Factoring out in algebra simplifies expressions such as quadratic equations into products of binomials or linear factors, sometimes using complex coefficients to achieve this if necessary.
The process of factoring out involves finding the numbers or expressions that divide evenly into the original expression. In the case of quadratic expressions like [tex]x^2 - 3x - 10[/tex], we look for two binomials that multiply together to give us the original quadratic. In algebra, a common method of factoring is looking for two numbers that multiply to give the constant term (in this case -10) and add up to the coefficient of the middle term (in this case -3). These two numbers are the factors of -10 that we use to split the middle term.
For example, the factors of -10 that add up to -3 are -5 and 2. Using these numbers, we can write [tex]x^2 - 3x - 10[/tex] as (x - 5)(x + 2). This is called factoring by grouping, wherein we factor common terms out of pairs of terms and then factor further if possible.
In the context of complex numbers, all second-order polynomials can be factored into linear factors. For instance, [tex]x^2 + 1[/tex] can be factored as (x - i)(x + i), utilizing complex roots i and -i. The fundamental theorem of algebra assures us that any polynomial can be factored completely into linear factors using the complex number system.
What is the measure of arc RS?
Answer:
60°, D
Step-by-step explanation:
(140-x)/2=40
140-x=40×2=80
x=140-80=60°
1. What is the center and radius of the circle?
(x-4)² + (x-7) ² - 49
Answer:
Center at (4, 7) and radius is √49, or 7
Step-by-step explanation:
Didn't you mean (x-4)² + (y-7) ² = 49?
Comparing (x-4)² + (y-7) ² = 49
to (x - h)^2 + (y - k)^2 = r^2, we see that the center is at (h, k) => (4, 7) and that the radius is √49, or 7.
What is the length of the shortest side of a triangle that has vertices at (4,6), (-2,0), and (-6,3)?
Answer:
5
Step-by-step explanation:
This is a 3, 4, 5 triangle
Answer: 5
If you graphed these three points on a graph you can see that the points (-2,0) and (-6,3) have the smallest length. First we want to find the slope of these points. We can use the formula y2 - y1 / x2 - x1. 3 - 0 / -6 - -2. 3-0 is 3 and -6 - -2 is -4. Two negatives make a postive. So the slope is 3/-4. We can't have a negative slope so change the -4 to a postive 4. Now square the slope 3/4 to get 9 and 16. We know the pythagoren therom formula is a^2 + b^2 = c^2. So square 3 and 4 to get 9 and 16 then add them to get 25. Square 25 and you get the answer 5.
Today, Isaac needs to walk his dog, water the garden, and feed his fish. DDD is the number of minutes it takes to walk his dog, GGG is the number of minutes it takes to water the garden, and FFF is the number of minutes it takes to feed his fish.
The expression G+(D+F)G+(D+F)G, plus, left parenthesis, D, plus, F, right parenthesis describes the total number of minutes it takes Isaac to do all three tasks. We can also use the expression (G+D)+F(G+D)+Fleft parenthesis, G, plus, D, right parenthesis, plus, F to represent the same quantity.
Match each amount in the situation with the expression that represents it.
For reference:
The dog is an animal, and he needs to go outside to walk.
The garden is a bunch of plants (not an animal), and it is outside.
The fish is an animal, and she lives in a water tank inside.
Situation
Expression
THIS IS FOR KHAN ACADEMY
Answer:
The total Minutes of the Inside tasks.-F (Fish)The total Minutes of the Outside tasks.-G+D (Garden and Dog)The total Minutes of the tasks involving animals.-D+F (Dog and fish)The total Minutes of the tasks not involving animals.-G (GardenStep-by-step explanation:
D is the number of minutes it takes to walk his dog
G is the number of minutes it takes to water the garden
F is the number of minutes it takes to feed his fish.
