Which expression is a factor of 4ab + 4a − 3b − 3?
b − 1
4a − 3
3b + 1
4a + 3b
(4a − 3) is a factor of 4ab + 4a − 3b − 3. Option B is correct. It is obtained by solving the given expression and taking the common terms.
What is the factored form of an expression?When an expression is written as the result of multiplication of some terms, then that multiplication form is called the factored form of that expression.
From the given expression;
[tex]= \rm 4ab + 4a - 3b - 3\\\\ =4a(b + 1) - 3(b+1) \\\\ = (b+1)(4a - 3)[/tex]
From the expression, (b+1) and (4a—3) are factors.
Hence, option B is correct.
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Find the missing lengths of the sides
Answer:
a) a = 9d, c = 18 yd
Step-by-step explanation:
The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.
Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.
In given figure, we are given the longer leg.
√3x = 9√3
From this we can find the value of x, which is the shorter leg.
Dividing both sides by √3, we get
x = 9
The shorter side, a = 9 yd
Now let's find the hypotenuse.
Plug in x = 9, in 2x, we get
= 2*9
= 18 yd
The hypotenuse "c" = 18 yd.
So the answer is a) a = 9d, c = 18 yd
Find the second of 3 consecutive integers if the sum of the first and the third is 26
what is (-5.62x - 0.8) + (1.12+ 1.4x)
state if the polygons are similar
Since you didn't provide a picture of the exact thing you're working on I'm not sure if this will help you but it will help anyone who has the same project as me
Use a graphing calculator to solve the equation in the interval from 0 to 2π Round your answers to the nearest hundredth. 1.21, 2.26, 3.31, 4.35, 5.40 3.64 1.21, 4.35 0.404, 1,452.5, 3.55, 4.59, 5.64
The solution to the equation at the given interval is x = 3.64
Using a graphing calculator to solve the equation
From the question, we have the following parameters that can be used in our computation:
[tex]3\tan(\dfrac 13\theta) = 8[/tex]
This can be expressed as
[tex]y = 3\tan(\dfrac 13\theta)[/tex]
y = 8
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection of the lines
This point is located at x = 3.64
Hence, the solution to the equation at the inverval is x = 3.64
Question
Use a graphing calculator to solve the equation
[tex]3\tan(\dfrac 13\theta) = 8[/tex]
in the interval from 0 to 2π Round your answers to the nearest hundredth.
What is the ratio of pennies to dimes in a dollar
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. What is the rectangle’s width and length?
Final answer:
To find the width and length of the rectangle, set the equation (5x + 2)(2x - 1) = 100, simplify to 10x² - x - 102 = 0, factor to find x = 6, then substitute back to find the dimensions: 32 feet by 11 feet.
Explanation:
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. To find the rectangle’s width and length, we need to solve for x using the area of a rectangle, which is the product of its length and width. The equation is:
(5x + 2)(2x - 1) = 100
First, expand the left side of the equation:
10x²- 5x + 4x - 2 = 100
Combine like terms:
10x² - x - 2 = 100
Subtract 100 from both sides to set the equation to zero:
10x² - x - 102 = 0
Now, we can use the quadratic formula, factorization, or a graphing utility to find the values of x that satisfy the equation. For simplicity, we are looking for integer solutions because the setup of the problem suggests that such solutions are likely.
Factoring the quadratic equation, we get:
(10x + 17)(x - 6) = 0
Setting each factor to zero gives us two potential solutions for x:
10x + 17 = 0 or x - 6 = 0
Solving these, we find:
x = -17/10 or x = 6
Since a negative width does not make practical sense for a rectangle, we discard the negative solution and keep x = 6.
Inserting x = 6 into the original expressions for width and length, we find:
Width = 5(6) + 2 = 32 feet
Length = 2(6) - 1 = 11 feet
Therefore, the rectangle's dimensions are 32 feet by 11 feet.
x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)
Answer: The correct answer is (1,-1).
Explanation:
The given equations are,
[tex]x-2y=3[/tex] ..... (1)
[tex]5x+3y=2[/tex] ..... (2)
Use elimination method to solve the equations.
