Answer:
\(\frac{61}{99}\)
Step-by-step explanation:
let x = 0.616161 (etc.)
make a second equation because you multiply by 100:
100x = 61.616161 (etc.)
subtract from each other
100x = 61.616161
x = 0.616161
you get
99x = 61
solve for x
\(\frac{61}{99}\)
If a+b=3, ab=2, the value of a^2+ab^2?
Answer:
hope u will understand
A set of twins purchase a small, oddly shaped plot of land for their retirement. They want to divide the parcel along the grid lines into two identical plots. Can they do it and how?
The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.
To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.
For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.
If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.
However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.
To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.
If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.
the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.
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Note the full question may be :
To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.
Please help me solve this, it’s the last question.
The value of the double integration is 7776 after solving and integration. the answer is 7776.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
Double integration (x + y) dA
y = x²
y² = 216x
y = √216 √x
∫∫(√216 √x + x²)
After solving:
\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)
=7776
Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.
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1. Vocabulary Define opposites.
Answer:
Opposite means: im going to do something but in "reverse" like opposite day.
Step-by-step explanation:
In △JKL , if m∠ J < 90° , then ∠K and ∠L are _____
Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.
In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.
An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.
In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.
Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.
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Find the domain of the inverse function w-1 (x) . Express your answer as in inequality
Answer:
ANSWER
Step-by-step explanation:
Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.
If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).
For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.
Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.
A bee can pull 300 times its weight. If a person could pull a load in this same proportion, how many pounds could you pull? i weigh 120 pounds
here is an example of how it has to be wrote out.ijust dont know how to rite my question out
Answer:
36,000lbs
Step-by-step explanation:
300 x 120
true/false. the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables
The statement " the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables" is true because continuity correction is used to adjust for the discrepancy between continuous and discrete variables when approximating a discrete distribution
The continuity correction is used when approximating a discrete distribution, such as the binomial distribution, with a continuous distribution, such as the normal distribution. The normal distribution assumes continuous variables, while the binomial distribution uses discrete variables.
The continuity correction helps to account for the fact that the normal distribution is continuous, whereas the binomial distribution is not. It adjusts the boundaries of the intervals used in the approximation, to better reflect the underlying discrete nature of the data.
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On 5 days, lisa swam 650 meters, 675 meters, 725 meters, 800 meters, and 900 meters. What was her average distance per day?
Answer:
Her average per day was 750 meters.
Step-by-step explanation:
To find the average, add all the numbers up in the set and divide by how many numbers there are.
650 + 675 + 725 + 800 + 900 = 3750. Divide it by 5 and you get 750
Answer:
750 meters
Step-by-step explanation:
Step 1: Add all the given data
650 + 675 + 725 + 800 + 900 = 3750
Step 2: Divide the result by the number of numbers she swam
3750/5 = 750
The average distance per day is 750 meters.
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
A particle in the ocean moves with a wave. The motion of the particle can be modeled by the cosine function. If a 14 in. wave occurs every 10 s, write a function that models the height of the particle in inches y as it moves in seconds x. What is the period of the function?
The required function y = 7 cos (2π * 0.1 * x) and period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.
How to find the cosine function of this problem?he cosine function can be used to model periodic motion, and its general form is:
y = A cos (Bx + C) + D
where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
In this case, we know that a 14 in. wave occurs every 10 s, so we can use this information to find the frequency, which is the reciprocal of the period. The period is the time it takes for one complete cycle of the wave, which in this case is 10 s.
Therefore, the frequency is:
\(f = \frac{1}{T}=\frac{1}{10} = 0.1 Hz\)
We can also see that the amplitude of the wave is 7 inches, since the wave has a height of 14 inches from its highest point to its lowest point.
Now we can write the function that models the height of the particle in inches y as it moves in seconds x:
y = 7 cos (2π * 0.1 * x)
Here, the frequency is expressed in radians per second (2π * 0.1 = 0.2π), since the cosine function takes radians as its argument. The phase shift and vertical shift are both zero in this case, since the wave starts at its highest point and has no vertical shift.
Therefore, the period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.
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Which Is the Best estimare of The área of The figure in square centimeters (as shown down) l need It in 5min
Answer:
38.28cm²
Step-by-step explanation:
The area of the figure can be determined by expression the figure as two shapes.
A semicircle and trapezium;
Area of shape = Area of semicircle + Area of trapezium
Now;
Area of semicircle = \(\frac{\pi r^{2} }{2}\)
Where r is the radius, which is \(\frac{4}{2}\) = 2cm;
Area of semicircle = \(\frac{3.142 x 2^{2} }{2}\) = 6.28cm²
Area of trapezium;
= \(\frac{1}{2} (a + b)h\)
a and b are the base length = 6cm and 10cm
h is the height = 4cm
Input the parameters and solve;
= \(\frac{1}{2} (6 + 10) 4\)
= 32cm²
The area of the shape = 6.28cm² + 32cm² = 38.28cm²
lim x>-1 x^2-x-2/x+1
Answer:
-3
Step-by-step explanation:
If we directly evaluate the function at -1, we get 0/0, meaning we may still have a limit to find.
