Answer:
(3f - 2)²
Step-by-step explanation:
Given
9f² - 12f + 4
Consider the factors of the product of the coefficient of the f² term and the constant term which sum to give the coefficient of the f- term.
product = 9 × 4 = 36 and sum = - 12
The factors are - 6 and - 6
Use these factors to split the f- term
9f² - 6t - 6t + 4 ( factor the first/second and third/fourth terms )
= 3f(3f - 2) - 2(3f - 2) ← factor out (3f - 2) from each term
= (3f - 2)(3f - 2)
= (3f - 2)²
Answer:
9f² - 12f + 4 = (3f - 2)²
Step-by-step explanation:
9f²-12f+4 =
= (3f)²-2×(3f)×(2)+2²
= (3f-2)²
The equation of a line is x + 3y = 14. What is the y-intercept of the line?
Answer:
First of all, before writing the y-intercept you need to make sure that the equation is in slope intercept form.
x + 3y = 14
3y = 14 - x
y = 14/3 -x/3
y= -x/3 + 14/3
14/3 is the y-intercept
The y-intercept of the line with equation x + 3y = 14 is 4.67.
Explanation:The equation of the line is in the form x + 3y = 14. To find the y-intercept, we need to set x = 0 and solve for y. Plugging in x = 0, we get 0 + 3y = 14. Simplifying the equation gives us 3y = 14. Dividing both sides by 3, we find that y = 4.67. Therefore, the y-intercept of the line is 4.67.
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A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales.Write an equation that gives the weekly income y in terms of sales x.
The equation y=0.02x+250 gives the weekly income y in terms of sales x.
Step-by-step explanation:
Given,
Weekly salary of real estate agent = $250
Commission rate = 2%
Let,
x be the sales per week.
y be the total weekly income.
Amount of commission = 2% of sales per week
Amount of commission = [tex]\frac{2}{100}*x[/tex]
Amount of commission = 0.02x
Total weekly income = Amount of commission + Weekly salary
[tex]y=0.02x+250[/tex]
The equation y=0.02x+250 gives the weekly income y in terms of sales x.
Keywords: equation, percentage
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The weekly income y of a real estate agent can be calculated using the equation y = 250 + 0.02x where 'y' is the weekly income, 'x' is the sales amount, '250' is the fixed salary and '0.02x' is the commission on sales.
Explanation:The weekly income y of a real estate agent is comprised of a fixed salary and a variable part which is a commission based on the amount of sales done. Given the fixed salary is $250 and the commission is 2% of sales, we can represent this as a mathematical equation:
y = 250 + 0.02x
Here, 'y' represents the weekly income, 'x' represents the amount of sales and '250' is the fixed salary. The term '0.02x' is the 2% commission of sales. So, for a given sales amount 'x', the weekly income 'y' can be computed using this equation.
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Help please I need the area and perimeter
the 17th term of an A.P is 13 times the second term.prove that the twelve term is five term the third term.
Answer:
T_12 = 5(T_3)
Step-by-step explanation
T_17 = 13(T_2)
T_n = a + (n-1)d; where a=first term and d=common difference
T_17 = a + 16d
T_2 = a + d
Therefore,
a + 16d = 13(a + d)
a + 16d = 13a + 13d
16d - 13d = 13a - a
3d = 12a
d = 4a
To prove that T_12 = 5(T_3)
a + 11d = 5(a + 2d)
a + 11d = 5a + 10d
since d = 4a
a + 11(4a) = 5a + 10(4a)
a + 44a = 5a + 40a
45a = 45a
Since LHS = RHS
Therefore; T_12 = 5(T_3)
A. (5, 7) and (-4,-2)
find the slope of a line
Answer: m = 1
Step-by-step explanation: Use the slope formula to find the slope m.
Hope this helps you out! ☺
Answer:
m = 1
Step-by-step explanation:
refer to attached picture for reference
we are given 2 points
(x₁, y₁) = (5,7)
(x₂,y₂) = (-4,-2)
simply substitute these into the given equation for slope
m = (y₂ - y₁)/(x₂-x₁)
= (-2 -7) / (-4 - 5)
= -9 / -9
= 1
is 40% of a class are girls. and 25% of girls play tennis, what is the percent of the class play tennis?
a. 10%
b. 15%
c. 20%
d. 40%
Answer: a. 10%
Step-by-step explanation:
Girls in the class = 40%
Girls play tennis = 25%
Percentage of class play tennis = 40%*25% = 0.4*0.25 = 0.1
Percentage of class play tennis = 10%
The percentage of the class that plays tennis is 70%.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying by 100.
