible values for p.
To find our solutions, we can use the process of factoring.
If we have an equation in the form:
[tex]x^2+bx+c=0[/tex]
We want to find two numbers, say, k and j, such that:
[tex]\displaystytle kj=c\text{ and } k+j=b[/tex]
After finding them, we can factor as such:
[tex](x+k)(x+j)[/tex]
So, -k and -j will be our zeros.
Therefore, for our equation, we will find two numbers k and j such that:
[tex]\displaystyle kj=12\text{ and } k+j=-(4+p)[/tex]
Notice that for the first criterion, we can simply list all the factors of 12.
So, according to the first equation, possible values of k and j are:
1 and 12; 2 and 6; or 3 and 4.
Then, our roots will be -1 and -12; -2 and -6; or -3 and -4, respectively.
However, remember that one of our roots is three times the other.
Therefore, the only candidates that work will be the second option.
Hence, k and j are 2 and 6.
Therefore:
[tex]k=2\text{ and } j=6[/tex]
With this information, we can now determine p. Since:
[tex]k+j=-(4+p)[/tex]
Then it follows that:
[tex]\begin{aligned}(2)+(6)&=-(4+p)\\8&=-(4+p)\\-8&=4+p\\p&=-12\end{aligned}[/tex]
Hence, our equation is:
[tex]x^2-(4+-12)x+12=0[/tex]
Or, factored:
[tex]x^2+8x+12=0 \text{ or } (x+6)(x+2)=0[/tex]
So, our roots are x=-6 and x=-2 when p=-12.
However, we also need to consider the negative factors of 12.
Factors of 12 also include -2 and -6.
Hence, our k and j can also be k=-2 and j=-6.
Then, in this case, our p is :
[tex]\begin{aligned} (-2)+(-6)&=-(4+p)\\-8&=-(4+p)\\8&=4+p\\p&=4\end{aligned}[/tex]
Therefore, for our second case, k=-2 and j=-6. Then p=4. So, our equation is:
[tex]x^2-(4+4)x+12=0[/tex]
Or, factored:
[tex]x^2-8x+12\text{ or } (x-2)(x-6)=0[/tex]
Hence, when p=4, our roots are x=2 and x=6.
Related Questions
The tables represent the functions f(x) and g(x).
Which input value produces the same output value for the two functions?
x = –12
x = –9
x = –6
x = –3
Answers
Answer:
x = -6 has the same output for both functions
Step-by-step explanation:
Here, we want to get the x value that has the same y-value for both functions
We can simply get this by substituting
Let’s take it one after the other
if x = -12
f(x) = 2/3(-12) + 7
= -8 + 7 = -1
2(-12) + 15 = -9
This is incorrect
for x = -9
g(x) = 2/3(-9) + 7
= -6 + 7 = 1
f(x) = 2(-9) + 15 = -3
for x = -6
g(x) = 2/3(-6) + 7 = 3
f(x) = 2(-6) + 15 = 3
So as we can see our answer is x = -6
Question 8 HELPPPPPPPPPPPPPP
Answers
Answer:
it would be at 3
cause double negatives cancel out- if u c something like -- or -(-) they would become a positive- so you would plot it at positive 3
hope this helps (again lol)
<33
Step-by-step explanation:
Answer:
plot at 3
Step-by-step explanation:
a negative number times another negative number will result in a positive number
therefore, - (-3)=3
Reba works at a starbucks coffee shop where a 120z cup of coffee costs $1.65, a 160z cup costs $1.85, and a 20oz cup cost $1.95. During one busy period, Reba served 55 cups of coffee, emptying six 1440z brewers while collecting a total of $99.65. How many cups of each size did reba fill?
Answers
Answer:
Cups of 120oz sold = 17
Cups of 160oz sold = 25
Cups of 200oz sold = 13
Step-by-step explanation:
We know that:
a 120z cup of coffee costs $1.65
a 160z cup costs $1.85
a 200oz cup cost $1.95
Let's define the variables:
A = # of 120z cups that she sold
B = # of 160oz cups that she sold
C = # of 200oz cups that she sold.
We know that:
"Reba served 55 cups of coffee"
A + B + C = 55.
