Factoring a trinomial means expanding an equation into the product of two or more binomials/monomials. It is written as (x + m) (x + n). A trinomial can be factorized in many ways.
A trinomial is ax²+bx+c=0
where,
a= the x^2 term coefficient
b= the x term coefficient
c= the constant value
Quadratic Trinomial in One Variable
In one variable, the general form of the quadratic trinomial formula is ax²+ bx + c, where a, b, and c are constant terms and neither a, b, nor c is zero. If b² - 4ac > 0, then we can always factorize a quadratic trinomial for the values of a, b, and c. It is equivalent to ax2 + bx + c = a (x + h)(x + k), where h and k are real numbers. Let's look at an example of factoring a quadratic trinomial.
Example: Factorize: 3x² - 4x - 4
Solution:
Step 1:- First multiply the coefficient of x² and the constant term.
3 × -4 = -12
Step 2:- Break the middle term -4x such that on multiplying the resulting coefficient numbers, we get the result -12 (obtained from the first step).
-4x = -6x + 2x
-6 × 2 = -12
Step 3:- Rewrite the main equation by applying the change in the middle term.
3x² - 4x - 4 = 3x²- 6x + 2x - 4
Step 4:- Combine the first two terms and the last two terms, simplify the equation and take out any common numbers or expressions.
3x2² - 6x + 2x - 4 = 3x (x - 2) + 2(x - 2)
Step 5:- Again take (x - 2) common from both the terms.
3x (x - 2) + 2(x - 2) = (x - 2) (3x + 2)
Therefore, (x - 2) and (3x + 2) are the factors of 3x² - 4x - 4.
Quadratic Trinomial in Two Variable
There is no specific way to solve a quadratic trinomial in two variables. Let's take an example.
Example: Factorize: x² + 3xy + 2y²
Solution:
Step 1: These types of trinomials also follow the same rule as above, i.e., we need to break the middle term.
x² + 3xy + 2y² = x² + 2xy + xy + 2y²
Step 2: Simplify the equation and take out common numbers of expressions.
x² + 2xy + xy + 2y² = x (x + 2y) + y (x + 2y)
Step 3: Again take (x + 2y) common from both the terms.
x (x + 2y) + y (x + 2y) = (x + y) (x + 2y)
Therefore, (x + y) and (x + 2y) are the factors of x² + 3xy + 2y²
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Which ordered pair is a solution to the equation y = –23x + 9?
A (−32,10)
B (0,10)
C (−1,1023)
D (23,10)
Answer: None of these
Step-by-step explanation:
A. If [tex]x=-32[/tex], then [tex]y=745[/tex], not [tex]10[/tex].
B. If [tex]x=0[/tex], then [tex]y=9[/tex], not [tex]10[/tex].
C. If [tex]x=-1[/tex], then [tex]y=32[/tex], not [tex]1023[/tex].
D. If [tex]x=23[/tex], then [tex]y=-520[/tex], not [tex]10[/tex].
please help me solve this asap
Answer: D. Vertical
Step-by-step explanation:
a dark eyed man marries a dark eyed woman, but they have a blue eyed child. what is the probability that their second child will have blue eyes?
The probability that their second child will have blue eyes is 1/4.
Here dark eye is dominant trait and blue eyes is recessive trait.
So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.
Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).
So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.
Hence we get the required answer.
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its finals week and im lost! help!
im so lost on this question, i need help, thanks!
Answer:
It should be to the right of 4 and the left of 6
Step-by-step explanation:
Solve for y in this diagram. Justify your answer.
The value of y in the isosceles triangle is AC = 6 cm
What Is an Isosceles Triangle?
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ABC
Now , the angle ∠ABC = 25°
The angle ∠ACB = 25°
So , the 2 angles of a triangle is 25° so , the third angle is 130°
So , the triangle is an isosceles triangle
And , the two sides of the triangle is AB = AC
The measure of side AB = 6 cm
The measure of side AC = measure of side AB
Therefore , the measure of side AC = 6cm
Therefore , the value of AC is 6 cm
Hence , the measure of side AC of triangle is 6 cm
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suppose that 15% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?