The percentage change is also calculated using the same method.
In percentage change we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We
If 40% of a class is girls, then 60% of the class must be boys.
Let's say there are 100 students in the class, so 40 of them are girls, and 60 are boys.
If 25% of the girls play tennis, that means 25% of 40, which is 10 girls, play tennis.
Therefore, the total number of students who play tennis is 10 girls + some number of boys.
We don't know how many boys play tennis, but we can find out what percentage of the whole class plays tennis by dividing the total number of tennis players by the total number of students:
(10 girls + X boys) / 100 total students
We know that 40% of the class is girls, so:
X boys = 60% of 100 total students = 60 students
So the total number of students who play tennis is:
10 girls + 60 boys = 70 students
And the percentage of the class that plays tennis is:
70 students / 100 total students = 70%
Therefore,
The percentage of the class that plays tennis is 70%.
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13.) Springfield Elementary is putting on a school play
to raise money for their field trip. They are selling
adult's tickets for $6 and children's tickets for $3.50.
They made a total of $550 for selling 125 tickets. Write
and solve a system to determine how many of each
type they sold.
45 adult tickets and 80 children tickets were sold
Solution:
Let "a" be the number of adult tickets sold
Let "c" be the number of children tickets sold
Cost of 1 adult ticket = $ 6
Cost of 1 children ticket = $ 3.50
They sold a total of 125 tickets
Therefore,
a + c = 125
c = 125 - a --------- eqn 1
They made a total of $550. Therefore, frame a equation as:
number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = 550
[tex]a \times 6 + c \times 3.50 = 550\\[/tex]
6a + 3.50c = 550 ----------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
6a + 3.50(125 - a) = 550
6a + 437.5 - 3.50a = 550
2.5a = 112.5
a = 45Substitute a = 45 in eqn 1
c = 125 - 45
c = 80Thus 45 adult tickets and 80 children tickets were sold
At any given football game that Burbank plays , the probability that Patrick plays during the first half of the game is 5/6 . he plays during the first half, there is only a 3/7 chance that he'll play again during the second half. (He gets tired if he plays all out in the first half.) If he doesn't play during the first half, there is a 5/ 7 chance that he'll play during the second half . Find the probability that Patrick played in the first half, given that he played in the second half.
Answer:
the probability answer will be 8/49.
Step-by-step explanation:
the answer probability would be equal to multiplication of the odd cases of the given probabilities.Therefore,for him to playin both the halves of the game would be 8/49.
Using Bayesian probability, we find that the probability of Patrick playing in the first half given that he played in the second half is 3/4 or 75%.
This was determined by calculating intermediate probabilities and applying Bayes' theorem.
Let's define the following events:F: Patrick plays during the first half.S: Patrick plays during the second half.We are given the probabilities:P(F) = 5/6P(S|F) = 3/7P(S|FC) = 5/7, where FC is the complement of event F (Patrick does not play in the first half).We need to find P(F|S), the probability that Patrick played in the first half given that he played in the second half, using Bayes' theorem.Bayes' theorem states:Therefore, the probability that Patrick played in the first half given that he played in the second half is 3/4 or 75%.
Melvin walked 5/8 mile to the library. He then walked 3/10 mile from the library to the store. About how far did Melvin walk?
Answer:
37/40 = 0.925 miles
Step-by-step explanation:
The total distance Melvin walked (in miles) was ...
5/8 + 3/10 = 25/40 + 12/40 = 37/40 . . . . miles
__
In decimal, the sum is ...
