The rate at which the area of this square increases when the area of the square is 9 cm is 24 cm²/s.
What is rate of change?The rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
How to calculate the area of a square?Mathematically, the area of a square can be calculated by using this formula;
A = s²
Where:
A represents the area of a square.s represents the side length of a square.Next, we would determine the side length of a square by making s the subject of formula as follows:
A = s²
s = √A
s = √9
s = 3 cm.
By applying chain rule of differentiation, the rate of change (da/dt) in area of this square with respect to time is given by:
dA/dt = 2 × s(t) × ds/dt
dA/dt = 2 × 3 × 4
dA/dt = 24 cm²/s.
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Jon earns $13.75 per hour at his landscaping job. if the hours he works is represented by the variable h, then which equation below could be solved to find out how many hours he must work to earn $50.(1) h/13.75 = 50/1. (3) 50h = 13.75(2) h + 13.75 = 50. (4) 13.75h=50
13.75h = 50 This is the answer
I think it euqation 4
There are 16 triangles and 12 squares. What is the simplest ratio of squares to triangles?
Answer: 3:4
Step-by-step explanation:
Which angle is congruent
Answer:
they can be acute, obtuse, exterior, or interior angles
Step-by-step explanation:
Congruent angles are two or more angles that are identical to each other. the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
Factor p(x) into linear factor
The two other linear factors of the polynomial when it is given that k = -1 is a zero of the given polynomial are (x+1)(x-4)
In the above question, A cubic polynomial is given as follows
P(x) = [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 7x - 4
K = -1
We need to find the, linear factors of the polynomial when it is given that k = -1 is a zero of the given polynomial
So, we got that ( x +1 ) is a one linear factor of P(x). As the highest degree of the polynomial is 3 so there will be three zeroes of the given polynomial. Therefore, We need to find others two
If we divide P(x) = [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 7x - 4 by ( x + 1 ) by long division method we'll get, [tex]x^{2}[/tex] -3x - 4
Now we'll solve the quotient by squaring method, to get the other two
Let's say h(x) = [tex]x^{2}[/tex] -3x - 4
h(x) = [tex]x^{2}[/tex] -3x - 4
h(x) = [tex]x^{2}[/tex] -( 4 -1) x - 4
h(x) = [tex]x^{2}[/tex] -4x + x - 4
h(x) = x( x-4) + 1( x -4 )
h(x) = (x+1)(x-4)
Therefore, the two other linear factors of the polynomial when it is given that k = -1 is a zero of the given polynomial are (x+1)(x-4)
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The quotient of b and 5 is -30.
[tex]b \div 5 = - 30 \\ \frac{b}{5} = - 30[/tex]
I CONVERTED b÷5 SO THAT I CAN USE CROSS MULTIPLICATION
[tex]b = - 30(5) \\ b = - 150[/tex]
b is -150
HOPE THIS HELPS.
HELP PLEASE URGENT I ONLY HAVE 30MINS PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE
Using the properties of parallel lines we find the value of x is 9 and the value of y is 13.
In geometry, parallel lines are coplanar, straight lines that never intersect.
Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect. If a line and a plane in three-dimensional Euclidean space do not intersect at a point, they are also said to be parallel. On the other hand, skew lines are two noncoplanar lines. A transversal is a line that crosses across two other lines in the same plane at two separate points. Transversals play a crucial role in establishing if two or more other lines in the Euclidean plane are parallel.15). In the given figure the two angles represented by 12x+1 and 15x -26 are equal. as they are alternate exterior angles.
We know from the property of parallel lines that they are equal.
Therefore:
12x+1 = 15x -26
or, 12x-15x = -26-1
or, -3x = -27
or, x = 9
Therefore the angles are 12x + 1 = 109
Now,
109 + 4y-9 +28 =180
or, 4y = 180 - 128
or, y = 13.
Therefore as the line l and m are parallel the value of x is 9 and the value of y is 13 .