We are required to match these situations to their respective expressions:
Situation
The total Minutes of the Inside tasks.The total Minutes of the Outside tasks.The total Minutes of the tasks involving animals.The total Minutes of the tasks not involving animals.Expression
D+FG+DGFMatch:
The total Minutes of the Inside tasks.-F (Fish)The total Minutes of the Outside tasks.-G+D (Garden and Dog)The total Minutes of the tasks involving animals.-D+F (Dog and fish)The total Minutes of the tasks not involving animals.-G (Garden)Abe creates a scatter plot showing students' ages on the x-axis and their heights on the y-axis. Which type (1 point)
of trend will the scatter plot show?
М.
a linear trend
a positive trend
a negative trend
no trend
The trend will be positive because as the students get older their heights tend to get taller.
Answer:
B
Step-by-step explanation:
As students grow older, they will naturally grow taller because their bodies are developing and maturing. This means that as the values on the x axis increase, the values on the y axis will also increase.
The result of these type of correlation is that there will be a line increasing to the right. This is known as a positive trend.
Hope this helps!
Simplify (-2x^4y^2)^3
Final answer:
The expression (-2x⁴y²)³ simplifies to -8x¹²y⁶, by individually raising the coefficient and each variable to the third power.
Explanation:
To simplify the expression (-2x⁴y²)³, you must raise both the numerical coefficient and the variables to the third power. Remember that raising a power to a power multiplies exponents and raising a negative number to an odd power results in a negative number.
First, raise -2 to the third power: (-2)³ = -8Then raise x⁴ to the third power: (x⁴)³ = x¹²Lastly, raise y² to the third power: (y²)³ = y⁶Putting it all together, the expression simplifies to -8x¹²y⁶.
If a normal distribution has a mean of 44 and a standard deviation of 8, what
is the z-score for a value of 46?
O A. 1.25
O B. 1.75
O c. 0.75
O
D. 0.25
Answer:
The answer to this question is gotta be 0
Step-by-step explanation:
Because a normal distribution gives an area between 0 and z and the area for P(X=46) = 0
The correct answer is option D: 0.25. The z-score for a value of 46 is 0.25.
To calculate the z-score for a given value in a normal distribution, we use the formula:
z = [tex]\frac{{x - \mu}}{{\sigma}}[/tex]
where:
x - the value
[tex]\mu[/tex] - the mean
[tex]\sigma[/tex] - the standard deviation
Given:
x - 46
[tex]\mu[/tex] - 44
[tex]\sigma[/tex] - 8
We can plug these values into the formula:
z = [tex]\frac{{46 - 44}}{{8}}[/tex]
z = [tex]\frac{{2}}{{8}}[/tex]
z = 0.25
So, the z-score for a value of 46 is 0.25.
The question is:
If a normal distribution has a mean of 44 and a standard deviation of 8, what is the z-score for a value of 46?
A. 1.25
B. 1.75
C. 0.75
D. 0.25
Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a.
r = 4 + cos(theta)
c.
r = 3 + 2 cos(theta)
b.
r = 2 + 3 cos(theta)
d.
r = 2 + 2 cos(theta)
Please select the best answer from the choices provided
A
B
C
D
Answer:
c. r = 3 + 2 cos(theta)
Step-by-step explanation:
At θ = 180°, the value of r is positive, but just a fraction of the value at θ = 0°. This eliminates choices 'b' and 'd'.
Choice 'a' would give r=3 and r=5 for those two cases, but the ratio of left extent to right extent looks smaller than 3/5. A graph of choice 'c' shows it matches the given figure.
Answer:
c. r = 3 + 2 cos(theta)
Step-by-step explanation:
*********PLEASE I NEED HELP ********
IN 1,2,3
What solid will this lesson focus on?
triangular prism
regular square pyramid
cone
rectangular solid
Answer:
Regular Square Pyramid
Step-by-step explanation:
I’m doing this question on odyssey ware it’s the title
how do you do question b?
