The rule of signs in binomial factors given a trinomial in the form :
[tex]x^2\pm bx\pm c[/tex]Note that b and c can be positive or negative.
And the factor may be :
[tex](x\pm m)(x\pm n)[/tex]First thing to do is to check the sign of c.
If it is positive, the signs of m and n can be both positive or both negative.
Since positive multiplied by positive is positive and
negative multiplied by negative is also positive.
[tex]\begin{gathered} (+)\times(+)=+ \\ (-)\times(-)=+ \end{gathered}[/tex]If the sign of c is negative, one of the factors must be negative and the other must be positive, because negative multiplied by positive is negative.
[tex](-)\times(+)=-[/tex]After considering the sign of c, next to check is the sign of b.
Case 1 :
If b and c are both positive, we know that the factors can be both negative or both positive.
And since the sign of b is positive, we must follow the sign of it which is positive.
So both m and n are positive
For example :
[tex]x^2+5x+6[/tex]The factor will be :
[tex](x+2)(x+3)[/tex]which are both positive.
Case 2 :
If b is negative and c is positive, we will follow the sign of b. m and n will be both negative.
For example :
[tex]x^2-5x+6[/tex]The factors are :
[tex](x-2)(x-3)[/tex]which are both negative
Case 3 :
Now the third case is tricky.
If c is negative, we know that one of m and n is negative and the other one is positive.
The sign of the larger number between m and n will follow the sign of b.
For example :
[tex]x^2-x-6[/tex]c is negative, so one factor must be negative and the other must be positive. The sign of b is negative, so the larger factor must be negative also.
The factor will be :
[tex](x-3)(x+2)[/tex]3 is larger than 2, so the negative sign of b will proceed to the factor 3.
In a small private school 3 students are randomly selected from 17 available students what is the probability that they are the three youngest students
Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex]
What is probability?The field of mathematics known as probability concerns with numerical representations of the possibility that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given data
Total number of students available = 17
Number of students selected = 3
C₍₁₈₋₃₎ = [tex]\frac{18!}{3!(18-3)!}[/tex]
C₍₁₈₋₃₎ = [tex]\frac{18(17)(16)}{3(2)(1)}[/tex]
C₍₁₈₋₃₎ = [tex]\frac{4896}{6}[/tex]
C₍₁₈₋₃₎ = 816
Number of ways where students selected are youngest = 1
Probability of three youngest student are selected
= [tex]\frac{1}{C}[/tex]₍₁₈₋₃₎
= [tex]\frac{1}{816}[/tex]
Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex].
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Simplify 2/5(14–27)+2^5÷16.
We can simplify the numerical expression to get:
(2/5)*(14 - 27) + (2⁵/16) = -16/5
How to simplify the numerical expression?Here we have the expression:
(2/5)*(14 - 27) + (2⁵/16)
Let's simplify the term in the right first, we know that:
2⁵ = 2*2*2*2*2 = 4*4*2 = 16*2 = 32
Replacing that we get:
(2⁵/16) = 32/16 = 2
Then we get:
(2/5)*(14 - 27) + (2⁵/16) = (2/5)*(14 - 27) + 2
Now we can simplify the term in the left:
(2/5)*(14 - 27) = (2/5)*(-13) = -26/5
Replacing that we get:
(2/5)*(14 - 27) + 2 = -26/5 + 2 = -26/5 + 10/5 = -16/5
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Find the value of r so the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2
The line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2, then the intersection with the domain is r = -5/3.
The line that passes through the pair of points has the given slope is,
( − 2 , 8 ) , ( r , 4 ) and m = -12
What is Slope :Slope, numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
m = rise/run
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where,
m = slope
[tex](x_{1} ,y_{1} )[/tex] = coordinates of first point in the line
[tex](x_{2} ,y_{2} )[/tex] = coordinates of second point in the line
Then, we can find the [tex]m_{1}[/tex]
We can use these two values, ( − 2 , 8 ) , ( r , 4 )
x1 = -2
y1 = 8
x2 = r
y2 = 4
m = [tex]\frac{4-8}{r-(-2)}[/tex]
[tex]m = \frac{-4}{r+2}[/tex]
We can substitute m= -12 value into m= -(4/r+2)
So,
We can write,
-12 = [tex]\frac{-4}{r+2}[/tex]
We can find the domain,
If the fraction is defined, the dominator can not be equal to zero.