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The grocery store is having a sale on frozen vegetables. 4 bags are being sold for
$11.96. At this rate, what is the cost of:
9 bags
Answer: $98.67
Step-by-step explanation:
Answer:
$26.91
Step-by-step explanation:
11.96 divided 4 = 2.99
2.99 x 9 = $26.91
Are all of these choices correct?
Answer:
Yep! Got it alllllll right.
Using the value 22/7 for π, Calculate the area of a flat ring whose inside and outside diameters are 4cm and 10cm respectively
The area of a flat ring whose inside and outside diameters are 4cm and 10cm is 66cm²
What is the area of the circle?The region encircled by a circle with radius r is known as πr² in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.
Circular ring's inner diameter (d) is equal to 4 cm.
Circular ring's inner radius (r) is 2 cm.
The circumference of the ring (D) is 10 cm.
Circular ring's (R) outer radius is 5 cm.
To locate
the circumference of the ring.
Solution:
The following formula can be used to calculate the area of a circular ring whose inner and outer diameters are given:
Area of a circle equals (R2 - r2).
= 22(5^2-2^2) / 7
= 66cm²
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Find the formula round your answer to two decimal places if necessary
Explanation
Give that
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ \\ g(x)=\frac{x+1}{3} \end{gathered}[/tex]To get the value of
[tex](fog)(x)[/tex]we will have
[tex](f\text{ o g})(x)=f\left(\frac{x+1}{3}\right)=\frac{3}{x+1}[/tex]The value (f o g) (x) is
[tex]\left(fog\right)x=\frac{3}{x+1}[/tex][tex]The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values\:for\:which\:the\:function\:is\:real\:and\:defined[/tex]The graph is
Thus, the Domain is
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\quad \mathrm{or}\quad \:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\cup \left(-1,\:\infty \:\right)\end{bmatrix}[/tex]H-E-B buys cases of almonds and walnuts. Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case. H-E-B orders no more than 200 bags of almonds and walnuts at a time. H-E-B pays $24 per case of almonds and $27 per case of walnuts, but will not order more than $300 total at any one time. H-E-B makes a profit of $8 per case on almonds and $9 per case on walnuts.a)Express the constraints in terms of x and y, where x is case of almonds and y is case of walnuts.b)Graph and find the feasible region, identify the vertices.c)Find the Objective Functiond)Using the objective function and the vertices of the feasible region, determine how many cases of almonds and how many cases of walnuts H-E-B should sell to maximize its profit.
x is case of almonds and y is case of walnuts.
Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.
H-E-B orders no more than 200 bags of almonds and walnuts at a time.
So,
x + y < 200
where x and y refers to the number of bags
=======================================================
H-E-B pays $24 per case of almonds and $27 per case of walnuts, but will not order more than $300 total at any one time.
But keep in mind that : Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.
So,
24 * (x/15) + 27 * (y/17) < 300
===========================================================
The constraints are:
x + y < 200
(24/15) x + (27/17) y < 300
So, the graph of the previous constraints is as following :
An object is dropped from a height of 144 feet off the ground. The height
h
of the object after
t
seconds can be found using the function
h
(
t
)
=
144
−
16
t
2
When will the height be 128 feet?
seconds
When will the object reach the ground?
seconds
Answer:
The height will reach 128 feet after 1 second.
The object will reach the ground after 3 seconds.
Step-by-step explanation:
Plug in the height into the equation: h(t)=144-16t^2
Solve for t.
Ex:
128=144-16t^2, subtract 144 on both sides
-16=-16t^2, divide -16 on both sides
1=t^2, find the square root of both sides
1=t
Sam borrowed money from a credit union for 3 years and was charged simple interest at an annual rate of 2%. The total interest that he paid was $48. How much money did he borrow?
show step by step
Answer:
the amount of money sam has borrowed was 2400
he paid interest 2%
total intreast 48$
48÷3 = $16 a year
2%= $16
16×5= $80 for 10%
$80× 10= 800
800×3= 2400 total amount was borrowed
so 2400-2%= 2352
2400- 2352= 48
which graph best represents the equation y=x-1i’ll send the other photo :)
The given equation is
[tex]y=x-1[/tex]This equation belongs to an uptrend line because the variable x is positive. The line has to have a y-intercept at -1 because that's the constant term.