Probability that both the person own the dog is equal to 0.0225.
What is Probability ?The likelihood that an event will occur is measured by probability. It is difficult to provide a complete prediction for many events. Using it, we are only able to estimate the likelihood that an event will occur, or the chance that it will. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probabilities.
Let event A denotes that a person own dog,
P(A) = 15% =15/100 = 0.15
If we pick two people at Random then Probability that they both own dog
= P(A)*P(A)
= 0.15 * 0.15
= 0.0225
Required Probability = 0.0225
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write a logarithmic equation (using only real numbers) that has no real solutions. explain why there are no real solutions.
The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.
This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.
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the average iq test scores of an srs of 31 seventh-grade girls in a midwest school district is 105.84. suppose that the standard deviation of iq scores in this population is known to be 15. iq scores in a broad population are supposed to have mean of 100. is there evidence that the mean in this district di ers from 100? use signi cance level
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
X = 89 represent the mean of seventh-grade girls in Midwest school district
s = 15 represent the standard deviation for the sample
n = 31 sample size
μ = 100 represent the value that we want to test
'a' represent the significance level for the hypothesis test.
't' would represent the statistic (variable of interest)
[tex]p_{v}[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses,
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis: μ = 100
Alternative hypothesis: μ ≠ 100
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] ) (Equation-1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]
t = -4.08
Calculate the P-value
First we need to calculate the degrees of freedom given by:
[tex]df = n-1[/tex]
[tex]df = 31 -1[/tex]
[tex]df = 30[/tex]
Since is a two tailed test the p value would be:
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )
[tex]p_{v}[/tex] = 0.00031
Therefore,
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
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A line has a slope of -9 and includes the points (6, 1) and (7, d). What is the value of d?
Answer:
-8
Step-by-step explanation:
1-d/6-7=-9 it becomes
1-d/-1=-9
-1+d=-9
d=-8
Rewrite one eighteenthx3y + seven eighteenthsxy2 using a common factor.
one thirdxy(6x2 + 7y)
one thirdx2y(6x2 + 9y)
one eighteenthxy(x2 + 7y)
one eighteenthx3y2(y + 7)
Answer:
C
Step-by-step explanation:
1/18 x³y + 7/18 xy²
1/18 xy (x² + 7y)
O
-200
Is the√8 a rational or irrational number?
irrational, because
its decimal
rational, because all
expansion does not radicals are rational
repeat
rational, because its
decimal expansion
eventually repeats
Sod
3980 207
irrational, because
all radicals are
irrational
Sign out
Dec 15
The square root of 8 is an irrational number, because it is not an exact square root.
What are rational and irrational numbers?The rational numbers are composed by the set of all numbers that can be represented by fractions, such as whole numbers, terminating decimals, or repeating decimals.
The irrational numbers, conversely, are composed by the set of numbers that cannot be represented by fractions, such as non-exact roots and non-terminating decimals.
The square root of 8 is non-exact, hence it is an irrational number, as the square root is then a non-terminating and non-repeating decimal.
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what is the correct congruence statement for triangles shown
Answer:
It is NLJ
Step-by-step explanation:
Trust me lol
What is the approximate value of y − x? 4.9° 6.2° 11.1° 17.2°
Answer:
Step-by-step explanation:
11.1
The approximate value of y - x is 17.2°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given a right triangle LMN.
Using the tangent function,
tan (y) = 19.1 / 14.1
= 1.3546
y = tan⁻¹ (1.3546) = 53.56°
We know that,
x + y = 90°, since the other angle is 90°.
x = 90 - 53.56° = 36.44°
y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°
Hence the value of y - x is 17.2°.
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Mayerlin has two summer jobs. During the week she works in the grocery store, and on the weekend she works at a nursery. She gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery. How many total hours does she work if she does 11 hours at the grocery store and 10 hours at the nursery? How many total hours does she work if she does g hours at the grocery store and n hours at the nursery?
The total number of hours Mayerlin worked is 21 and (g + n) respectively.
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. When two whole numbers are added, the sum or total of those values is obtained.
Given that, Mayerlin gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery.