Answer:
Step-by-step explanation:
Not sure
PlEASE HELP PRONTO WIL GIVE BRANLIEST!!!
Kevin drew a picture of a house and then built a model. The x-axis shows the size of different segments in the drawing, and the y-axis shows the size of the same segments in the model.
Write an equation showing the relationship between x and y.
A) y = 2x
B) y = x + 2
C) y = x + 3
D) y = 1/2x
Answer:
(A) y = 2x
Step-by-step explanation:
hope this helps
|
Find the amplitude and period of f(t)= 1/2sin3t
Answer:
Step-by-step explanation:
hello :
note : y = A sin(Bt + C) + D
• amplitude is A
• period is 2π/B
in this exercice : f(t)= 1/2sin3t
amplitude is A =1/2
period is 2π/3
Mary is creating valentine’s Day card for her friends and can choose from white,red,or pink construction paper to create a heart.On the heart she can use a black blue or green marker to write out her message and she can’t finish the valentine by sprinkling gold or silver glitter.Wh is the probability that her valentine to her friend will be on either red or pink construction paper with. black market and gold glitter?
Answer:
(1/9)
Step-by-step explanation:
Mary can choose from white,red,or pink construction paper to create a heart.
And she can use black, blue or green marker to write out her message and she can’t finish the valentine by sprinkling gold or silver glitter.
The probability that her valentine to her friend will be on either red or pink construction paper with black marker and gold glitter.
The probability that she uses red or pink construction paper = (2/3)
(since red or pink are two out of the total 3 sample spaces available for construction paper)
Probability that she uses black marker = (1/3)
(Black is one of the 3 sample spaces for markers)
Probability that she uses gold glitter = (1/2)
(Gold glitter is one of two sample spaces for glitters)
The required probability is then
(2/3) × (1/3) × (1/2) = (1/9)
Hope this Helps!!!
In the figure below, BD and EC are diameters of circle P. What is the arc measure of AE in degrees?
Pls helppp
Answer:
27°
Step-by-step explanation:
Since BD is a diameter then arc BD = 180°
∠ APE = 180° - (90 + 63)° = 180° - 153° = 27°
The measure of the arc AE is equal to the angle at the centre subtended by it.
arc AE = ∠ APE = 27°
find the sum of−2 5/10 and−5 4/15. then, in two or more complete sentences, explain the steps you used to add the mixed numbers.
Answer:
- 7 23/30
Step-by-step explanation:
-2 5/10 + -5 4/15
First simplify the fractions if possible
-2 1/2 + -5 4/15
Then, we need to get a common denominator
The common denominator in this case is 30
-2 1/2*15/15 + - 5 4/15*2/2
-2 15/30 + -5 8/30
Since the signs are alike we add
First the whole numbers
2+5 =7
Then the fractions
15/30+8/30 = 23/30
Add the fraction and the whole number together
7 23/30
Take the sign
- 7 23/30
If the fraction was improper, we would change it to a mixed number and add the whole numbers together
Final answer:
To find the sum of −2 5/10 and −5 4/15, convert them to improper fractions, find a common denominator, add them with the negative signs, and simplify if needed, resulting in −7 23/30.
Explanation:
To find the sum of −2 5/10 and −5 4/15, we first convert the mixed numbers into improper fractions. The first step is to add the whole numbers together, and then add the fractions separately.
Since both numbers are negative, when we add them, the answer will also have a negative sign, following the rule that when two negative numbers add, the answer has a negative sign. We find the common denominator for the fractions, which in this case is 30, and convert them accordingly. After adding the converted fractions, we simplify the result if possible.
To illustrate, for the whole numbers: −2 + (−5) = −7. For the fractions: −(5/10 × 3/3) + −(4/15 × 2/2) = −(15/30) + −(8/30) = −(23/30). Thus, the sum is −(7) − (23/30) or −7 23/30.
what is the hourly difference in median income for a male versus female with an advanced degree?
