- Cubic Function | 3-degree
- Domain & Range | Domain and Range both are all set of Real Numbers.
- End Behavior | When x approaches positive infinity, f(x) approaches positive infinity as well. When x approaches negative infinity, f(x) approaches negative infinity too.
- Intervals of Increasing/Decreasing | Increases at (-∞, 2) U (6,∞) and Decreases at (2,14/3) aka 2 < x < 14/3
- Intervals of Positive/Negative
Positive when x > 6 or (6,+∞)
Negative when 2 < x < 6 and x < 2 or (2,6) U (-∞,2)
- Turning Points are (2,0) and (14/3, -256/27)
- Zeros and Multiplicity | Factoring the polynomial as we get (x-2)(x-2)(x-6). Therefore, the zeros are multiplication of 2 and 6.
Multiplicity will affect the graph for x-axis. When the multiplicity kicks in, the graph will turn either decreasing on increasing on x-axis immediately.
Also I was plotting the graph so It might take too long.
What is the answer for this and why? Show work
Answer: (-4.5,-3)
Step-by-step explanation:
(-9,-2) (9,-6) 1:3
[tex]\displaystyle\\\boxed {x=\frac{x_1+\lambda x_2}{1+ \lambda} \ \ \ \ \ \ y=\frac{y_1+\lambda y_2}{1+\lambda} }[/tex]
[tex]\displaystyle\\x_1=-9\ \ \ \ x_2=9\ \ \ \ \ y_1=-2\ \ \ \ \ \ y_2=-6\ \ \ \ \ \lambda=1:3=\frac{1}{3} \\\\x=\frac{-9+(\frac{1}{3})(9) }{1+\frac{1}{3} } \\\\x=\frac{-9+3}{\frac{(1)(3)+1}{3} } \\\\x=\frac{-6}{\frac{3+1}{3} } \\\\x=\frac{(-6)(3)}{4} \\\\x=\frac{-18}{4}\\\\x=-4.5 \\\\y=\frac{-2+(\frac{1}{3} )(-6)}{1+\frac{1}{3} } \\\\y=\frac{-2+(-2)}{\frac{4}{3} } \\\\y=\frac{(-4)(3)}{4} \\\\y=-3\\Thus,(-4.5,-3)[/tex]
Please help!! I don't know what I'm doing
answer:
1/5^2
=
1/25
step-by-step
1) 5^5/5^7=
5*5*5*5*5
-------------------
5*5*5*5*5*5*5
2) aka
1/5^2= 1/25 (.04)
In an Examination, 1.100 Boys and 900 Girls appeared, 50% percent of the Boy and Girls passed the examination. The fail percentage is?
54.5 % students got failed
• Percentage in mathematics is defined as the number or ratio which can be expresses as a fraction of 100. If we want to calculate the percent of the number, we need to divide the number by the whole and multiply by 100.
• Percentage are dimensionless quantity. Percentage means pert per hundred. Percentage can also be represented in fraction form such as 0.5% or 0.25%.
• For example Prince got 98% marks in Maths which means that he has scored 98 marks out of 100.
According to the Question
Number of boys = 1100
Number of girls = 900
%age of boys passed = 50%
%age of girls passed = 40%
No of boys failed = ((100-50)*1100)/100
= 550
No of girl failed = ((100-40)*900)/100
= 540
Total number of students =1100+900 = 2000
Total number of students failed = 1090
Percentage of students failed = 1090/2000 *100 = 54.5
54.5 % students got failed
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dimetri says that a function that is made of terms where the variable is raised only to an odd power will be an odd function. do you agree with dimetr
The given function is not the odd function.
According to the statement
We have to find about the odd function.
So, For this purpose, we know that the
The odd function is that the function f is odd if the subsequent equation holds for all x and −x within the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ) Geometrically, the graph of an odd function has rotational symmetry with relevance the origin, meaning that its graph remains unchanged after a rotation of 180∘ about the origin.
From the given information:
dimetri says that a function that's fabricated from terms where the variable is raised only to an odd power are going to be an odd function
Then
Algebraically, an odd function is one where f(-x) = -f(x). this suggests that if we substitute -x for each x within the function, it should be the identical as switching every sign up the function. This doesn't always work.
