When a polynomial has four or more terms, the easiest way to factor it is to use grouping.
Grouping can be understand more better with an example:
for eg: factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:
Break up the polynomial into sets of two. You can go with (x^3 + x^2) + (–x – 1). Put the plus sign between the sets, just like when you factor trinomials. The square x2 is the GCF of the first set, and –1 is the GCF of the second set. Factoring out both of them, you get x^2(x + 1) – 1(x + 1).one can Factor again as many times as you can. The two terms you’ve created have a GCF of (x + 1). When factored out, you get (x + 1)(x^2 – 1).However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).
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Complete the table for an object that goes 3/4 miles in 6 minutes.
Write any fraction as follows: 1/2 for one half
The speed of Ana is in miles per hour 7.5mph
By dividing the distance Ana covered by the amount of time she spent running, one may calculate her speed in miles per hour. Since the question asks for the speed to be calculated in miles per hour, an hour rather than a minute would be utilized as the unit of time.
Speed = distance ÷ time
Distance = 3/4
Time = 1/10
Speed = 3/4 ÷ 1/10
Speed = 3/4 x 10 = 15/2 miles per hour
or, 7.5mph
Divide the distance Ana covered by the time she ran to get her speed.
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The question is incomplete
Ana runs 3/4 mile in 6 minutes or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour
What is the solution for the following set of equations 6x 2y 8 3x 7y 68?
The solution of the set of equations: 6x - 2y = 8; 3x + 7y = 68 is (4,8)
The problem can be solved using elimination - substitution method.
Set of equations:
6x - 2y = 8 .... (equation 1)
3x + 7y = 68 ..... (equation 2)
Divide equation 1 by 2
3x - y = 4 ..... (equation 3)
Eliminate x by substracting equation 3 from equation 2:
3x + 7y = 68
3x - y = 4 _
8y = 64
y = 64/8
y = 8
Substitute y = 8 into equation 3:
3x - 8 = 4
3x = 12
x = 12/3
x = 4
Hence, the solution is (4,8)
Your question is incomplete, but most probably your question was:
What is the solution for the following set of equations 6x - 2y = 8; 3x + 7y = 68 ?
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Is x2 4x 4 a perfect square trinomial?
x² + 4x + 4, this is a perfect square trinomial, which is expressed as
(x + 2)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 4x + 4
= (x)² + 2(2x) + 4
= (x)² + 2(x)(2) + 2²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 2)²
= (x + 2) (x + 2)
so, this is a perfect square trinomial.
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(X-5)-1 substitute the 9 for x and evaluate
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
The definition of a linear equation.A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.
Here,
Given : (X-5)-1
Thus,
after substituting the value of x with 9
We get,
=> (X-5) -1
=>(9-5)-1
=> 4 -1
=> 3
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
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can someone help me find two true statements!
1. In a triangle line parallel to one side will divides other two sides in the same ratio
2. 8/x = 12/18
x = 12
How do you find a linear equation from two points?Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
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Can you make a triangle with 3 different length sides?
Yes, you can make a triangle with three different length sides.
1. Draw three lines of different lengths on a piece of paper.
2. Connect the ends of the lines to form a triangle.
3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.
4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.
5. Measure each side of the triangle with a ruler and add them together.
6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.
7. Once the triangle is valid, it will be a triangle with three different length sides.
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What is the area of right triangle with base 10 cm and height 5 cm?
Answer:25cm
Step-by-step explanation:area of triangle=1/2 × base× height
=1/2×10×5
= 25cm^2
Mario has 3/4 cups of chocolate chips needs 1/3 cup to make a batch of cookies how many batches can Mario make if he uses all of his chocolate chips
In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.
How to find the given equation?First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).
[tex]3/4 cups * 1 = 3/4 cups\\[/tex]
Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:
[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]
Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:
[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]
Mario can make 2.25 batches of cookies using all of his chocolate chips.
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Geometry Questions....need help pls
This given figure carries onto themself at 360, 180, and 60 degrees respectively.
What does carrying a figure onto itself mean?If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.
Given three figures those figures have rotational symmetry from their center point. The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.
for figure 1
figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.
for figure 2
figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.
for figure 3
figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.
therefore, the given figures have 1, 2, and 6 rotational symmetry.
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I GIVE THANKS AND MARK BRAINLIEST
What is the correct answer?
Please help.
Answer:if the siblings are less and the child are more u should remove the percent from the difference and put it to the another one the one from down there so the difference is 70% so try the same from down there is 18 so it got to be 20
Answer:20
What is the value of x?
3/4(x−8)= −1/2
Answers:
x = -26/3
x = 10
x = 22/3
the value of x would be 22/3 after simplification.
What is simplification?The acts or process of simplifying something such that it is simpler to accomplish or understand, or the item that is the consequence of such simplifying: The group offers suggestions on how to make trade procedures simpler. In mathematics, we generally use the PEMDAS method to simplify the values.