Following the characteristics of the equation, we can deduct that the correct graph is A.
help it’ll be greatly appreciated:(
The complete table of the algae area is:
Day 1 2 3 4 5 6
Area 1/2 1 2 4 8 16
What is meant by an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
The initial area exists given as;
A(1) = 1/2 square meters
When it doubles every day, we have:
A(n) = 2 × A(n - 1) where A(1) = 2
So, we contain the following values
A(2) = 1/2 × 2 = 1
A(3) = 1 × 2 = 2
A(4) = 2 × 2 = 4
A(5) = 4 × 2 = 8
A(6) = 8 × 2 = 16
Therefore, the complete table is:
Day 1 2 3 4 5 6
Area 1/2 1 2 4 8 16
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Select ALL the correct answers. Consider the graph given below. A diagonal curve declines from (negative 2, 10), (0, 6), (1, 4), (2, 2), (3, 0), (4, negative 2), (5, negative 4), (6, negative 6), (7, negative 8),and (8, negative 10) on an x y coordinate plane. Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2
The sequence of transformations needed to transform the parent function f(x) into the linear function g(x) = 6 - 2x is given as follows:
Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units.Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units.Linear function and transformationA linear function is defined according to the following rule:
y = mx + b.
In which:
m is the slope of the function, which is by how much y changes by when x changes by 1.b is the intercept of the function, which is the value of y when x = 0.From the stated graph, we have that when x = 0 and y = 6, and when x increases by 1, y decays by 2, hence the function is defined as follows:
y = -2x + 6.
The parent function is:
f(x) = x.
Then, to generate the transformed function, we have that:
x -> -x, hence the function was reflected over any of the axis.-x -> -2x, hence there was a vertical stretch by a factor of 2.-2x -> -2x + 6, meaning that the function was shifted up 6 units.Using these three bullet points, the correct options were chosen.
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Answer:
Your welcome
Step-by-step explanation:
patterns in proportional relationships, need help with the graph and the process table, i need to find a algebraic rule that represents the relationship between the number of pizzas, x, and the total cost, y.
Since the cost of each medium pizza is $7, then
Assume that the number of pizzas is x and the total cost is y, then
Multiply x by x to find y
The algebraic rule is
[tex]y=7x[/tex]a) Let us complete the table
x: Process: y
0 0 x 7 = 0 0
1 1 x 7 = 7 7
2 2 x 7 = 14 14
3 3 x 7 = 21 21
4 4 x 7 = 28 28
a) We need to find the cost of 10 pizzas, then
Substitute x by 10 in the algebraic rule
[tex]\begin{gathered} y=7(10) \\ y=70 \end{gathered}[/tex]The cost of the 10 pizzas is $70
b) If you have exactly $84, then substitute y by 84 to find x
[tex]\begin{gathered} y=84 \\ 84=7x \end{gathered}[/tex]Divide both sides by 7 to find x
[tex]\begin{gathered} \frac{84}{7}=\frac{7x}{7} \\ 12=x \end{gathered}[/tex]You can buy 12 pizzas buy $84
c) If you buy 0 pizza, then the cost of it is
[tex]\begin{gathered} x=0 \\ y=7(0) \\ y=0 \end{gathered}[/tex]Since zero multiplied by any number give zero
The cost of zero pizza is zero
Because 0 x $7 = $0
Given a pair of points on each line, use the slope formula to determine whether AB and CD are parallel. perpendicular, or neither. AB: A(-2,-5) and B(4.7) CD: C(0, 2) and D(8,-2)
Answer:
Perpendicular
Explanation:
Given the coordinates
A(-2,-5), B(4.7) C(0, 2) and D(8,-2), we are to determine whether AB is parallel, perpendicular to CD or neither
To do this, we need to find he slope of AB and CD first. Using the formula for calculating slope as shown;
m = y2-y1/x2-x1
For AB:
slope = 7-(-5)/4-(-2)
Slope = 7+5/4+2
Slope of AB = 12/6
Slope of AB = 2
For CD
Slope of CD = -2-2/8-0
Slope of CD = -4/8
Slope of CD = -1/2
Note that for AB to be perpendicular to CD, the product of their slope must be -1.
