Answer:
yous welcome
Step-by-step explanation:
6. is 2
7. is 1
8. is 100
The equation 3x + 7y = 105 represents the number of bags of sand (x) and bags of mulch (y) that can be bought with $105. If no bags of sand are bought, how many bags of mulch can be bought with $105?
Show work to support your answer.
Answer:
15 bags
Step-by-step explanation:
3(0) + 7y=105
7y=105
y=15
Graph f(x) = 2(2)x please help fast
The graph of the exponential function is in the image at the end.
How to graph the exponential function?Here we want to graph the function:
f(x) = 2*2ˣ
To do so, we need to evaluate the function in some values, and then we can find some points in the graph, and then we can use these points to sketch the graph.
When x = 0 we get.
f(x) = 2*2⁰ = 2 ----> (0, 2)
when x = -1
f(-1) = 2*2⁻¹ = 1 ---> (-1, 1)
When x = 1
f(1) = 2*2¹ = 4 ----> (1, 4)
And so on, when you have enough points, you can graph them and connect them with a curve, the graph you will get is something like the one below.
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problem 3 [2pts] verify that the function y(t) = 1 cos(t) is a solution to the differential equation d 2y dt2 = 2y 3 − y
The function y(t) = 1/cos(t) is a solution to the differential equation d2y/dt2 = 2y3 - y if it satisfies the equation when substituted into it. To verify this, we can substitute the function into the equation and simplify.
First, let's find the first and second derivatives of the function:
dy/dt = (sin(t))/(cos^2(t))
d2y/dt2 = (2sin^2(t))/(cos^3(t)) - (1/cos^3(t))
Now, let's substitute these derivatives and the original function into the differential equation:
(2sin^2(t))/(cos^3(t)) - (1/cos^3(t)) = 2(1/cos(t))^3 - (1/cos(t))
Simplifying the right side of the equation gives us:
(2sin^2(t))/(cos^3(t)) - (1/cos^3(t)) = (2/cos^3(t)) - (1/cos(t))
Combining like terms on the right side gives us:
(2sin^2(t))/(cos^3(t)) - (1/cos^3(t)) = (2 - cos^2(t))/(cos^3(t))
Since sin^2(t) + cos^2(t) = 1, we can substitute 1 - cos^2(t) for sin^2(t) to get:
(2(1 - cos^2(t)))/(cos^3(t)) - (1/cos^3(t)) = (2 - cos^2(t))/(cos^3(t))
Simplifying the left side gives us:
(2 - 2cos^2(t))/(cos^3(t)) - (1/cos^3(t)) = (2 - cos^2(t))/(cos^3(t))
Combining like terms on the left side gives us:
(1 - cos^2(t))/(cos^3(t)) = (2 - cos^2(t))/(cos^3(t))
Since both sides of the equation are equal, we can conclude that the function y(t) = 1/cos(t) is a solution to the differential equation d2y/dt2 = 2y3 - y.
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3. In the figure below, find the values of x, y, and z.
Answer:
z= 13
x= 36
y= 18
Step-by-step explanation:
Solving for z.
We know that 108 degrees and (8z+4) are alternate exterior angles, so they are equal to each other.
We can set both of those angles equal to each other, and solve for our missing side, z.
108= 8z+4
104=8z
z= 13
Solving for x.
We know that 108 degrees and (3x) are alternate interior angles, so they would equal each other.
We can set both of these angles equal to each other, and solve for our missing side, x.
3x=108
x= 36
Solve for y.
We know that (4y) and (3x) are same side interior angles, so they would make 180 degrees. We know that (3x) would equal 108.
4y+108=180
4y= 72
y= 18
Find the first derivative for each of the following:
y = 3x2 + 5x + 10
y = 100200x + 7x
y = ln(9x4)
The first derivatives for the given functions are:
For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.
For \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.
For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.
To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.
For the function\(y = 3x^2 + 5x + 10:\)
Taking the derivative term by term:
\(d/dx (3x^2) = 6x\)
d/dx (5x) = 5
d/dx (10) = 0
Therefore, the first derivative is:
dy/dx = 6x + 5
For the function y = 100200x + 7x:
Taking the derivative term by term:
d/dx (100200x) = 100200
d/dx (7x) = 7
Therefore, the first derivative is:
dy/dx = 100200 + 7 = 100207
For the function \(y = ln(9x^4):\)
Using the chain rule, the derivative of ln(u) is du/dx divided by u:
dy/dx = (1/u) \(\times\) du/dx
Let's differentiate the function using the chain rule:
\(u = 9x^4\)
\(du/dx = d/dx (9x^4) = 36x^3\)
Now, substitute the values back into the derivative formula:
\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)
Therefore, the first derivative is:
dy/dx = 4/x
To summarize:
For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.