The hourly difference in median income between males and females with an advanced degree is approximately $9.62/hr.
To determine the hourly difference in median income between males and females with an advanced degree, we need to know the median income for each gender and the number of hours worked. If you can provide the median income values for both males and females with an advanced degree, I can calculate the difference for you.
For illustration, let's assume the following median income values:
- Median income for males with an advanced degree: M dollars per year
- Median income for females with an advanced degree: F dollars per year
- Average hours worked per week: H hours
- Number of weeks worked per year: W weeks (usually 52)
Here's how to calculate the hourly difference:
1. Convert annual median incomes to hourly incomes:
[tex]\text{Hourly income for males} = \frac{M}{H \times W} \\\\\text{Hourly income for females} = \frac{F}{H \times W}[/tex]
2. Calculate the difference in hourly incomes:
[tex]\text{Hourly difference} = \text{Hourly income for males} - \text{Hourly income for females}[/tex]
Let's plug in hypothetical numbers for illustration:
- Median income for males: M = 100,000 dollars per year
- Median income for females: F = 80,000 dollars per year
- Average hours worked per week: H = 40 hours
- Number of weeks worked per year: W = 52
Calculate the hourly incomes:
[tex]\text{Hourly income for males} = \frac{100,000}{40 \times 52} = \frac{100,000}{2080} \approx 48.08 \text{ dollars/hour} \\\\\text{Hourly income for females} = \frac{80,000}{40 \times 52} = \frac{80,000}{2080} \approx 38.46 \text{ dollars/hour}[/tex]
Calculate the hourly difference:
[tex]\text{Hourly difference} = 48.08 - 38.46 = 9.62 \text{ dollars/hour}[/tex]
So, the hourly difference in median income between males and females with an advanced degree is approximately $9.62/hr. To provide an exact answer, please supply the specific median income values for males and females with an advanced degree.
The complete question is:
What is the hourly difference in median income for a male versus female with an advanced degree?
$_____/hr
What is the slope of the line shown?
a. slope = 2
b. slope= 1/2
c. slope = -1
d. slope= 1
Answer:
the answer is b, 1/2.
Step-by-step explanation:
1-0 divided by 4-2 is 1/2
Veronica surveyed her classmates about which types of pets they own. The graph shows her data.
A circle graph titled Pets. 32 percent is dogs, 26 percent is cats, question mark is fish, 13 percent is lizards, 18 percent is no pet.
Something is missing. Veronica found the percentages of her classmates who have dogs, cats, and lizards, but she has not calculated the percentage who have fish.
What percent of her classmates own fish?
Answer:
11% own fish
Step-by-step explanation:
I will give U 15 pt Please help the last 2 answers are
The height of the brush after t seconds
The time it takes for the brush to hit the ground
We have the height h(t) as
h(t) = -16t² + 1024
16t² is how far we've fallen as a function of time; since we started 1024 feet up the height is 1024-16t².
Answer: the distance the brush falls in t seconds, first choice
a and b are positive integers and a−b = 2. Evaluate the following:
4^(1/2a) / 2^b
Answer:
4
Step-by-step explanation:
4^(1/2a)/2^b
[tex]\frac{4^{\frac{1}{2} a} }{2^b}\\=\frac{(2^{2})^{\frac{1}{2}a} }{2^b}\\=\frac{2^{2 \times \frac{1}{2}a } }{2^b} \\=\frac{2^a}{2^b} \\=2^{a-b} \\=2^2\\=4[/tex]
If sally got 28 questions correct and received 70% on the exam, how many questions were on the exam
Answer: 40
Step-by-step explanation:
Number of correct questions Sally got = 28 questions
Percentage of correct questions answered= 70% on the exam,
Total number of questions in the exam = Unknown
Let the total questions in the exam be represented as y.
Since Sally got 70% correctly, this will be:
70% of y = 28
70/100 × y = 28
0.7 × y = 28
0.7y = 28
Divide both side by 0.7
0.7y/0.7 = 28/0.7
y = 40
There are 40 questions in the exam.