Since Mayerlin works 11 hours at the grocery store and 10 hours at the nursery, the total number of hours she worked is:
11 + 10
= 21
Now, if, Mayerline works g hours at the grocery store and n hours at the nursery, the total number of hours she worked is:
g + n
Hence, the total number of hours Mayerlin worked is 21 and (g + n) respectively.
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Which equation represents a hyperbola with a center at (0,0) a vertex at (-48,0) and a focus at (50,0)
The equation of hyperbola will be;
⇒ x²/48² - y²/14² = 1
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
In hyperbola,
The value of center = (0, 0)
The value of vertex = (- 48, 0)
The value of focus = (50, 0)
Now,
We know that;
The equation of hyperbola is,
⇒ (x - h)²/a² - (x - k)²/b² = 1
Where, (h, k) is center, (h ± a, k) is the vertex.
Here, The value of center = (0, 0)
The value of vertex = (- 48, 0)
The value of focus = (50, 0)
So, h = 0, k = 0
a = 48, c = 50
We get;
⇒ (x - 0)² / 48² - (y - 0)² / b² = 1
⇒ x² / 48² - y² / b² = 1
Since, c = √a² + b²
⇒ b = √c² - a²
⇒ b = √50² - (-48)²
⇒ b = √196
⇒ b = 14
Hence, We get;
⇒ x² / 48² - y² / b² = 1
⇒ x² / 48² - y² / 14² = 1
Thus, The equation of hyperbola is;
⇒ x²/48² - y²/14² = 1
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The area of the caribbean sea is 2.7182 × 106 km2. the area of the south atlantic ocean is 4.027 × 107 km2. find the total area. write the final answer in scientific notation with the correct number of significant digits. 4.29882 × 108 km2 4.299 × 107 km2 3.75518 × 1013 km2 3.755 × 1013 km2
The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²
Calculating total areaFrom the question, we are to determine the total area of the water bodies.
From the given information
"The area of the Caribbean sea is 2.7182 × 10⁶ km²"
and
"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"
To determine the total area, we will add up the two areas
Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²
Total area = 4.29882 × 10⁷ km²
Total area ≈ 4.299 × 10⁷ km²
Hence, the total area is 4.299 × 10⁷ km²
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Answer:
Hence, the total area is 4.299 × 10⁷ km²
Step-by-step explanation:
Sydney is going to the amusement park. where she has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money
Sydney will spend is given by the equation y = 18 + 4r. where y represents the
total amount of money, in dollars and cents, and a represents the number of rides Sydney goes on. What could the number 4 represent in the equation?
The number 4 could represent the cost of each ride Sydney goes on in the equation
How to determine what the number 4 could represent in the equation?From the question, we have the following parameters that can be used in our computation:
y = 18 + 4r
Where
y = total amount of money, in dollars and cents, r = the number of rides Sydney goes onThe equation y = 18 + 4r is a linear equation
A linear equation in its slope-intercept form can be represented as
y = c + mx
Where x and y are the variables
So, we have
Slope = m
By comparing the equations, we have
m = 4
This means that
Slope = 4
In this case, the slope is 4
So, the interpretation is that 4 is the cost of each ride
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Write an equation to represent the graph below
The zeros of a parabola are -5 and 2, and it passes through the point (1, -18). What inequality represents all the ordered pairs outside the parabola?
The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains al the ordered pairs outside the parabola.
What is the quadratic inequality of the parabola?
In this problem we must determine a quadratic inequality of the form:
a · x² + b · x + c < y
Where a, b, c are the real coefficients of the inequality.
First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:
25 · a - 5 · b + c = 0
4 · a + 2 · b + c = 0
a + b + c = - 18
(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)
Second, write the quadratic inequation:
(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
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Which shows the expression below in simplified form?
(6.3 × 1011) ÷ (7 × 105)
A.
9 × 105
B.
-0.7 × 105
C.
9 × 104
D.
9 × 107
Answer: It's D.
Step-by-step explanation: When you simplify you get the answer D.