In this case, factoring the polynomial at the top would be helpful.
The polynomial can be factored to (x+1)(x-2), so the function would now turn out to be (x+1)(x-2)/(x+1)
The (x+1) cancel out, leaving you with (x-2), which you can directly evaluate by plugging in x as -1:
-1-2 = -3
Quick disclaimer: the function is still undefined at -1; it's just that the function gets closer and closer to -3 as you approach -1.
I hope this helped you.
the sum of 1/2 and 1/5 is between 1/2 and 1 yes or no
Answer:
no
Step-by-step explanation:
vertex to standard form
The quadratic function y = 7(x + 1)² + 1 in standard form is y = 7x² + 14x + 2.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is -
y = 7(x + 1)² + 1
Solve the equation to get the standard form.
First solve using the formula (a + b)² = (a² + 2ab + b²) -
y = 7(x + 1)² + 1
y = 7(x² + 2x + 1) + 1
Now, open the brackets -
y = 7x² + 14x + 1 + 1
Now, add the like terms -
y = 7x² + 14x + 2
Therefore, the value is obtained as 7x² + 14x + 2.
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What’s the answer to this?
Answer:
your answers will be options B and E
Step-by-step explanation:
hope this helps have a nice day!!
Tom is showing his work in simplifying (5.2 - 8.5) - 0.5 + 6.8. In which step did Tom make an error? (5 points)
Step 1:: (5.2 - 8.5) - 0.5 + 6.8
Step 2: 5.2 + (-8.5 - 0.5) + 6.8 (distributive property)
Step 3: 5.2 - 9 + 6.8
Step 4: 5.2 + 6.8 - 9 (commutative property)
Step 5: 12 - 9 = 3
Answer:
Step 2; he wrote distributive instead of associative
Step-by-step explanation:
Given the values A, B and C, the following expression is true about associative property
(A+B)+C = A+(B+C) [Associative property]
We can see that according to this property, we only regrouped the values without changing their positions.
Applying this in Tom's solution, we will find out that he made an error in step 2. The property he used was associative property not distributive property because all he did was to re-group the values with changing their positions.
From Step 1 and 2:
Step 1:: (5.2 - 8.5) - 0.5 + 6.8
Step 2: 5.2 + (-8.5 - 0.5) + 6.8 (Associative property)
Hence Tom made an error in step 2 where he wrote distributive instead of associative property.
water stations will be placed every 400 metets of a 5 kilometer racehow many water staions are neeedded
13 water stations will be placed every 400 meters of a 5 kilometer.
Given: Water stations will be placed ; every 400 meters
Also the total distance = 5 km = 5000 meters
Thus if a water station is supposed to be kept at every 400 meter distance then that means we can find out this distance by using unitary method
this means by using unitary method we get;
Number of water stations needed is = 5000 divided by 400
12.5 = 13 water stations would be required.
Thus 13 water stations will be placed every 400 meters of a 5 kilometer.
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Which expression is equivalent to 20 + 8y − 9y − 21
Answer:
-y-1
Step-by-step explanation:
12.
Find the equation of the circle which touches the line 3y-4x-24 = 0 at the point
(0,8) and also passes through the point (7,9). Prove that this circle also touches the
x-axis. Find the equation of the tangents to this circle which are perpendicular to the
line 3-4x-24=0.
The equation of the circle is (x-3)^2 + (y-4)^2 = 85.the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.
What is the equation of the circleFirst, we find the center of the circle. Since the circle touches the line 3y-4x-24=0 at the point (0,8), the center must lie on the line perpendicular to this line and passing through (0,8), which has the equation 4y + 3x - 32 = 0. The intersection of this line with the line passing through (7,9) and perpendicular to the line 3y-4x-24=0 gives us the center of the circle:
Solving the equations 3y - 4x - 24 = 0 and 4y + 3x - 32 = 0 gives us the point (3,4), which is the center of the circle.
Now, we can find the radius of the circle by using the distance formula between the center (3,4) and the point (7,9):
r = √((7-3)^2 + (9-4)^2) = √(85)
So the equation of the circle is (x-3)^2 + (y-4)^2 = 85.