Subtract:
88 – (–35)
Question options:
A)
–53
B)
–123
C)
53
D)
123
Answer:
it's answer is D 123
Step-by-step explanation:
Here
88 - ( -35)
When it comes our of bracket - *- = +
So
88 + 35
= 123
Hope it will help you :)
Answer:
D ) 123
Step-by-step explanation:
88 – (–35) =
= 88 + 35
= 123
The exterior walls and roof of a barn are to be painted. The barn is in the shape of a rectangular prism, with an isosceles triangular prism for a roof. Calculate the total area to be painted. PLEASE HELP! I WILL MARK YOU BRAINLIEST!
Given:
The rectangular prism has a length of 25 feet, a width of 10 feet and a height 55 feet.
The triangular prism has a base length of 25 feet, a height of 8 feet, and a prism height of 55 feet.
To find:
The total area to be painted.
Solution:
There are 4 external surfaces for the rectangular prism and 4 external surfaces for the triangular prism.
The rectangular prism has 4 rectangles out which there are 2 sets of similar rectangles.
There are two rectangles with lengths of 25 feet and widths of 10 feet while the other two rectangles have lengths of 55 feet and widths of 10 feet.
The area of a rectangle with a length of 25 feet and a width of 10 feet [tex]= 25(10)= 250[/tex] square ft.
The area of two such rectangles [tex]= 2(250) = 500[/tex] square feet.
The area of a rectangle with a length of 55 feet and a width of 10 feet [tex]= 55(10)= 550[/tex] square feet.
The area of two such rectangles [tex]= 2(550) = 1100[/tex] square feet.
The triangular prism has 2 triangles and 2 rectangles.
The triangles have base lengths of 25 feet and heights of 8 feet while the rectangles have lengths of 55 feet and heights of 14.8 feet.
The area of a triangle with a base length of 25 feet and a height of 8 feet [tex]= \frac{1}{2}(25)(8)= 100[/tex] square feet.
The area of two such triangles [tex]=2(100)= 200[/tex] square feet.
The area of a rectangle with a length of 55 feet and a width of 14.8 feet [tex]= 55(14.8)= 814[/tex] square feet.
The area of two such rectangles [tex]= 2(814) = 1628[/tex] square feet.
The total area to be painted [tex]=500+1100+200+1628 = 3128[/tex] square feet.
So an area of 3128 square feet is to be painted.
An area of 3128 square feet is to be painted.
The rectangular prism has a length of 25 feet, a width of 10 feet and a height 55 feet.
The triangular prism has a base length of 25 feet, a height of 8 feet, and a prism height of 55 feet.
To find:
The total area to be painted.
There are 4 external surfaces for the rectangular prism and 4 external surfaces for the triangular prism.
The rectangular prism has 4 rectangles out which there are 2 sets of similar rectangles.
There are two rectangles with lengths of 25 feet and widths of 10 feet while the other two rectangles have lengths of 55 feet and widths of 10 feet.
The area of a rectangle with a length of 25 feet and a width of 10 feet = 25(10)= 250 square ft.
The area of two such rectangles = 2(250) = 500 square feet.
The area of a rectangle with a length of 55 feet and a width of 10 feet = 55(10)= 550 square feet.
The area of two such rectangles = 2(550) = 1100 square feet.
The triangular prism has 2 triangles and 2 rectangles.
The triangles have base lengths of 25 feet and heights of 8 feet while the rectangles have lengths of 55 feet and heights of 14.8 feet.
The area of a triangle with a base length of 25 feet and a height of 8 feet = (1)/(2)(25)(8)= 100 square feet.
The area of two such triangles =2(100)= 200 square feet.
The area of a rectangle with a length of 55 feet and a width of 14.8 feet = 55(14.8)= 814 square feet.
