[tex]y = \frac{1}{4} {x}^{4} + \frac{5}{2} {x}^{2} - 18x + k[/tex]
Step-by-step explanation:
[tex]dy = ( {x}^{3} + 5x - 18)dx[/tex]
Integrating the above expression, we get
[tex]y = \int( {x}^{3} + 5x - 18)dx[/tex]
[tex] = \frac{1}{4} {x}^{4} + \frac{5}{2} {x}^{2} - 18x + k[/tex]
where k is the constant of integration
The president of a small company
made $72,000 last year. She cut her
salary this year to $60,000 because
the company was not doing as well.
What was the percent decrease in
her salary to the nearest percent?
Answer:
17%
Step-by-step explanation:
Percent decrease
[tex] = \frac{72000 - 60000}{72000} \times 100 \\ \\ = \frac{12000}{72000} \times 100\\ \\ = \frac{1200000}{72000} \\ \\ = 16.67 \% \\ \\ \approx \: 17 \%[/tex]
I didn’t mean to click C but yea I need help
Answer:
C.
Step-by-step explanation:
It says from least to greatest. You start off looking at the whole numbers and 1 is the least. Your going to start at 1 2/5 (that rules off A and B). The next number you need to compare is 3/10 and 5/8. Since 5/8 is bigger than 3/10 the answer would be C.
Rhombus JKLM is shown below. Find m∠KLM.
A.36°degree
B.38°degree
C,72°degree
D.76°degree
Answer:
Option D
Step-by-step explanation:
Properties of a rhombus,
1). Diagonals of a rhombus bisect the opposite angles.
2). Sum of adjacent two angles of a rhombus is 180°.
By property (1),
Diagonal JL will bisect the angles ∠MJK and ∠KLM.
Therefore, m∠KLM = 2(5x + 3)°
Similarly, diagonal KM will bisect the angles ∠JKL and JML.
Therefore, m∠JKL = 2(9x - 11)°
By property (2),
2(9x - 11)° + 2(5x + 3)° = 180°
9x - 11 + 5x + 3 = 90
14x - 8 = 90
14x = 98
x = 7
Since, m∠KLM = 2(5x + 3)°
= 2(5×7 + 3)°
= 76°
Therefore, Option D will be the answer.
Solve the following equation for x.
18 – 4.x = 10 - 2x
A x = -4
B) x = -1
C) x = 1
D) x =4
Answer:
D) x = 4
Step-by-step explanation:
18 - 4x = 10 - 2x
10 - 2x = 18 - 4x
10 - 2x + 4x = 18 - 4x + 4x
10 + 2x = 18
10 - 10 + 2x = 18 - 10
2x = 8
2x ÷ 2 = 8 ÷ 2
x = 4
Help,please, thank you!
Answer:
x=64°
Step-by-step explanation:
x=180-90-26 (angles on a str line)
=64°
Answer:
64 is the answer to this question
Step-by-step explanation:
180÷2=90
90-26=64
CORRECTLY ANSWER PLEASE AND THANK YOU
9514 1404 393
Answer:
(-3, 4)
Step-by-step explanation:
The midpoints of the diagonals of a parallelogram are coincident. This means the sums of coordinates at the ends of the diagonals are the same. For missing point P, we must have ...
P +(0, -3) = (-6, -6) +(3, 7)
P = (-6, -6) +(3, 7) -(0, -3)
P = (-6 +3 -0, -6 +7 -(-3))
P = (-3, 4)
PLEASE HELP How can you make different triangles with the same angle measures?
Form different triangles with angle measures 90°, 75°, and 15°
How can you make different triangles with the same angle measures?
O A. Make triangles with the same angle measures and the same side lengths
OB. It is not possible to make different triangles with the same angle measures.
OC. Make triangles with the same angle measures but different side lengths
OD. Make triangles with the same side lengths but different angle measures
Help me please! It’s timed
Answer:
x=36.08
Step-by-step explanation:
Given: From the given triangle DEF, ∠E=[tex]90^{0}[/tex]
DF=55
and DE= x
To find the value of x
According to trigonometry rule,
[tex]\frac{x}{55} =cos49^{0} \\x=55(cos 49^{0} )\\x=55(0.656)\\x=36.08[/tex]
Therefore, the value of x will be 36.08
see attachment :)) I've been stuck on this question forever... I do not understand how they got 2r^2-60r-45=0. I know the formula for the area of the circle is r^2 pi... but still... Can someone answer the question with explanation?
Answer:
2r² - 60r - 45 = 0
Step-by-step explanation:
Hang on this is going to be convoluted
------------------------------
Area of pond
a = πr²
Area of path
a = πr²/10
Combined Area
a = πr² + πr²/10
a = π(r² + r²/10)
---------------------------
The Combined Area can also be expressed as
a = π(r + 1.5)²
a = π(r² + 3r + 2.25)
-----------------------------
Set the areas equal
π(r² + r²/10) = π(r² + 3r + 2.25)
Divide both sides by π
r² + r²/10 = r² + 3r + 2.25
Subtract r² from both sides
r²/10 = 3r + 2.25
Multiply both sides by 20
2r² = 60r + 45
Subtract 60r + 45 from both sides
2r² - 60r - 45 = 0
I’ll mark brinaliest if the answe is correct. I need those two answers that are blank
Answer:
blue marbles: 4/15
red marbles: 8/15
Step-by-step explanation:
add all the marbles together then put how many marbles in front as the numerator.
What is the sum of the polynomials below ? 3y^5-2y+8 2y^5 - 4y^3-7
Answer:
[tex](3 {y}^{5} - 2y + 8) + (2 {y}^{5} - {4y}^{3} - 7) \\ = 5 {y}^{5} - 4 {y}^{3} - 2y + 1[/tex]
Which number is rational?
Answer:
Option D, [tex]\sqrt{16}[/tex], since the answer is 4 which is a rational number considering that it's a whole number
Hope this helps!
Susan and Katie are running an ultra marathon. Susan averages 5 miles per hour. Katie averages 5.2
miles per hour. If Susan gets a 45 minute head start, then exactly how many hours after Katie begins
running will she catch up to Susan?
Answer:
Katie will catch up to Susan after running 33.4 h.
Step-by-step explanation:
We can find the time that takes Katie to catch up to Susan by using the following equation:
[tex] x_{f_{k}} = x_{0_{k}} + v_{0_{k}}t + \frac{1}{2}at^{2} [/tex]
Where:
[tex] x_{f_{k}} [/tex]: is the final position of Katie
[tex] x_{0_{k}} [/tex]: is the initial position of Katie = 0
[tex] v_{0_{k}}[/tex]: is the initial speed of Katie = 5.2 mi/h
a: is the acceleration = 0 (she is moving at constant speed)
t: is the time
Since Katie will catch up to Susan, the final distance traveled by Katie will be equal to the final distance traveled by Susan.
[tex] x_{f_{s}} = x_{0_{s}} + v_{0_{s}}t + \frac{1}{2}at^{2} [/tex]
[tex] x_{0_{k}} + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Since Susan gets a 45 minutes head start, in that time she traveled the following distance:
[tex] d = \frac{v}{t} = \frac{5 mi/h}{45 min*\frac{1 h}{60 min}} = 6.67 mi [/tex]
So, this will be the initial position of Susan.
[tex] 0 + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Hence, the time will be:
[tex] 5.2t = 6.67 + 5t [/tex]
[tex] t = 33.4 h [/tex]
Therefore, Katie will catch up to Susan after running 33.4 h.
I hope it helps you!
PLEASE I REALLY NEED HELP
Plans for a new school call for classrooms directly across the hall from each other to be congruent. This computer printout shows a math classroom. If the vertices of a science classroom are located at (-3x¹,y¹). (-3x²,y²), (-3x³, y³), and (-3x⁴, y⁴), will the science classroom be congruent to the math classroom?
The lengths of the horizontal sides of the science class is larger than the
length of the horizontal side of the math class.
The correct option is; No, the the transformation applied was not a rigid motion.
Reasons:
The given vertices of the science classroom are;
(-3·x₁, y₁), (-3·x₂, y₂), (-3·x₃, y₃), and (-3·x₄, y₄)
The coordinates of the vertices math classroom are;
(x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄)
Whereby x₁ = x₄, we have;
Length of the vertical side of the rectangular math class = y₁ - y₄
Length of the horizontal side, [tex]L_M[/tex] = x₂ - x₁
Similarly;
The length of the horizontal side of the science class is, [tex]L_S[/tex] = -3·x₂ - (-3·x₁)
Therefore;
[tex]L_S[/tex] = 3·(x₁ - x₂) = [tex]\mathbf{3 \cdot L_M}[/tex]
The length of a side of the science is three times the length of the side of
the math class, which gives that the dimensions of the science class are not
the same as the the dimensions of the math class.
Therefore;
The science class and the math class are not congruent
The the correct option is, no the transformation that gives the science class from the math class is not a rigid transformation.Learn more about non-rigid transformation here:
https://brainly.com/question/2396426
which of the following is the slope of a line perpendicular to the line y = -2/3 x +5
Answer:
-2/3x is the slope
Step-by-step explanation:
y=mx+b is the equation to follow
If f(x)=3x^2 and g(x)=4x^3+1 what is the range of (f°g)(x)?
Someone pls help
Answer:
= 3*(4x^3+1)^2
= degree 6
Step-by-step explanation:
Amber and Ruben play a game with one 6-sided die. Ruben gets a point if he rolls a prime number. Amber gets a point if she rolls a number that is a factor of 6. Is this game fair? Explain.
Answer:
Explain what?
Step-by-step explanation:
The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors?
This question is incomplete
Complete Question
A varsity boys' basketball team has a ratio of seniors to juniors that is 7:4.
The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors
Answer:
The boys' team has more seniors
Step-by-step explanation:
If each team has 12 juniors,
Step 1
For the boys' basketball team, lets find the total number of people on the team
A varsity boys' basketball team has a ratio of seniors to juniors that is
7:4 = seniors : juniors
Sum of proportion
= 7 + 4 = 11
Let the total number of people on the team = x
Hence:
4/11 × x = 12
4x/11 = 12
Cross Multiply
4x = 11 × 12
x = 11 × 12/4
x = 33 members
The number of seniors is calculated as
33 members - 12 juniors
= 21 seniors
Step 2
For the girls' basketball team, lets find the total number of people on the team
The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2.
= 3:2 = seniors : juniors
Sum of proportion
= 3+2 = 5
Let the total number of people on the team = x
Hence:
2/5 × x = 12
2x/5 = 12
Cross Multiply
2x = 5 × 12
x = 5 × 12/2
x = 30 members
The number of seniors is calculated as
30 members - 12 juniors
= 18 seniors
Therefore, from our above calculations, the boys' team has more seniors
A - y = -2x + 40
B - y = 2x + 40
C y = 1/2x + 40
D - y=-1/2x +40
Answer:
c y=1/2x+40
because it's positive (up). /
whats the value of x? 8(-6 + 6x) = 240
Answer:
x = 6
Step-by-step explanation:
8(-6 + 6x) = 240
Distribute the 8
-48 + 48x = 240
Add 48 to both sides
48x = 288
Divide both sides by 48
x = 6
if cos a>0 and cot a is undefined then where does the terminal side of a located?
A. Quadrant II
B.quadrant III
C.negative x axis
D.negative y axis
E.no such angle a exists
Answer:C
Therefore: In Quadrant I, cos(θ) > 0, sin(θ) > 0 and tan(θ) > 0 (All positive). For an angle in the second quadrant the point P has negative x
Step-by-step explanation:
consider the equation k over x equals 12 where k is any number between 20 and 65 and X is a positive integer what are the possible values for x
Factories the following expression correctly 8x2 +4x
Answer:
4x(2x+1)
Step-by-step explanation:
8x^2+4x
x(8x+4)
4x(2x+1)
Answer:
4x(2x + 1)
Step-by-step explanation:
8x² + 4x
4(2x² + x)
4x(2x + 1)
Jim, Carla and Tomy are members of the same family. Carla is 5 years older than Jim. Tomy is 6 years older than Carla. The sum of their three ages is 31 years. How old is each one them?
We are given these three people age below:
Jim's ageCarla's ageTomy's ageWe define the age of Jim as any variable, because the problem doesn't give any specific age. I will define Jim's age as x.
Jim's age = xNext, Carla is 5 years older than Jim. That means if Carla is 5 years older, her age would be x+5.
Carla's age = x+5Then Tomy is 6 years older than Carla. That means the age would be 6+(x+5).
Tomy's age = 6+(x+5)The sum of their three ages is 31 years old. That means we add all these ages and equal to 31.
[tex] \large{x + x + 5 + 6 + x + 5 = 31}[/tex]
Combine like terms and solve for x.
[tex] \large{3x + 16 = 31} \\ \large{3x = 31 - 16} \\ \large{3x = 15} \\ \large{x = 5}[/tex]
Then we substitute the value of x in ages to find these three people ages.
Jim's age = x = 5Carla's age = x+5 = 5+5 = 10Tomy's age = 6+(x+5) = 6+(5+5) = 6+10 = 16.Answer
Jim's age = 5Carla's age = 10Tomy's age = 16I have 2 more days to live what to do :(
Answer:
I would say, spend time with your family and friends and get ready for the time, I'm so sorry that this is happening to you and i hope you had an amazing life.
What is the equation of the translated function, g(x), if
f(x) = x2?
g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x – 2)2 + 5
g(x) = (x – 5)2 + 2
Answer:
D
Step-by-step explanation:
g(x) = (x+4)^2 +6
Helppppp meeeeeeeeeeeee
Answer: B
Step-by-step explanation:
And also why do you have only 1 hour out of 16 to complete a test?
Choose the attributes that are true for all quadrilaterals.
four angles
four right angles
four sides
opposite sides equal in length
opposite sides parallel
Answer:
four angles
four sides
Step-by-step explanation:
express 81 as sum of odd numbers.
Step-by-step explanation:
[tex]1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17[/tex]
Solution all the odd no. show sum is 81At the dance shoe store, they sell Tap, Point, and Ballet shoes. A pair of point shoes are double the price of ballet shoes. The tap shoes are $10 more than ballet shoes. If the total price of all the shoes is $648, how much is each shoe
Answer:
a pair of Tap shoes costs $169.50
a pair of Point shoes costs $319.00
a pair of Ballet shoes costs $159.50
Step-by-step explanation:
first tell your teacher, that the problem description is misleading.
as a shoe store has more than one pair per type. so, "all the shoes" would mean all the sites in the store. but that is for sure not meant here.
what your teacher hopefully meant was that the total price of buying one pair of each of the shoe types is $648.
and your teacher was hopefully asking for the price of pairs of shoes, and not actually single shoes.
my solution bases on these assumptions.
so, we got Tap (t), Point (p) and Ballet (b) shoes.
buying one pair each is
t + p + b = 648
now we know some other information.
p = 2×b (Point shoes are double the price of Ballet shoes)
t = b + 10 (Tap $10 more than Ballet)
so, we can replace t and p by expressions of b and get
b + 10 + 2×b + b = 648
4×b + 10 = 648
4×b = 638
b = 159.50
p = 2×159.50 = 319.00
t = 159.50 + 10 = 169.50