Given, the equation in the form of x is 3/4(x−8)= −1/2
For the value of x
3/4(x−8)= −1/2
multiply by 4 on both sides
3(x - 8) = -2
divide by 3 into both the sides
x - 8 = -2/3
add 8 on both sides
x = -2/3 + 8
x = 22/3
therefore, the value of x for the given equation 3/4(x−8)= −1/2 is 22/3.
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I
Student council is selling personal pan pizzas to raise money for a field trip. They
make a profit of $1. 50 for each pizza they sell. If they already have $235, what is the
minimum number of pizzas must they sell in order to have at least $300?|
The minimum number of pizzas must they sell in order to have at least $300 is 44.
What is the profit?
The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.
The student council needs to raise $300 - $235 = $65 to reach their goal.
They make a profit of $1.50 for each pizza they sell.
so they need to sell $65 / $1.50 = 43.333 pizzas to reach their goal.
As you cannot sell a fractional number of pizzas, they need to sell at least 44 pizzas to raise enough money for the field trip.
Hence, the minimum number of pizzas must they sell in order to have at least $300 is 44.
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Sergio purchased 4 items for $1.50 each. Sales tax was 8.25%. What was the total price?
please explain if you can, thxs!
Answer:
6.495.Step-by-step explanation:
The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.
The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.
So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.
If a coin is tossed 4 times, the odds of it coming up either heads every time or tails every time are 1:7.
What is the probability the coin comes up all heads or all tails after 4 tosses?
The probability the coin comes up all heads or all tails after 4 tosses is 12.5%.
What is probability?Probability refers to the ratio, chance, likelihood, or odds that an expected outcome is achieved when there are many possible outcomes.
Probability is a fractional value, especially when the odds of the occurrence of the expected event are not 100% uncertain or certain.
In this case, probability lies between zero and one.
Odds of a coin coming up either heads or tails every time = 1:7
The sum of ratios = 8 (1 + 7)
Thus, the probability of the coin coming up with all heads or all tails = 12.5% (1/8 x 100)
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the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trains per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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The annual cost of Randall coverage is 4900. The college pays 62% of the cost. How much is Devi red from his biweekly paycheck for medical insurance?
$1862 is Devi red from his biweekly paycheck for medical insurance
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The annual cost of Randall coverage is 4900.
The college pays 62% of the cost.
We need to find How much is Devi red from his biweekly paycheck for medical insurance
Let us convert 62% to decimal value by dividing with 100
62/100=0.62
Now multiply 0.62 with 4900
0.62×4900
3038
Now subtract 3038 from 4900
4900-3038
1862
Hence, $1862 is Devi red from his biweekly paycheck for medical insurance
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Which statements are correct when translating this phrase into a variable expression?
The product of 8 and y decreased by 10
A 8y + 10
B Product means to multiply
C 8y-10
D product means to multiply
E y/x - 10
Therefore , the solution of the given problem of algebra comes out to be
Product means to multiply and decreased means to subtract so option C only seems valid
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
Product means to multiply and decreased means to subtract so option C only seems valid
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Hanna is recovering
hundreds of treasure chests from an ancient
shipwreck. She is able to
récover 8 chests every 4 hours.
Complete the table using equivalent ratios.
Treasure chests
Hours
8
10
Answer:
12
5
Step-by-step explanation:
if 8 chests = 4hrs
then X chests= 6hrs
cross multiply
48=4x
divide by 4
X= 12
repeat the same for the second using any and you'd get 5
9. Expand :
(i) (3x - 4y + 5z)² (ii) (2a-5b-4c)²
(iii)
(5x + 3y)³
(iv) (6a - 7b)³
What is elimination method example?
The elimination method is used for solving linear equations. Here we make use of the addition property of equality, that is when same number is added on both sides of equation, it still remains equal.
Lets look into some examples.
Example 1x + y = 10
x - y = 2
By adding both equations,
x + y + x - y = 10 + 2
+ y and - y are cancelled or y term is eliminated.
2x = 12
x = 6
Example 22x + 3y = 10
-3x + 3y = 15
Here to eliminate y, we have to add the additive inverse of second equation.
2x + 3y + 3x - 3y = 10-15
5x = -5
x = -1
Example 3x + 4y = 5
3x - y = 2
To equalize the y term we multiply the second equation by 4
12x - 4y = 8
Adding both equations,
x + 4y + 12x - 4y = 5 + 8
13x = 13
x = 1
So elimination method is used for solving linear equations.
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A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the cat cover in taking 12 steps
According to unitary method, cat takes 12 steps to cover 9 feet.
How do you translate distance in steps?Measure your stride length or assume that it is 2.2 feet for women and 2.5 feet for men to determine it. Add the stride length to the number of steps, for example, 2.2 feet multiplied by 1,000 feet equals 2,200 feet. The answer is 2,200 ft / 5,280 0.42 mi when expressed in miles.
Given, it takes a dog three steps to cover the same distance as a cat four steps.
4 steps of a cat = 3 steps of a dog
12 cat steps equal (3/4)*12 to 9 dog steps.