For y = 100200x + 7x, the first derivative is dy/dx = 100207.
For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.
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Problem 15.73. Give a combinatorial proof for this identity: n m Σ(0)(...)-("") (" *) k-r r=0
The combinatA combinatorial proof for the identity Σ(n-m+r choose r) (r=0 to m) = (n+1 choose m+1) is as follows:
Consider a set of (n+1) distinct objects labeled from 0 to n. We want to count the number of ways to choose a subset of (m+1) objects from this set.
On the left-hand side of the identity, we can break down the sum as follows:
Σ(n-m+r choose r) (r=0 to m)
Each term in the sum represents choosing a different number of objects from the first (n-m) objects. The term (n-m+r choose r) represents choosing r objects from the first (n-m) objects, where r ranges from 0 to m.
Now, let's consider the right-hand side of the identity, (n+1 choose m+1). This represents choosing (m+1) objects from the set of (n+1) objects.
We can interpret the left-hand side as counting the number of ways to choose a subset of (m+1) objects from a set of (n+1) objects using combinatorial reasoning. The right-hand side represents the same count directly by using the binomial coefficient. Therefore, both sides of the identity represent the same quantity, and the combinatorial proof verifies the given identity.
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40% off $800
25% off $600
Answer:
40% of $800 = 320
25% of $600 = 150
The graph shows depth of water in a tank over time.
Calculate the rate at which the depth is decreasing.
Give your answer as a decimal.
PLEASE HELP ASAP!!!
maria and charlie can deliver 45 papers in 3 hours. how long would it take them to deliver 51 papers
The time which both of take to deliver 51 papers is 3.4hours.
Since, we have time which Maria and Charlie are taking to deliver 45 papers.
Whenever some relation is given for any object with time and it is asking same relation at any other time, we need to use unitary methods.
So, we use unitary method.
45 papers are delivered in =3 hours
1 paper is delivered in =(3/45)hours
Therefore, 51 papers are delivered in :
=(3/45)×51hours
=(51/15)hours
=17/5hours
=3.4hours
Hence, 3.4 hours will be taken by both to deliver 51 papers.
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Which statement best describes a characteristic of money market accounts?
A. Money market accounts have a predetermined time limit before a withdrawal can be made.
B. Money market accounts allow for more withdrawals than regular savings accounts but with higher interest rates.
C. Money market accounts have higher interest rates than regular savings accounts but with more restrictions.
D. Money market accounts have no withdrawal minimums.
Answer:
Correct answer is C- Money market accounts have higher interest rates than regular savings accounts but with more restrictions
Step-by-step explanation:
took the quiz
What is the radius of a hemisphere with a volume of 165\text{ cm}^3,165 cm 3 , to the nearest tenth of a centimeter?
Answer:
4.3cm
Step-by-step explanation:
the radius of the hemisphere can be determined its volume
volume of a hemisphere = (2/3) x (n) x (r^3)
n = 22/7
r = radius
(2/3) x (22/7) x( r^3) = 165 cm^3
44/21 x r^3 = 165
divide both sides of the equation by 21/44
165 x 21/44
r^3 = 78.75
find the cube root
r = 4.2863 cm
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
the 100th terms, 8 is greater than 6, so add 1 to 2. this give 4.3cm
please help me
Which measurements could create more than one triangle?
A. A triangle with sides measuring 5 cm and 10 cm and an included angle measuring 40°
B. A triangle with sides measuring 4 inches, 8 inches, and 15 inches
C. A triangle with sides measuring 6 inches, 8 inches, and 10 inches
D. A triangle with angles measuring 75°, 60°, and 45°
Answer:
your answer is up there
Step-by-step explanation:
Sorry for not being some help i really am Red Riot out
What are the roots of the quadratic equation 0 = 2x² + 12x-14?
1,6, -7
2,12,-14
-7,1
-1,7
The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.
What is a quadratic equation?Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.
In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
So, the roots of 0 = 2x² + 12x-14 are:
2x² + 12x-14 = 0
2x² + 14x - 2x -14
2x(x + 7) - 2(x + 7)
(2x - 2) (x + 7)
Now, use the zero product property as follows:
2x - 2 = 0
2x = 2
x = 2/2
x = 1
And
x + 7 = 0
x = -7
Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.
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Correct question:
What are the roots of the quadratic equation 0 = 2x² + 12x-14?
a. 1,6, -7
b. 2,12,-14
c. -7,1
d. -1,7
Barbara has some dimes and quarters. If she has 16 coins worth a total of $2.50, how many of each type of coin does she have?
Answer:
10 dimes and 6 quarters.
Step-by-step explanation:
2.50-25-25=2.00-10 dimes = 1.00-4 0.25=0
so
10 dimes and 6 quarters.
