Answer:
Option D.
Step-by-step explanation:
We need to find the circumstances that would likely make factoring the best method for solving a quadratic equation.
A quadratic equation is prime if its factors can not possible. So, option A is incorrect.
In a quadratic equation leading coefficient can not be zero. So, option B is incorrect.
For large numbers (coefficient or constant), quadratic formula is best method. So, option C is incorrect.
The difference of 2 perfect squares is:
[tex]x^2-a^2=(x-a)(x+a)[/tex]
In this case factoring is the best method.
Therefore, the correct option is D.
The endpoints of a line segment graphed on a coordinate plane are (8, 5) and (10, 1). What are the coordinates of the midpoint of the line segment?
Answer:
(9,3)
Step-by-step explanation:
(8+10)/2. (5+1)/2
18/2. 6/2
9,3
simplify 2(3x+7)-4(7+x)
Answer:
[tex] \boxed{ \bold { \huge{ \boxed{ \sf{2x - 14}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2(3x + 7) - 4(7 + x)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{6x + 14 - 4(7 + x)}[/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{6x + 14 - 28 - 4x}[/tex]
Collect like terms
⇒[tex] \sf{6x - 4x + 14 - 28}[/tex]
⇒[tex] \sf{2x + 14 - 28}[/tex]
Calculate
⇒[tex] \sf{2x - 14}[/tex]
Hope I helped!
Best regards!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(3x + 7) - 4(7 + x)}}\\\\{\mathsf{= 2(3x) + 2(7) - 4(7) - 4(x)}}\\\\\mathsf{= 6x + 14 - 28 - 4x}\\\\\mathsf{= (6x - 4x) + (14 - 28)}\\\\\mathsf{= 2x - 14}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{2x - 14}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A cash box of $1 and $5 bills is worth $45. The number of $1 bills is 3 more than the number of $5 bills. How many of each bill does it contain?
Answer:
There are 10 $1 bills and 7 $5 bills
Step-by-step explanation:
7($5 bills) x 5
=35
7+3 (3 more $1 bills)
=10
10+35
=45
Answer:
$1: 10
$5: 7
Step-by-step explanation:
To find out how many of each bill is in the cash box, create an expression
x = the dollar bills
This makes the $5 bills 5x and the $1 bills x (this can also be 1x)
When it says "The number of $1 bills is 3 more than the number of $5 bills" This means that the number of $1 is x + 3 and the number of $5 is 5x
When you put it together the expression will be x + 3 + 5x = 45
First add x and 5x, making it 6x
Next subtract 3 from each side, which makes the equation 6x = 42
Lastly, divide 6 from each side, this means that x = 7
To find out how many bills there are substitute 7 wherever there is an x
This mean that the number of $1 is 7 + 3 (10), and the number of $5 bills are 5x7 (35), but its just 7 because they are $5 each
3 times the sum of 1/3 of
a number and 8 is 11
Answer:
I guess this is how to do it....
3×(1/3 of x + 8)=11.
use the 3 to multiply the numbers in the bracket.
3x+24=11.
3x=11-24.
3x=-13.
x= -13/3.
x= -4.33.
Hannah and Zach together earn $950 for an
advertising drop. They earn equal hourly rates
of pay. If Hannah worked for 10 hours and
Zach for 9 hours, how much
did Zach earn?
Answer:
$450
Step-by-step explanation:
First, write out an equation. We know that Hannah and Zach together earnes $950 and they get payed in equal hourly rates, so for now, in this step of solving the problem, we will be adding the number of hours each person worked together.
Hannah worked 10 hrs and Zach worked 9 hrs, so add 10+9 to get 19 hrs worked in all between the two of them.
Let "x" represent the amount of money made each hour, and form your equation.
Your equation would be: [tex]19x=950[/tex]
Then, just solve for "x". Divide both sides by 19.
[tex]\frac{19x}{19}=\frac{950}{19}\\x=50[/tex]
The "x=50" means that Hannah and Zach each earn $50 per hour.
Now, the question asks us to find the amount of money that Zach made. So, multiply 50 by only the number of hours Zach worked, which is 9.
[tex]50*9=450[/tex]
That means that Zach made a total of $450.
A bricklayer is able to set 2.5 bricks in one minute. How many bricks can he set in 8 hours?
2,000
O 150
O 20
O
1, 200
0
120
Answer:
1200
Step-by-step explanation:
First we need to figure out how many bricks can be set in an hour, so you do 2.5*60, since there are 60 min. in an hour. That's 150.
Now we do 8 hours. You do 150*8, which is 1200.
Hope this helps.
Answer:
1200
Step-by-step explanation:
The reason behind this answer is because you first multiply 2.5 by 60 for the 60 minutes in an hour and ultimately get 150 then you multiply that answer by 8 to get 1200.
what I need to Know is 5003×5984= can you answer my question please thanks
Answer:
29,937,952 mark me as brainliest
Step-by-step explanation:
If f(x) = 2x + 3 and g(x) =4x - 1, find f(4).
Solve the "f" function with substitute 4 and solve the "g" function with what we get for the "f" function.
f(4) = 2(8) + 3
f(4) = 16 + 3
f(4) = 19
g(19) = 4(19) - 1
g(19) = 76 - 1
g(19) = 75
Best of Luck!
Find the value of each of the following quantities.
(a) C(5, 4)
(b) C(5, 0)
(c) P(5, 1)
(d) P(5, 5)
Answer: (a) 5 (b)1 (c)5 (d)120
Step-by-step explanation:
Formula for combinations: [tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]
Formula for permutations: [tex]C(n,r)=\dfrac{n!}{(n-r)!}[/tex]
(a) C(5, 4) = [tex]\dfrac{5!}{4!(5-4)!}=\dfrac{5\times4!}{4! (1)}=5[/tex]
(b) C(5, 0) = [tex]\dfrac{5!}{0!(5-0)!}=\dfrac{5!}{5! }=1[/tex]
(c) P(5, 1) = [tex]\dfrac{5!}{(5-1)!}=\dfrac{5\times4!}{4! }=5[/tex]
(d) P(5, 5) = [tex]\dfrac{5!}{(5-5)!}=\dfrac{5!}{1}=5!= 5\times4\times3\times2\times1=120[/tex] [as 0!=1]
Hence, the required answer is
(a) 5 (b)1 (c)5 (d)120
Does a point have a location?
A point in geometry is a location.
It has no size, width, length or depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions.
(5x+3)(7x-7) how do find x
We can use the FOIL method to solve.
(5x + 3)(7x - 7)
(5x * 7x) + (5x * -7) + (3 * 7x) + (3 * -7)
35x - 35x + 21x - 21
0 + 0
0
Best of Luck!
Find the distance between (-7,-2) and (11,3)
Answer:
The answer is
[tex] \sqrt{349} \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-7,-2) and (11,3)
The distance between the points is
[tex]d = \sqrt{ ({ - 7 - 11})^{2} + ({ - 2 - 3})^{2} } \\ = \sqrt{ ({ - 18})^{2} + ({ - 5})^{2} } \\ = \sqrt{324 + 25} \\ [/tex]We have the final answer as
[tex] \sqrt{349} \: \: units[/tex]Hope this helps you
PLLLSSSS HELP which one is greater a or b. ?
Answer:
The rate of change for A is 4. For B, it is 2
Step-by-step explanation:
the slope of A is 4 and for B it is 2. Slope is the same as rate of change.
You want to have $2 million in real dollars in an account when you retire in 35 years. The nominal return on your investment is 9.94% and the inflation rate is 3.2%. What is the real amount you must deposit each year to achieve your goal?
a. $20,403.
b. $7,482.
c. $16,017.
d. $18,887.
e. $19,711.
Answer:
b. $7,482.
Step-by-step explanation:
20,403 nets $5,996,106 after 35 years.
7,482 nets $2,198,837 after 35 years.
$7,482 is over 2 million and the smallest amount, so you don't have to solve for the other ones.
The real amount that must deposit each year to achieve your goal is $16,017 option (c) is correct.
What is invested amount?An investment is a payment made to acquire the securities of other firms with the intention of making a profit.
First, we will calculate the real rate of interest:
r = [(1+nominal rate)/(1+inflation rate)] - 1
Nominal rate = 9.94% = 0.094
Inflation rate = 3.2% = 0.032
r = [(1+0.094)/(1+0.032)] - 1
After calculating,
r = 0.0653 or 6.53%
Deposit amount each year:
Future value = PV[(1+r)ⁿ - 1]/(r)
2000000 = PV[(1+0.0653)³⁵ - 1]/(0.0653)
After calculating,
PV = $16020.544
The value $16020.544 is near the $16,017.
Thus, the real amount that must deposit each year to achieve your goal is $16,017 option (c) is correct.
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15 points?
Solve
(7-w)(5w-8) = 0
(if there is more that one solution, separate them with commas.)
Please state what w is...
━━━━━━━☆☆━━━━━━━
▹ Answer
(w = 7, w = 8/5)
▹ Step-by-Step Explanation
(7 - w)(5w - 8) = 0
Separate:
7 - w = 0
5w - 8 = 0
Solve:
w = 7
5w - 8 = 0
(w = 7, w = 8/5)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
w = 7, 8/5
Step-by-step explanation:
(7 - w) (5w - 8) = 0
(7 - w) × (5w - 8) = 0
7 × 5w - 7 × 8 - w × 5w + w × 8 = 0
35w - 56 - 5w² + 8w = 0
- 5w² + 43w - 56 = 0
5w² - 43w + 56 = 0
5w² - 35w - 8w + 56 = 0
5w(w - 7) - 8(w - 7) = 0
(w - 7) (5w - 8) = 0
w - 7 = 0 OR 5w - 8 = 0
w = 7 OR w = 8/5
Thus, the value of w is 7, 8/5
The price of a cup of coffee was $2.10 yesterday. Today, the price rose to $2.25. Find the percentage increase. Round your answer to the nearest tenth
of a percent.
Answer:
Easy-peasy.
Step-by-step explanation:
2.45/2.10 = 1.167 (rounded to the nearest tenth of a cent).
That is, 2.45 is 116.7% of 2.10
Since $2.10 is 100% of 2.10,
2.45 is a 16.7 increase.
The solution is 7.1 %
The percentage increase in the price of the coffee is 7.1 %
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the percentage increase in the price of the coffee be represented as A
Now , the value of A is calculated by
Let the initial price of the coffee be = P
The value of P = $ 2.10
The increased price of the coffee be = Q
The value of Q = $ 2.25
Now , the equation will be
The percentage increase in the price A = ( increased price of the coffee - initial price of the coffee / initial price of the coffee ) x 100
Substituting the values in the equation , we get
The percentage increase in the price A = ( ( 2.25 - 2.10 ) / 2.10 ) x 100
The percentage increase in the price A = ( 0.15 / 2.10 ) x 100
The percentage increase in the price A = 0.0714 x 100
The percentage increase in the price A = 7.14 %
Therefore , the percentage increase is 7.1 %
Hence , the percentage increase in the price is 7.1 %
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please help for this question. Thank you
Answer:
A. 8.3
B.18.7
C. 10.4
D. 1.04
Step-by-step explanation:
p(x) = 0.03x² + 0.56x + 6.35
A. Determination of p(3)
p(x) = 0.03x² + 0.56x + 6.35
x = 3
p(3) = 0.03(3)² + 0.56(3) + 6.35
p(3) = 0.03(9) + 1.68 + 6.35
p(3) = 0.27 + 1.68 + 6.35
p(3) = 8.3
B. Determination of p(13)
p(x) = 0.03x² + 0.56x + 6.35
x = 13
p(13) = 0.03(13)² + 0.56(13) + 6.35
p(13) = 0.03(169) + 7.28 + 6.35
p(13) = 5.07 + 7.28 + 6.35
p(13) = 18.7
C. Determination of p(13) – p(3)
From A and B above,
p(13) = 18.7
p(3) = 8.3
p(13) – p(3) = 18.7 – 8.3
p(13) – p(3) = 10.4
D. Determination of p(13) – p(3) / 13 – 3
From C above,
p(13) – p(3) = 10.4
p(13) – p(3) / 13 – 3 = 10.4/ 13 – 3
= 10.4 / 10
= 1.04
Simplify (x + 3)(x − 3)
Answer:
x^2 -9
Step-by-step explanation:
(x + 3)(x − 3)
FOIL
first x*x =x^2
outer -3x
inner 3x
last -3*-3 =-9
Add together
x^2 -3x+3x -9
Combine like terms
x^2 -9
PLZ HELP WILL MARK BRAINLIEST
What is the function g(x) created from f(x) = x2 by moving the graph left 7 units, adding vertical compression by a factor of 1 6 , and shifting the graph down 8 units?
Answer:
g(x) = (1/6)(x +7)^2 -8
Step-by-step explanation:
The transformation ...
g(x) = a·f(x -h) +k
represents vertical scaling by a factor of 'a', right shift by h units, and up shift by k units. You want the function g(x) for f(x) = x^2, a = 1/6, h = -7, and k = -8. Those transformations give you ...
g(x) = (1/6)(x +7)^2 -8
The square of a number is 3 less than four times the number. Which values could be the number?
Answer:
The numbers are 1 and 3Step-by-step explanation:
Let the number be x
The statement
The square of a number is 3 less than four times the number is written as
x² = 4x - 3
Solve the quadratic equation
We have
x² - 4x + 3 = 0
Write - 4x as a difference
That's
x² - x - 3x - 3 = 0
Factorize the expression
That's
x( x - 1) - 3( x - 1) = 0
( x - 1)( x - 3) = 0
x - 1 = 0 x - 3 = 0
x = 1 x = 3
The numbers are 1 and 3
Hope this helps you
Answer:
1 and 3
Step-by-step explanation:
Please help me how to convert fraction to decimal? easy method plz.
Which of the following is NOT a rational number?
7.11
4.333...
8/11
-2852664798743...
Answer:
A rational number is a number that can be written as a fraction.
A. 7.11
=> 711/100
So, the 1st option is a rational number.
B. 4.333....
=> 4 1/3
=> 13/3
So, the 2nd option is a rational number.
C. 8/11
=> This is in its fractional form.
=> So, the 3rd option is a rational number.
D. -2852664798743
=> This can't be written in a fractional form.
=> So, the 4th option is NOT a rational number.
112,783 expanded form
Answer:
100,000 + 10,000+ 2,000+ 700+ 80+ 3
Find the largest value of $n$ such that $5x^2+nx+48$ can be factored as the product of two linear factors with integer coefficients.
Answer:
[tex]n = 241[/tex]
Step-by-step explanation:
Given
[tex]5x^2 + nx + 48[/tex]
Required
Determine the highest value of n
From the given equation, 5 is a prime number;
So, the factors of x² is 5x and x or -5x and -x
Since [tex]5x^2 + nx + 48[/tex] has all shades of positive terms, we'll make use of 5x and x
The factorized expression can then be:
[tex](5x + a)(x + b)[/tex]
Open the brackets
[tex]5x^2 + ax + 5bx + ab[/tex]
Equate this to the given expression
[tex]5x^2 + ax + 5bx + ab = 5x^2 + nx + 48[/tex]
[tex]5x^2 + (a + 5b)x + ab = 5x^2 + nx + 48[/tex]
By direct comparison;
[tex]5x^2 = 5x^2[/tex]
[tex](a + 5b)x = nx[/tex]
[tex]a + 5b = n[/tex] ---- (1)
[tex]ab = 48[/tex] --- (2)
From (2) above, the possible values of a and b are:
[tex]a = 1, b = 48[/tex]
[tex]a = 2, b = 24[/tex]
[tex]a = 3, b = 16[/tex]
[tex]a = 4, c = 12[/tex]
[tex]a = 6, b = 8[/tex]
[tex]a = 8, b = 6[/tex]
[tex]a = 12, b = 4[/tex]
[tex]a = 16, b = 3[/tex]
[tex]a = 24, b = 2[/tex]
[tex]a = 48, b = 1[/tex]
Of all these values; the value of a and b that gives the highest value of n is;
[tex]a = 1, b = 48[/tex]
So;
Substitute 1 for a and 48 for b in (2) [tex]a + 5b = n[/tex]
[tex]1 + 5 * 48 = n[/tex]
[tex]1 + 240 = n[/tex]
[tex]241 = n[/tex]
[tex]n = 241[/tex]
Hence, the largest value of n is 241
Answer:
Step-by-step explanation:
The two factors of $5x^2+nx+48$ must be in the form $(5x+A)(x+B)$. $A$ and $B$ must be positive integers to form the largest value of $n$. Therefore, $AB=48$ and $5B+A=n$. To form the largest value of $n$, $B$ must equal $48$. Therefore, $A=1$. \[5B+A=5(48)+1=\boxed{241}\]
Jenna bought a coat on sale for $120, which was 2/3 of the original price. What was the original price of the coat?