2 + r ≠ 0
Rearrange variables to the left side of the inequality,
r ≠ -2
Append the inequality as the domain,
r ≠ -2
We can solve the equation,
-12 = [tex]\frac{-4}{r+2}[/tex]
Multiply both sides of equation by the common denominator,
-12 (r+2) = -4(r+2)/ (r+2)
Reduce the fractions,
-12 (r+2) = -4
Apply the distributive property,
-12r - 24 = -4
Rearrange variable to the left side of the equation,
-12r = -4 + 24
Calculate the sum or difference,
-12r = 20
Divide both sides of the equation by the coefficient of variables,
r = - 20/12
r = -5/3
Therefore,
The intersection with the domain is r = -5/3, so the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 12.
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Can anyone help me get through this problem I’ve tried using my knowledge but it’s not much. PLEASE HELP.
The scissor has intersecting lines with angles 1,2,3,4.The angles are ∠1=159° and ∠3 is 159°. We got the angle ∠2=21° and ∠4=21°.
Given that,
In the picture there is a scissor.
The scissor has intersecting lines with angles 1,2,3,4.
∠1=159° and ∠3 is 159°.
We have to find the angles ∠2 and ∠4.
Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees. There is a unique connection between the angles created when lines intersect.
The straight line has 180°
∠1+∠2=180°
159°+∠2=180°
∠2=180°-159°
∠2=21°
Now,
∠3+∠4=180°
159°+∠4=180°
∠4=180°-159°
∠4=21°
Therefore, the angle ∠2=21° and ∠4=21°.
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1. The graph shows the height of a plant after a certain amount of time measured in days. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. The graph shows how much snow fell after a certain amount of time measured in hours. 2. Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning.
Due to different rates of change in each case, neither graph shows a proportional relationship.
When does a graph represents a proportional relationship?A graph represents a proportional relationship if the output variable y in the y-axis can be written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
Item 1Between days 0 and 10, the plant grew by 4 centimeters.Between days 30 and 40, the plant grew by 8 centimeters.For the first case, the rate of change is of:
k = 4/10 = 0.4.
For the second case, the rate of change is of:
k = 8/10 = 0.8.
Different rates, hence cannot be written as proportional relationship.
Item 2Between hours 0 and 2, the amount of snow grew by 2 inches.Between days 2 and 4, the amount of snow remained constant at 2 inches.Hence the rates for each interval are given as follows:
Hours 0 - 2: 2/2 = 1 inch a hour.Hours 2 - 4: 0/2 = 0 inches a hour.Different rates, hence it is not a proportional relationship.
What is the missing information?The graphs are missing and are given by the image inserted at the end of the answer.
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Chloe had 3/4 of a pizza left. Addie ate 1/6 of Chloe's pizza. How much pizza did Addie eat?
Answer: 3/24 or 1/8 of the pizza
Step-by-step explanation:..
3x^2 + 36x + 11 = 0
Hello, could you please help me factorise this / complete the square?
Answer:
x = +/-[tex]\frac{\sqrt{291} }{3} -6[/tex]
Step-by-step explanation:
1. Check whether the following is closure under multiplication : 7×12 = 72
2. The sum of two integers is -38,one of them is -22.Find the other.
3. In a competitive exam, Gopi gets 4 marks for each correct answer and -2 for each wrong answer. If he gives 32 correct answers and 8 wrong answers, what will be his total score?
7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.
1)
Closure property of multiplication:
It states that if two real numbers a and b are multiplied, then the product will be a real number as well.
We have 7 × 12 = 72
7, 12 and 72 all are real numbers.
So, it is a closure property under multiplication.
2)
Sum = - 38
a = - 22
We need to find b
a + b = - 38
- 22 + b = - 38
b = - 38 + 22
b = - 16
3)
1 correct answer = 4 marks
1 incorrect answer = - 2 marks
Number of correct answers = 32
Number of incorrect answers = 8
Total score = 32 × 4 + (- 2) × 8
= 128 - 16
= 112 marks.
Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.
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Solve the following inequality:
4c<14-3c
Answer: x < 2
Step-by-step explanation:
To solve this, we will isolate the variable c.
Given:
4c < 14 - 3c
Add 3c to both sides of the equation:
7x < 14
Divide both sides of the equation by 7:
x < 2
1. How would you subtract a negative fraction from a positive
decimal?
Answer:
you could either make the fraction a decimal or my personal like is to make the decimal a fraction
Step-by-step explanation:
convert the fraction to a decimal or decimal to fraction
which lines are parallel if angle 4 = angle 5? justify your answer
r and s are the parallel lines, if ∠4 equals ∠5.
Given,
The figure with,
Four lines: Line r, Line s, Line l and Line m.
Angles: ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8
Here, we have to find the parallel lines when ∠4 = ∠5
Lets see:
Angle 1 and angle 4 are the same because the opposite angles created by two crossing lines are identical. As a result, angle 1 also equals angle 5.