Answer:
0.9 x 10^6
Step-by-step explanation:
6.3 divided by 7 is 0.9
10^11 ÷ by 10^5 is 10^6
how much less is the value including 13% VAT in Rs.3200 than Rs.3820
The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."
Here, we have VAT.
A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.
Value on Rs. 3200 with 13% VAT
= 3200 + 30% of 3200
= 3200 + 960
= 4160 rupees
Now, the less value,
= 4160 - 3820
= 340 rupees.
Therefore, the less value is 340 rupees.
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What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answer:
a. [tex]\frac{x+2}{x+6}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]
help????????????????
sinC = 72/97
What is right triangle?
A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.
Given right angle triangle ABC ∠B is a right angle
AB=72
BC=65 and
AC = 97
sin C = perpendicular/hypotenuse = p/h
sinC = 72/97
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Answer:
Just so we can help each other out!
A circle has a circumference of 145 units. Find the length of the arc intercepted by a central angle of 125°.
Round to the nearest tenth.
Step-by-step explanation:
20° units circle a circumference
A circle has a circumference of 145 units. Then the length of the arc intercepted by a central angle of 125° which is round to the nearest tenth is 50
The length of an arc depends on the radius of a circle and the central angle θ. We know that for the angle equal to 360 degrees (2π), the arc length is equal to circumference. Hence, as the proportion between angle and arc length is constant, we can say that:
L / θ = C / 2π
L / θ = 2πr / 2π
L / θ= r
As circumference C = 2πr,
145=2πr
r=145/2π
r=23.07746675
We find out the arc length formula when multiplying this equation by θ:
L = r * θ
as θ=125°
θ=2.18166(radians)
L=23.07746675x2.18166
L=50.34718611
Length round to nearest tenth is 50
Therefore, the value of length round to nearest tenth is 50
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20 newspapers in 4 piles = newspapers per pile
Answer: 5
Step-by-step explanation:
20/4 = 5
7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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7
10
1
2/5
Cedric has
3
of the pie
of the pie
of the pie
of the nie
4
of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
C
PR
The fraction of the pie left that each friend will receive is; 3/8 of the pie
How to divide fractions?Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.
The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.
For example, 3/8 divided by 3/4 would be;
3/8 divided by 3/4 = 3/8 * 4/3
Now, we are told that cedric has 3/4 of a pie left.
Now, he wants to share equally among two of his friends, it means that;
Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8
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Complete question is;
Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
A hockey goaltender has a save percentage of 0.920. This
means that the probability of any single shot taken on the
goaltender being a goal is 0.08. What would be the
expected number of goals scored on this goaltender in a
game where she faced 35 shots?
2.8 goals
2.0 goals
3.4 goals
1.5 goals
Answer:
2.8 goals
Step-by-step explanation:
35 * 0.08 = 0.35*8
0.35*8=2.8
The expected number of goals scored on the goaltender would be 2.8.
Explanation:The expected number of goals scored by the goaltender can be calculated using the formula:
Expected goals = Total shots * Probability of a goal
Therefore, for a goaltender with a save percentage of 0.920 (which means the probability of a goal is 0.08), and facing 35 shots:
Expected goals = 35 * 0.08Expected goals = 2.8The expected number of goals scored on this goaltender in a game where she faced 35 shots would be 2.8 goals.
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A car traveled at an average speed of 60 mph for two hours. how far did it travel? responses 30 miles 30 miles 60 miles 60 miles 120 miles 120 miles 150 miles
Answer: 120 miles
Step-by-step explanation:
If a car goes 60 miles per hour then in two hours (60×2) it will go 120
1 point
Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales
of soft drinks and hot dogs?
The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220 * 2
How to determine the calculation that will give the closest estimateFrom the question, we have the following parameters that can be used in our computation:
Time = one week
Number of cans = 362
Unit price of soft drink = $1.75
Number of hot dogs = 221
Unit price of hot dogs = $2.35
The calculation that will give the closest estimate is represented as
Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs
Substitute the known values in the above equation, so, we have the following representation
Estimate = 362 * 1.75 + 221 *2.35
Approximate
Estimate = 360 * 2 + 220 * 2
Hence, the expression is 360 * 2 + 220 * 2
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