The measure of side OP in rectangle MNOP is 30 units.
What is dilation?Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.
Given that, rectangle MNOP is dilated by a scale factor of 1/3 to form rectangle M'N'O'P' and side O'P' measures 10, we need to find the measure of side OP.
Since, the scale factor is less than 1 therefore, the dilation is a reduction.
Therefore,
O'P' / OP = 1/3
OP = 3 × 10
OP = 30
Hence, the measure of side OP in rectangle MNOP is 30 units.
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In the example for “solving right triangles using trigonometric ratios”, students solved for a triangle given angle 0 = 48 and b = 10 using cosine and secant. Use the diagram below as a reference
using trigonometric ratios, following is the proof.
In what way may I locate trigonometric ratios?You can determine trigonometric ratios by either utilizing the provided acute angle or by figuring out the ratios of the right-angled triangle's sides. The formula for trigonometric ratios is sin = Perpendicular/Hypotenuse. base/hypotenuse = cos.
Its given that
θ = 48 , b = 10
Cos θ = b/c
Cos 48 = 10/c Equation (A)
Sec 48 = c/b
sec 48 c/10 Equation (B)
Equation (A) × Equation (B)
Cos 48 × Sec 48
10/c × c/10
1 =1
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for his birthday, bert gets a box that holds $125$ jellybeans when filled to capacity. a few weeks later, carrie gets a larger box full of jellybeans. her box is twice as high, twice as wide and twice as long as bert's. approximately, how many jellybeans did carrie get?
Carrie has 1000 jellybeans in the box.
The volume of Carrie's box is 8 times larger than the volume of Bert's box because 2 x 2 x 2 = 8. Thus, Carrie's box can hold 8 times more jellybeans than Bert's box, which means it can hold approximately 8 x 125 = 1000 jellybeans.
Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank.
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Carrie has 1000 jellybeans in the box.
The volume of Carrie's box is 8 times larger than the volume of Bert's box because 2 x 2 x 2 = 8. Thus, Carrie's box can hold 8 times more jellybeans than Bert's box, which means it can hold approximately 8 x 125 = 1000 jellybeans.
Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank.
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Write a function rule for the statement: The output is seven more than one-third of the input
The function rule for the statement "The output is seven more than one-third of the input" can be written as: y = 1/3x + 7
The pattern represented in the input/output table must be represented by the function rule when it is written from the data in the table. Start by searching for a pattern between the input and output numbers. The output numbers' values are quite similar to the input number multiplied by three.
Let x be the input, and y be the output.
As we have the statement as:
The output is seven more than one-third of the input
So, we can write the function as:
y = 1/3x + 7
This represents the relationship between the input and the output,
where the output is seven more than one-third of the input.
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what point on the line 3x-y=4 is closest to (-2,3) symnolab
Point on the line 3x-y=4 is closest to (-2,3) are:
(19/10, 51/30)
Now, According to the question:
The equation for the line in slope-intercept form:
y=3x - 4
The slope of this line is m = 3.
A line perpendicular to this line passing through point A(-2,3) has a slope m= -1/3.
The y-intercept for this perpendicular line [go down 2/3 and over 2 from A(-2,3) which is calculated from the slope to get to x-0] is
(-2,3) + (2,-2/3) = (0, [tex]2\frac{1}{3}[/tex] ), so b = 2 1/3.
The equation for this perpendicular line is
y=(-1/3)x + [tex]2\frac{1}{3}[/tex] or
x+3y=7
Solving the system of two linear equations with two unknows substituting y=3x-4 into this equation:
x+3(3x-4)=7
Solve for x:
10x-12=7
x=19/10
19/10 + 3y = 7
30y=70-19
y = 51/30
Hence, Point on the line 3x-y=4 is closest to (-2,3) are:(19/10, 51/30)
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What are all values of x for which the function f defined by f(x) = (x2 - 3)e-x is increasing?.
The function f is increasing for x > 3/2.
To determine the values of x for which the function f is increasing, we need to find the critical points of f, which are the values of x where the function changes from increasing to decreasing or vice versa.
The first step is to find the derivative of f:
f'(x) = (2x - 3)e-x
Next, we need to find the critical points by setting f'(x) = 0 and solving for x:
(2x - 3)e-x = 0
2x - 3 = 0
x = 3/2
This is the only critical point of f. To determine the behavior of f near this critical point, we need to find the second derivative of f:
f''(x) = (2 - 3e-x)
For x < 3/2, f''(x) < 0, which means f is concave down and f'(x) is decreasing. This means that f is decreasing for x < 3/2.
For x > 3/2, f''(x) > 0, which means f is concave up and f'(x) is increasing. This means that f is increasing for x > 3/2.
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A college is currently accepting students that are both in-state and out-of-state. They plan to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 200 and y > 400
0 < x and y < 200
0 < x ≤ 200 and 0 < y ≤ 400
The constraints to represent the incoming students at the college, 0 < x ≤ 200 and 0 < y ≤ 400. So Option D is correct.
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
A college is currently accepting students that are both in-state and out-of-state
They are accepting two times as many in-state students as out-of-state
They can accept only 200 out-of-state students
Suppose,
the number of in-state students = y
the number of out-of-state students = x
According to given condition,
y = 2x
They can accept only 200 out-of-state students,
So, 0 < x ≤ 200
They plan to accept two times as many in-state students as out-of-state,
So, 0 < y ≤ 400
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How do you find the intersection of the diagonals of a trapezoid?
The diagonals of these quadrilaterals are bisectors of one another, the point of intersection can be identified by locating the middle of two obliquely opposing vertices.
How do you find the point of intersection of a diagonal?Given is a trapezoid ABCD with sides that are parallel to one another. The diagonals' point of intersection is parallel to both AB and CD's midpoints.
Unlike with rhombi and squares, the diagonals of an isosceles trapezoid are not always perpendicular. Congruence exists between them, though. The two diagonals are always congruent whenever you discover an isosceles trapezoid. A trapezoid that is isosceles has congruent diagonals.
A trapezoid that is isosceles has congruent diagonals. A line connecting the middle points of the non-parallel sides of a trapezoid is called the midsegment. A trapezoid has one and only one midsegment. The fact that it is situated midway between the bases means that it will be parallel to them.
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Each of thee equation repreent the ame function written in different form. Standard Form: f(x)=x2−10x24
Factored Form: f(x)=(x−4)(x−6)
Vertex Form: f(x)=(x−5)2−1
The zero of a function are the value of x for which the function i equal to zero. Which form of the equation make it eaiet to ee the zero of the function?
The factored form makes it easiest to see the zeros of the function, as they correspond to the roots (x-intercepts) of the equation. In this form, the zeros are x=4 and x=6.
Form for Function ZerosTo find the zeros of a function from its factored form:Set each factor equal to zero:(x-4) = 0 or (x-6) = 0
Solve for x:x = 4 or x = 6
These values correspond to the x-intercepts, or zeros, of the function.
The zeros of a function are the values of x where the function intersects the x-axis, or where the value of the function is equal to zero. In a factored form, each factor is equal to zero at specific values of x. These values correspond to the x-intercepts of the function, which are the zeros.
By setting each factor equal to zero and solving for x, we find the x-intercepts of the function, which are the zeros. This is why the factored form makes it easiest to see the zeros of a function.
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What i the lope of the line that pae through the point (2, 8)(2,8) and (-3, 14)(−3,14)? Write your anwer in implet form
The slope of the line that passes through points (2, 8) and (-3, 14) is -1.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Given:
The coordinates of point = (2, 8) and (-3, 14),
Calculate the slope of the line from the formula given below,
m = (y₂ - y₁) / (x₂ - x₁)
Here m is the slope.
Substitute the values,
m = (13 - 8) / (-3 - 2)
m = −1
Therefore, the slope of the line that passes through points (2, 8) and (-3, 14) is -1.
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Your younger brother is getting stickers from a vending machine at the local supermarket. A proportion of stickers have the phrase "Girls Rule!" If there are 12 stickers with this message in a sample of 36 stickers, what is the 95% confidence interval for this proportion?
The confidence interval is (0.732, 0.318).
Total samples = E = 36
Number of outcomes = 12
Calculating the probability
= 12/36
= 0.333
The probability that a population parameter would fall between a set of values for a specified percentage of the time is described by a confidence interval. Analysts typically employ confidence intervals that cover 95% or 99% of projected observations.
Value of z for 95% confidence interval = 1.96
Interval = p ± z ( p√ 1 - p/ E)
Taking positive sign
= 0.333 + 1.96 ( 0.333√ 1 - 0.333/ 36)
= 0.318
Taking negative sign
= 0.333 - 1.96 ( 0.333√ 1 - 0.333/ 36)
= 0.732
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If b = 5.4 yards and c = 7.5 yards, what is the perimeter? If necessary, round to the nearest
tenth.
The perimeter of the triangle would be 18.1 yards.
What is Pythagorean theorem ?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Given the information in the problem, we can use the Pythagorean theorem to find the length of the other leg, a:
[tex]c^2 = a^2 + b^2\\\\7.5^2 = a^2 + 5.4^2\\\\56.25 = a^2 + 29.16\\\\56.25 - 29.16 = a^2\\\\27.09 = a^2\\\\a = \sqrt{27.09} \\\\a = 5.2\ yards[/tex]
The perimeter of the triangle is the sum of the lengths of all its sides:
Perimeter = a + b + c
Perimeter = 5.2 + 5.4 + 7.5
Perimeter = 18.1 yards (rounded to the nearest tenth)
Therefore, The perimeter of the triangle would be 18.1 yards.
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Seventy-five (75) customers at Crummy Burger today were entered in a drawing. Three names will be drawn, and each will win a prize.
Determine the number of ways that the prizes can be distributed if all 3 prizes are a $10 gift card.
Bonus**** If a pair of fair six-sided dice are tossed, what is the probability that the sum is even OR greater than 7?
The number of ways in which the prizes are allocated is 67,525.
Combinations are the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given that
Number of customers = 75
Number of prizes = 3
And, the value of the gift card = $10
Based on the above information,
The number of ways in which the prizes are allocated is shown below:
=⁷⁵C₃
=[tex]\frac{75!}{(3!*(75-3)!}[/tex]
After solving this the number of ways that came is 67,525
Hence, the number of ways in which the prizes are allocated is 67,525
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The breed. Com moondhedegas dome tetembe eggs to find the Seed Yes creo A5x4 OON 8. 9x8 Ore O No Yes No C 5 -- D8x9 O O No L-8X9 Yes No Yes No P A bookstore has 7 copies of their top selling book in their window display. The store has 10 times the amount in stock. If the store sells 17 of the books, how many books would be left in stock? Cicle the equations you can use to solve the problem. Then circle the solution 10 + 7 First, solve 2x17 - Then solve 119 - 17 - b. 7x10 70 There are 10 books left in stock 53
The answer to the question is: 10 books left in stock.The equation that used to solve this problem is 7 + 10 = x - 17.
This question can be solved by using an equation. The equation that used to solve this problem is 7 + 10 = x - 17. This equation can be solved by first multiplying both sides by 2. This will give us 2x17 = x. Then, subtract 17 from both sides, which gives us x = 119 - 17. Finally, subtract 7 from both sides to get 10 = x - 17. Therefore, the answer to the question is 10 books left in stock.
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What is the value of cos-1(1/2)
Answer: The value of cos-1(1/2) is equal to 60 degrees in degrees or π/3 radians in radians.
Step-by-step explanation:
A hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.
a. What is the volume of the cylinder?
b. What is the volume of the cone?
c. Estimate the volume of the hemisphere by calculating the average of the volumes of the cylinder and cone.
Answer:
guys i have no idea
Step-by-step explanation:
The volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, a hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.
Since, all of them are tightly packed in one another therefore, radius of all them will be equal,
And, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.
r = radius of cylinder = 8 cm and
h = height of cylinder = radius of hemisphere = 8 cm
We know that,
Volume of a cylinder = π × radius² × height
Volume of a cone = 1/3 × π × radius² × height
Therefore,
a) The volume of cylinder =
π × 8² × 8 = 512π cm³
b) The volume of cone =
1/3 × π × 8² × 8 = 170.6π cm³
c) Volume of the hemisphere = (512π + 170.6π) / 2
= 341.3π cm³
Hence, the volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.
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Is "Johann Sebastian Bach is the greatest of all the Baroque composers" a proposition? Why?
"Johann Sebastian Bach is the greatest of all the Baroque composers"
a proposition, The proposition is a meaningful statement. without any question,
Mathematical reasoning techniques are laid forth in the rules of mathematical logic. The father of logical reasoning was the Greek philosopher Aristotle. The theoretical foundation for many branches of mathematics, and hence computer science, is provided by logical reasoning. It is used in the design of computing devices, artificial intelligence, the definition of data structures for programming languages, and many other practical areas of computer science.
Statements to which the truth values "true" and "false" can be given are the focus of propositional logic. The objective is to evaluate these claims, either singly or collectively.
"Johann Sebastian Bach is the greatest of all the Baroque composers"
a proposition
The proposition is a meaningful statement. without any question,
in our case, Johann is the greatest composer, is truth statement,
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simplify the expression, assume that no variable is zero
The simplification of the expression are :
a. 1/-5z
b. -5b/3c
c. 2a/9x
What is simplifying expression?Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
A. To simply 2xy/-10xyz
we divide through by 2xy which is the common factor
= 1/-5z
B. -15ab/9ac
we divide through by 3a, which is the common factor
= -5b/3c
C. -6ac/-27cx
we divide through by -3c, which is the common factor
= 2a/9x
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Square ABCD has vertices at A(-2,1), B(2,7), C(8,3), and D(4, -3).
ch
1
2
3
4
5
© 2016 Strong Mind. Created using GeoGebra.
How many units is the perimeter of square ABCD?
104
1615
24
The perimeter of square ABCD is 8 [tex]\sqrt{13}[/tex] units.
Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)
A square's perimeter is equal to the sum of its four sides or the product of four and one of its sides.
Therefore, the square's perimeter is equal to a + b + c + d.
4 × any of the sides because the sides of a square are equal to one another.
Since ABCD is a square:
Perimeter of a square = 4 × (length of a side)
=4 × AB
Formula to calculate the distance between two points [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] is, [tex]$\mathrm{d}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex]
Therefore, distance between two points A(-2, 1) and B(2, 7) will be,
AB = [tex]\sqrt{(2+2)^2+(7-1)^2} \\[/tex]
AB = [tex]\sqrt{4^2+6^2} \\[/tex]
AB = [tex]\sqrt{52} \\[/tex]
AB = 2[tex]\sqrt{13}[/tex]
Hence the perimeter of square ABCD can be calculated as 4 × AB
Now Perimeter of a square ABCD = 4 × 2[tex]\sqrt{13}[/tex]
= 8 [tex]\sqrt{13}[/tex] units
Therefore the answer is 8 [tex]\sqrt{13}[/tex] units
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Square ABCD has vertices at A(−2,1), B(2,7), C(8,3), and D(4,−3). How many units is the perimeter of square ABCD?
Let V and W be vector spaces over a field F. Let Z = {(v, w): v ∈ V and w ∈ W}. Prove that Z is a vector space over F with the operations(v1, w1)+(v2, w2)=(v1 + v2, w1 + w2) and c(v1, w1)=(cv1, cw1).
Z is a vector space over F with the operations(v1, w1)+(v2, w2)=(v1 + v2, w1 + w2) and c(v1, w1)=(cv1, cw1) is proved.
A vector is a mathematical object that can be added and multiplied by a number, also known as a scalar.
In this case, we have two vector spaces, V and W, which are sets of vectors that can be added and scaled in a certain way, with the scalars taken from a field F.
=> (v1, w1)+(v2, w2)=(v1 + v2, w1 + w2)
We then define a new set, Z, which consists of ordered pairs of vectors, one from V and one from W. With the operations of adding two vectors element-wise and scaling a vector by a scalar, we can show that Z is also a vector space over F.
=> c(v1, w1)=(cv1, cw1).
To do this, we need to verify that Z satisfies the properties of a vector space, such as closure under addition and scalar multiplication, associativity and commutativity of addition, the existence of an additive identity and inverse, and distributivity of scalar multiplication over vector addition.
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graph and solve 10c+5≤45
Answer: c ≤ 4, graph is attached.
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
10c + 5 ≤ 45
Subtract 5 from both sides of the equation:
10c ≤ 40
Divide both sides of the equation by 10:
c ≤ 4
Next, since the symbol is less than or equal to, we will have a closed circle. Next, it's less than, so our graph will represent all numbers less than 4.
in which of these rows of the truth table is the compound proposition (p ∧ r) → ¬(q ∨ p) true? The row where both p and q are true, but ris false. The row where both p and rare true, but q is false. The row where p q and rare all false. The row where p, q and r are all true.
By using the truth table The correct options are (a) The row where both p and q are true, but r is false and (c) The row where p, q and r are all false.
Given, (p ^ r) -> ~(q v p)
Creating truth table:
=> p ^ r will return true if both the values of p and r are true else will return false.
=> q v p will return true if at least one of the values of q or p is true else will return false.
=>~(q v p) will return true if the truth value of q v p is false else will return false.
=>(p ^ r) -> ~(q v p) will return false if truth value of p ^ r is true and truth value of ~(q v p) is false else will return true.
p q r (p ^ r) (q v p) ~(q v p) (p ^ r) -> ~(q v p)
F F F F F T T
F F T F F T T
F T F F T F T
F T T F T F T
T F F F T F T
T F T T T F F
T T F F T F T
T T T T T F F
=> Option (a) is correct because according to the row number 7 where p = q = T and r = F, the result = T
=> Option (b) is wrong because according to row number 6, where p = q = T and q = F, the result = F
=>Option (c) is correct because according to row number 1, where p = q = r = F the result = T
=>Option (d) is wrong because according to the row number 8 where p = q = r = T the result = F
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When considering stand-alone risk, the return distribution of a less risky investment is more placed ("tighter") than that of a riskier investment. What shape would the return distribution have for an investment witha) completely certain returns andb) completely uncertain returns?
For an investment with completely certain returns, the return distribution would be a very tight, vertical line at the predetermined return. This is because the risk associated with the investment is zero, meaning the return will not vary regardless of market conditions.
For an investment with completely uncertain returns, the return distribution would be a flat line with no particular shape. This is because the risk associated with the investment is very high, meaning the return could be anything, as it is impossible to predict the returns with any degree of accuracy.
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Pls help with this pleaee
Answer:
bjrjrjrjrjjrjrkjrjrjrjrjfjfj
Step-by-step explanation:
nbgnntntnthththththt
Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side
The change in the scale factor is 4/5.
A scale factor is defined as the ratio between the scale of a given original object and a new object.
12 / 15
12 ÷ 3 = 4
15 ÷ 3 = 5
4/5
Answer key: The change of scale means that 1 inch represented 4 feet, but now 1 inch represents 5 feet.
1 inch represents 4 feet which factors 12 feet.
4 cannot factor 15 feet.
5 can factor 15 feet.
1 inch would represent 5 feet then.
15 ÷ 5 = 3 inches
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35. Find the perimeter and area of each composite figure. 10 in 6 in 14 in
A shipping company charges a $5.75 handling fee in addition to $0.31 per pound to ship a package. Using X for the weight in pounds and for the cost of shipping in dollars, write a linear function that determines the cost of shipping based on weight.
The Shipping Company Cost, y=$(5.75+0.31x) is a linear function that determines the cost of shipping based on weight.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
A shipping company charges a $5.75 handling fee in addition to $0.31 per pound to ship a package.
Using X for the weight in pounds and for the cost of shipping in dollars
Let the number of pounds being shipped=x
Shipping Company charges $5.75 plus an additional $0.31 per pound to ship a package.
Shipping Company Cost = $5.75 + ($0.31 X Number of Pounds)
Shipping Company Cost, y=$(5.75+0.31x)
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Ms. Avila got blue ribbons to give to participants at the school science fair. She ordered 120
blue ribbons from the Smart Start school supplier. Since this was a bulk order, Smart Start
reduced the price of each blue ribbon by $0.75. The total came to $60.
Which equation can you use to find the amount of money, b, Smart Start normally charges
for a blue ribbon?
555
Step-by-step explanation:55
WILL GIVE BRAINLEST, PLEASE HELP
Which of the following gives the correct range for the graph?
A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.
−4 ≤ x ≤ 2
−3 ≤ x ≤ 5
−4 ≤ y ≤ 2
−3 ≤ y ≤ 5
The range of the graph is -4 ≤ y ≤ 2.
Option C is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
A coordinate plane with a segment going from the point (-3, 2) to (0, 1) and another segment going from the point (0, 1) to (5, -4).
This means,
(-3, 2) to (5, -4)
The range of the graph is the y-coordinate.
So,
-4 to 2
This can be written as,
-4 ≤ y ≤ 2
Thus,
The range is -4 ≤ y ≤ 2.
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Isaac owns a food truck that sells tacos and burritos. He only has enough supplies to make 130 tacos or burritos. He sells each taco for $4.25 and each burrito for $8.50. Isaac must sell a minimum of $850 worth of tacos and burritos each day. If x represents the number of tacos sold and y represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
By solving linear equation, it can be calculated that x = 60 , y = 70 is one possible solution of the linear equation.
What is linear inequation?Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥
A one degree inequation is known as linear inequation.
Let the number of tacos sold be $x and the number of burrito sold be $y
He only has enough supplies to make 130 tacos or burritos.
x + y ≤ 130 ... (1)
He sells each taco for $4.25 and each burrito for $8.50.
Isaac must sell a minimum of $850 worth of tacos and burritos each day.
4.25x + 8.5y ≥ 850
x + 2y ≥ 200 ... (2)
The inequalities has been solved graphically as;
One possible solution is x = 60, y = 70
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Algebraically determine the limit. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.) lim (4 + b)2-82 DO h
Limit, (4 + b)² - 8², Algebraically Determining Limits, h approaches 0, Expansion Formula for Square, Lim [(4 + b + h)² - 8² = (4 + b)² - 64.
To algebraically determine the limit, we can use the definition of a limit.
The limit of (4 + b)²-8² as h approaches 0 is equal to the limit of (4 + b + h)² - 8² as h approaches 0 minus (4 + b)² - 8².
Using the expansion formula for a square, we can write:
(4 + b + h)² - 8² = (4 + b)² + 2(4 + b)h + h² - 64
Now, taking the limit as h approaches 0:
lim [(4 + b + h)² - 8²] = lim [ (4 + b)² + 2(4 + b)h + h² - 64 ] = (4 + b)² - 64
So,
lim (4 + b)² - 8² as h approaches 0 = lim [(4 + b + h)² - 8²] - (4 + b)² + 64 = lim [(4 + b + h)² - 8²]
Hence,
lim (4 + b)² - 8² as h approaches 0 = lim [(4 + b + h)² - 8² = (4 + b)² - 64.
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