For example, if f(x)=x³+7:
f(-x)=(-x)³+7=-x³+7.
However, since the 7 did not become -7, it is not the same as -f(x), so it is not an odd function.
So, The given function is not the odd function.
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writing and graphing linear equations glass art
The graph of Linear Equation is always a straight line .
In 40 minutes; diane walks 2.5 miles and sue walks 1.5 miles. in miles per hour , how much diane walking?
Answer:
3.75 miles per hour
Step-by-step explanation:
Diane is walking 2.5 miles in 40 minutes.
2.5/40 = 0.0625 miles per minute
There are 60 minutes in an hour.
0.0625 * 60 = 3.75
Diane is walking at a speed of 3.75 miles per hour.
Here, we have to calculate the walking speed of Diane in miles per hour, we need to convert the time from minutes to hours since the walking distance is given in miles.
Diane walks 2.5 miles in 40 minutes.
To convert 40 minutes to hours, we divide by 60 (since there are 60 minutes in an hour):
40 minutes ÷ 60 = 2/3 hours
Now, we can calculate Diane's walking speed (or rate) in miles per hour:
Diane's walking speed = Distance / Time
Diane's walking speed = 2.5 miles / (2/3) hours
To divide by a fraction, we can multiply by its reciprocal:
Diane's walking speed = 2.5 miles * (3/2) hours
Now, simplify:
Diane's walking speed = 7.5 miles / 2 hours
Finally, divide:
Diane's walking speed = 3.75 miles per hour
So, Diane is walking at a speed of 3.75 miles per hour.
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Tanner's parents give him x dollars per month for his allowance. however, since his birthday is in february, he gets an extra 20% bonus that month. pick all the expressions that represent how much tanner's allowance is in february. 120x x+0.2x x+1.2x 1.2x
it is given in question that Tanners parent give him x dollars per month plus 20% extra in February therefore the amount become 0.2x
What do you mean percentage?
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Tanner's parents give him x dollars per month for his allowance.
however, since his birthday is in february
he gets an extra 20% bonus that month.
pick all the expressions that represent how much tanner's allowance is in february month
20% = 20/100
= 2/10
=1/5
= 0.2
since it is given in question that Tanners parent give him x dollars per month plus 20% extra in February
therefore the amount become 0.2x
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inspection of a random sample of 25 aircraft showed that 17 needed repairs to fix a wiring problem that might compromise safety. (a) how large a sample would be needed to estimate the true proportion of jets with the wiring problem, with 90 percent confidence and an error of ± 5 percent?
The random sample proportion.
Probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.
at 90% confidence interval: The Central 90% of any normal distribution is: Z_(α/2) = 1.960
Error = E = ±5% = ±0.05
Applying the normal Probability distribution
= 0.70 ≤ P≤ 0.77(this means that we are 90% confident that the true proportion of jet with wiring problem fall with 0.70 and 0.77, hence there is no need for the airline to conduct further sampling, rather, they should just inspect all the planes)
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Tony is making a tiered cake for a party. He use 9 cups of butter from the refrigerator to make 4 cakes. We want to find how butter he needs to put in each cake. This situation can be represented by the expression -9 divided by 4. Find the solution, and explain what it means in the context of the problem.
The amount of butter that Tony needs to put in each cake will be 2.25 cups.
How to illustrate the information?From the information, Tony is making a tiered cake for a party and he use 9 cups of butter from the refrigerator to make 4 cakes.
The amount of butter that he needs to put in each cake will be:.
= Number if cups / Number of cakes
= 9 / 4.
= 2.25 cups
Therefore, the amount of butter that Tony needs to put in each cake will be 2.25 cups.
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A family is polled to see the mean of the number of hours per day the television set is on. The results, starting with Sunday, are 5, 2, 1, 2, 1, 2, and 6 hours. What is the average number of hours the family had the television set on to the nearest whole number?
The average number of hours the family had the television set on is 3 hours.