"emptying six 1440z brewers while"
A*120oz + B*160oz + C*200oz = 6*1440oz
"collecting a total of $99.65"
A*$1.65 + B*$1.85 + C*$1.95 = $99.65
Then we have a system of equations:
A + B + C = 55
A*120oz + B*160oz + C*200oz = 6*1440oz
A*$1.65 + B*$1.85 + C*$1.95 = $99.65
To solve this, the first step is to isolate one of the variables in one of the equations, let's isolate A in the first one:
A = 55 - B - C
Now we can replace that into the other two equations:
(55 - B - C)*120oz + B*160oz + C*200oz = 6*1440oz
(55 - B - C)*$1.65 + B*$1.85 + C*$1.95 = $99.65
Now we can rewrite those equations as:
B*40oz + C*80oz = 8640oz - 55*120oz = 2040oz
B*$0.20 + C*$0.30 = $99.65 - 55*$1.65 = $8.90
Now we have the system:
B*40oz + C*80oz = 2040oz
B*$0.20 + C*$0.30 = $8.90
Now we need to isolate another variable in one of the equations, let's isolate B in the first one:
B = 2040oz/40oz - C*80oz/40oz = 51 - 2*C
Now we can replace this in the other equation and get:
(51 - 2*C)*$0.20 + C*$0.30 = $8.90
Bow we can solve this for C.
$10.20 - C*$0.40 + C*$0.30 = $8.90
$10.20 - $8.90 = C*$0.10
$1.30 = C*$0.10
($1.30/$0.10) = C = 13
Now we can replace this in the equation:
B = 51 - 2*C = 51 - 2*13 = 25
And for A, we had:
A = 55 - B - C = 55 - 25 - 13 = 17
Then:
Cups of 120oz sold = 17
Cups of 160oz sold = 25
Cups of 200oz sold = 13
help Please ill give branliest.
The juniors and seniors at a high school are ordering class shirts. The amounts ordered in each size are shown in the two-way frequency table below.
Small Medium Large X-Large Total
Juniors 65 84 68 23 240
Seniors 51 62 79 28 220
Total 116 146 147 51 460
Which statement is true about the information represented in the table?
A The percentage of Seniors who ordered a large shirt is greater than the percentage of students who ordered a large shirt who are also in the Senior class.
B The percentage of Seniors who ordered a small shirt is the same as the percentage of students who ordered a small shirt who are also in the Senior class.
C The percentage of Juniors who ordered a medium shirt is greater than the percentage of students who ordered a medium shirt who are also in the Junior class.
D The percentage of Juniors who ordered a medium shirt is less than the percentage of students who ordered a medium shirt who are also in the Junior class.
Answers
Answer:
it b
Step-by-step explanation:
To determine which statement is true, we need to calculate the percentages for each option and compare them and option c is correct.
Option A: The percentage of Seniors who ordered a large shirt is greater than the percentage of students who ordered a large shirt and are also in the Senior class. To calculate the percentage of Seniors who ordered a large shirt, we divide the number of Seniors who ordered a large shirt by the total number of Seniors:
Percentage of Seniors who ordered a large shirt =[tex](79 / 220) * 100 = 35.91[/tex]% To calculate the percentage of students who ordered a large shirt and are also in the Senior class, we divide the number of Seniors who ordered a large shirt by the total number of students who ordered a large shirt: Percentage of students who ordered a large shirt and are also in the Senior class [tex]= (79 / 147) * 100 = 53.74[/tex]% Since the percentage of students who ordered a large shirt and are also in the Senior class is greater than the percentage of Seniors who ordered a large shirt, statement A is false.
Similarly, we can calculate the percentages for the other options: Option B: The percentage of Seniors who ordered a small shirt is the same as the percentage of students who ordered a small shirt and are also in the Senior class. Percentage of Seniors who ordered a small shirt [tex]= (51 / 220) * 100 = 23.18[/tex]% Percentage of students who ordered a small shirt and are also in the Senior class [tex]= (51 / 116) * 100 = 43.97[/tex] % Since the percentages are not the same, statement B is false.
Option C: The percentage of Juniors who ordered a medium shirt is greater than the percentage of students who ordered a medium shirt and are also in the Junior class. Percentage of Juniors who ordered a medium shirt [tex]= (84 / 240) * 100 = 35[/tex]% Percentage of students who ordered a medium shirt and are also in the Junior class [tex]= (84 / 146) * 100 = 57.53[/tex]% Since the percentage of students who ordered a medium shirt and are also in the Junior class is greater than the percentage of Juniors who ordered a medium shirt, statement C is true.
Hence the correct option is C.
