Answer:
0.51
Step-by-step explanation:
0.55 - (0.9 - 0.8) x 4
0.55 - 0.1 x 4
0.55 - 0.4
0.51
Carla has a rectangular garden in her backyard. The width of the garden is 9 meters. The area of the garden is 360 square meters. What is the length of the garden? Show your work.
Answer:
l = 40 m
Step-by-step explanation:
The formula for area of a rectangle is
A = lw, where
A is the area in square units,l is the length,and w is the widthStep 1: Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):
360 = 9l
Step 2: Divide both sides by 9 to solve for l
(360 = 9l) / 9
40 m = l
Optional Step 3: We can check our answers by checking that the product of 40 and 9 is 360
40 * 9 = 360
360 = 360
So What is the square meters of this shape
Answer:
6 square units
Step-by-step explanation:
area of a triangle = 1/2( base length x height )
The height of the triangle shown is 6 units
And the base length is 2 units
So the area would be 1/2 ( 6 * 2 )
6 * 2 = 12
12 * 1/2 = 6
The area is 6 square units
It takes 2 minutes to print out 3 posters at Carla's school.How long would it take to print out 14 posters
Prove this is a parallelogram
Answer:
please which class are you
simplify: sin theta {1/sin theta - 1/cosec theta}
Answer:
SORRY I DIDN'T KNOW
Step-by-step explanation:
PLEASE SOLVE THIS PROBLEM
imagine attached choose one
Answer:
R
Step-by-step explanation:
Using Pythagoras' theorem, calculate the length of YZ.
Give your answer in centimetres (cm) to 1 d.p.
17 cm
5 cm
The length of two sides is given as 17 cm and 5 cm, then the length of side YZ by Pythagoras' theorem will be equal to 16.25 cm.
What is a Pythagoras' Theorem?According to the Pythagoras theorem, the square on the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of squares of the remaining two sides.
As per the given values in the question,
The length of two sides is given as 17 cm and 5 cm.
As per Pythagoras' theorem,
h² = p² + b²
17² = 5² + b²
b² = 289 - 25
b = √264
b = 16.25 cm.
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Question 12 of 15
Solve: 8+=(x-4) - 1
A. x = -24
B. There are infinitely many solutions.
C. x = 40
D. x=-40
the solution of the system of equation where x = -40.
What is a System of Equations?
A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.
8+x/2 =1/4(x-4) - 1
⇒8+x/2 = x/4 -1 -1
⇒x/2-x/4 = -10
⇒x/4 = -10
⇒x = -40
Hence the solution of the system of equation where x = -40.
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Solve the following:
(If you answer for the points I will be reporting you)
(2x3 + 4x3 - ) - (-7x2 + x -5)
(-6y2 + 2y - 2) - (y2 - 3y +10)
(5x2 -4x +11) + (-12x2 +4x -1)
(10x2 -5x +3) - (8x2 + 6x + 4)
Answer:
Bellow
Step-by-step explanation:
(2x³ + 4x³ - ) - (-7x² + x -5)
= 6x³ + 7x² - x + 5
(-6y² + 2y - 2) - (y² - 3y +10)
= -6y² + 2y - 2 - y² + 3y - 10
= -7y² + 5y - 12
(5x² -4x +11) + (-12x² +4x -1)
= -7x² + 0x + 10
= -7x² + 10
(10x² -5x +3) - (8x² + 6x + 4)
= 10x² - 5x + 3 - 8x² - 6x - 4
= 2x² - 11x - 1
I hope this helps!
The expressions are s
6x³ + 7x² - x + 5
-7y² + 5y - 12
-7x² - 8x + 10
2x² - 11x -1
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of coefficients, variables, constants, terms and factors.
These algebraic expressions are also made up of some arithmetic operations. These operations are;
BracketParenthesesMultiplicationSubtractionAdditionDivisionFrom the information given, we have that;
1. (2x3 + 4x3 - ) - (-7x2 + x -5)
expand the bracket
6x³ + 7x² - x + 5
2. (-6y2 + 2y - 2) - (y2 - 3y +10)
expand the bracket
-6y² + 2y -2 - y² + 3y - 10
collect the like terms
-7y² + 5y - 12
3. (5x2 -4x +11) + (-12x2 +4x -1)
expand the bracket
5x² - 4x + 11 - 12x² - 4x - 1
-7x² - 8x + 10
4. (10x2 -5x +3) - (8x2 + 6x + 4)
expand the bracket
2x² - 11x -1
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Find the percent cost of the total spent on each equipment $36, fees $158, transportation $59
Percent cost of the total spent on
each equipment = 14.23%,fees=62.45% and transportation = 23.32%.