Given
mAB = 2
mCD = -1/2
Taking their product
mAB * mCD = 2 * -1/2
mAB * mCD = -1
Since the product is -1, hence AB is PERPENDICULAR to CD
Graph the equation of a line y= X/6 -3
Solution
To graph the line y = x/6 - 3,
Since the y-intercept is -3
This picture should be of help
weiyr the coordinates of the two points on the line then find the slope
ANSWER:
two points are (3,4) and (3,0)
the slope is undefined or indeterminate
SOLUTION:
since the denominator of the slope (change in x) is 0, the slope, change in y over change in x is indeterminate
The difference of a number and 9 is fewer than 4
Answer:
x-9<4
a number=x
difference = -
9=9
x-9
fewer than - < 4
x-9<4
Solve by substitution.2x + y = -9(3x + 5y = 4([?],[])
The given system is
[tex]\mleft\{\begin{aligned}2x+y=-9 \\ 3x+5y=4\end{aligned}\mright.[/tex]Let's isolate y in the first equation.
[tex]\begin{gathered} 2x+y=-9 \\ y=-9-2x \end{gathered}[/tex]Then, we replace the equation we've got in the second equation of the system.
[tex]3x+5(-9-2x)=4[/tex]Now, we solve for x.
[tex]\begin{gathered} 3x-45-10x=4 \\ -7x=4+45 \\ -7x=49 \\ x=\frac{49}{-7} \\ x=-7 \end{gathered}[/tex]We use this value to find y.
[tex]\begin{gathered} y=-9-2(-7) \\ y=-9+14 \\ y=5 \end{gathered}[/tex]Therefore, the solutions are x = -7 and y = 5.Find the equation for the line through points (2,0) and (8,4) use y=Mx+b
Explanation:
To find the equation with the form y = mx + b, we can use the following equation:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and it is ca
Find the measures of the sides of the sides of triangle JKL then classify it by its sides if J(-7, -7), K(-9 1), L(-1, -1)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ J(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-7})\qquad K(\stackrel{x_2}{-9}~,~\stackrel{y_2}{1}) ~\hfill JK=\sqrt{(~~ -9- (-7)~~)^2 + (~~ 1- (-7)~~)^2} \\\\\\ ~\hfill JK=\sqrt{( -2)^2 + ( 8)^2} \implies \boxed{JK=\sqrt{ 68 }}[/tex]
[tex]K(\stackrel{x_1}{-9}~,~\stackrel{y_1}{1})\qquad L(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill KL=\sqrt{(~~ -1- (-9)~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill KL=\sqrt{( 8)^2 + ( -2)^2} \implies \boxed{KL=\sqrt{ 68 }} \\\\\\ L(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad J(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-7}) ~\hfill LJ=\sqrt{(~~ -7- (-1)~~)^2 + (~~ -7- (-1)~~)^2} \\\\\\ ~\hfill LJ=\sqrt{( -6)^2 + (-6)^2} \implies \boxed{LJ=\sqrt{ 72 }}[/tex]
well, let's notice, the triangle has two sides that are twins, JK and KL, that means is an isosceles, and isosceles triangle is a triangle with twin sides.
What is the exact circumference of a
circle with diameter 48 millimeters?
The circumference of circle is 150.72 millimetres.
In simpler terms, circumference in the perimeter of circle. Thus, it will represent the measure of length of the line of circle. The relationship between circumference of circle and it's diameter will be represented as formula -
C = πd, where C is circumference and d is diameter.
Keep the value of diameter in the formula to find the exact circumference of the circle.
Circumference = 3.14×48
Performing multiplication to find the circumference of the circle
Circumference = 150.72 millimetres.
Therefore, the circumference of the circle with 48 millimetres diameter is 150.72 millimetres.
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A political gathering in South America was attended by 8,475 people. Each of South America's 12 countries and 3 territories was equally represented. How many representatives attended from each country?
