The instantaneous rate of change at x = 2 is 0
at x = 3 is negative
0 <= x <= 4 is 0
a function has an instantaneous rate of change of 0 at a maximum or minimum
the instantaneous rate of change at x = 3 being negative means it goes down after the maximum or minimum meaning it is a maximum
the average rate of change on the interval is 0, so the function goes up and then down
these all sound like a parabola
y = -2(x - 2)^2 + 10 is a parabola that fits the requirements
A cheeseburger it’s twice the price of a slice of pizza and order of three cheeseburgers and four slices of pizza is $15 right in the Quetion for for the green information
Answer: 45+x = 45x
Step-by-step explanation:
What is 100 times 95 times 38
Answer: 361000
Step-by-step explanation:
Let Ln denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the given function on the indicated interval. (Round your answer to four decimal places.) L4 for f(x) = 1/x-1on [3, 4] L4 =
The indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.
Let Ln denote the left-endpoint sum using n sub intervals.
We are given that
[tex]f(x) = \frac{1}{x-1}[/tex] [3,4]
We have to find L4
It means n = 4
x = [tex]\frac{b-a}{n} = \frac{4-3}{4} = \frac{1}{4}[/tex] = 0.25
Now, intervals are
[3, 3.25], [3.25, 3.50], [3.5, 3.75], [3.75, 4]
Now,
[tex]L_{4} = f(x_{0}) \triangle x+f(x_{1})\triangle x +f(x_{2})\triangle x+f(x_{3})\triangle x\\ \\ L_{4} = \frac{1}{3-1} (0.25)+\frac{1}{3.25-1}(0.25)+\frac{1}{3.5-1}(0.25)+\frac{1}{3.75-1}(0.25)\\ \\ L_{4} = 0.7595[/tex]
Hence the answer is the indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.
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1. {(1, -2), (-2, 0), (-1, 2), (1, 3)}2. {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15}}Is the relation a function
To find if a relation is a function, identify if there is more that one value of y for the same value of x (if there are more than one value for one value of x is not a function)
Ordered pairs (x,y)
1.
x y
1 -2
-2 0
-1 2
1 3
As there are two values of y when x=1. (1 , -2) and (1 ,3). The relation is not a function2.
x y
1 1
2 2
3 5
4 10
5 15
As there are no more than one value of y for the same value of x. The relation is a function.13+v+2v=v+3+4combine like termsmove letters to the leftwhat's left?add or subtract constantwhat's left?divide coefficientanswer
13+v+2v=v+3+4
Combine like terms
13+3v=v+7
Move letters to the left
13+3v-v =7
13+2v=7
Subtract constant
2v=7-13
2v=-6
divide both side by 2
2v/2 = -6/2
v = -3
If a spring is stretched 10cm by a weight of 8kg how much will it be stretched by 3kg
The amount of string that can be stretched by 3 kg weight is 5/ 4× 3
= 15 / 4 = 3.75 cm
Given ; The string is attached to a weigh whose weight is 8 kg
the length of the string which is being stretched is 10 cm
The amount of string that can be stretched by 3 kg weight can be calculated by unitary method
According to the unitary method ;
the string when attached to a 1 kg weight the length will be = 10 / 8 = 5 /4
Thus the amount of string that can be stretched by 3 kg weight is 5/ 4× 3
= 15 / 4 = 3.75 cm
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multiply: 1/6 (-3/7) answer in simplest form
1/6 (-3/7)
[tex]\frac{1}{6}\cdot\frac{-3}{7}=\frac{-3}{6\cdot7}=\frac{-3}{2\cdot\text{ 3 }\cdot\text{ 7}}=\frac{-1}{2\cdot7}=\frac{-1}{14}[/tex]Answer:
-1 /14
[tex]\frac{-1}{14}[/tex]Juan always saves the same amount of money from his weekly allowance. This table shows how much he has saved in dollars at different times. Which equation represents the situation, where ex is the time and why is the amount saved?
The equation represent the given situation is y=3x+10.
What is equation?
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. 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.
Here let us take the values of time and amount as x and y. Then take any two points ,
[tex](x_1,y_1)=(3,19)\\(x_2,y_2)=(6,28)[/tex]
Now using slope formula,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = 9/3 = 3
Now using equation formula ,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-19=3(x-3)
=>y-19=3x-9
=>y=3x-9+19
=>y=3x+10
Hence the correct option is A)y=3x+10.
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If a number is tripled and then subtracted from 15 the result is 5 more than twice the number?
The number in the word problem is 2
How to find the number
let the number be x
from the question it is deduced that
If a number is tripled and then subtracted from 15 = 15 - 3x
5 more than twice the number = 2x + 5
equating both sides
15 - 3x = 2x + 5
collecting like terms
15 - 5 = 2x + 3x
10 = 5x
x = 2
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The inequality 2c−3<9 represents the amount of money a student can spend on c candy bars. Select the values that best complete the sentence. The solution to the inequality is , and it represents that the student can buy a maximum of whole candy bars.
He can buy 5 candy at most with this inequality 2c-3<9 as the inequality will result in c<6 as the definition of inequality says, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another".
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. The greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols. Take the same amount away from both sides. Add the same positive number to both sides. Subtract the same positive number from both sides. Reverse the sign and multiply both sides by the same negative number.
Here,
2c-3<9
add 3 both side,
2c-3+3<9+3
2c<12
divide both side by 2,
c<6
According to the definition of inequality, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another," he can only purchase a maximum of 5 candies with the inequality 2c-3<9.
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3) Sketch a graph, labelling and scaling the axes, of the line y = 2x – 3.
y = 2x - 3
Put x = 0 and solve
y = 2(0) - 3
y = 3
We have a point (0, 3)
Put y = 0 and solve for x
0 = 2x - 3
2x = 3
x = 3/2
x = 1.5
The second point is (1.5, 0)
Below is the graph
Choose the point on the terminal side of 135º.
We are given the following information.
We also know that the general equation of a line is given by
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the point at which it crosses the y axis.
Since the line given goes through (0,0), b=0. Now we just need to find m.
This can be done via the formula
[tex]m=\tan (\theta)[/tex]In this case
[tex]m=\tan (135)=-1[/tex]And so, the equation of the line given is
[tex]y=-x[/tex]Now we simply need to see which of the options fit this equation. We can do this easily, because x and y are equal except for their sign.
As such, the point of the terminal side of 135° is (-1,1).
A linear function can be modeled using the equation 2x-y=2.
What is the Zero of this function
If linear function can be modeled using the equation 2x-y=2. Then x=1 is the Zero of this function
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
2x-y=2
We need to write this in slope intercept form
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
y=2x-2
m=2 and y intercept is -2
Now take the values of x and y
x 0 1 2 3
y -2 0 2 4
Hence the zero of this function is x=1
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]
Simplify the expression 2n/6n+4 times 3n+2/3n-2
Answer:11n^3/9-2n^2/3+44n/3-8Step-by-step explanation:
Step-by-step explanation:
15)The demand equation for a certain product is given by the formulap = 32-10.0001x+1where x is the number of units sold in a month and p is the price perunit. If the price is set at $14.75 for the month, how many units will be sold?
The demand equation is given to be:
[tex]p=32-\sqrt{0.0001x+1}[/tex]where p is the price and x is the number of units sold.
If the price per unit is $14.75, the number of units will be calculated as follows:
[tex]\begin{gathered} p=14.75 \\ \therefore \\ 14.75=32-\sqrt{0.0001x+1} \end{gathered}[/tex]Subtracting 32 from both sides, we have:
[tex]\begin{gathered} -\sqrt{0.0001x+1}=14.75-32 \\ -\sqrt{0.0001x+1}=-17.25 \end{gathered}[/tex]Multiply both sides by -1:
[tex]\sqrt{0.0001x+1}=17.25[/tex]Square both sides:
[tex]\begin{gathered} 0.0001x+1=17.25^2 \\ 0.0001x+1=297.5625 \end{gathered}[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 0.0001x=297.5625-1 \\ 0.0001x=296.5626 \end{gathered}[/tex]Divide both sides by 0.0001:
[tex]\begin{gathered} x=\frac{296.5625}{0.0001} \\ x=2965625 \end{gathered}[/tex]The number of units sold will be 2,965,625 units.
9=4/t Math Answer 6th grade problem
9=4/t
To solve for t
multiply both-side of the equation by t
That is;
[tex]9\times t=\frac{4}{t}\times t[/tex]9t = 4
divide both-side of the equation by 9
That is;
[tex]\frac{9t}{9}\text{ =}\frac{4}{9}[/tex][tex]t=\frac{4}{9}[/tex]PLEASE HELP!!! thank you
The congruent statement for the triangle is ΔVXW ≅ ΔRPQ
What are congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .
In other words, two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.
Therefore, for the two triangles the to be congruent the corresponding sides are and the angles are equals also.
Hence,
∠V ≅ ∠R
∠W ≅ ∠Q
∠X ≅ ∠P
Therefore, ΔVXW ≅ ΔRPQ
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Suppose at 21 inches of wire cost $.84 at the same rate how much incense for 14 inches of wire cost
Step 1:
Concept:
The cost of wire varies directly to the length in inches
Step 2:
[tex]\begin{gathered} \text{If 21 inches cot \$0.84} \\ \text{Then 1 inches will cost = }\frac{0.84}{21}\text{ = 0.04 \$/inch} \end{gathered}[/tex]Final answer
14 inches will cost = 14 x 0.04 = $0.56 = 56 cents
56 cents
what is the area of a circle with the diameter of 16 cm
Answer:
201.06 square centimeters.
Explanation:
The formula for finding the area of a circle is:
[tex]\text{Area}=\pi r^2[/tex]Given that the diameter = 16 cm
[tex]\begin{gathered} \text{Radius,r}=\text{Diameter}\div2 \\ =16\div2 \\ r=8\operatorname{cm} \end{gathered}[/tex]Next, substitute r=8cm into the formula for area.
[tex]\begin{gathered} A=\pi\times8^2 \\ =64\pi \\ =201.06\operatorname{cm}^2 \end{gathered}[/tex]The area of the circle is 201.06 square centimeters.
i really really need help on this qustion
The coordinates of R are (7, -3).
What is meant by ordered pair?An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), with two values written within parentheses in a fixed order. It aids visual comprehension by locating a point on the Cartesian plane.An ordered pair's numeric values can be integers or fractions. An ordered pair is a pair of two numbers (or variables) separated by a comma and written inside brackets. (1, 2) is an ordered pair, for example.It represents a point in coordinate geometry and an element of a relation/cartesian product in set theory.Ordered pairs are also known as 2-tuples or sequences (or lists in a computer science context).Therefore,
R are (7, -3)
P are (4,-3)
Q are (4,4)
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Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD.A. 18B. 32C. 16D. 6
For the given parallelogram, the diagonals AC and BD intersect at point E. That means;
[tex]\begin{gathered} BE=DE \\ \text{Also,} \\ AE=CE \end{gathered}[/tex]Substitute for the given values and we'll have;
[tex]\begin{gathered} BE=DE \\ y+10=4y-8 \\ \text{Collect all like terms and you'll have;} \\ y-4y=-8-10 \\ -3y=-18 \end{gathered}[/tex]Divide both sides by -3 and you'll have;
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-18}{-3} \\ y=6 \end{gathered}[/tex]Note that line segment BD is made up of;
[tex]\begin{gathered} BD=BE+DE \\ BD=(y+10)+(4y-8)_{} \\ BD=y+10+4y-8 \\ BD=4y+y+10-8 \\ BD=5y+2 \\ \text{When y=6, we now have} \\ BD=5(6)+2 \\ BD=30+2 \\ \text{BD}=32 \end{gathered}[/tex]Therefore, the answer is option B
6x2−2x=0
The 1st x is to the 2nd power
Answer:
x = 0 x = 1/3
a test has 30mmultiple choice questions with 4 choices each. how many different ways can the question be answered
The answer will be [tex]4^{30}[/tex] different ways can the question be answered using permutation.
What is permutation?
A permutation is both an ordered combination and an ordered arrangement of results. For instance, 3 people are to sit in each of the 5 chairs. The first person can be seated in five different ways, the second person in four different ways, and the third person in three different ways. Accordingly, generalising this, we obtain n alternatives to fill the first chair, n-1 options to fill the second, and n-2 options to fill the third chair. As a result, nPr = n! / (n - r)! can be used to represent how many different permutations (arrangements) there are when there are r individuals and n chairs.
Each question has four choices. So, the total number of ways in which the questions can be attempted is [tex]4^{30}[/tex]
Hence the number of ways the question be answered is [tex]4^{30}[/tex].
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a coffee machine can be adjuste4d to deliver any fixed numer of ounces of coffee. if the machine has a standard deviation of 0.4 ounces, what should be the mean setting so that an 8 ounce cup will overflow only 0.5% of the time?
The mean μ=9 is the setting so that an 8 ounce cup will overflow when only 0.5% of the time.
A Z-score indicates how far a given value is from a standard deviation. A Z-score (standard value) is the number of standard deviations that a particular data point is above or below the mean. Standard deviation essentially reflects the amount of variability within a given data set.
The average is calculated as: From the Z-score formula:
z=(x-μ)/σ
Z-score associated with 0.5% is 0
(8μ)/0.4=0
Solving for x gives:
μ=9
For μ=9, an intermediate setting such that the 8 ounce cup overflows 0.5% of the time.
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What are the roots of 2x^2+4x+7 ? Show your work.
The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.
Define quadratic function.A quadratic function has the generic form f(x)=ax²+bx+c. A parabola, a kind of two-dimensional curve, is the graph of a quadratic function. A polynomial function of degree two in one or more variables is known in algebra as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.
Function:
2x² + 4x + 7 = 0
ax² + bx + c = 0
x = [tex]\frac{-b +-\sqrt{}b^{2}- 4ac }{2a}[/tex]
a = 2
b = 4
c = 7
Using quadratic function,
x = [tex]\frac{-4\sqrt{} 4^{2} -4(2)(7)}{2(2)}[/tex]
x = [tex]\frac{-4+-\sqrt{-40} }{4}[/tex]
So,
i = √-1
x = [tex]\frac{-4+-2i\sqrt{10} }{4}[/tex]
Simplifying,
x = -1 +-√10/2
Roots are:
x = -1 + i√10/2
x = -1 - i√10/2
The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.
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Hello! I need some assistance with this homework question for precalculus, please?HW Q27
The expression is given to be:
[tex]\log_55^{86}[/tex]Recall the rule of logarithms:
[tex]\log a^b=b\log a[/tex]Thus the expression becomes:
[tex]\log_55^{86}=86\log_55[/tex]Recall the rule:
[tex]\log_aa=1[/tex]Hence, we have the expression to be:
[tex]86\log_55=86[/tex]The answer is 86.
In a bakery, the ratio of fruit scones to cheese scones is 3:4.
a) Given that there are 24 cheese scones, how many fruit scones are there?
b)
If 6 fruit scones were sold, what would be the new ratio of fruit scones to cheese scones?
Answer:
a) 18 and b)1:2
Step-by-step explanation:
for a i divided 24 by 4 (24:4) and got 6 the i multiplied 3 by 6 and got 18. also you could do a proportion and fruit scones would be x so you have to calculate x. if you don't know how to do proportions you can ask me i can explain.
for b since i got the count was 18:24. i took away those six from 18 and got with the ratio 12:24. i divided both sides by twelve and got 1:2
Answer:
a) 18 fruit scones
b) 6:8
Step-by-step explanation:
a) The ratio is 3:4 given that there 3 fruit scones to 4 cheese scones so if there are 24 cheese scones, 24/4=6, 3*6=18 so there 18 fruit scones.
b) The ratio is 3:4 given that there 3 fruit scones to 4 cheese scones so if there are 6 fruit scones, 6/3=2, 2*4=8 so there are 8 cheese scones. The new ratio would be 6:8
Which ordered pair does NOT belong to any quadrant?
(1, 3)
(-1, -3)
(1, -3)
(0, 3)
The ordered pair (0, 3) does not lie onto any of the four quadrants.
What is the sign convention for quadrants?We know in the cartesian plane there are four quadrants.
In the first quadrant (x, y).
In the second quadrant (- x, y).
In the third quadrant (- x, - y).
In the fourth quadrant (x, - y).
Given are some ordered pairs. We know when x = 0 the point lies onto the x-axis and when y = 0 the point lies onto the x-axis.
Out of the given ordered pairs (0, 3) does not belong to any quadrant as it lies onto the y-axis only at 3.
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The average 12 ounce cola contains 33 grams of sugar. How many grams of sugar are contained in a 68 ounce bottle of soda?
Answer:
There are 55 grams of sugar in a 20-ounce bottle of soda.
Step-by-step explanation:
So if your looking for a 68 ounce bottle of soda we know there would be about 165 grams of sugar just in 60 ounces. as then you would find the amount of 8 grams of sugar.