The corresponding angles are identical when two parallel lines cross across a line. To put it another way, if r and s are parallel, the angles created when l intersects r and s are same. Angle 1 equals Angle 5, Angle 2 equals Angle 6, etc. We can infer that r and s are parallel since we know that angle 1 Equals angle 5.
So, we can conclude that if ∠4 equals ∠5, then r and s are the parallel lines.
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Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? what is the equation of the asymptote? decay; y = 0 growth; y = 0 decay; x = −3 growth; x = −3
The exponential function given in this problem represents an exponential decay, and it's asymptote is of y = 0.
What is an exponential function?An exponential function is modeled according to the rule given as follows:
[tex]y = ab^x + c[/tex]
The parameters of the function are defined as follows:
a + c is the y-intercept, which is the value of the function when x = 0.b is the rate of change of the function.c is the asymptote of the function.To verify if the function represents growth or decay, we have to check parameter b as follows:
If |b| > 1, the function represents exponential growth.If |b| < 1, the function represents exponential decay.In the context of this problem, the function is defined as follows:
[tex]y = 14\left(\frac{1}{2}\right)^x[/tex]
Hence the parameters of the given function are as follows:
a = 14, b = 0.5, c = 0.
Then:
Since |b| = 0.5 < 1, the function represents exponential decay.The asymptote of the function is of y = c = 0.More can be learned about exponential functions at https://brainly.com/question/25537936
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Answer:
Answer down bellow
Step-by-step explanation:
Q's asked: Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? What is the equation of the asymptote?
Answer: Decay; y = 0
hope this helps
~~Wdfads~~
Estimate the quotient of 72.4 ÷ 9.38.
8
9
10
11
Answer: 80
Step-by-step explanation:
72.4 = 724/10
9.38=
938/10.
72.4/9.38
= 7.7
=8 approximately
The estimated quotient of 72.4 ÷ 9.38 is 8
Estimation is the process of calculating the approximate value to make the calculation easier and simple.
The rounding off a number is the process of putting a number up or down to the nearest whole number or the nearest tens, hundred, thousand, etc
First number is 72.4
Round the number to the nearest whole number
72.4 = 72
Second number is 9.38
Round the number to the nearest whole number
9.38 = 9
Divide the number 72 by 9
72/9 = 8
The quotient is 8
Hence, the estimated quotient of 72.4 ÷ 9.38 is 8
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Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
50x + 35 = 190; x = 3.1 hours
50x − 35 = 190; x = 4.5 hours
35x + 50 = 190; x = 4 hours
35x − 50 = 190; x = 6.9 hours
The equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Jerald is having drain issues at his home and decides to call a plumber.
The plumber charges $35 to come to his house and $50 for every hour they work.
Let x be the number of hours:
190 = 35 + 50x
50x = 155
x = 3.1 hours
Thus, the equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.
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The number of students at Longview Middle School decreased by 0.75% from the number of students the previous year. To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares. How many of the smaller squares will be shaded to represent 0.75%?
The area of Nevada is about 245% of the area of Ohio. How many squares would be shaded on 10 × 10 grids to represent 245%?
The number of the smaller squares which would be shaded to represent 0.75% as given in the task content is; 75.
The number of squares to correctly represent 245% on the grid is; 245.
What is the number of smaller squares which would be shaded to represent 0.75%?It follows from the task content that; To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares.
Since each Square in the 10 × 10 grid represents 1%, it follows that on division of one of the squares in the grid into 100 smaller squares;
The percentage, 0.75% can be represented by shading 75 smaller squares.
Also, the number of squares to be shaded on 10 × 10 grids to represent 245% according to the task content is; 245. This follows from the fact that, all 100 squares on the on 10 × 10 grids represent 100%.
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Two angles are supplementary if their sum is 180°. The larger angle measures three degrees more than twice the measure of a smaller
angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.
Which of the following is the definition for permutation?
A. Selections of objects in which the order of the objects doesn't
matter.
B. The probability of an event where order doesn't matter when
selecting the objects.
C. Selections of objects in which the order of the objects matters.
D. The probability of an event where order matters when selecting
the objects.
SUBMIT
Frank is riding his bicycle for 6 hours at a speed of 9.6 kilometers per hour. For how many kilometers does he ride?
Maria and Jamal each have gardens. The area of Maria’s garden is represented by the expression 8x2 – 3x. Jamal’s garden is a rectangular plot with the width and length represented by the expressions 3x and 4x – 2.
Which expressions give how much bigger or smaller Jamal’s garden is compared to Jessica’s? Check all that apply.
4x2 – 9x
–4x2 + 3x
4x2 – 3x
12x2 – 6x – 8x2 – 3x
12x2 – 6x – 8x2 + 3x
The expression will be given as -4x² + 3x. Thus, option B is correct answer.