What is the average number of hours?The average of a set of numbers is calculated by adding the numbers together and dividing it by the total number. Average is also known as mean. Average is a measure of central tendency. Other measures of central tendency are mode and median.
Average = sum of the numbers / total number
Average = (5 + 2 + 1 + 2 + 1 + 2 + 6) / 7 =
19 / 7 = 2.714 hours
To round off a number to the nearest whole number, if the tenth digit is equal to 5 or greater than five, add one to the units digit. If this is not the case, the unit digit remain unchanged. In both cases, the tenth digit is replaced with o.
Because the tenth digit in 2.714 is greater than 5, the number becomes 3 hours.
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At a grocery store, a customer pays a total of $9.70 for 1.8 pounds of potato salad and 1.4pounds of coleslaw. another customer pays a total of $6.55 for 1 pound of potato salad and 1.2pounds of coleslaw. how much do 2 pounds of potato salad and 2 pounds of coleslaw cost?
use long divison to find the quotient below (4x^ - 7x - 2) / (x-2)
The quotient of the expression is 4x+1.
What is expression?An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined
Given:
The expression is
[tex](4x^{2} - 7x - 2) / (x-2)[/tex]
By long division method the following steps are :
Divide the tens column dividend by the divisor. Then Multiply the divisor by the quotient in the tens place column ,Subtract the product from the divisor then at last Bring down the dividend in the ones column and repeat.
We have to find the quotient of the expression.
According to given question we have
[tex](4x^{2} - 7x - 2) / (x-2)\\\\=(x-2)(4x+1)/(x-2)\\\\=4x+1[/tex]
Therefore, the quotient of the expression is 4x+1.
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An arithmetic sequence has this recursive formula:
| a₁ = 4
| an = an-1 - 7
What is the explicit formula for this sequence?
[tex]a_n = 4+ (n-1)(-7)[/tex] is the explicit formula for the sequence | a₁ = 4
| an = an-1 - 7
We have given [tex]a_1 = 4[/tex]
If [tex]a_n = a_{n-1} - 7[/tex]
Then, [tex]a_2 = a_{(2-1)} - 7[/tex]
⇒ [tex]a_2 = a_1 - 7[/tex]
⇒ [tex]a_2 = 4 - 7[/tex]
⇒ [tex]a_2 = -3[/tex]
Now, common difference (d) = [tex]a_2 - a_1[/tex] = -3 - 4 = -7
The explicit formula for arithmetic sequence is expressed as
[tex]a_n = a+ (n-1)d[/tex] Where a is the 1st term, [tex]a_n[/tex] is the nth term and d is the common difference.
With given information explicit formula:
[tex]a_n = 4+ (n-1)(-7)[/tex]
What is an explicit formula?Without expressing the other terms of the sequence, explicit formulas are always utilized to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence.
A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way. Without knowing the prior term in the series, the explicit formula makes it simple to locate any term. The explicit formulas for various sequences are provided here:
An = a + (n - 1) d, where a is the first term and d is the common difference, an is the arithmetic sequence.
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Help-Khan academy geometry-mapping shapes
The sequence of transformations that maps triangle DEF into triangle ABC is:
A 90º rotation about point F, then a translation along the directed line segment FC.
What are transformations on the graph of a function?Transformations in the graph of a function are classified as follows:
Translation: Translation left/right or down/up, changing just the position.Reflections: Over one of the axes or over a line, changing just the orientation.Rotations: Over a degree measure, changing the orientation or the inclination.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, changing the side lengths of the figure.For this problem, we have that:
The orientation was changed, hence first it underwent a rotation.Then the position changed, hence after the rotation it underwent a translation.Thus the correct sequence is given by Sequence B.
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Can someone please help mee (20 points
brainliest!!!)
Answer:
i hope this is the answer
Step-by-step explanation:
I’m so confused please help!!
Answer:
(3,1)
Step-by-step explanation:
Y axis = Arrow that goes up and Down
X axis = Arrow that goes from left to right
To find point J, you have to go up 3 on the Y axis.
Then, go to the right once.
now that your on point J, you have to write the coordinates.
(Y axis, X axis) = (3,1)
solve the compound inequality 2x<4x-5<15
The answer of the given inequality is 5/2<x<5
To solve this given inequality we need to 1st understand what is inequality then we will be easily able to solve this sum.
It is a relationship between inequal values. the word inequality means not equal. to compare the values whether it is less or greater than then different inequalities are used. We can easily identify when an equation is called an inequality equation when we will see the sign ≤ , ≥ ,< ,>. This sign means that the expression is an inequality.
Here in the sum we will be solving the equation in two parts in the 1st part we will be taking the part 2x<4x-5 and in the 2nd part we wil take the equation 4x-5<15
On solving the 1st part :
∴ 2x<4x-5
=> 2x-4x<-5
=> -2x<-5
=> 2x>5 [Multiplying boyh sides by minus sign]
=> x>5/2
On solving the 2nd part :
∴ 4x-5<15
=> 4x<15+5
=> 4x<20
=> x<5
So on solving the inequality we got that 5/2<x<5
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Find the area of the triangle
The area of the triangle is 5√11 cm²
How to find the area of a triangle?The area of a triangle can be found as follows:
area of a triangle = 1 / 2 bh
where
b = base of the triangleh = height of the triangleTherefore,
b = base of the triangle = 2(√6² - 5²) = 2(√36 - 25) = 2√11 cm
h = height of the triangle = 5 cm
area of the triangle = 1 / 2 × 2√11 × 5
area of the triangle = 5√11
area of the triangle = 5√11 cm²
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se repartio 8 qintos de bizcocho entre 4 ninos Que parte dl bizcocho recibio cada uno
Answer:
Step-by-step explanation:
Es de dividir 8/5 entre los 4 niños, tipo:
8/5 ÷ 1/4 =8/20 esto sale de multiplicar 8x1 y 4x5 debido a que cuando divides fracciones, se multiplican los factores.
Luego 8/20 se simplifica dividiendo todo por 4 y queda 2/5 que es el resultado.
Respuesta: Cada niño comió 2/5
Espero te sirva!
π x 910(10)
PLEAS ENEMOPOEJDHE HELP
Answer:
The correct is the 9100πx
delroy is going to a dog adoption day at his local animal shelter. he wants to make 4 batches of dog biscuits for the dogs. it takes 1 3of a cup of margarine to make a batch. how many cups of margarine will he need?
4/3 cups of margarine will he need to make 4 batches of dog biscuits.
What is a fraction in math?A fraction is a piece of the entire. The number is shown as a quotient in mathematics, in which the numerator and denominator are split. Both are integers in a straightforward fraction. The numerator, as well as the denominator of a complex fraction, as well as the denominator of a complex portion, is a fraction.
What is a whole number in math?Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of corresponding positive numbers, which are additive, are the negative numbers. The blackboard bold math b Z or boldface Z is a common way to represent the set of integers in mathematical terminology.
According to the given information:There are four batches of dog biscuits.
Making a batch requires 1/3 cup of margarine.
As we can see that for 1 batch of dog biscuits required 1/3 cup of margarine.
So to make 4 batches of dog biscuits:
= (1/3)*4
= 4/3
4/3 cups of margarine will he need to make 4 batches of dog biscuits.
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-20=4x-6x
solve equation
Answer:
X=10
Step-by-step explanation:
-20=4x-6x
4x-6x=-20
[tex]\frac{-2x}{-2} =\frac{-20}{-2}[/tex]
X=10
Answer:
x = 10
Step-by-step explanation:
STEPS FOR SOLVING LINEAR EQUATION
−20=4x−6x
Combine 4x and −6x to get −2x.
−20=−2x
Swap sides so that all variable terms are on the left hand side.
−2x=−20
Divide both sides by −2.
x=
−2
−20
Divide −20 by −2 to get 10.
x=10
$600 son repartidos entre 3 amigos en la razón (2w + 3) : (w + 2) : (3w + 4), en donde w es un número positivo.
a) Si la menor parte es $125, forma una ecuación en términos de w y resuélvelo.
b) Luego, expresa la razón en la forma más simple.
c) Los 3 amigos deciden donar $50 cada uno a una caridad. Determina la razón de sus partes luego de la donación
The equation will be (2w ,+ 3) + (w + 2) + (3w + 4) = 600
The ratio in lowest term will be 2:1:3
When they donate $50, the ratio will be 1:4.