The area of two such rectangles = 2(814) = 1628 square feet.
The total area to be painted =500+1100+200+1628 = 3128 square feet.
So an area of 3128 square feet is to be painted.
What does a machine change to make work easier? Select three options.
the amount of work done
the amount of force applied
the time needed to do the work
the direction of a force
the distance over which a force is applied
Answer: the amount of force applied
The direction of a force
The distance over which a force is applied
The machine will work easier when force, the direction of the force and the displacement increased. Options B, D, and E are correct.
What is Work?It is defined as the transfer of energy from one object to the other.
The work is equal to the product applied Force and the displacement.
The formula of the work is,
W = Fs
Where
W = work
F = force
s = Displacement
Therefore, the machine will work easier when force, the direction of the force and the displacement increased.
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If the state legislature cannot agree on a state budget, what would MOST LIKELY happen?
State employees would not receive salaries.
A temporary spending authority would be passed.
The governor would suspend the state legislature.
D)
Spending on government services would come to a halt
When a state legislature cannot agree on a state budget, the most probable outcome is the passing of a temporary spending authority, allowing the government to maintain operations while negotiations continue. Other, more drastic measures occur in extreme cases.
Explanation:If the state legislature cannot agree on a state budget, the most likely outcome would be that a temporary spending authority would be passed, also known as a continuing resolution. This temporary resolution authorizes the government to continue operations at the current funding level until a new budget can be agreed upon. Without this, essential government services could be disrupted, including wages for state employees and spending on other government services.
Halting all government spending or suspending the state legislature is highly unlikely and would typically only happen in extreme situations. It's also important to note that the specifics of what happens when a budget isn't passed can vary from state to state, as the processes for managing this situation are defined by each state's constitution and laws.
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You have $13 and earn $0.50 for each cup of orange juice you sell .write an equation that represents the total amount A (in dollars )you have after selling j cups of orange juice
Answer:
13 plus .50 times J =A
Step-by-step explanation:
i dont really know how to explain this but here we go...
you already have $13 and if you get .50 for every cup you sell (J) then thats it really...
A = 13+ 0.50j is the equation which represents the total amount A you have after selling j cups of orange juice.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that you have $13 and earn $0.50 for each cup of orange juice you sell .
We have to find an equation which represents the total amount A (in dollars )you have after selling j cups of orange juice
A = 13+ 0.50j
13 is the initial amount and 0.50 is the slope of the given equation.
Hence, A = 13+ 0.50j is the equation which represents the total amount A you have after selling j cups of orange juice.
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A contractor has $3,285 to spend for doors and hammers. Doors cost $75 each. He bought the greatest number of doors that he could buy. He will use the money he has remaining to buy hammers that cost $15 each. What is the greatest number of hammers the contractor can buy with the money he has remaining?
Answer:
4 hammers
Step-by-step explanation:
step 1
Find out the greatest number of doors that the contractor could buy
Divide the total amount by the cost of each door
so
[tex]\$3,285/\$75=43.8[/tex]
That means ----> The greatest number of doors that the contractor could buy are 43
step 2
Find the remaining money
The remaining money is equal to
[tex]3,285-43(75)=\$60[/tex]
step 3
Find the greatest number of hammers that the contractor can buy with the remaining money
Divide the remaining money by the cost of each hammer
[tex]\$60/\$15=4\ hammers[/tex]
0.12m/s =_____km/h
0.3g/cm^3=____km/m^3
Answer:
a)0.12m/s=0.432km/h
b)0.3g/cm²=300
Step-by-step explanation:
a)multiply the speed value by 3.6
b)multiply the mass / volume value by 1000
Hope this helps :)
need help ASAP I don't understand this....will mark brainliest
Answer:
C
Step-by-step explanation:
All parabolas (U shaped graphs) have domains of All Real Numbers
Answer:They y axis runs up and down so on the verticle lind where is says -2 plotthe point.
Step-by-step explanation: