Factor trinomials using the ‘ac’ method 9z^2 + 15z + 4
Answers
Hello there. To solve this question using the AC method, we'll have to remember some properties about factorizing numbers.
Given the trinomial:
\(9z^2+15z+4\)We start by labeling the numbers. The AC method requires that you find the A, B, C coefficients in:
\(Ax^2+Bx+C\)In this case, it is easy to see that:
\(A=9,B=15,C=4\)Now, we multiply A and C:
\(A\cdot C=9\cdot4=36\)And we factorize this number in all the possible ways as a product of two numbers:
In the right column, you add the factors
And the numbers we'll choose are those that the sum is equal to B, in this case, 3 and 12 adds up to 15, that is the value of B we're looking for.
Now, we split the middle term in these factors:
\(9z^2+3z+12z+4\)And we can factor some terms as follows:
\(\begin{gathered} 3z\cdot(3z+1)+4\cdot(3z+1) \\ (3z+4)(3z+1) \end{gathered}\)This is the factorization of this trinomial.
Related Questions
What is 6 1/3 divided by 1/6 equal to?
Answers
Rewrite 6 1/3 as an improper fraction:
6 1/3 = 19/3
Now you have 19/3 divided by 1/6
When dividing by a fraction flip the fraction over and multiply:
19/3 x 6/1 = (19 x 6) / (3x1) = 114/3 = 38
The answer is 38
Answer:
38
Step-by-step explanation:
6 x 3 is 18
18 + 1 is 19 so you have 19/3
3 x 2 = 6
19 x 2 = 38
38/6 divided by 1/6 is 38
38!!!!!!!!
At an after-season sale on winter clothes, I found a bunch of really cute hats and scarves. I decided to buy two hats and two scarves for myself to have for next year. I spent $72. When I told my friends about the sale, they asked me to go back and get something for them. I ended up spending $46 on one hat and two scarves. What was the price of a single hat and a single scarf?Write two integers separated by comma, no spaces, no dollar sign
Answers
ANSWER
One hat costs $26 and one scarf costs $10
EXPLANATION
Let the price of one hat be h.
Let the price of one scarf be s.
Two hats and two scarves cost $72. This implies that:
\(2h+2s=72\)One hat and two scarves cost $46. This implies that:
\(h+2s=46\)From the second equation, make h the subject of the formula:
\(h=46-2s\)Substitute that into the first equation and solve for s:
\(\begin{gathered} 2(46-2s)+2s=72 \\ 92-4s+2s=72 \\ \Rightarrow92-72=4s-2s \\ 2s=20 \\ \Rightarrow s=\frac{20}{2} \\ s=\$10 \end{gathered}\)Substitute the value of s into the equation for h and solve for h:
\(\begin{gathered} h=46-2(10) \\ h=46-20 \\ h=\$26 \end{gathered}\)Hence, one hat costs $26 and one scarf costs $10.
What is 27 ÷ 4 rounded to the nearest tenth?
Answers
Answer:
6.8
Step-by-step explanation:
27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.
A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 109 and standard deviation 11. His profit on each bar sold is $0.12, and it costs him $10 per week to maintain the machine and rent the space for it. What are the mean and standard deviation for Y= the profit he earns from this machine in a randomly selected week?
Answers
Answer:
10
Step-by-step explanation:
PLEASE HELP!! DUE TONIGHT!!!
Answers
Answer:
Step-by-step explanation:
Even ( I think)
positivie ( I think )
x intercept - (0,0)(-2,0)(-4,0)
y intercept - (0,0)
SOMEONE HELP ME
Solve. 35.1 = 12.9 + 10.2x Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
Step-by-step explanation:
35.1-12.9=22.2
22.2/10.2=x
2.17647059
2 1764059
------------------
10000000
Please help me! Thanks.