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In a basketball game, the home team was down by 9 points at the end of the game. They only scored 6 points for every 7 points the visiting team scored. What was the final score of the game? Type both answers with a comma inbetween. Show your work below.
Answers
The final score of the basketball game is (54, 63).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, They only scored 6 points for every 7 points the visiting team scored
and they differ by a total of 9 points.
Therefore, The final score would be 6×9, 7×9.
= (54, 63).
If we take the difference between 63 and 54 it would be 9.
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Richard and Linda enjoy visiting Hilton Head Island, South
Carolina. The distance from their home to Hilton Head is
975 mi, so the drive takes them 2 days. Richard and Linda
travel twice as far the first day as they do the second day.
How many miles do they travel each day?
Answers
Answer:
first day: 650, second day: 325
Step-by-step explanation:
Let x be the number of miles travelled on the second day and 2x the number of miles travelled on the first day. They add up to 975.
2x+x=975
3x=975
x=325
x represents the number of miles travelled on the second day so they travelled 650 miles on the first day and 325 miles on the second day.
Answer:
650 miles the first day, 325 miles the second day
Step-by-step explanation:
We can call the distance they traveled on the first day as 2x and the distance they traveled on the second day as x. The former is 2x because they traveled twice as far the first day compared to the second day. Since the total distance traveled is 975 miles, we can write the following equation to solve for x:
[tex]2x + x = 975[/tex]
[tex]3x = 975[/tex] (Simplify LHS; 2x + x = 3x)
[tex]\frac{3x}{3}=\frac{975}{3}[/tex] (Divide both sides of the equation by 3 to get rid of the coefficient on x)
[tex]x = 325[/tex] (Simplify)
Therefore, [tex]2x = 2 * x = 2 * 325 = 650[/tex] so the final answer is they traveled 650 miles the first day and 325 miles the second day. Hope this helps!
6. Which graph best represents the solution set of y>3 x-4?
Answers
The required graph of the solution to the given inequality y>3 x-4 has shown.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Given inequality,
y > 3x-4
Illustrating the above inequality on the coordinate plane, the yellow shaded region shows the solution of the given inequality y > 3x-4.
Thus, the required graph of the solution to the given inequality y>3 x-4 has shown.
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A school is purchasing new athletic uniforms for the basketball team. Each uniform costs the school $50.00. The school pays a $80.00 flat shipping fee. If the school spends $830.00 on the order, how many uniforms, did they purchase? Write an equation and explain how you used it to find your answer
Answers
jo jo mera padha ye lhika huwa uski bhen randi aur uski ma maha randi
Answer:
They bought 15 uniforms
Step-by-step explanation:
Equation-
50x + 80 = 830
Subtract 80 from both sides
50x = 750
Divide both sides by 50
x = 15
plz help asap i need help fast asap i will mark you brainlist
Answers
Answer:
What do you need help with?
What is the right angle postulate? Definition and how to use it
Answers
Answer:
Search it up!
Step-by-step explanation:
A speeding automobile is traveling 55 miles/hour, and a highway trooper, 2 miles behind, is chasing it at a speed of 70 miles/hour. How long will it take the trooper to overtake the speeding car if they both maintain these speeds?
Answers
10 minutes of chasing is needed i think
♦⭐Will mark brainliest⭐♦
Solve for x. 2/5x=6/5
A. x = 12/25
B. x = 12/5
C. x = 3
D. x = 6
Answers
Answer:
C. X = 3
Step-by-step explanation:
Multiply both sides by 5 to remove fractions
2x = 6
divide by 2
x = 3
what’s the answer did anyone figure it out ?
Answers
Answer:
NAswer to what
Step-by-step explanation:
Plsss help meeeeeeeeeeeee
Answers
Answer:
x = 8
y = 14
Step-by-step explanation:
It's given in the question,
ΔABC ≅ ΔDEF
Therefore, by the property of congruence,
EF = BC, AB = ED and AC = FD
And m∠E = m∠B
Since, m∠E = m∠B
(6y - 4) = 80
6y = 80 + 4
6y = 84
y = 14
Since, AB = ED
10 = 3x - y
10 = 3x - 14
3x = 24
x = 8
Plz help me I need this in less than a hour :<
Answers
Plz Help The function shown models the total number of insects in a colony x months after a small number of the insects are brought into a region.
What was the total number of insects in the colony when they were first brought into the region ? Enter your answer in the box
Answers
Answer:
I think it's 25? If I can edit I'll come back with answer..(if it's not 25.)
Step-by-step explanation:
In a science test. Devi scores 16 marks more than Ali. lf
Devi obtains twice as many marks as ali find the marks Ali obtains.
Answers
Let the marks of Devi be x and Ali be y.
So, the equations:
2y = x and y + 16 = x
So,
2y = y + 16. [ because we know equals are equal to equals]
=> 2y - y = 16
=> y = 16
Check
Ali's marks are half of Devi's marks.
Devi's marks are 16 more than alis.
So, Devi's marks will be 16×2 = 32 and 32 is 16 greater than 16 (16+16=32).
someone please help me with this work
Answers
Answer:
-34degrees
Step-by-step explanation:
PLEASE HELP I WILL GIVE GBRAINLIEST
Answers
Find the slope by using 2 sets of x,y values from the table.
Slope is change in y over change in x:
Slope = (-6 - -9) / (1 - -2) = 3/3 = 1
Then the y intercept is the value of y when x is 0. Looking at the table when x is 0 y is -7
The equation would be y = x-7
1
Which point on the number line represents 3?
-1
В
0
о
ООО
Answers
Answer: C
A is -1 and 1/3
B is -2/3
C is -1/3
D is 1/3
so it’s C
Hope this helps
JT has coordinates J (-2,-5) and T (2,3). The segment is rotated 180° about the origin to form J'T'. Then J'T' is translated 6 units to the right and 3 units down to form J''T''. What are the coordinates of J'T' and J''T''?
Answers
Answer:
(2,5)) ,(-2,-3),(8,2),(4,-6)
Step-by-step explanation:
it is rotated by 180 degree so evrything becomes positve beside the -6
-= 20 Points For this Question! =-
First Question: Find an equation of the line with slope 3 that contains the point (-7, 11).
Second Question: Find an equation of the line with slope 3/5 that contains the point (10, -6).
Answers
Ricardo borrows $1850 for 8 months at 12% interest.
What is the amount he will pay back at the end of the
loan period?
How do you know?
Answers
Answer:
Ricardo will have to pay $1776 at the end of the loan period.
I know this because if you multiply 12% to 1850 you get 222.
Now you multiply 222 to 8 which gives you an answer of 1776.
Hope this helps. :)
What is the measure of DC?
1. 61
2. 119
3. 122
4. 360
Answers
Answer:
61 it is because it is in first
Is this correct? Please Help!
Answers
PLEASE HELP ME ASAPP !! I HAVE 10 MINUTES LEFT !! When Erin first planted the cherry tree in her yard, it was 40 feet tall. Now it is 35% taller. How tall is the tree now?
Answers
Answer: 54 feet tall
Step-by-step explanation:
Answer:
it would be 54 feet tall now
Step-by-step explanation
35% of 40 is 14
40+14=54
54 feet
Compare 6 ⋅ 108 to 3 ⋅ 106
6 ⋅ 108 is 2,000 times larger than 3 ⋅ 106.
6 ⋅ 108 is 200 times larger than 3 ⋅ 106.
6 ⋅ 108 is 20 times larger than 3 ⋅ 106.
6 ⋅ 108 is 2 times larger than 3 ⋅ 106.
Answers
Answer:
6 ⋅ 108 is 2 times larger than 3 ⋅ 106.
(6 x 10^8) ÷ (3 x 10^6) = 200
So the answer is 6 ⋅ 10^8 is 200 times larger than 3 ⋅ 10^6.
Hopes it helps.
Divide x³-4x²+5x-2 by x-2
Answers
Answer:
p(x)=x^3-4x^2+5x-2
=(2)^3-4(2)^2+5(2)-2
=8-4(4)+10-2
=8-16+10-2
=0
hope it helps mark as brainliest
Answer:
remainder is zero
quotient is x^2-2x+1
Step-by-step explanation:
Is this a function?
Answers
nah buddy
Step-by-step explanation:
The product of two numbers has a 5 in the ones digit. Are the two numbers even or odd
Answers
The ones digit of the product of two numbers has an odd 5 in it.
What are products?
The outcome of one or more multiplications is referred to as a "product." For instance, the mathematical statement "times equals" would be written with the multiplier, the multiplicand, and their product as the variables.According to our question,
You might perform a simple calculation like 5x5 to get the odd value of 25, as 5 is odd.hence,The ones digit of the product of two numbers has an odd 5 in it.
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