How to calculate the value?a. The equation based on the information will be:
(2w + 3) + (w + 2) + (3w + 4) = 600
6w + 9 = 600
6w = 600 - 9
6w = 591
Divide
w = 591/6
w = 98.5
b. Therefore, (2w + 3) = 2×98.5 + 3 = 200
(w + 2) = 98.5 + 2 = 100.5
(3w + 4) = 3(98.5) + 4 = 299.5
The ratio in lowest term will be 2:1:3.
c. When they donate $50, the ratio will be:
= (50 × 3)/600
= 150/600
= 1:4
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i need help with this
if you could send a picture that would be great
The value of input are {1, 2, 3, 4, 5}.
The value of output are {4, 5}.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
The points are given as;
{(1, 5) , (2, 4) , (3, 5) , (3, 4) , (4, 4) , (5, 5)}
Now, All points are shown in graph.
Clearly, The input of points are,
x = {1, 2, 3, 4, 5}.
And, The output of points are,
y = {4, 5}
So, The value of input are {1, 2, 3, 4, 5}.
The value of output are {4, 5}.
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laura measured a picnic area near the river and made a scale drawing. the scale she used was 3 inches : 2 yards. if the picnic area is 90 inches wide in the drawing, how wide is the actual picnic area?
The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.
Let the actual width of the picnic area be x yards.
According to the given question.
Laura measured a picnic area near the river and made a scale drawing.
The scale she used was 3 inches : 2 yards.
⇒ The scale is 3 inches : 2 yards
The width of the picnic area in the drawing is 90 inches.
As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.
Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by
3inches : 2 yards = 90inches : x
⇒ 3x = 180
⇒ x = 60yards
The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.
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4(y-2)²-9=0 find the perfect square
Answer:
(2(y-2)+3) (2(y-2)-3)
Step-by-step explanation:
In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra.
Hugo grapes triangle PQR and (Rt*T<3,1>)(truabgle PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error
The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.
What is a triangle?In geometry, a triangle is defined as the shape which has three sides and also has three angles. We can say that a triangle is a type of polygon with three sides and three vertex. Triangle follows angle sum theorem.
Triangle Angle-Sum TheoremAccording to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.
Some important formula of triangles:
Area of triangle = 1/2 . base .heightPerimeter of triangle = sum of side lengthsNumber of vertices = 3Number of edges = 3In the question given,
the equation of line is y=2
The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.
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The complete question is :
Hugo grapes triangle PQR and (Rt*T<3,1>)(Δ PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error.
a garden is in the shape of a square with a perimeter of 60 feet. the garden is surrounded by two fences. one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside. if the material used to build the two fences is $ 1.15 per foot, what was the total cost of the fences?
Answer: The total cost of the fences=$165.6
Step-by-step explanation:
Let a = the length of the side if the square.
The perimeter of the square is 60 ft
4a = 60ft
divide both sides by
4a = 60/4
a = 15 ft
The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside
Expand to get:
4*a + 4(a + 2*3)
Replace a with 15 to get:
= 4*15 + 4(15 + 6) 60 + 4(21) 60+84
= 144ft
The cost of the fence is $1.15 per foot
The cost of 144 ft fence will be:
= 144*1.15
= $165.6
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solve the system y=x and 2x+3y=15
The value of x and y can be written as x=y=3. Therefore, the value of both x and y is equal to 3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two the system of equations as follows,
y = x
2x + 3y = 15
Now, if we substitute the value of y from the first equation in the second, then we can write,
2x + 3y = 15
2x + 3x = 15
5x = 15
x = 15/5
x = 3
Therefore, the value of x and y can be written as x=y=3.
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I need help asap!!!!
Answer:
Step-by-step explanation:
You multiply the weight per gallon by the number of gallons, which is 3205.
So, 8.34 x 3205