Multiply equation (1) by 5.
[tex]5(x-2y)=5(3)[/tex]
[tex]5x-10y=15[/tex] ..... (3)
Subtract equation (3) from equation (2).
[tex]5x+3y-(5x-10y)=2-15[/tex]
[tex]5x+3y-5x+10y=-13[/tex]
[tex]13y=-13[/tex]
[tex]y=-1[/tex]
The y-coordinate is -1.
Put y=-1 in equation (1).
[tex]x-2(-1)=3[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
The x-coordinate is 1.
Therefore the intersection point is (1,-1).
Tabitha defines a sphere as the set of all points equidistant from a single point. Is Tabitha's definition valid?
Answer: Yes, Talid's definition is valid.
Step-by-step explanation:
Definition of sphere:- In geometry , a sphere is a perfectly round three-dimensional shape . It is defined as the set of points that are all at the same distance which is known as radius from a given point in a 3-dimensional space. Talid's definition:- A sphere as the set of all points equidistant from a single point.
Hence, Talid's definition is valid.
y = 2x2 - 3x - 20?
A) x = -5 and 2
B) x = 5 and -2
C) x = -2.5 and 4
D) x = 2.5 and -4
Tim’s bank requires its customers to have a 4-digit personal identification number (PIN) to access their accounts. If each digit can be a value from 0 to 9, and a 4-digit number is randomly generated, what is the probability that the number 1234 will be Tim’s PIN? A. 1 6,561 B. 1 5,040 C. 10,000 D.1 10,000
Answer:
1/10000
Step-by-step explanation:
There are 10 choices for each of the 4 digits. This means the total number of choices for the PIN are
10(10)(10)(10) = 10000
The number 1234 will only appear 1 time in this list; this makes the probability it is Tim's PIN 1/10000.
Hence, the probability that the number [tex]1234[/tex] will be Tim’s PIN is
What are digits?
A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system.
The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base [tex]10[/tex] numeral system, i.e. the decimal digits.
From the given information,
We have [tex]10[/tex] choices for each of the four digits.
This means that the total number of choices for the PIN is:-
[tex]10(10)(10)(10) = 10000[/tex]
The number [tex]1234[/tex] will only appear one time in this list which makes the probability of the form Tim's PIN [tex]\frac{1}{10000}[/tex].
Hence, the probability that the number [tex]1234[/tex] will be Tim’s PIN is [tex]\frac{1}{10000}[/tex].
To know more about digits
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A triangle has an area of 1102 m², and two of the sides of the triangle have lengths 60 m and 56 m. find the angle included by these two sides.
write the equation of the line that passes throughout (-1,5) and has a slope of 3 in point-slope form
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
The Jensen family took a road trip in September.the dad fills up the tank,he records the miles on the SUV as 24,033.he pays $83.58 to fill up the tank. what is the size of the SUV's tank in gallons, rounded to the nearest whole number. One gallon of gas cost $3.79,
Please help asap! 44 pts (:
Mark has a bag containing a mixture of 30 green and white marbles. Without looking, he guesses that half of the marbles in the bag are green. He randomly selected 1 marble from the bag, recorded the color, and returned the marble to the bag. After 15 trials, Mark has drawn 10 green marbles and 5 white marbles. Which of the conclusions below is BEST supported by his data?
The bag contains more white than green marbles.
The bag contains 10 green marbles and 20 white marbles.
The bag contains an equal amount of each color.
The bag contains more green than white marbles.
PLEASE HELP!
You work for a landscaper that has a customer needing to seed an area of land 80 feet by 40 feet in size. The garden center has 5-pound bags of grass seed. Each bag of seed can cover 25 square yards of land.
You calculate that the area you need to seed is 3200 square feet. You divide by 25 to find that you need 128 bags to seed the area. Is this correct?
A) Yes.
B) No, you need to convert the 3200 square feet to yards by dividing by 3. Then calculate the number of bags.
C) No, you need to convert the 3200 square feet to yards by dividing by 9. Then calculate the number of bags.
D) No, you need to convert the 3200 square feet to yards by multiplying by 9. Then calculate the number of bags.
Answer:
Since the mulch is measured in yards you need to either convert the area to be seeded to yards or the bag to feet. No, you need to convert the 3200 square feet to yards by dividing by 9. Then calculate the number of bags.
in 56 years, kevin will be 9 times as old as he is right now. how old is he right now?
The pentagons JKLMN and PQRST are similar find the length x of TP
Answer:
the answer is 2.8 assuming you had the same messurments and questions as me
Step-by-step explanation:
25 points need help ASAP!!!
For this question, any non-integer answers should be entered as decimals, rounded to the hundredths place. Consider this data set. 25.5 26 18.2 15.3 28.5 27 20.7 20.2 26.1 18.2 21.4 17.9 24.3 22.6 19.6 The mean of the data set is , and the sample proportion of numbers less than the mean is .
Answer:
Step-by-step explanation:
this is it
50x = 100 what does x equal??
I need to make a matrix in reduced row echelon form
A real estate agency offers three apartments for rent in New Mexico City. The expected total revenue per month from monthly rentals for the three apartments is $1,600. The individual owners of these apartments bear the monthly maintenance costs of 20% of the rent for the first two apartments and 25% of the rent for the third apartment, which is a total amount of $345. The agency charges a monthly fee equal to 10% of the rent for apartments 1 and 3 and a fee equal to 20% of the rent for apartment 2. The monthly rent plus agency fees totals $1,820. Let x, y, and z represent the monthly rental for the first, second, and third apartments, respectively.
Let the three apartments be A, B & C
The rent of A is $x
The rent of B is $y
The rent of C is $z
So x + y + z = 1600 .......(1)
Now
Maintenance of A is 20% of x = 0.20x
Maintenance of B is 20% of y = 0.20y
Maintenance of C is 25% of z = 0.25z
0.20x + 0.20y + 0.25z = 345
Multiplying by 100 we get
20x + 20y + 25 z = 34500
Dividing by 5 we get
4x + 4y + 5z = 6900 .......(2)
Monthly fee of A is 10% of x = 0.10x
Monthly fee of B is 20% of y = 0.20 y
Monthly Fee of C is 10% of z = 0.10z
Now
0.10x + 0.20y + 0.10 z= 1820 - 1600
0.10x + 0.20y + 0.10z = 220
Multiplying by 100 we get
10x + 20y + 10z = 22000
Dividing by 10
x + 2y + z = 2200 ....(3)
Making a Matrix of equation (1), (2) & (3)
[tex] \left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right] [/tex]
is the required matrix
Help why did I get this wrong? Corrections!!! Janie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?
The following expression models the total money earned by setting up a food stall at a funfair, where x represents the number of cheeseburgers sold.
Answer:
C is correct option.
The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
Step-by-step explanation:
We are given expression [tex]\dfrac{6x}{x+3}+10[/tex]
Let us suppose f(x) is total money earned by setting up a food stall at a funfair.
where, x represents the total number of cheeseburger were sold.
Therefore, [tex]f(x)=\dfrac{6x}{x+3}+10[/tex]
We need to collect the information about constant 10.
If we put x=0 into f(x)
f(0)=10
10 is a money earn when no cheeseburger sold.
It means 10 would be initial cost of setting up of Food stall.
Thus, The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
The sum of three consecutive odd integers is 153. what is the value of the largest of the integers?
The value of the largest of the integers will be 53.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of three consecutive odd integers is 153.
Let x be the odd number. Then the other two odd numbers will be x + 2 and x + 4. Then the equation will be
x + x + 2 + x + 4 = 153
3x + 6 = 153
3x = 147
x = 49
Then the other two odd numbers will be
x + 2 = 49 + 2 = 51
x + 4 = 49 + 4 = 53
The value of the largest of the integers will be 53.
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You are a lab technician and it takes you 1 hour 30 minutes to complete a lab test. At this rate, how many hours would it take you to complete 5 of the lab tests?
The second step in the process for factoring the trinomial x2-5x-36 is to
Answer:
Find the sum of the factors of 36
Step-by-step explanation: