Answer:
d^2y/dx^2 = 2
Step-by-step explanation:
We take the derivative with respect to x twice here. Find the first derivative, simplify the results and then differentiate that result again with respect to x.
(d/dx)(2x^2+2y=17+ → 4x + 2(dy/dx) = 0. Simplifying, we get:
dy/dx = -2x
Now take the derivative of this new equation, obtaining:
d^2y/dx^2 = 2
Find the area of right triangle RST
Check the picture below.
Answer:
B. 7.5 square units.
Step-by-step explanation:
We have been given an image of a right triangle. We are asked to find area of our given triangle.
We can see that base of our given triangle is 5 units as difference between point S and point T is 5 units.
[tex]2--3=2+3=5[/tex]
The height of our given triangle (RT) is 3 units.
[tex]1--2=1+2=3[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{5 units}\times \text{3 units}[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times 15\text{ units}^2[/tex]
[tex]\text{Area of triangle}=7.5\text{ units}^2[/tex]
Therefore, area of our given triangle is 7.5 square units and option B is the correct choice.
Measure the sides and angles of the two triangles. Are the two triangles similar? Yes, corresponding angles are congruent. Yes, all sides have been increased by 1 unit. Yes, corresponding sides are proportional. No, corresponding angles are not congruent and corresponding sides are not proportional.
Answer:
D) No, corresponding angles are not congruent and corresponding sides are not proportional.
;]
Step-by-step explanation:
Answer:
the answer is D i just answered it with D and its correct
good luck on your assignment :)
Step-by-step explanation:
Which of the following functions has the largest value when x = 3?
c(x) = 3x2 + 5x + 22
j(x) = 12x
a(x) = 9x
All the functions are equal at x = 3.
c(x)
j(x)
a(x)
Answer:
c(3) is the largest
Step-by-step explanation:
For positive values of x, j(x) > a(x), so the comparison is between c(x) and j(x).
Without evaluating the functions, you can subtract 5x from them to get ...
c'(x) = c(x) -5x = 3x² +22
j'(x) = j(x) -5x = 7x
Now the question is whether c'(3) is larger than j'(3). The latter is ...
j'(3) = 7·3 = 21
Since c'(3) has an added constant of 22 and x² will be positive, we know that ...
c(3) > j(3) > a(3)
The function with the largest value at x=3 is c(x).
_____
You can, of course, simply evaluate the functions:
c(3) = (3·3 +5)·3 +22 = 14·3 +22 = 42 +22 = 64j(3) = 12·3 = 36a(3) = 9·3 = 27c(3) > j(3) > a(3) . . . . . . . c(3) is the largest
Answer:
It’s D
Step-by-step explanation:
a(x)
3 less than 3 times a number is 12, what is it?
The number is 3.
3x3 is 9, which is 3 less than 12.
Answer:
The number is 5.
Step-by-step explanation:
12 plus 3 is 15.
5 x 3 = 15
15 - 3 = 12
3 less than 3 times a number is 12.
It sounds like 3 less from a number IS 12. So adding 3 to 12 will get 15, and 15 divided by 3 equals 5.
I hope this is correct and that it helps! :)
Write the equation of the line, in slope-intercept form, that contains the points (-1, -2) and (1, 2). Use the box provided or the upload option to submit all of your calculations and final answer.
Which statement describes a strong U.S. dollar?
Answer:
I can tell you that B is NOT correct as I got it wrong. I bet the right answer is C as it is holding steady at 1:95.
Step-by-step explanation:
These are the choices for Plato
A. The exchange rate between the U.S. dollar and the yen changes from 1:95 to 1:102.
B. The exchange rate between the U.S. dollar and the euro changes from 1:95 to 1:92. - Wrong answer
C. The exchange rate between the U.S. dollar and the euro remains 1:95
Devaughn is 11 years younger than Sydney. The sum of their ages is 83. What is Sydney's age?
To solve for Sydney's age, we used an equation based on the relationship that Devaughn is 11 years younger than Sydney and the sum of their ages is 83. Solving the equation 2S - 11 = 83, we found that Sydney is 47 years old.
To find Sydney's age, we need to set up and solve an equation based on the information given: Devaughn is 11 years younger than Sydney, and the sum of their ages is 83.
Let's let Sydney's age be represented by S and Devaughn's age be represented by D. Given that Devaughn is 11 years younger than Sydney, we can express Devaughn's age as D = S - 11.
The sum of their ages is given as 83, so we can write the following equation: S + D = 83.
Substituting Devaughn's age in terms of Sydney's age, we get: S + (S - 11) = 83. This simplifies to 2S - 11 = 83. Solving for S, we add 11 to both sides, resulting in 2S = 94, and then we divide by 2 to find S = 47.
Therefore, Sydney's age is 47 years old.
Eight white balls and twenty black balls are in a bag. What is the probability of the drawing a black ball in one draw?
Answer:
20/28 which is about 71%
Step-by-step explanation:
so first you add up how many balls there are. 8+20=28. So 28 is the denominator for the fraction. there are 20 black balls, so that is the numerator. so 20/28 is the fraction. then you divide 20 by 28 to get the rounded percent.
Which expression gives the volume of a sphere with radius 5?
Answer:
it is d
Step-by-step explanation:
formula of sphere=4/3* pi*r cubed
Answer:
D
Step-by-step explanation:
A is nothing.
B is the surface area
C is nothing
D is the volume of a sphere.
What is the magnitude of the vector (7, -4) to the nearest tenth?
2.4
5.7
8.1
9.0
Answer:
Step-by-step explanation:
Apply the Pythagorean Theorem: hyp² = 7² + (-4)² = 49 + 16 = 65.
The magnitude of this vector <7, -4> is 8.1, to the nearest tenth.
Which statement is true about the ray passing
through points B and C?
The ray extends infinitely in one
direction
The ray extends infinitely in both
directions
The ray has a finte length that can
be measured
There are only two points on the
entire ray
Cosidering the ray BC.
It is clear that:
1) A ray starts from one point and extends infinitely in ONE direction.
2) The ray BC cannot be measured. But the line-segment BC can be Measured.
3) B and C are the only two points on the given ray.
Hence the statement: "There are only two points on the entire ray" is the correct one.
Hope it helps...
Regards;
Leukonov/Olegion.
The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered so options (A), and (D) are true.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
Given,
A ray is passing through points B and C.
(A) The ray extends infinitely in one direction which is True.
(D) There are only two points on the entire ray which is also true.
Hence, The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered.
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Mags is 2 years older than Vector.Which equation will help you find Mags' age (m) if you know Vector's age (v)?
Answer:
Step-by-step explanation:
m = megs age
v = vectors age
meg is 2 years older than vector + 2
therefore
m = v +2
On a sunny morning, Ishaan rode his bicycle to a farm that sold baskets of apples for $ 9 . 1 2 $9.12dollar sign, 9, point, 12 each and baskets of eggplants for $ 9 . 5 4 $9.54dollar sign, 9, point, 54 each. Ishaan decided to buy a basket of apples and a basket of eggplants . How much did Ishaan need to pay for his produce? $
Answer:18.66
Step-by-step explanation:
HELP ASAP!!!!! PLEASE
Find the area of the square, which has a side length of 2.
Area of square = 2 x 2 = 4
Now multiply the area by the length b
Volume = 4 x 5 = 20 square units total.
Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the questions below. Show all your work for full credit. Use the correct units with your answers
Answer:
Step-by-step explanation:
From what I understand about parabolic motion in the English system, the equation for flight is
[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]
where [tex]v_{0}t[/tex] is the initial upwards velocity and
[tex]h_{0}[/tex] is the initial height from which the object was launched. Filling in that equation with those values gives you
[tex]s(t)=-16t^2+64t+3[/tex]. That's a.
In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function. The absolute max is the heighest that the ball will go. Completing the square is the way to solve this. Begin by setting the equation equal to 0, the moving the 3 over by subtraction:
[tex]-16t^2+64t=-3[/tex]
Now factor out the -16 since the leading coefficient HAS to be a positive 1:
[tex]-16(t^2-4t)=-3[/tex]
Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:
[tex]-16(t^2-4t+4)=-3[/tex]
BUT since you added in a 4*-16 on the left you have to add it in on the right:
[tex]-16t^2(t^2-4t+4)=-3-64[/tex]
which simplifies to
[tex]-16(t-2)^2=-67[/tex]
Now bring the 67 over by addition and you have your vertex:
[tex]s(t)=-16(t-2)^2+67[/tex].
The vertex is (2, 67). The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.
How long it will be in the air is found by factoring to find the zeros. These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046
So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at
x = 4.05 seconds. Which makes sense if you know anything about parabolic motion and physics. The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark. Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds. And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters). Sorry it's so long, but it's not a question that can be answered with just a few sentences.
[tex]log_{13} 244=\frac{ln244}{ln13}[/tex] ≈ [tex]2.143[/tex]
A. 2.143
B. 0.453
C. 3.949
D. 2.209
Answer:
A.
Step-by-step explanation:
The question is on laws of logarithms
For example to find the log₁₀ 100
⇒log₁₀ 100 = 2................how?
we take In 100 / 1n l0 = 2
where 10²=100
⇒Thus logₓ y = In y / In x
I'm this many years old, and I would like to know what 1+1 is. I have to answer this correctly because if I don't my mommy will put me in the oven again.
the answer is 3 I bet the oven is hot tbh
Title: The Infallible Logic of 1 + 1 = 2
Introduction:
The seemingly simple equation, 1 + 1 = 2, holds a profound and fundamental place in mathematics and logic. Its truth is evident, self-evident, and indisputable, serving as a cornerstone for mathematical reasoning and human understanding. In this essay, we explore the underlying principles and irrefutable logic behind the statement that 1 + 1 equals 2.
Body:
Basic Arithmetic Principles:
At its core, mathematics is a system of rules and principles that govern the manipulation of numbers and quantities. The equation 1 + 1 = 2 is a fundamental expression of these principles. It demonstrates the addition of two individual units (1) to form a collective sum (2). This is a foundational concept in arithmetic.
Axiomatic Truth:
In the realm of mathematics, certain statements are considered axioms—self-evident truths that do not require proof. 1 + 1 = 2 is one of these axioms. It is a statement that is true by definition and serves as a building block for more complex mathematical operations.
Logical Proof:
One way to understand why 1 + 1 equals 2 is through logical proof. We can start with the premise that we have one unit (1) and add another unit (1) to it. The result, by definition, is two units (2). This logical progression is simple and irrefutable.
Set Theory:
In set theory, a branch of mathematics that deals with sets and their relationships, the equation 1 + 1 = 2 is rigorously defined. In set theory, 1 represents a set containing a single element, and adding another set with one element results in a set with two elements. This is a formalized representation of why 1 + 1 equals 2.
Real-World Application:
The equation 1 + 1 = 2 has practical applications in various fields, including science, engineering, economics, and everyday life. It reflects the way we count and aggregate objects, making it essential for quantitative analysis and problem-solving.
Conclusion:
The equation 1 + 1 = 2 is not merely a mathematical expression; it is a reflection of the logical and axiomatic foundation upon which mathematics and much of human reasoning are built. Its undeniable truth serves as a testament to the precision and consistency of mathematics. The simple act of adding one to one resulting in two exemplifies the elegance and power of mathematical logic, making it an enduring principle in our understanding of the world. In a universe governed by mathematical laws, 1 + 1 will always equal 2, and this irrefutable truth is a testament to the beauty and reliability of mathematics.
The population of a city has increased by 36% since it was last measured. If the current population is 51000 , what was the previous population?
So if we have the number after the 36% increase in population, we would want to subtract that 36% from 51000.
36% of 51000 can be found by multiplying 51000 by 0.36 (0.36 is the decimal equivalent of 36%)
51000 x .36 = 18360
So you simply subtract 18360 from 51000, which is 32,640.
Natasha is driving at a rate of 4 miles every 3 minutes how fast is Natasha driving
Answer:
80 mph
Step-by-step explanation:
Since Natasha is driving at a rate of 4 miles every 3 minutes, we are asked to find her speed in mph. Since there are 60 minutes in an hour, we can make a proportion: 4/3 = x/60. Solving for x, we get x to be 80. So Natasha is driving at 80 miles an hour.
Answer:
80 miles per hour
Step-by-step explanation:
60 / 3 = 20
4 x 20 = 80
Enter the equation of the circle described below.
Center (-3, 0), radius 5
Answer:
[tex](x+3)^2 + y^2 =25[/tex]
Step-by-step explanation:
The general equation of a circle has the form:
[tex](x-h)^2 + (y-k)^2 =r^2[/tex]
Where the point (h, k) is the center of the circle and r is the radius
In this case the center is (-3, 0) and the radius is [tex]r=5[/tex]
So [tex]h=-3\\k=0[/tex]
Finally the equation of the circle is:
[tex](x-(-3))^2 + (y-0)^2 =5^2[/tex]
[tex](x+3)^2 + y^2 =25[/tex]
(X+3)^2 +y^2 =25
This is the correct answer
Check on Desmos
-0.18x + y = -6.54
-2.8x - y = -2.4
Answer:
The solution is (-3, 10.8)
Step-by-step explanation:
While it's rather obvious that you want to solve this system of linear equations, you should share that instruction when you post the problem.
To solve this system using elimination by addition and subtraction, combine the two equations as shown below (to eliminate y):
-0.18x + y = -6.54
-2.8x - y = -2.4
--------------------------
-2.98x = -8.94
Dividing both sides by -2.98, to isolate x, yields: x = -8.94 / (-2.98) = -3.
Then x = 3. Find y from -2.8x - y = -2.4: -2.8x + 2.4 = y, and here,
y = -2.8(-3) + 2.4 = 8.4 + 2.4 = 10.8
Then the solution is (-3, 10.8)
Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. Kelly ran at an average speed of 8 miles per hour. b If Kelly finished the race in 1 1/2 hours, how long did it take Ava to finish the race?
Answer:
2
Step-by-step explanation:
Kelly ran at an average speed of 8 miles per hour. If she finished the race in one and a half hours that means she ran 12 miles.
8=x
?=3/2x
12=x
We now know the road is 12 miles long. Ava has an average speed of 6 miles so she will finish it in 12/6 hours.
12/6=2
It takes Ava to finish the race in 2 hours.
Kelly ran at an average speed of 8 miles per hour.
If she finished the race in one and a half hours that means she ran 12 miles.
What is the formula for the average speed?
The average speed is the distance traveled divided by the time taken.
8=x
12=x
We now know the road is 12 miles long.
Ava has an average speed of 6 miles so she will finish it in 12/6 hours.
12/6=2hours
Therefore, It takes Ava to finish the race in 2 hours.
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Best Deal 1
Quantity of Flour Price
3 pounds $5.25
5 pounds $9.75
7 pounds $12.60
10 pounds $14.20
12 pounds $18.24
A baker purchases flour each week from a wholesale warehouse. The chart shows the quantities and prices available this week. If the caterer decides to buy the BEST deal, how much will he save per pound of flour over the most expensive deal?
A) $0.28
B) $0.37
C) $0.47
D) $0.53
d. $0.53 because..
3/5.25 = 1/1.75
5/9.75 = 1.95
7/12.60 = 1.80
10/14.20 = 1.42
12/18.24 = 1.52
then do ;
most expensive deal - least expensive deal = how much he’ll save
1.95 - 1.42 = .53
Answer: The answer would be D.
like she said down there !
!
Step-by-step explanation:
A carpenter contracts to do a job. The costs for the job are $2000 for materials, $500 for labor, and $150 for equipment rental. What would be the total cost of materials were increased by 15%
Answer:
$2950
Step-by-step explanation:
Add together the following three items:
Materials: $2000 plus 15%, or 1.15($2000), or $2300
Labor: $500
Equipment Rental: $150
Total: $2300 + $500 + $150 = $2950
Please help! I would appreciate it <3
Answer:
Final answer is E. 10
Step-by-step explanation:
Apply Pythagorean theorem to the given right triangle.
[tex]\left(Hypotenuse\right)^2=\left(Leg_1\right)^2+\left(Leg_2\right)^2[/tex]
[tex]\left(h\right)^2=\left(5\sqrt{2}\right)^2+\left(5\sqrt{2}\right)^2[/tex]
[tex]\left(h\right)^2=50+50[/tex]
[tex]\left(h\right)^2=100[/tex]
take square root of both sides
[tex]h=10[/tex]
Hence final answer is E. 10
ANSWER
E. 10
EXPLANATION
Using Pythagoras Theorem, which says the hypotenuse squared is equal to the sum of squares of the two shorter legs.
[tex] {h}^{2} = {(5 \sqrt{2} )}^{2} + {(5 \sqrt{2} )}^{2} [/tex]
Evaluate the squares on the RHS.
[tex] {h}^{2} = 25 \times 2 + 25 \times 2[/tex]
[tex] {h}^{2} = 50 + 50[/tex]
Simplify:
[tex] {h}^{2} = 100[/tex]
Take positive square root.
[tex]h = \sqrt{100} [/tex]
[tex]h = 10[/tex]
The hypotenuse is 10 units.
The correct answer is E
Whats this answer ? Help
Answer:
True
Step-by-step explanation:
A negative exponent turns into positive when it is put into fraction form.
5^-2 = 1/5^2
5^-2 = 1/25
Answer:
Step-by-step explanation:
It's true. A minus power means that you put the denominator in the numerator and the numerator in the denominator. For example
(5/3)^(-2) = (3/5)^2 = 9/25
Consider the hyperbola represented by the equation: (picture)
The center of the hyperbola is _______
The left vertex, if the hyperbola opens horizontally, or the bottom vertex, if it opens vertically, is ______
The other vertex is ______
Answer:
- The center of hyperbola is (-2 , 3)
- The left vertex, if the hyperbola opens horizontally, or the
bottom vertex, if it opens vertically, is (-6 , 3)
- The other vertex is (2 , 3)
Step-by-step explanation:
* Lets study the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (h , k) and transverse axis parallel to the x-axis is
(x - h)²/a² - (y - k)²/b² = 1, Where
- The length of the transverse axis is 2a
- The coordinates of the vertices are (h ± a , k)
- The length of the conjugate axis is 2b
- The coordinates of the co-vertices are (h , k ± b)
- The coordinates of the foci are (h ± c , k), where c² = a² + b²
* Now lets solve the problem
∵ (x + 2)²/4² - (y - 3)²/5² = 1
∵ (x - h)²/a² - (y - k)²/b² = 1
∴ a = 4 , b = 5
∴ h = -2 , k = 3
∵ The center of the hyperbola is (h , k)
∴ The center of hyperbola is (-2 , 3)
∵ The coordinates of the vertices are (h + a , k) , (h - a , k)
∴ The coordinates of the vertices are (-2 + 4 , 3) , (-2 - 4 , 3)
∴ The coordinates of the vertices are (2 , 3) , (-6 , 3)
∴ The left vertex, if the hyperbola opens horizontally, or the
bottom vertex, if it opens vertically, is (-6 , 3)
∴ The other vertex is (2 , 3)
The center of a hyperbola is determined by the coordinates (h, k) in its equation. The vertices are the points where the hyperbola intersects its major axis, and their positions depend on whether the hyperbola opens horizontally or vertically. If it opens horizontally, the left vertex is at (h - A, k), and if it opens vertically, the bottom vertex is at (h, k - B).
Explanation:In the equation of a hyperbola, the center of the hyperbola can be found by identifying the coordinates (h, k). These are the constants in the denominators of the fractions on the left-hand side of the equation. For instance, in the equation ((x-h)²/A²) - ((y-k)²/B²) = 1, the center would be at the point (h, k).
The vertices of the hyperbola are the points where the hyperbola intersects its major axis. If the hyperbola opens horizontally, the left vertex will be located at the coordinate (h - A, k), and the other vertex will be at (h + A, k). If the hyperbola opens vertically, the bottom vertex will be at the coordinate (h, k - B), with the other vertex at (h, k + B).
Remember, A represents the distance from the center to a vertex along the major axis, and B represents the distance from the center to a vertex along the minor axis.
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name the property illustrated by (3c x 6)2=3c(6 x 2)
BRAINLIEST REWARD!!!
Answer:
Associative property of multiplication
Explanation:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.
Quadrilateral KLMN has vertices of K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4) Find the length of MN
Answer:
The length of MN is [tex]\sqrt{5}[/tex] units.
Step-by-step explanation:
The given Quadrilateral KLMN has vertices at K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4).
We use the distance formula to find the length of MN.
[tex]|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We plug in the values to get
[tex]|MN|=\sqrt{(-4--2)^2+(-4--5)^2}[/tex]
[tex]|MN|=\sqrt{(-2)^2+(1)^2}[/tex]
[tex]|MN|=\sqrt{4+1}[/tex]
[tex]|MN|=\sqrt{5}[/tex]
The length of MN is [tex]\sqrt{5}[/tex] units.
Answer:
B
Step-by-step explanation:
PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
C
Step-by-step explanation:
Using the coefficients of each term and evaluating for h = - 4
- 4 | 1 - 7 - 7 20
↓ - 4 44 - 148
---------------------------
1 - 11 37 - 128 ← remainder
Quotient = x² - 11x + 37 , R - 128