0.625 + 0.30 = 0.925 . . . . miles
triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC
Answer:
[tex]DC=\frac{8}{3}\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The triangle ABD is an isosceles triangle
because
AB=BD
The segment BM is a perpendicular bisector segment AD
so
In the right triangle ABM
Applying the Pythagorean Theorem
[tex]BM^2=AB^2-AM^2[/tex]
we have
[tex]AB=5\ units\\AM=x\ units[/tex]
substitute
[tex]BM^2=5^2-x^2[/tex]
[tex]BM^2=25-x^2[/tex] -----> equation A
In the right triangle BMC
Applying the Pythagorean Theorem
[tex]BM^2=BC^2-MC^2[/tex]
we have
[tex]BC=7\ units\\MC=AC-AM=(9-x)\ units[/tex]
substitute
[tex]BM^2=7^2-(9-x)^2[/tex]
[tex]BM^2=49-(81-18x+x^2)[/tex]
[tex]BM^2=49-81+18x-x^2[/tex]
[tex]BM^2=-x^2+18x-32[/tex] ----> equation B
equate equation A and equation B
[tex]-x^2+18x-32=25-x^2[/tex]
solve for x
[tex]18x=25+32\\18x=57\\\\x=\frac{57}{18}[/tex]
Simplify
[tex]x=\frac{19}{6}[/tex]
Find the length of DC
[tex]DC=AC-2x[/tex]
substitute the given values
[tex]DC=9-2(\frac{19}{6})[/tex]
[tex]DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units[/tex]
fred thinks of a number that is greater than 110 and less than 120. he can make his number with same number of hundreds,tens and ones. what is freds number?
The number Fred thinks of is 111
Solution:
Given that, Fred thinks of a number that is greater than 110 and less than 120
He can make his number with same number of hundreds,tens and ones
To find: Fred's number
Given that the number is greater than 110 and less than 120
The possible numbers are:
111 , 112, 113, 114, 115, 116, 117, 118, 119
But he can make his number with same number of hundreds,tens and ones
So the numbers in ones, tens and hundreds place are same
So the only possible number is 111
Thus the number Fred thinks of is 111
Final answer:
Fred's number is 111, as it is the only number that is greater than 110 and less than 120 and has the same number of hundreds, tens, and ones.
Explanation:
The number Fred thinks of must be greater than 110 and less than 120. Additionally, it must have the same number of hundreds, tens, and ones. To meet these conditions, the only number that fulfills this is 111. This is because it's the only number between 110 and 120 that has the same digit in the hundreds, tens, and ones place.
Fred's number is unique in this range because it is represented with three identical digits, showcasing an interesting property of numbers in our base-ten system where a digit's value depends on its position. Hence, 111 is the number Fred is thinking of, which consists of one hundred, one ten, and one one.
A real estate agent received a 1.5% commission for a house that sold for $250,000. How much was the agent's commission?
Answer:
$3,750
Step-by-step explanation:
1.5% of 250,000 is 3,750
The question does NOT ask for the total price. It is just asking for commission.
How would you write out 3x6+7x4=46 to make it correct?
Answer:
3x6+7x4=46 it’s correct
we can rewrite it this way : (3x6)+(7x4)=46
I’m confused on what’s going on here, so if someone could explain it I would be super grateful.
Given AB = 4x + 5, BC = 3x - 2 and AC 9x -5
The sum of the length of any two sides of a triangle is greater than the length of third side.
Case I
AB + BC > AC
⇔4x +5 +3x -2 > 9x -5
⇔7x + 3 >9x - 5
⇔ 7x -9x > -5 -3
⇔-2x > -8
⇔x <4
Case II
if AB+AC > BC
4x +5 +9x -5> 3x -2
⇔13x >3x -2
⇔ 13x -3x> -2
⇔10x > -2
⇔x >[tex]-\frac{1}{5}[/tex]
Case III
AC+BC > AB
⇔9x - 5 +3x - 2 > 4x +5
⇔6x -7 > 4x +5
⇔6x -4x >5+7
⇔2x > 12
⇔x > 6
for each sequence, find the first 4 term and the 10th term 2nsquard (algbra) pls can sm1 answer me plis
Answer:
see explanation
Step-by-step explanation:
To find the terms of the sequence substitute n = 1, 2, 3, 4, 10 into the rule.
n = 1 → 2(1)² = 2(1) = 2
n = 2 → 2(2)² = 2(4) = 8
n = 3 → 2(3)² = 2(9) = 18
n = 4 → 2(4)² = 2(16) = 32
n = 10 → 2(10)² = 2(100) = 200
The first 4 terms are 1, 8, 18, 32 and the 10 th term is 200
Answer:
2, 8, 18, 32.
10th term = 200.
Step-by-step explanation:
The first 4 terms of 2n^2 are
2(1)^2, 2(2)^2, 2(3)^2, 2(4)^2
= 2, 2*4, 2*9, 2*16
= 2, 8, 18, 32.
The 10th term = 2(10)^2
= 200.