Area may be defined as the total amount of space which is covered by an entity. The area for a square will be given by the product of its sides and the area of the rectangle will be given as the product of its length and breadth. It is given that the area of Maria's garden is 8x² - 3x and the length and breadth of Jamal's garden are 4x - 2 and 3x respectively. The area of Jamal's garden is given by A = l×b = (4x - 2) × 3x = 12x² - 6x.
Now, difference between Maria's garden and Jamal's garden is given by
(8x² - 3x) - (12x² - 6x)
= 8x² - 3x - 12x² + 6x
=> -4x² + 3x which is the required answer.
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Simplify: 3√5•√10+11√5•√10-√5
choices:
A) 14√15-√5
B) 6√35
C) 26√50
D) 14√50-√5
The value of the numbers 3√5•√10+11√5•√10-√5 based on the information is D. 14✓50 - ✓5
How to illustrate the information?It should be noted that based on the information given, we simply want to simplify 3√5•√10+11√5•√10-√5.
This will be illustrated as:
= 3√5•√10+11√5•√10-√5
It should be noted that the numbers inside the square roots will be multiplied. This will be:
= (3√5•√10) + (11√5•√10) -√5
= 3✓50 + 11✓50 - ✓5
= 14✓50 - ✓5
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Estimate the quotient of 72.4 ÷ 9.38.
8
9
10
11
Answer:
7.719
Step-by-step explanation:
HELP FOR 40 PTS AND BRAINLY :)
Answer:
A. 183Step-by-step explanation:
To solve this problem, use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract112-38*14÷14+109
First thing you do is multiply.
[tex]\sf{38*14\div14}[/tex]
38*14=532
532÷14=38
112-38+109
Add and subtract the numbers from left to right.
[tex]\sf{112-38+109}[/tex]
[tex]\sf{112-38=74}[/tex]
[tex]\sf{74+109=\boxed{\sf{183}}[/tex]
[tex]\Rightarrow \boxed{\sf{183}}[/tex]
Therefore, the correct answer is A. 183.
I hope this helps, let me know if you have any questions.
Answer:
I’m believing it is A. 183
Step-by-step explanation:
is correct don’t you;)
In the figure below, m
m
rjdjdjdufjfjfjfjfuuf
how many groups of 5/8 are in 15/16? Show all your work.
surface area of a cuboid with dimensions of 9cm 5cm and 7cm
x - 2(x - 6) = -x + 12
The value of x in the equation given as x - 2(x - 6) = -x + 12 is 0
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the equation?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
x - 2(x - 6) = -x + 12
Open the bracket
So, we have
x - 2x + 12 = -x + 12
Evaluate the like terms
So, we have
x - 2x = -x
This gives
x = 0
Hence, the solution of x in the equation is 0
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2/3c - 2 = 2 + c
Solve for C.
Answer:
c=-12
Step-by-step explanation:
Let's solve your equation step-by-step.
2/3c−2=2+c
Step 1: Simplify both sides of the equation.
2/3c−2=2+c
2/3c+−2=2+c
2/3c−2=c+2
Step 2: Subtract c from both sides.
2/3c−2−c=c+2−c
−1/3c−2=2
Step 3: Add 2 to both sides.
−1/3c−2+2=2+2
−1/3c=4
Step 4: Multiply both sides by 3/(-1).
(3/−1)*(−1/3c)=(3/−1)*(4)
c=−12
Answer:
c=−12
Someone help with geometry please the answer I put isn’t correct
The △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.
What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.So, △ABC ≅ △DCB:
CB = CB (Common line - Given)AC = DB (Similar lines - Given)∠ABC = ∠DCB = (Right angle - Given)So, △ABC ≅ △DCB is under SAS condition.
Therefore, the △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.
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A local pizza shop has a membership program for frequent buyers. the membership costs $20 per month and members get a discounted price of $1.75 per slice of pizza. robert purchased a membership to this pizza shop. how much would robert have to pay the pizza shop if he bought 6 slices of pizza this month? what would be the monthly cost for xx slices of pizza?
Answer: $10.50
Step-by-step explanation:
Cot of 1 slice a pizza = $1.75
Cost of 6 slices of pizza = 6 × $1.75
=$10.50
Hence, Robert will pay $10.50 for the 6 slices of pizza and $20 for the membership.
Melissa is having a party. She has $126 to spend on ice cream. Each container of ice cream costs $6. How many containers of ice cream will she be able to purchase?
Answer: 21 containers of ice cream
Step-by-step explanation: simple problem, take 126 and divide it by 6 to get your answer