Answer:
10 Dimes and 6 Quarters.
Step-by-step explanation:
Important info:
16 Coins
Total = $2.50
Note:
Dimes = 0.10 Cents
Quarters = 0.25 Cents
Question to answer:
How many of each type of coin does she have?
Solution:
10 Dimes = $1.00
6 Quarters = $1.50
$1.00+$1.50 = $2.50
Therefore 10 Dimes and 6 Quarters = $2.50 and = 16 Coin.
which number is not a perfect square?
A.1
B.25
C.30
D.36
Answer:
C. 30
Step-by-step explanation:
1 times 1 is 1
5 times 5 is 25
6 times 6 is 36
Answer:
The answer is 30
Step-by-step explanation:
what is the axis of symmetry of the graph of the function f(x)=3x^2+12x-4
Answer:
Step-by-step explanation:
Use the equation x = -b/2a => x = -12/6 = -2.
if a number is added to the numerator of (11)/(35) and twice the number is added to the denominator of (11)/(35), the resulting is equivalent to (1)/(3). find the number
For the statement to happen, the number should be 2.
An algebraic expression is is defined as the combination of numbers and variables in solving a particular mathematical question. Variable, usually letters, are used to denote the unknown quantity.
Let x = number
Based on the information given, add the number to the numerator of 11/35 and add twice the number to the denominator of 11/35, and the result should be equal to 1/3.
Hence, (11 + x) / (35 + 2x) = 1/3.
Simplify and solve for the value of x.
3(11 + x) = (35 + 2x)
33 + 3x = 35 + 2x
3x - 2x = 35 - 33
x = 2
number = 2
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if u have 10 and add 20 and add 10
Answer:
It will be 40
Step-by-step explanation:
Hope this helped have an amazing day!
The given statement is,
→ if u have 10 and add 20 and add 10.
In mathematical expression,
→ (10 + 20) + 10
→ 30 + 10
→ 40 is the answer.
help asap if you can pls an thank u!!!!!!!
The value of angle S is 53°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.
With this theorem we can say that
7x+2 = 4x+13+19
collecting like terms
7x -4x = 13+19-2
3x = 30
divide both sides by 3
x = 30/3
x = 10
Since x = 10
angle S = 4x+13
angle S = 4(10) +13
= 40+13
= 53°
Therefore the measure of angle S is 53°
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If a square has sides of 10 meters each, what is the perimeter?
Answer:
p= 4s
40 m
Step-by-step explanation:
Answer:
You would multiply 10 by 4 or add 10 4 times. A square has 4 sides and if each side is 10 meters, the answer would be
40 meters
:)
An umbrella top is composed of 8 equal triangles of fabric. What is the sum of the interior angles of the umbrella top?
Answer:
480 cm2
Step-by-step explanation:
8 isosceles triangles of sides 13cm,13cm,10cm
By Heron's Formula,
Area =
s(s−a)(s−b)(s−c)
Where s=
2
a+b+c
s=
2
13+13+10
=18
Area of triangle =
18×(18−13)×(18−13)×(18−10)
(Heron's formula)
Area of triangle =
18×5×5×8
=5
144
Area of triangle =60cm
2
Area of cloth made of 8 triangles =60×8
=480cm2
use the dual simplex method to find a solution to the linear programming problem formed by adding the constraint 3xi 5x3> 15 to the problem in example 2.
Using the dual simplex method to find a solution to the linear programming problem formed by adding the constraint 3xi 5x3> 15 to the problem. The final solution is:
xi = 20
x2 = 0
x3 = 15
x4 = 0
x5 = 40
Adding the constraint 3xi + 5x3 > 15 does not affect the optimal solution, as none of the variables involved in the new constraint are in the basis. Therefore, the final solution remains the same.
To use the dual simplex method to find a solution to the linear programming problem formed by adding the constraint 3xi + 5x3 > 15 to the problem in example 2, we need to follow these steps:
1. Rewrite the problem in standard form by adding slack variables:
Maximize 4xi + 3x2 + 5x3
Subject to:
2xi + 3x2 + 4x3 + x4 = 60
3xi + 2x2 + x3 + x5 = 40
xi, x2, x3, x4, x5 >= 0
2. Calculate the initial feasible solution by setting all slack variables to 0:
xi = 0
x2 = 0
x3 = 0
x4 = 60
x5 = 40
3. Calculate the reduced costs of the variables:
c1 = 4 - 2/3x4 - 3/2x5
c2 = 3
c3 = 5 - 2/3x4 - 1/2x5
c4 = -2/3x1 - 1/2x2
c5 = -3/2x1 - 1/2x2
4. Choose the entering variable with the most negative reduced cost. In this case, it is x1.
5. Calculate the minimum ratio test for each constraint to determine the leaving variable:
For the first constraint: x4/2 = 30, x1/2 = 0, so x4 is the leaving variable.