As given in the question,
Money spent on
Each equipment = $36
Fees = $158
Transportation = $59
Total money spent = $( 36 + 158 + 59)
= $253
Percent cost of the total spent on
Each equipment = (36/253) × 100
= 14.23%
Fees = (36/253) × 100
= 62.45%
Transportation =(36/253) × 100
= 23.32%
Therefore, percent cost of the total spent on
each equipment = 14.23%,fees=62.45% and transportation = 23.32%.
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How can you find the diameter and radius if you know the circumference.
Answer:
If we say the circumference is 1600 pi, and this is equal to pi times the diameter, we can just divide both sides by pi to get the diameter, which is going to be 1600.
Step-by-step explanation:
Circles are all similar, and "the circumference divided by the diameter" produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).
I need to get an answer for this …(2x − 3)² = 4x − 6
Expanding the square terms and rearranging the expressions for simplification , we can solve for x. The answer is x = \(\frac {5}{2}\) or \(\frac {3}{2}\) .
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
How to solve quadratic equation?Write the quadratic equation in standard form, ax2 + bx + c = 0. Write the Quadratic Formula. Then substitute in the values of a, b, c.Simplify.Check the solutions.\((2x-3)^2 = 4x-6\\4x^2 -12x+9 =4x-6\\4x^2 - 16x +15 =0\\4x^2-10x-6x+15 =0\\2x(2x-5)-3(2x-5)=0\\(2x-5)(2x-3)=0\)
x = \(\frac {5}{2}\) or \(\frac {3}{2}\)
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a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years. what is the 95% confidence interval estimate for the average number of years served by all supreme court justices? place your limits, rounded to 1 decimal place,
"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.
The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,
we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)
= 13.8 ± (1.96 × 1.088)
= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13
= 15.9313.8 - 2.13
= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].
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an experiment of study times versus test scores found a correlation coefficient of r = 0.49. how would you describe this relationship?
The correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores. This suggests that as study times increase, there is a tendency for test scores to also increase. However, the relationship is not extremely strong.
The correlation coefficient, denoted by 'r', ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other tends to increase as well. In this case, the correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores.
It's important to note that the correlation coefficient of 0.49 falls between 0 and 1, closer to 1. This suggests that there is a tendency for test scores to increase as study times increase, but the relationship is not extremely strong. Other factors may also influence test scores, and the correlation coefficient does not imply causation.
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What is SSS SAS ASA and AAS?
SSS - Side - Side - Side
SAS - Side - Angle - Side
ASA - Angle - Side - Angle
AAS - Angle - Angle - Side
The above theorems can be used to compare two triangles.
SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.
That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.
A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.
While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.
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SSS, SAS, ASA, and AAS are four types of triangle congruence.
SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.
SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.
ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.
AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.
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Here are two circles, Circle A and Circle D. Segment AD connects the two centers and is 10 inches long. Segment AD is a side to square ABCD. What is the area of the shaded region.
Answer:
the answer is, area of the square - a half of area of the circle
C=circle and S =square
radius of C is 10
so Area Of C is =
\(\pi r^{2} = \pi{10}^{2} = 100\pi\)
area of S = 10×10 = 100
so the answer is
\(s - \frac{c}{2} = 100 - \frac{100\pi}{2} = 100 - 50\pi\)
Write a quadratic equation in the form x^2+bx+c=0
ax^2 + bx + c = 0
a=1
b=4
c=-8
x^2 + 4x - 8 = 0
(I thought I was wrong but I might be correct lol)
which point is on the graph of the function y=8x+4
The point (0, 4) is on the graph of the function y = 8x + 4.
What is the graph of a function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.
The point on the graph of the function y = 8x + 4 depends on the values of x that you plug into the equation.
For any value of x, you can find the corresponding y-value using the equation.
For example:
x = 0, y = 8 * 0 + 4 = 4
So the point (0, 4) is on the graph of the function y = 8x + 4.
Similarly, for any other value of x, you can plug it into the equation and find the corresponding y-value to determine the point on the graph of the function.