To prove that the circle also touches the x-axis, we need to show that the distance from the center (3,4) to the x-axis is equal to the radius. The equation of the x-axis is y=0, so the distance from (3,4) to the x-axis is simply 4. Since the radius is sqrt(85), which is also approximately equal to 9.22, we can see that 4 is indeed equal to the radius, so the circle touches the x-axis.
To find the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0, we first find the slope of this line, which is 3/4. The slope of a line perpendicular to this line is the negative reciprocal, which is -4/3.
To find the points of tangency, we need to find the intersection points of the line passing through (3,4) with slope -4/3 and the circle (x-3)^2 + (y-4)^2 = 85. This gives us two points of tangency: (0,7) and (6,1).
The tangent lines at these two points can be found using the point-slope form of the equation of a line, with the slope equal to the negative reciprocal of the slope of the line 3y-4x-24=0:
At (0,7), the tangent line has the equation y - 7 = (-4/3)(x-0), which simplifies to y = (-4/3)x + 7 + 4 = (-4/3)x + 11.
At (6,1), the tangent line has the equation y - 1 = (-4/3)(x-6), which simplifies to y = (-4/3)x + 9.
Therefore, the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.
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Complete the equation describing how x
and y are related.
Х у
y = [? ]x +
07
1 9
2 11
3 13
4 15
5 17
Enter the answer that
belongs in [?]
Answer:
Hello,
Answer 2
Step-by-step explanation:
7=2*0+7
9=2*1+7
11=2*2+7
13=2*3+7
15=2*4+7
17=2*5+7
y=2*x+7
An other way:
\(points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\\)
The complete equation is \(y = 2x+7\).
What is equation?An equation is a condition on a variable such that two expressions in the variable should have equal value.
What is substitution?Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
\(y = ax + b\)
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
\(\implies 7 = a(0) + b\\\implies b = 7\)
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
\(\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2\)
substitute the value of a and b in the equation y = ax + b.
\(\implies y = 2x+ 7\)
Therefore, the complete equation is \(y = 2x+7\).
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What is the exact value of sin165° ?
Which of the following is the point and slope of the equation y + 2 = 2(x - 8)?
-8, 2), 2
(2, -8), 2
(8, -2), 2
(-2, 8), 2
PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
The function rule for g(x) is h(x) = (x - 0)² - 7.
How to determine the vertex form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:
f(x) = a(x - h)² + k
2 = a(-3 - 0)² - 7
2 + 7 = 9a
9 = 9a
a = 1
Therefore, the required quadratic function in vertex form is given by:
h(x) = a(x - h)² + k
h(x) = (x - 0)² - 7
h(x) = x² - 7
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Please help with my music math
10. A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of _______ inch.
A. 3
B. 1/2
C. 1
D. 11/2
A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).
To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.
The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.
Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.
The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.
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How many solutions does the system of equations below have? y=-3/4x+1/6
The solution is the point (0, 1/6) y = 1/6
Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.
In this case, the equation is in slope-intercept form (y = mx + b),
where m represents the slope (-3/4) and b represents the y-intercept (1/6).
The slope-intercept form allows us to determine various properties of the equation.
Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.
Each pair of x and y values that satisfy the equation represents a solution.
For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:
y = (-3/4)(0) + 1/6
y = 1/6
Therefore, the solution is the point (0, 1/6).
In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.
Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.
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A negatively charged balloon moves close to another balloon. They then repel each other. What can be said about the other balloon?
Answer: B: It has a negative charge.
Step-by-step explanation:
According to theory espoused by the French physicist, Charles-Augustin de Coulomb, like charges charges will repel each other and unlike charges will attract one another.
This means that objects with negative charges will repel each other. As the first balloon in the question was negatively charged, it would only repel the other balloon if it was negatively charged as well.
Answer:
b
Step-by-step explanation:
i got it correct sorry if it wasnt helpful have a good day:)
One month Pablo rented 5 movies and 3 video games for a total of $39. The next month he rented 2 movies and 12 video games for a total of 75 . Find the rental cost for each movie and each video game.
we get that the rental cost for each movie is $ 4.5 and each video game is $ 5.5.
Let the cost of number of movies be x and the cost of number of video games be y.
So, the equations are:
5 x + 3 y = 39
2 x + 12 y = 75
2 x = 75 - 12 y
x = 75/2 - 6 y
Put it in the first one, we get that:
5 ( 75/2 - 6y) + 3y = 39
375/2 - 30 y + 3 y = 39
27 y = 187.5 - 39
27 y = 148.5
y = 148.5 / 27
y = $ 5.5
x = 75/2 - 6 y
x = 37.5 - 6 (5.5)
x = 37.5 - 33
x = $ 4.5
Therefore, we get that the rental cost for each movie is $ 4.5 and each video game is $ 5.5.
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On a certain hot summer's day, 310 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $718.00. How many children and how many adults swam at the public pool that day?