Perform the indicated operation.
h(x) = 3x - 1
g(x) = 2x – 4
Find (hog)(x)
Answer:
[tex]\large\boxed{(h\circ g)(x)=6x-16}[/tex]
Step-by-step explanation:
[tex]h(x)=3x-1\\\\g(x)=2x-4\\\\(h\circ g)(x)=h\bigg(g(x)\bigg)\\\\\text{Substitute instead of x the expression (2x - 4) to h (x):}\\\\(h\circ g)(x)=3(2x-4)-4\qquad\text{use the distributive property}\\\\(h\circ g)(x)=(3)(2x)+(3)(-4)-4\\\\(h\circ g)(x)=6x-12-4\\\\(h\circ g)(x)=6x-16[/tex]
41,464,700+?=50,000,000
Answer:
8,535,300
Step-by-step explanation:
the answer is 41,464,700 + 8,535,300 = 50,000,000
Find the slope determined by the following pair of points
(19/4,2) , (1,3/4)
Answer:
1/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3/4-2)/(1-19/4)
m=(3/4-8/4)/(4/4-19/4)
m=(-5/4)/(-15/4)
m=(-5/4)(-4/15)
m=20/60
m=2/6
m=1/3
Answer:
1/3
Step-by-step explanation:
If you want to make 2 1/2 Batches of cookies and you need one and 1 2/3 cups of flour per cookie batch how much flower do you need
Answer:
you need 4 1/3 cups of flower
What is the area of this parallelogram?
A.
2.9 cm2
B.
5.8 cm2
C.
8.7 cm2
D.
6.0 cm2
Answer:
5.8
Step-by-step explanation:
Which shows the correct first step to solving the system of equations in the most efficient manner ? 3x+2y=17 x+4y=19
The correct answer is option 1: x = -4y+19
Step-by-step explanation:
Given equations are:
[tex]3x+2y=17\ \ \ Eqn1\\x+4y=19\ \ \ \ Eqn2[/tex]
When we have to solve a system of equations using substitution method we look for a variable in both of equations that is without any co-efficient as it is easy to isolate that variable in the equation and then using substitution method to solve it
We can see that in equation 2, x is without any co-efficient
So,
[tex]x+4y = 19[/tex]
Subtracting 4y from both sides
[tex]x+4y-4y = 19-4y\\x = 19-4y\\[/tex]
Can also be written as:
[tex]x = -4y+19[/tex]
Hence,
The correct answer is option 1: x = -4y+19
Keywords: Linear equations, variables
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Answer:
The correct answer is option 1: x = -4y+19
Step-by-step explanation:
Show how to solve the problem mentally.
A student has a monthly budget of $120 to spend on either burritos, which cost $6 each, or sodas, which cost $4 each. What is the largest number of burritos that a student could afford to purchase in one month ?
Answer:
Step-by-step explanation:
he has 120 bucks...burritos are 6 and sodas are 4
the largest number of burritos a person can afford to purchase....
120/6 = 20....he can purchase 20 burritos....but then he doesn't get any soda because thats gonna take all his money
The largest number of burritos a person can afford to purchase is 20.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
It is given that:-
He has 120 bucks...burritos are 6 and sodas are 4The largest number of burritos a person can afford to purchase:-
120 / 6 = 20.
He can purchase 20 burritos....but then he doesn't get any soda because that's gonna take all his money.
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If a = b and e = f, what is the value of y
A. 87
B.88
C. 91
D. 92
Answer:
it’s 92 on edge
Step-by-step explanation:
Which form of equation models the data if a is a negative integer and b is a positive integer?
A.) b = ax/y
B.) y = ab^x
C.) y = ax+b
D.) y = ab^-x
* ^ = exponent *
Answer:
y=ax+b
Step-by-step explanation:
i got it right on TTM
Answer:
C
Step-by-step explanation:
darren got 42 out of the 56 question correct on the test. what percent of the questions did he get correct? please help ....
Answer:
75%
Step-by-step explanation:
42/56 = [tex]\frac{42}{56}[/tex]
Convert to decimal form:
42÷56 = 0.75
= 75%
Darren got 75% of the questions correct on his test, as 42 out of 56 simplifies to 3/4 or 75%. This percentage might place him in a higher percentile, indicating good performance.
Explanation:Darren scored 42 out of 56 questions correctly on his test. To find what percent of the questions he got correct, you set up a fraction of correct answers over the total number of questions and then convert it to a percentage. The fraction for Darren's test is 42/56, which simplifies to 3/4 or 0.75 when divided. To convert this to a percentage, you multiply by 100, giving Darren a score of 75% correct on his test.