Additionally, a dog's step covers one foot.
The dog moves nine feet in nine steps.
So a cat takes 12 steps to cover 9 feet.
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Please help!!!
if 7^9/7^n = 7^3 then n is ___?
Answer:
n= 6
Step-by-step explanation:
7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3
distance of -6,8 and 1,7
Answer:
d ≈ 7.07 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )
d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]
= [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]
= [tex]\sqrt{7^2+1}[/tex]
= [tex]\sqrt{49+1}[/tex]
= [tex]\sqrt{50}[/tex]
≈ 7.07 units ( to 2 decimal places )
A town has a population of 4000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 4500?
=========================================================
Work Shown:
x = number of years
y = population
y = 4000*1.02^x
4500 = 4000*1.02^x
4500/4000 = 1.02^x
1.125 = 1.02^x
log(1.125) = log(1.02^x)
log(1.125) = x*log(1.02)
x = log(1.125)/log(1.02)
x = 5.94784893412128
Rounding to the nearest year, it takes about 6 years for the population to reach 4500 people.
---------------
Check:
Plug in x = 5
y = 4000*1.02^x
y = 4000*1.02^5
y = 4416.3232128
y = 4416
We come up a bit short. Now try x = 6
y = 4000*1.02^x
y = 4000*1.02^6
y = 4504.649677056
y = 4505
We go a bit over the target, but it's better to go over rather than come up short.
This confirms the answer is approximately 6 years.
$710 is invested in an account earning 3.7% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
The function for the amount after {t} years can be written as -
[tex]$710(1 + 0.45/12nt)^{nt}[/tex]
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
where -
[A] = final amount
[P] = initial principal balance
[r] = interest rate
[n] = number of times interest applied per time period
[t] = number of time periods elapse
Given is that $710 is invested in an account earning 3.7% interest (APR), compounded monthly.
We can write -
A = 710(1 + 0.37/12)¹²⁽¹⁾
A = 710(1 + 0.037/12)¹²
A = 710(1 + 0.031)¹²
A = 710(1.031)¹²
A = 710 x 1.45
A = 1029.5
Let the annual growth rate be R. Then, we can write the function for annual growth rate after {t} years as -
1029.5 = [tex]$ 710(1 + R/1)^{t}[/tex]
1029.5 = [tex]$710(1+R)^{t}[/tex]
1.45 = [tex]$(1 + R)^{t}[/tex]
1.45 = 1 + tR + ..... {Binomial expansion}
Neglecting the binomial series from the third term as the value of the terms become negligible -
1.45 = 1 + tR
R = 0.45/t
Function for the amount after t years can be written as -
[tex]$710(1 + 0.45/12nt)^{nt}[/tex]= A
Therefore, the function for the amount after {t} years can be written as -
[tex]$710(1 + 0.45/12nt)^{nt}[/tex]
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3. The difference between the digits in a two-digit numeral is 3. The units’ digit is twice the tens’ digit. Find the numeral.
Answer:
36
Step-by-step explanation:
let the number be 10x+y
x - y = 3 (eq 1)
given: y = 2x (eq 2)
putting 2 in 1
x - 2x = 3
-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)
y = 6
number is 36
Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving?(Heavy Cream: 36.7%, Light Cream 19.2%, Whole Milk 3.5%, Low-Fat Milk 1.5%, Skim Milk 0.05%)
The Light cream with 19.2% content will have 15.36g of milk.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here Light cream as 19.2% of 80g
∴ 0.192×80=15.36g
Hence, The Light cream with 19.2% content will have 15.36g of milk.
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A karate studio offers a 6 week session for
$175. How much would you expect to pay for
a 9 week session?
Answer:
262.5 $
Step-by-step explanation:
A karate studio offers a 6 week session for
$175. How much would you expect to pay for
a 9 week session?
find the cost of 1 session175 : 6 = 29.16
multiply by the number of weeks29.16 x 9 = 262.5
or
175 : 6 = x : 9
x = 175 x 9 : 6
x = 262.5
. The length of one line segment is 9cm and the length of a parallel line segment is 3cm. What scale factor would you need to use to map the first line segment onto the second line
semgment?
O 9/3=3
O 9x3=27
O 3/9=0.33
O 9/9=1
Scale factor required to map the first line segment onto second line segment is 3/9=0.33
What is scale factor?The scale factor is the ratio of the length of the image to the length of the pre-image.
In this case, we're looking for the that would map the first line segment (length 9cm) onto the second line segment (length 3cm).
To find the scale factor, we can divide the length of the image by the length of the pre-image:
scale factor = length of image / length of pre-image
In this case:
[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]
[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]
So the scale factor to map the first line segment onto the second line segment is 1/3.
It means the 1st line is 3 times longer than the second one.
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3 ratios equivalent to 6/18
Answer:
Step-by-step explanation:
divide them both by 2
which is 3/ 9
divide them both by 3
whic is 2/6
and finally divide them both by 6
which is 1/3
you can multiply them both by an number as well
take care