Hence, the point (0, 4) is on the graph of the function y = 8x + 4.
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U 3
4
5
a) Solve by factorisation
6
7
8
3x²+2x80
9
Note: Please write your answers on the same line
separated with a comma, eg............
b) Solve the equation
2x² + 7x 80
Give each value correct to 2 decimal places.
Note: Please write your answers on the same line
separated with a comma, eg......
F *****
+
+
[3]
[3]
The solutions of equations 3x² + 2x - 80 and 2x² + 7x - 80 are x = -20/3 or x = 4, and x = -16/2 or x = 5, respectively.
What is equation?Equation is an expression that states the equality of two values. It is composed of symbols and numerical constants, as well as operators. Equations can be used to represent physical laws, mathematical relationships, or other types of relationships. Equations are used to describe the relationships between different variables, enabling us to solve problems by finding the values of those variables. Equations can also be used to describe the behavior of objects or systems.
a) 3x² + 2x - 80 = 0 can be factorized as (3x + 20)(x - 4) = 0. Therefore, the two solutions are x = -20/3 or x = 4.
b) 2x² + 7x - 80 = 0 can be factorized as (2x + 16)(x - 5) = 0. Therefore, the two solutions are x = -16/2 or x = 5.
From the above, it can be concluded that the solutions of equations 3x² + 2x - 80 and 2x² + 7x - 80 are x = -20/3 or x = 4, and x = -16/2 or x = 5, respectively.
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Choose the correct horizontal asymptote of f(x)=X +3/x² + 4
Answer:
I need the options mate to chose which is correct
Step-by-step explanation:
Under which condition can the work done by a force be calculated by taking the dot product of the force vector with the displacement vector?.
The work done by a force can be calculated by taking the dot product of the force vector with the displacement vector whether the force and displacement vectors are consecutive or anti-congruent.
The formula of the dot product is-
A ⋅ B = |A| |B| cos(θ)
Here A and B are the vectors |A| and |B| which represent their magnitudes, and θ is the angle between them.
The angle between the force and displacement vectors is either 0 degrees (cos(0) = 1) or 180 degrees (cos(180) = -1) depending on whether they are parallel or antiparallel. The dot product becomes: in these circumstances.
A ⋅ B = |A| |B| (1) = |A| |B| (cos(0)) = |A| |B|
When the vectors are parallel or antiparallel, the angle is 0 or 180 degrees, respectively, and the cosine term is 1 or -1. This occurs since work done is defined as the dot product of the force and displacement vectors multiplied by the cosine of the angle between them.
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(70 points)------------------
Answer:
Wait I don't understand the question... It looks like it is already answered- :(
Step-by-step explanation:
HELP!! Dr. Montgomery recently graduated from medical school and his wife bought him an engraved stethoscope. The stethoscope cost $160.00. The sales tax in his city is 8%. What is the total cost of the stethoscope in dollars and cents including sales tax?
Answer:
$172.8
Explanation
Divide 160 ÷ 100 to get 1.6 then multiply it by 8 to get 12.8 then add 160 to get 172.8
Consider the wave packet: ψ(x)=[ 2πa 2
1
] 1/2
exp[− 4a 2
(x−⟨x⟩) 2
+i ℏ
px
]. Calculate the uncertainties ⟨Δx 2
⟩=⟨( x
^
−⟨x⟩) 2
⟩ and ⟨Δp 2
⟩=⟨( p
^
−⟨p⟩) 2
⟩, where ⟨ A
^
⟩ denotes the expectation value ⟨ψ∣ A
^
∣ψ⟩ of the observable A
^
on the state ∣ψ>.
The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.
The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.
To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.
Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
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Error Analysis Sarah said the vertex of the function f(x) = (x + 2)² is (2, 6). Is she correct? Explain.
No, Sarah's claim that the vertex of the function\(f(x) = (x + 2)^2\) is (2, 6) is incorrect. The correct vertex of the function f(x) = (x + 2)² is (-2, 0)
Comparing the given function \(f(x) = (x + 2)^2\) with the general form, we can see that the function has a transformation of shifting 2 units to the left (h = -2) and no vertical shift (k = 0). Therefore, we expect the vertex to be at the point (-2, 0).