Some students might be interested in how this compares to percentile ranks. For example, if the 70th percentile for a test is 16 correct answers out of 20, this means that 70% of the students answered 16 or fewer questions correctly. Darren's score of 75% would likely place him in a higher percentile since he got a larger proportion of the questions correct, which is generally considered good.
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Solve x^2=2x+3 by factoring
The solution is x = 1 and x = -3
Solution:
Given that we have to solve the given equation by factoring
Given equation is:
[tex]x^2=2x + 3\\\\x^2 - 2x - 3 = 0[/tex]
[tex]\text{Consider the form } x^2+bx+c[/tex]
Find a pair of integers whose product is c and and whose sum is b
[tex]\text{Compare } x^2-2x-3 = 0 \text{ with } x^2+bx +c\\\\\text{We get } b = -2 \text{ and } c = -3[/tex]
Now find, a pair of integers whose sum is -2 and product is -3
The integers that satisfies this condition is -1 and 3
When we add - 1 and 3 we get 2
When multiply -1 and 3 we get -3
Thus the pair of integers are -1 and 3
Write the factored form using these integers.
[tex](x-1)(x+3) = 0[/tex]
The Zero Product Property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0
Set the factors equal to 0
[tex]x - 1 = 0 \text{ and } x + 3 = 0[/tex]
x = 1 and x = -3
Thus the solution is x = 1 and x = -3
Place the following steps in order to complete the square and solve the quadratic equation x2-6x+7=0
Answer:
The solved expression is [tex]x=3+\sqrt{2}[/tex] and [tex]x=3-\sqrt{2}[/tex]
Therefore [tex]x=3\pm\sqrt{2}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]x^2-6x+7=0[/tex]
To solve the given equation by using completing the square :
[tex]x^2-6x+7=0[/tex]
Rewritting the above equation as below :
[tex]x^2-6x+7+2-2=0[/tex]
[tex](x^2-6x+7+2)-2=0[/tex]
[tex](x^2-6x+9)-2=0[/tex]
[tex](x^2-6x+3^2)-2=0[/tex]
[tex](x^2-2(x)(3)+3^2)-2=0[/tex] ( it is of the form of [tex](a-b)^2=a^2-2ab+b^2[/tex] heere a=x and b=3 )
[tex](x-3)^2-2=0[/tex]
[tex](x-3)^2=2[/tex]
Taking square root on both sides we get
[tex]\sqrt{(x-3)^2}=\pm\sqrt{2}[/tex]
[tex]x-3=\pm\sqrt{2}[/tex]
[tex]x=\pm\sqrt{2}+3[/tex]
[tex]x=3\pm\sqrt{2}[/tex]
Therefore [tex]x=3+\sqrt{2}[/tex] and [tex]x=3-\sqrt{2}[/tex]
The middle school golf team is selling golf balls to raise $850 for new equipment. They sell golf balls for two dollars each. A case has 24 packs of golf balls. Each pack has six golf balls. How many cases of golf balls does the team need to sell to raise enough money for new equipment.
Answer:
3 cases
Step-by-step explanation:
Total Money Needed = $850
Each Golf Ball = $2
Total Balls needed = 850/2 = 425 balls
Case = 24 Pack
Pack = 6 balls
So a Case has:
24 * 6 = 144 balls
They need 425 balls to sell and each case has 144 balls, so number of case needed would be:
425/144 = 2.95
We can't have 2.95 cases, so we round up to 3 cases
Is 3 a factor of 81? Use divisibility rules to explain
Answer:
Step-by-step explanation:
yes it is a factor because 31 is a factor and if u add there is a one
Final answer:
Yes, 3 is a factor of 81 because the sum of 81's digits (8 and 1) is 9, which is divisible by 3. Also, since 81 is 3 raised to the power of 4, 3 is repeatedly a factor of 81.
Explanation:
To determine if 3 is a factor of 81, we can use the concept of divisibility. A number is divisible by 3 if the sum of its digits is divisible by 3. The number 81 only consists of the digits 8 and 1, and when added together (8 + 1), they equal 9. Since 9 is divisible by 3, so is 81. Therefore, 3 is indeed a factor of 81.
Additionally, the three-factor product rule can confirm this, as combining the factors 3, 3, and 3 (since 3 x 3 x 3 = 27, and 27 x 3 = 81), you end up with 81, which proves that 3 is a factor of 81.