Answers
Answer: Answer:
The perimeter of the polygon are
PQ = 5
RS = 5
PR = √74 = 8.60
QS = √74 = 8.60
QR = 7
Step-by-step explanation:
To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula
d = √(x _2 - x_1)^2 + (y_2 - y_1)^2
Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = 4
PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2
= √ 5^2 + 0^2
= √ 25
= 5
Between R( 5 , -3) and S ( 0 , -3)
x_1 = 5
y_1 = -3
x_2 = 0
y_2 = -3
RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2
= √( -5)^2 + ( -3 + 3)^2
= √ 25 + 0
= √ 25
= 5
Between P( 0 , 4) and R (5 , -3)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = -3
PR = √( 5 - 0)^2 + ( -3 - 4)^2
= √ 5^2 + (-7)^2
= √ 25 + 49
= √ 74
= 8.60
Between Q ( 5 , 4) and S(0 ,-3)
x_1 = 5
y_1 = 4
x_2 = 0
y_2 = -3
QS = √ ( 0 - 5)^2 + ( -3 - 4)^2
= √ -5^2 + -7^2
= √ 25 + 49
= √ 74
= 8.60
Between Q( 5,4) and R(5 , -3)
x_1 = 5
y_1 = 4
x_2 = 5
y_2 = -3
QR = √ (5 - 5)^2 + ( -3 - 4)^2
= √ 0^2 + (-7)^2
= √ 0 + 49
= √ 49
= 7
Step-by-step explanation:
Solve for c.
y= ax2 + bx + c
Answers
Answer: c=−ax^2−bx+y
Step-by-step explanation:
Answer: a= \(\frac{-bx-c+y}{x^{2} }\)
Step-by-step explanation: Step 1: Flip the equation.
ax²+bx+c=y
Step 2: Add -bx to both sides.
ax²+bx+c+−bx=y+−bx
ax²+c=−bx+y
Step 3: Add -c to both sides.
ax²+c+−c=−bx+y+−c
ax²=−bx−c+y
Step 4: Divide both sides by x^2.
\(\frac{ax^{2} }{x^{2} }\) = \(\frac{-bx-c+y}{x^{2} }\)
If I Helped, Please Mark Me As Brainliest, Have A Great Day :D
Math nerds help me out
Answers
Answer:
the 3rd one
y= (x-1)(x-6)
Step-by-step explanation:
Answer:
y=(x-1)(x-6)
Step-by-step explanation:
from the factorised form (x-1)(x-6) we can easily derive the roots of 1 and 6
it crosses the x axes on the roots, which happens at 1 and 6 on the graph
write an algorithm, using pseudocode, to make the robot: 1. stand up 2. walk forward until it senses a wall 3. turn around 4. walk back to the chair 5. sit down in its original starting position finally, output the total number of steps taken.
Answers
We had written an algorithm, using pseudo code.
//Define the required variables.
total_number_of_steps = 0
number_of_steps = 0
//robot stands up to walk.
stand
//the robot moves forward till the wall is not reached.
while (wall is not reached)
//the robot senses the wall with the help of arms.
raise arms
sense_the_wall
if (wall is not there)
//if the wall is not found, the robot lowers the arms
lower arms
//if wall is not detected, the robot moves forward.
step_forward
//increment the number of steps forward.
number_of_steps=number_of_steps+1
//increment the total number of steps.
total_number_of_steps=total_number_of_steps+1
else
exit
end if
end while
//else if the wall is found, lower the arms
lower arms
//the robot turns 90 degrees right once.
turn_right_90
//the robot turns 90 degrees right again.
turn_right_90
//till the number of steps does not reach 0, move
for (number_of_steps! = 0)
step
//increment the total number of steps.
total_number_of_steps=total_number_of_steps+1
//the robot moves backwards on detecting the wall, so
//decrement the number of steps.
number_of_steps = number_of_steps-1
//end the for loop.
end for
//the robot turns 90 degrees left once.
turn
//the robot turns 90 degrees left again.
turn
//the robot sits down.
sit
//display the total number of steps taken by robot
display total_number_of_steps
The last line ends the pseudocode
Stop
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6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answers
Answer:
65/100 that is the answer to this question
\( - 4x + 7 = 2y - 3\)
a. only 2,1
b. only 5,-5
c. both
d. neither
Answers
mart math math math math
Answers
Explanation:
Segment AW bisects angle CAD.
This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.
Therefore, angle CAD = 40 degrees.
The supplement of this is angle DAX
(angle CAD) + (angle DAX) = 180
angle DAX = 180 - (angle CAD)
angle DAX = 180 - 40
angle DAX = 140 degrees
A baseball player had 4 hits in 8 games At this rate how many hits will the baseball player have in the next 28 games?
O 14
O 24
O 28
O 56
Answers
Please,can you help me with this one?
Parker has 4 different piggy banks
one each for pennies, nickels,dimes, and quarters
If there are twenty coins in each of his 4 piggy banks,
what is the average amount of money contained in
each piggy back?
Answers
Answer:
Just multiply two with the value of one penny,one,nickel,one dimes,one quarters and add them you will get the ans.
What is the sum of
1
8
+
5
16
+
3
8
?
A.
9
32
B.
13
32
C.
9
16
D.
13
16
Answers
Answer:
18 + 516 + 38 = 572
Answer:
0.8125 =13/16
Step-by-step explanation:
1/8 +5/16 +3/8= 0.8125
0.8125 as a fraction is 13/16
Martina, Ahmad, and Ryan served a total of 87 orders Monday at the school cafeteria. Ahmad served 9 fewer orders than Martina. Ryan served 2 times as many orders as Martina. How many orders did they each serve?
Answers
Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.
Calculating Unknown Quantity:To find an unknown quantity in a problem we use the algebraic expression. These are combinations of variables and constant terms. Here variables are used to represent the Unknown Numbers.
Here we have
Martina, Ahmad, and Ryan served a total of 87 orders
Since we don't how many orders served each one
Let's assume that each of them with different variables
Martina served 'm' orders
Ahmad served 'a' orders
Ryan served 'r'
Given that
Ahmad served 9 fewer orders than Martina
=> a = m - 9 ---- (1)
Ryan served 2 times as many orders as Martina.
=> r = 2m --- (1)
Given that total served orders = 87
=> m + a + r = 87
=> m + m - 9 + 2m = 87 [ from (1) and (2) ]
=> 4m = 87 + 9
=> 4m = 96
=> m = 24
Number of orders served by Ahmad, a = 24 - 9 = 15
Number of orders served by Ryan, r = 2(24) = 48
Therefore,
Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.
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A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $6 a pound? To get a mixture worth $6 a pound, pounds of coffee should be added. (Type an integer, proper fraction, or mixed number.) what is this answer please need help
Answers
The weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds the mixture will be 15 pounds
Let the weight of coffee worth $10 to be added to mixture be x pounds
The weight of coffee worth $4 to be added to mixture is 30 pounds
We want a mixture that worth $6 a pound
The weight of mixture of coffee worth $ 6 is the sum of $10 coffee and $4 coffee
= x + 30
From the above equation we can form a linear equation
X 10 + 30 ×4 = (x+ 30) 6
10x + 120= 6x +180
10x-6x= 180 -120
4x = 60
X= 15
Hence, the weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds
what's a linear equation ?
A linear equation only has one or variables. No variable in a linear equation is raised to a strength greater than 1 or used because the denominator of a fraction. while you discover pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all the factors lie at the same line
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Overview
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Question Progress
Homework Progress
22/44 Marks
Round the number 125.3546 to 1 decimal place.
Answers
Answer:
125.4
Step-by-step explanation:
Given
\(Number = 125.3546\)
Required
Round to 1 decimal place
Up till the first decimal place, the number is:
\(Number = 125.3\)
The digit after .3 is 5
The conditions for approximation are:
If n > 4, approximate to 1Else: approximate to 0In this case: 5 > 4, so we approximate to 1
Add this "1" to the last digit of 125.3. This becomes 125.4
Hence: when the number is approximated to 1 decimal place, the digit is 125.4
What is the solution for the following question? \(\sqrt{13} +3x = x-5\)
Answers
Answer:
≈ -4.3028.
Step-by-step explanation:
sqrt(13)+3x=x-5;
2x=-5-sqrt(13);
2x≈ -8.6056;
x=-4.3028.
Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?
Responses
3.5 meters
3.5 meters
45meters
7 meters
Answers
The distance he would've covered is 32.02m if he ran through a straight line.
What is Pythagoras's Theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
\(x^2 = y^2 + z^2\\\)
Let's substitute the values into the equation and solve.
\(x^2 = 20^2 + 25^2\\x = 32.02m\)
Jimmy would've jogged 32.02m if he ran through a straight line.
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On one day at a local minigolf course, there were 320 customers who paid a total of $2,900. If the cost for a child is $7 per game and the cost for an adult is $10 per game, write a system of equations to model this scenario, where x represents the number of children and y represents the number of adults who played that day.
7x + 10y = 2900
x + y = 320
7x + 10y = 320
x + y = 2900
10x + 7y = 2900
x + y = 320
10x + 7y = 320
x + y = 2900
Brainiest for correct answer
Answers
A system of equations to model this scenario is given as follows -
x + y = 320
7x + 10y = 2900
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.The general equation of a straight line is → y = mx + c{m} - slope {c} - intercept along the y - axis.
Given is that on one day at a local minigolf course, there were 320 customers who paid a total of $2,900. The cost for a child is $7 per game and the cost for an adult is $10 per game.
Let {x} represents the number of children and {y} represents the number of adults who played that day. We can write the given system of equations as -
x + y = 320
7x + 10y = 2900
Therefore, a system of equations to model this scenario is
x + y = 320
7x + 10y = 2900
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Please help me solve this.
Answers
\(\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions\)
A software development company is voting to elect a president, a secretary, a treasurer, and three directors. If a total of 11 qualified candidates applied for these positions, in how many ways can the positions be filled?
Answers
The ways to elect the candidates from the total is 462
How to determine the ways of selection?From the question, we have
Total number of candidate, n = 11Numbers to selection, r = 6 i.e. the president, a secretary, a treasurer, and three directorsThe number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 11 and r = 6
Substitute the known values in the above equation
Total = ¹¹C₆
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 11!/5!6!
Evaluate
Total = 462
Hence, the number of ways is 462
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how many solutions are there to the system 8x=12y-9 and 27y+18x=21?
Answers
There is one solution in the system of equation
How to determine the number of solutions?The system of equations is given as:
8x=12y-9 and 27y+18x=21
Divide 8x=12y-9 by 8
x = 1/8(12y-9)
Substitute x=1/8(12y-9) in 27y+18x=21
27y + 18 * 1/8(12y-9) =21
Expand
27y + 27y - 20.25 =21
Evaluate the like terms
54y = 41.25
Divide by 54
y = 0.7639
Hence, there is one solution in the system of equation
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In a survey of 2266 adults, 736 say they believe in UFOs. Construct a 90% confidence interval for the population proportion of adults who believe in UFOs. A 90% confidence interval for the population proportion is ( ?, ?).
(Round to three decimal places as needed.)
Part 2
Interpret your results. Choose the correct answer below.
A.
With 90% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.
B.
The endpoints of the given confidence interval shows that 90% of adults believe in UFOs.
C.
With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
D.
With 90% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
Answers
The 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
To construct a 90% confidence interval for the population proportion of adults who believe in UFOs, we can use the formula:
Confidence Interval = Sample Proportion ± Margin of Error
First, we calculate the sample proportion:
Sample Proportion \(\hat{p}\) = Number of adults who believe in UFOs / Total number of adults surveyed = 736 / 2266 ≈ 0.324
Next, we need to calculate the margin of error.
Since we are dealing with a large sample size, we can use the formula for a 90% confidence interval:
Margin of Error\(= Z \times \sqrt{(\hat{p} \times (1 - \hat{p}) / n)}\)
Here, Z represents the z-value for a 90% confidence level, which corresponds to a z-value of 1.645. n represents the sample size.
Margin of Error\(= 1.645 \times \sqrt{(0.324 \times (1 - 0.324) / 2266)}\) ≈ 0.015
Finally, we can construct the confidence interval:
Confidence Interval = 0.324 ± 0.015 = (0.309, 0.339)
Therefore, the 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
Now, let's interpret the results.
The correct answer is:
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
This means that we are 90% confident that the true proportion of adults who believe in UFOs falls within the range of 0.309 to 0.339.
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what is the measure of pQs
Answers
Find the quotient.
(6x ^2 + 23x + 20) ÷ (5 + 2x)
a) 3x - 4
b) 3x + 4
c) 3x +19
Answers
Answer:
3x+4
Step-by-step explanation:
25 POINTS PLEASE HELP ME !!!!Graph the image of this triangle after a dilation with a scale factor of 1/2centered at (−5, 1) .Use the Polygon tool to graph the dilated triangle.
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
The first thing is to determine the vertices of the triangle shown:|
\(\)
Solve x^2 - 4x + 1 = 0.
Answers
=
4.23606797
…
,
−
0.23606797
…