For the second constraint: x5/3 = 40/3, x1/3 = 0, so x5 is the leaving variable.
6. Update the solution by performing the pivot operation:
- Pivot on x1 and x4 in the first constraint: x1 = 20, x4 = 0, x2 = 0, x3 = 15, x5 = 40/3
- Pivot on x1 and x5 in the second constraint: x1 = 0, x4 = 0, x2 = 0, x3 = 15, x5 = 40
7. Repeat steps 3-6 until all reduced costs are non-negative or all minimum ratio tests are negative.
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Solve the system of equations using elimination: x-3y=-14x−3y=−14 and x-7y=-26x−7y=−26.
Answer:
2x - 10y = - 40
Step-by-step explanation:
x - 3y = -14
x - 7y = -26
2x - 10y = - 40
The length of two sides of a right triangle are leg: 12 m anli hypotenuse: 15
m. What is the area of the triangle. Round your answer to the nearest tenth
if necessary. *
Answer:
54m²
Step-by-step explanation:
Pythagorium theory
15²=12²+x²=> x=square root of 15²-12²
x=square root of 81
x=9
12*9/2=54m²
solve the given differential equation by undetermined coefficients. y'' 5y' 4y = 8
To solve the given differential equation by the method of undetermined coefficients, first identify the form of the equation: y'' - 5y' + 4y = 8.
This is a second-order linear homogeneous differential equation with constant coefficients. Since the right-hand side is a constant, we guess a particular solution of the form: yp = A, where A is an undetermined coefficient. Now we can find the first and second derivatives: yp' = 0
yp'' = 0
Substitute these values back into the original differential equation: 0 - 5(0) + 4A = 8
This simplifies to: 4A = 8
Now we can solve for the undetermined coefficient: A = 8 / 4
A = 2
So the particular solution is: yp = 2
Now we can find the complementary solution by solving the homogeneous equation: y'' - 5y' + 4y = 0
The characteristic equation is: r^2 - 5r + 4 = 0
Factoring this equation gives: (r - 4)(r - 1) = 0
So the roots are r1 = 4 and r2 = 1. The complementary solution is given by: yc = C1 * e^(4x) + C2 * e^(x)
Finally, the general solution is the sum of the complementary and particular solutions:
y(x) = C1 * e^(4x) + C2 * e^(x) + 2
where C1 and C2 are constants determined by initial conditions (if provided).
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Please HELP!!!! Asappppp thank you!!!!
Answer:
Step-by-step explanation:
The answer is C
Billy is ordering 7 identical sandwiches and a drink. The drink costs $2.5 and the entire order costs $140.5. Write an equation you can use to find the price of a sandwich.
Answer: $17.92/sandwich
Step-by-step explanation:
Let S be the price of a sandwich ($/sandwich).
7S is the total cost of the sandwiches. Add a drink for $2.50 to find the total cost, which we are told comes to $140.50
7S + $2.50 = $140.50
7S = $138
S = $19.7143
It is odd that this includes a fraction of a single penny (0.43 cents). Something is incorrect in the data given, since this should equal a whole number. For now, I'll round up to $19.72. The additional 7*($0.0043) = 4 cents will be treated as a tip.
Someone plz help me giving brainliest
Answer:
B. 5 2/5
Step-by-step explanation:
Use the long division solution to convert the original fraction ( 27/ 5 ) to a mixed number. The whole number portion of the mixed number will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction ( 5 ) , and the fraction portion of the mixed number will be the remainder of the original fraction division ( 2 ) over the denominator of the original fraction ( 5 )
What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures 80 degrees?
\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =80 \end{cases}\implies \begin{array}{llll} A=\cfrac{(80)\pi (8)^2}{360}\implies A=\cfrac{128\pi }{9} \\\\\\ A\approx 44.68~in^2 \end{array}\)
11. Stan Still is trying to record the dimensions of a "flag plot" (a triangular piece of land) where a house will be built. He has found that two consecutive sides of the plot have lengths of 70 yards and 95 yards. He has also determined that the angle between the two side is 82 degrees. To the nearest yard, what is the length of the final side of the plot?
Answer: 110 yards.
Step-by-step explanation:
According to the cosine formula,
In a triangle, if a and b are two consecutive sides and x is the angle between them, then the measure of the third side (c) is given by:-
\(c=\sqrt{a^2+b^2-2ab\cos x}\)
As per given, a= 70 yards , b= 95 yards , x= 82 degrees
The final side = \(\sqrt{(70)^2+(95)^2-2(70)(95)\cos 82^{\circ}}\)
\(=\sqrt{4900+9025-13300(0.139173)}\\\\=\sqrt{13925-1851} \\\\=\sqrt{12074}\\\\\approx110\text{ yards}\)
I.e. the length of the final side of the plot is 110 yards.