To find the vertex explicitly, we can set the derivative of the function equal to zero and solve for x. The derivative of\(f(x) = (x + 2)^2\) is\(f'(x) = 2(x + 2).\)Setting f'(x) = 0, we find x = -2. Plugging this value into the original function, we get f(-2) = (0)² = 0. So, the vertex is indeed located at (-2, 0).
In conclusion, the correct vertex of the function \(f(x) = (x + 2)^2\) is (-2, 0), not (2, 6). Sarah's claim is incorrect, likely due to a misunderstanding of the vertex form of the quadratic function.
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Evaluate the integral after changing to spherical coordinates.∫30∫√9−y2−√9−y2∫√9−x2−y20(x2z+y2z+z3)dzdxdy
To change to spherical coordinates, we can use the following formula:
x = ρ sin φ cos θ
y = ρ sin φ sin θ
z = ρ cos φ
We also note that the region of integration is a hemisphere with radius 3, and that the integrand contains x^2z+y^2z+z^3. Since we are integrating over a hemisphere, the bounds of ρ can be from 0 to 3, φ can be from 0 to π/2, and θ can be from 0 to 2π.
Next, we need to express the integrand in terms of ρ, φ, and θ. Substituting x, y, and z, we get:
x^2z + y^2z + z^3 = ρ^4 sin^2 φ cos^2 θ (ρ cos φ) + ρ^4 sin^2 φ sin^2 θ (ρ cos φ) + (ρ cos φ)^3
Simplifying, we get:
x^2z + y^2z + z^3 = ρ^5 cos^2 φ + ρ^3 cos^3 φ
Thus, the new integral is:
∫0^(2π) ∫0^(π/2) ∫0^3 (ρ^5 cos^2 φ + ρ^3 cos^3 φ) ρ^2 sin φ dρ dφ dθ
Integrating with respect to ρ, we get:
∫0^(2π) ∫0^(π/2) [ 1/6 ρ^6 cos^2 φ + 1/4 ρ^4 cos^3 φ ]_|ρ=0^3 sin φ dφ dθ
Simplifying and integrating with respect to φ, we get:
∫0^(2π) [ 9/5 sin^5 φ - 27/14 sin^7 φ ]_|φ=0^(π/2) dθ
Evaluating the limits, we get:
∫0^(2π) [ 9/5 - 27/14 ] dθ
Finally, evaluating the integral, we get:
∫0^(2π) [ 33/35 ] dθ = 66π/35
Therefore, the value of the integral after changing to spherical coordinates is 66π/35.
The first three terms of a sequence are given. round to the nearest thousandth (If necessary). 15,18,108/5 Find the 7th term pls help
The sequence 15, 18, 108/5 is a geometric sequence
The value of the 7th term is \(44\frac{2468}{3125}\)
How to determine the 7th term?The sequence is given as:
15, 18, 108/5
The above sequence is a geometric sequence with the following parameters:
First term, a = 15
Common ratio = 18/15
The nth term of a geometric sequence is:
an = a * r^(n - 1)
So, the 7th term is:
a7 = a * r^6
This gives
a7 = 15 * (18/15)^6
Evaluate
\(a_7 = 44\frac{2468}{3125}\)
Hence, the value of the 7th term is \(44\frac{2468}{3125}\)
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Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5
The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.
To convert the given equation from standard form to vertex form, we need to complete the square.
The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.
Given equation: y = x² - 6x + 14
Move the constant term to the right side:
y - 14 = x² - 6x
Complete the square by adding and subtracting the square of half the coefficient of x:
y - 14 + 9 = x² - 6x + 9 - 9
Group the terms and factor the quadratic:
(y - 5) = (x² - 6x + 9) - 9
Rewrite the quadratic as a perfect square:
(y - 5) = (x - 3)² - 9
Simplify the equation:
y - 5 = (x - 3)² - 9
Move the constant term to the right side:
y = (x - 3)² - 9 + 5
Combine the constants:
y = (x - 3)² - 4
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Please help it’s due tomorrow!
What is the most simplified expression for 4 c squared d + 3 d c minus 2 (d c squared + c d) + 6 c squared d squared?
2 c squared d + d c + 6 c squared d squared
2 c squared d + 5 d c + 6 c squared d squared
3 c squared d + 3 d c + 6 c squared d squared + c d
3 c squared d + 2 d c + 6 c squared d squared minus 2 cd
Answer: 2 c squared d + d c + 6 c squared d squared
Step-by-step explanation: I looked it up