There were 707 representatives who attended political gatherings from each country in South America.
We have been given that a political gathering in South America was attended by 8,475 people.
Each of South America's 12 countries and 3 territories were equally represented.
The number of representatives attended from each country is the ratio of the total number of people in the gathering to the total number of countries.
The number of representatives :
⇒ total number of people in the gathering / total number of countries
The number of representatives = 8,475 / 12
The number of representatives = 706.25 ≈ 707
Hence, there were 707 representatives who attended political gatherings from each country.
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Solve the equation for x, accurate to three decimal places: e4x − e2x = 12.x = 1.280x = 1.866x = 0.549x = 0.693
Given:
[tex]e^{4x}-e^{2x}=12[/tex]To Determine: The value of x
Solution
[tex]\begin{gathered} e^{4x}-e^{2x}=12 \\ (e^x)^4-(e^x)^2=12 \end{gathered}[/tex][tex]\begin{gathered} let:a=e^x \\ Therefore, \\ (e^x)^4-(e^x)^2=12 \\ a^4-a^2=12 \\ a^4-a^2-12=0 \end{gathered}[/tex]Solve the derived equation by factorizing completing
[tex]\begin{gathered} a^4-a^2-12=0 \\ a^4-4a^2+3a^2-12=0 \\ a^2(a^2-4)+3(a^2-4)=0 \\ (a^2-4)(a^2+3)=0 \\ a^2-4=0,or,a^2+3=0 \end{gathered}[/tex][tex]\begin{gathered} a^2-4=0 \\ a^2-2^2=0 \\ diiference\text{ of two square is expanded as} \\ a^2-b^2=(a-b)(a+b) \\ Therefore \\ a^2-2^2=0 \\ (a-2)(a+2)=0 \\ a-2=0,or,a+2=0 \\ a=2,a=-2 \end{gathered}[/tex][tex]\begin{gathered} Also,a^2+3=0 \\ a^2=-3(No\text{ solution because square root of a negative number is an imaginary number\rparen} \end{gathered}[/tex]Therefore
[tex]a=2,or,a=-2[/tex][tex]\begin{gathered} e^x=a \\ e^x=2,or,e^x=-2(no\text{ solution\rparen} \\ x=ln2 \\ x=0.693 \end{gathered}[/tex]Hence, the value of x is 0.693
What is the relationship between 7.0/10^2 and 7.0/10^3
[tex]7/10^2[/tex] is ten times [tex]7/10^3[/tex] or [tex]7/10^3[/tex] is one-tenth of [tex]7/10^2[/tex].
[tex]10^2[/tex] and [tex]10^3[/tex] are written in the exponent form.
Exponent
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
We are given two numbers [tex]7/10^2[/tex] and [tex]7/10^3[/tex].
We have to find the relationship between the two given numbers.
We know that,
[tex]7/10^2[/tex] can be written as 7/100 and [tex]7/10^3[/tex] can be written as 7/1000.
We can write,
7/1000 = (7/100) *(1/10)
Hence, 7/1000 is one-tenth of 7/100.
Also, we can write,
7/100 = (7/1000)*10
Hence, 7/100 is ten times 7/1000.
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Solve 3 < 2x + 1 ≤9 I’m so confused
Answer:
1 < x ≤4
Step-by-step explanation:
3 < 2x + 1 ≤9
Solve for x
Subtract 1 from all sides
3-1 < 2x + 1-1 ≤9-1
2 < 2x ≤8
Divide by 2
2/2 < 2x/2 ≤8/2
1 < x ≤4
Find the area of the figure (Please respond I need help)
Answer: 32 unit squared
Step-by-step explanation:
To find the area you multiply the amount of unit squares on one side of the shape and multiply it by the amount of unit squares at the top of the shape.
Answer:
to find the area of a shape you want to use the formula A=wl which is area is equal to width multiplied by length.
for this exact problem you want to count the squares on one short side and one long side. when you get the two numbers you multiply them
answer is: 4x8=32hope this helped!