Answer:
$
180
Step-by-step explanation:
The original price is the quotient between $120 and 2/3, we get:
P = $180
What is the original price?
We know that 2/3 of the original price is $120, then to get the original price, we need to take the quotient between $120 and 2/3.
[tex]P = \frac{\$120}{2/3} = (3/2)*\$ 120[/tex]
By taking that quotient we will see that the original price of the coat is:
[tex]P = (3/2)*\$120 = $180[/tex]
We conclude that the original price of the coat is $120.
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i need help asap !!!!!!!!!!!
Answer:
3 a : YES
3 b : NO
4:
F
D
E
5:
IH
GH
IG
Step-by-step explanation:
3 a) Yes The sum of any two sides is larger than the third side
3 b). NO The sum of 3 ft + 4 ft gives 7ft which is not larger than 10 ft
4 Recall that larger angles opposite larger sides, and smaller angles oppose smaller sides in the triangle. Therefore, the smallest angle must be that opposite the 1 1/4 side that is angle [tex]\angle F[/tex] then angle d must follow (opposes side of length 2) and lastly angle E (since it opposes the largest side of length 2 1/8
5:
Notice that the third angle which is not given must verify the following:
[tex]\angle I = 180^o-59^o-61^o=60^o[/tex]
Therefore following the same concept as explained in the previous problem the order of these angles from smallest to largest must be:
IH
GH
IG
James works in a post office and is paid $8 per hour. Last week, he worked
32 hours and this week he worked 33.25 hours. How much should his
biweekly (every 2 weeks) paycheck be for?
Answer:
James will receive a paycheck in the amount of $522.
Step-by-step explanation:
There are 2 ways you can go at finding the answer. The first way is by adding 32 hours and 33.25 hours together to get a total of 65.25 hours. Then multiply 65.25 hours by $8 to get $522. The second way is multiplying 32 hours by $8 and get $256. Then multiply 33.25 hours by $8 to get $266. Finally add $256 and $266 up and you get $522. I hope this helps you!
A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711 , the explained variation is 18.592 , and the unexplained variation is 2.119 . Find the coefficient of determination.
Answer:
0.898
Step-by-step explanation:
The formula for the Coefficient of determination = ratio of explained variation to Total variation
From the above question, we have the following values
Explained variation = 18.592
Total variation = 20.711
The coefficient of determination = 18.592 : 20.711
= 18.592/20.711
= 0.8976872194
Approximately ≈ 0.898
Therefore, the coefficient of determination is 0.898
i nee help so bad math
Answer:
2L - the third picture
2W - the fifth picture
4 - the first picture
L+2 - the 6th picture
W - the 7th picture
Step-by-step explanation:
2L - the third picture
2W - the fifth picture
4 - the first picture
L+2 - the 6th picture
W - the 7th picture
Subtract 5y ^2−6y−115, y, squared, minus,
Answer:
y^2+8y+16
Step-by-step explanation:
6y^2 +2y +5 - ( 5y^2 -6y-11)
Distribute the minus sign
6y^2 +2y +5 - 5y^2 +6y+11
Combine like terms
y^2+8y+16