The differentiation of the given equations is [tex]\frac{d}{dx}x^{2}=2x[/tex].
Given that, [tex]\frac{d}{dx}x^{2}[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
Differentiate using the Power Rule which states that [tex]\frac{d}{dx}x^{n}=nx^{n-1}[/tex].
1) [tex]\frac{d}{dx}x^{2}=2x[/tex]
2) [tex]\frac{d}{dx}(3x^{5})=15x^4[/tex]
3) [tex]\frac{d}{dx}(9x^{2})=18x[/tex]
4) [tex]\frac{d}{dx}(3x^{3})=9x^{2}[/tex]
5) [tex]\frac{d}{dx}(2x^{7})=14x^6[/tex]
6) [tex]\frac{d}{dx}(x^{7})=7x^6[/tex]
Therefore, the differentiation of the given equations is [tex]\frac{d}{dx}x^{2}=2x[/tex].
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PLEASE HELP IMMEDIATELY
What is the equation of the line that passes through Point (-2, 1) and has a Slope of 1.
Answer:
[tex]y=x+3[/tex]
Step-by-step explanation:
Using Point-Slope form: Y-y1=m(X-x1)
Slope(m) = 1, Point(x1,y1) = (-2,1)
y-1=1(x+2)
y=x+2+1
y=x+3
:]
(ps. Brainliest would be greatly appreciated lol)
Step-by-step explanation:
1.given gradient (slope) make formula of straight line
[tex]y = 1x + c[/tex]
2.substitute in y and x values in order to work out c
[tex]1 = 1( - 2) + c[/tex]
[tex]c = 3[/tex]
3. equation of line is
[tex]y = 1x + 3[/tex]
I messed up and didn’t show this for my last question, so sorry on my part.
Evaluate the function for the following values
f(-2)=
f(0)=
f(3)=
Answer:
1 , 7 , 7
Step-by-step explanation:
to evaluate f(- 2) means what is the value of y when x = - 2
locate x = - 2 on the x- axis , go vertically up to meet the graph at (- 2, 1)
f(- 2) = 1
similarly
f(0)
locate x = 0 , at the origin, go vertically up to meet the graph at (0, 7 )
f(0) = 7
f(3)
locate x = 3 on the x- axis , go vertically up to meet the graph at (3, 7 )
f(3) = 7
Wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.
The domain of the given question is; 20 to 25.
If she is paid $9 per hour, the range is; $180 to $225.
How to find the domain and range?The independent quantity is defined as the quantity that causes a change in the dependent quantity.
Now, In this question, the defined quantities are hours worked and weekly pay. Applying the concept of independent and dependent quality, the number of hours she works causes her weekly pay to change. This means that hours worked is the independent quantity and weekly pay is the dependent quantity.
We are told that she plans to work between 20 and 25 hours. This means that;
The domain is 20 to 25.
Now, as she is paid $9 per hour, this makes the range;
9(20) = $180 to 9(25) = $225.
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Juniper has a monthly budget that breaks down as follows 40% for rent 15% for food 18% free utilities 15% for savings for person for entertainment and 8% for personal items juniper has a net income of 3,250 each month calculate the amount of money that juniper has each month for rent
Juniper spends $1300 out of the monthly income of $3250 on rent
Total income of Juniper = 3250 each month
Income is the money that an individual or organization receives in return for their services or goods. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.
Percentage of expenditure on rent = 40%
Percentage of expenditure on food = 15%
Percentage of expenditure on utilities = 18%
The percentage for savings = 15%
Percentage of expenditure for personal items = 8%
Money Juniper spends on rent each month out of total income:
= Income per month*40%
3250*40%
= $1300
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Calculate the height of a pyramid if the volume is 168 cm³ and the area of the base in 36 cm².
V
=
Bh, V = volume, B = area of the base, h = height
The volume of a pyramid is v = 1/3base area × height
height = 3volume/ base area
height = 3×168cm^3/ 36cm^2
height = 14cm
What is a pyramid?A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles which are called lateral faces. The number of lateral faces equals the number of sides on its base.
The volume of a pyramid is given by
v= 1/3base area × height
= 3×168 = 36h
therefore the height =3x168/36
= 14cm
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Alex is fourteen years old and he is also nine years older than his sister Kristen. How old is Kristen?
Answer:
5
Step-by-step explanation:
If Alex is 14 and he's 9 years older than his sister Kristen,then Kristen is 5
14-9=5
Answer:
14-9 = 5, so Kristen is 5 years old
Please help. See picture attached.
The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.
A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.
t = 1/2ah + 1/2bh
Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.
t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h
A ring is now reduced to £840.
This is a saving of 40% of the original price.
b) Work out the original price of the ring.
Answer:
The original price was $864
Step-by-step explanation:
if the ring is now $840 $40 u do $40 - %40 = %24
$24 + $840 = $864
Orlando makes a trail mix for his hiking trip. He uses 1 \frac{5}{6}1 6 5 pounds of cashews, 1.6 pounds of sunflower seeds, 1 \frac{1}{8}1 8 1 pounds of raisins, and 1.625 pounds of pecans. Which answer choice shows these weights in order from least to greatest ? DUE TODAY NEED NOW WILL GIVE BRAINLIEST PART OF TEST REALLY NEED
An answer choice shows these weights in order from least to greatest is:
1 1/8 pounds of raisins.1.6 pounds of sunflower seeds.1.625 pounds of pecans.1 5/6 pounds of cashews.What is a numerical data?A numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
In order to arrange the given numerical data (weights) in order from least to greatest, we would convert the fractions into a decimal number as follows:
1 5/6 pounds of cashews = 11/6 = 1.8333 pounds.1.6 pounds of sunflower seeds = 1.6 pounds.1 1/8 pounds of raisins = 9/8 = 1.125 pounds.1.625 pounds of pecans = 1.625 pounds.Now, we can arrange the numerical data in order from least to greatest based on the weight of each item:
1.125 pounds = 1 1/8 pounds of raisins.1.6 pounds = 1.6 pounds of sunflower seeds.1.625 pounds = 1.625 pounds of pecans.1.8333 pounds = 1 5/6 pounds of cashews.Read more on greatest numbers here: brainly.com/question/24654699
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About 30% of people age 50 to 60 suffer from mild depression. A researcher is interested in determining if a vitamin d supplement will increase or decrease the proportion of people that have mild depression. The researcher randomly selects 500 people between the ages of 50 and 60 and ask them to take a vitamin d supplement for 6 months. At the end of the six months, the participants are asked to complete a survey. A psychologist then classifies each participant as either depressed or not. The psychologist classifies 158 people as depressed. Is the proportion of people that are classified as depressed different from 0. 30? what is the null and alternative hypothesis?.
The null and alternative hypothesis is H₀ : p = 0.30 and Hₐ : p ≠ 0.30 respectively.
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.
One of the ideas put out in the hypothesis test is the alternate hypothesis.
Mild depression affects about 30% of adults in the 50 to 60 age range.
500 people between the ages of 50 and 60 are chosen at random by the researcher, and they are instructed to take a vitamin D pill for six months.
The psychologist classifies 158 people as depressed.
The null hypothesis will be:
H₀ : p = 0.30 and;
The alternative hypothesis is,
Hₐ : p ≠ 0.30
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How many solutions does this equation have?
–4k − 13 = 19 − 8k + 20
Answer: k = 13
Step-by-step explanation:
PLEASE HELP ME THANK YOU
The area of half circle is 14.13 sq.unit
The total area of the figure is 86.13 sq.unit
Given,
The figure is combined by a triangle, rectangle and a half circle.
The area of triangle = 18 sq.units
The area of rectangle = 54 sq.units
We have to find the area of half circle to get the total area of the figure;
Here,
Area of circle = π r²
Then,
Area of half circle = π r² / 2
Here,
r = 6/2 = 3 units
Now,
Area = π r² / 2 = π × 3² / 2 = 28.27/2 = 14.13 sq.units
That is,
The area of half circle is 14.13 sq.unit
Then,
The total area of figure = Area of [triangle + rectangle + half circle]
The total area of figure = 18 + 54 + 14.13 = 86.13 sq.units
Therefore,
The total area of the figure is 86.13 sq.unit
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the table show the total cost to be a member of the gym for different numbers of months.number of months. total costs3. $53.976. $77.9412. $125.88create a function that gives the total cost C,in dollars to be a member of the gym given the number of months M of member ship.
The table shows the total cost to be a member of the gym for different numbers of months.
Number of months. total costs
3. $53.97
6. $77.94
12. $125.88
Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.
_____________________________________
Total cost = M* (factor per month ) + b
_____________________________________
The expression for a linear equation is
*The slope-intercept form.
y = mx + b
m= (y2-y1)/ (x2-x1) (I)
y-intercept is (0, b)
*and the point-slope form
y- y1 = m(x-x1) (II)
________________________
Point 1 (3, 53.97)
Point 2 (12, 125.88)
Replacing in (II)
The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99
y - 53.97 = 7.99* (x- 3)
y = 7.99 x - 7.99* 3 + 53.97
y = 7.99x + 30
____________________
Verifying
y = 7.99x + 30
x= 3
y = 7.99*3 + 30
y= 53.97
x= 6
y = 7.99*6 + 30
y= 77.94
x= 12
y = 7.99*12 + 30
y= 125.88
_________________________
Answer
The linear function is y = 7.99x + 30
PLEASE HELP I LITERALLY HAVE 10 MINUTES!! 40 POINTSSS
The graph that matches the data on the table, representing the altitude and time of a hawk is the straight line graph in the second option.
What is a straight line graph?A straight line graph is the graph of a linear function or relationship
From the he values in the given, we have;
The difference between the consecutive altitude values (the first difference) = 70 - 80 = 60 - 70 = 50 - 60 = -10 is constant
The difference between consecutive time values = 1
Therefore;
The relationship is a linear relationship and the graph is a straight line.
Slope of the graph = -10/1 = -10
The equation in point and slope form is therefore;
(y - 80) = (-10) × (x - 1) = -10•x + 10
(y - 80) = -10•x + 10
y = 80 + 10 - 10•x = 90 - 10•x
y = 90 - 10•x
The y–intercept = 90
The slope = -10
The correct option is therefore the second graph that has the altitude (ft) on the the vertical axis and the time (s) on the horizontal axis, with a straight line decreasing from left to right starting at the point (0, 90) on the left
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I need help so I get good grades
Answer: 9
Step-by-step explanation:
I am assuming that the grid units equal 1 inch.
We have to solve for x. For the width,
60 = 20/3 x
To divide by a fraction is to multiply by its reciprocal.
x = 60 * 3/20 = 180/20 = 9
Samuel was preparing for the triathlon. He did 3 activities every morning: ran for 30 minutes, covering 4.5 miles swam for 20 minutes, covering 2 3 mi biked for 45 minutes, covering 9 miles What was Samuel's average speed during his morning training?
Samuel's average speed during his morning training is 0.41 miles/minute.
Here we have to find the average speed of Samuel. We can solve this problem by following a few steps.
According to the problem, Samuel was preparing for the triathlon. He did 3 activities every morning; ran for 30 minutes, covered 4.5 miles; swam for 20 minutes, covered 2.3 miles biked for 45 minutes, and covered 9 miles.
We have to recall the formula of average speed as,
average speed = total covered distance/ total time
The total distance which has been covered is,
4.5 miles by running,2.3 miles by swimming,9 miles by biking.The total covered distance is, ( 4.5 + 2.3 + 9 ) = 36.5 miles.
The total time which has been spent is,
30 minutes for running,20 minutes for swimming,45 minutes for biking.The total spent time is, (30+ 20+ 40) = 90 minutes.
Now, we can easily calculate the average speed. Which is (36.5/90) = .41 miles/minute.
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What equation could be used to solve the problem below?
If three times a number is increased by 24, the result is 4 less than seven times the number.
solve. 2-6: MathXL for School: Practice & Problem Solving (Grade 8 Pre-Algebra)
The area of the rectangle is [tex]b^2[/tex] +9b square feet
The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees
The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..
The length of the rectangle = (5/3)b+15 feet
The width of the rectangle = (3/5)b feet
The area of the rectangle = The length of the rectangle × The width of the rectangle
Substitute the values in the equation
The area of the rectangle = [(5/3)b+15] ×(3/5)b
Apply the distributive property in the equation
[(5/3)b+15] ×(3/5)b = [tex]b^2[/tex] +9b square feet
Hence, the area of the rectangle is [tex]b^2[/tex] +9b square feet
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which of these expressions are equal to 3/5×6?Explain why the others aren't equal to this expression.3×(6÷5)3÷(5×6)(3×6)÷53×6/5
Answer:
(3×6)÷5
Step-by-step explanation:
We are given the following expression:
(3/5)*6
The 6 can also be written as a fraction(6/1).
So we have a multiplication of fractions, is which we multiply the numerators and denominators.
So
(3*6)/5
The fraction sign means division
So the answer is:
(3×6)÷5
The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator. PLEASE HELP ASAP
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
x^2+x^2=16
x^2=8
x= 2sqrt2
:]
I l over here and I have no idea
Mr majors ordered 6 boxes of candy and a bucket of pop corn at the concession stand. if the pop corn was $3.20 and the total was $18.20, what was the price of one candy box
The price of one candy box was $2.50 if the popcorn were of $3.20 and the total amount was $18.20.
The price of one candy box can be determined using an algebraic expression. An algebraic expression can be defined as one that consists of both numbers and letters.
As he ordered 6 boxes of candy and a bucket of popcorn and the popcorn was of $3.20 and the total was $18.20, an algebraic expression can be given as;
6(x) + 3.20 = 18.20
Here x is the price of one candy box
Solving for x;
6x = 18.20 - 3.20
6x = 15
x = 15 / 6
x = 2.50
Hence the price of one candy box is calculated to be $2.50.
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Aaden has a bag that contains strawberry chews, apple chews, and watermelon
chews. He performs an experiment. Aaden randomly removes a chew from the bag,
records the result, and returns the chew to the bag. Aaden performs the experiment
31 times. The results are shown below:
A strawberry chew was selected 4 times.
A apple chew was selected 7 times.
A watermelon chew was selected 20 times.
Based on these results, express the probability that the next chew Aaden removes
from the bag will be a flavor other than apple as a fraction in simplest form.
The probability that the next chew Aaden removes from the bag will be a flavor other than apple is 24/31.
What is Probability?Probability is a branch of mathematics concerned with determining the likelihood of an event occurring. Probability assesses the likelihood of an event occurring and is equal to the number of favorable events divided by the total number of events.
Given:
Number of times Aaden performs the experiment = 31 times
A strawberry chew was selected 4 times.
An apple chew was selected 7 times.
A watermelon chew was selected 20 times.
So,
Probability of selecting a strawberry chew = 4/31
Probability of selecting an apple chew = 7/31
Probability of selecting a watermelon chew = 20/31
So, the probability that the next chew Aaden removes from the bag will be a flavor other than apple i.e. it can be strawberry or watermelon chew.
Probability of selecting a strawberry chew + Probability of selecting a watermelon chew
= 4/31 + 20/31 = 24/31
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Answer:
24/31
Step-by-step explanation:
Based on these results, express the probability that the next chew Aaden removes from the bag will be a flavor other than apple as a fraction in simplest form.
The experiment occurred 31 times, a flavor other than apple was selected 4+20=24 times. Probability the next chew will be a flavor other than apple:
24/31
=
The probability as a fraction in simplest form is
24/31
"Every angle subtended at the circumference of a semicircle by the diameter is a roght angle." Which other circle theorem proves this?
The angle subtended by an arc is twice the angle it subtends.
The angle is 90 degrees.
What is diameter of circle?
diameter is circle is twice the radius of circle.
The theorem to solve the given statement is :
The angle subtended by an arc is twice the angle it subtends.
let suppose, O be the center of circle,
The diameter AB forms on the circle and point P on the periphery of circle ,
so we have:
To prove : ∠APB=90°
We know that angle subtended by an arc at center is double the angle subtended at any point or circumference.
that is:
Angle subtended by arc AB at O = Double the angle subtended at P
⇒∠AOB=2∠APB
∵AOB is a straight line.
∠AOB=180°
2∠APB=180°
∠APB=90°
Angle formed by arc AB or semi circle is 90°
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Find x 109° x 31° 35°
No need to help anymore. I figured out the answer.
The value of x is 43.
As per the property of exterior angles, the exterior angle is equal to sum of opposite interior angles. Also, the rightmost interior angle of triangle will be 35°. This will be according to the property that opposite angles are equal. Now, forming the equation for sum of exterior angles.
109 = x + 31 + 35
Performing addition on Right Hand Side of the equation
109 = x + 66
Rearranging the equation
x = 109 - 66
Performing subtraction on Right Hand Side of the equation
x = 43
Therefore, as per the angles of triangle, the value of x is 43.
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Answer the questions below to find the total surface area of the can..
The total surface area of the cylinder is equal to 117.8 in^2
Total Surface Area of Cylinder
The total surface area of a cylinder can be calculated using the formula
[tex]TSA = 2\pi rh + 2\pi r^2[/tex]
h = height of cylinderr = radius of cylinderLet's substitute the values and proceed to solve.
[tex]TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2[/tex]
The total surface area of the cylinder is 117.8 squared inch.
The area of each circle is
[tex]A = \pi r^2 \\A = 19.6in^2[/tex]
And there are two identical circle in the diagram and this will have a total area of
[tex]A = 2 * 19.6\\A = 39.2in^2[/tex]
The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2
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Name a pair or vertical angles.
Answer:
There are two pairs:
1 and 3
2 and 4
Step-by-step explanation:
Verticle angles are angles opposite to each other when two lines intersect.
Write (9m) to the power of 4 without exponents.
6561m⁴ is the value of the expression (9m)⁴ without applying the exponent property.
What is an exponent?
The type of mathematical shorthand known as exponential notation enables us to write complex expressions more concisely. The base, which can be either a number or letter, is an exponent. It implies that the base is to be raised to a specific level of power. While n is the power, X is the base.
The expression is (9m)⁴.
The value of the expression (9m)⁴ without applying the property of the exponent will be
→ 9m × 9m × 9m × 9m
(we've simply expanded (9m)⁴ )
which on further simplifying gives,
→ 6561m⁴
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(02.05 MC)
Given f(x) and g(x) = f(kx), use the graph to determine the value of k.
-3
-1/3
1/3
3
Using the graph obtained value of k is 1/3. Option C is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that
f(x) and g(x) = f(k-x),
The standard equation of a line is,
y = mx + b
The slope of the line for the coordinate points are (1, 2) and (1.5, 5)
m = 5-2/1.5-1
m = 3/0.5
m = 6
The y-intercept of the line is,
2 = 6(1) + b
2 - 6 = b
b = -4
As a result the obtained equation is g(x) = 6x - 4
For the other coordinate point (3, 2) and (2, 0), the slope is
m = 0-2/2-3
m = -2/-1
m = 2
The y-intercept of the line is,
2 = 2(3) + b
2 - 6 = b
b = -4
As a result the obtained equation will be f(x) = 2x - 4.
Substitute xk at the place of x in the function as
f(xk) = 2(xk)- 4
If g(x) to f(k⋅x)
6x + 4 = 2(xk)- 4
6x = 2xk
6 = 2k
k = 1/3
Thus, using the graph obtained value of k is 1/3. Option C is correct.
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a triangle with a base of 6cm has an area of 30cm squared. What is its perpendicular height?
The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.
1/2(6)h = 30
3h = 30
Isolate h.
3h/3 = 30/3
h = 10
PLEASE HELP DUE IN A FEW MINUTES! THANK YOU!!
Step-by-step explanation:
5 - (-7) = 5 + 7
because 2 negatives added together make positive.
Answer:
+ 7
Step-by-step explanation:
the rule of signs for addition/ subtraction
a + (- b ) = a - b
a + (+ b) = a + b
a - (+ b) = a - b
a - (- b) = a + b
Then
5 - (- 7 ) = 5 + 7