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What will be the values of x if the distance between the
points (x, 4) & (3, x) be 131/2 ?
The values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.
To find the values of x if the distance between the points (x, 4) & (3, x) be 131/2, we can use the distance formula:
D = √((x2 - x1)² + (y2 - y1)²)
Where D is the distance, (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the given values, we get:
131/2 = √((3 - x)² + (x - 4)²)
Squaring both sides and simplifying, we get:
169 = (3 - x)² + (x - 4)²
Expanding and rearranging, we get:
2x² - 14x - 110 = 0
Using the quadratic formula, we can find the values of x:
x = (-(-14) ± √((-14)² - 4(2)(-110))) / (2(2))
x = (14 ± √(196 + 880)) / 4
x = (14 ± √1076) / 4
x ≈ 9.39 or x ≈ -4.39
So the values of x are approximately 9.39 and -4.39.
Therefore, the values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.
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1. A wife works three days then a day off while his husband works five days then a day off. If the couple has a day-off together today, how many days after will they have another day off together?
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth. If a man weighs 180 pound on the surface of the earth, what would his weight be at an altitude 1000 miles? Assume the radius of the earth to be 4000 miles
3. Two turtles A and B start at the same time move towards each other at a distance of 150 m. The rate of turtle A is 10 m/s while that B is 20 m/s. A fly flies from one turtle to another at the same time that the turtles start to move toward its each other. The rate of the fly is constant at 100 m/s. determine the total distance traveled by the fly until the two turtles met?
1). 15 days
2). 115.2 pounds.
3). 500 meters
1. To find out when the couple will have another day off together, we need to find the least common multiple (LCM) of their work schedules. The LCM of 3 and 5 is 15, so the couple will have another day off together after 15 days.
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth.
This means that W = k/D^2, where k is a constant.
To find k, we can plug in the values given in the question: 180 = k/4000^2.
Solving for k gives us k = 180*4000^2 = 2880000000. Now we can plug in the new distance, 4000 + 1000 = 5000 miles, to
find the new weight: W = 2880000000/5000^2 = 115.2 pounds.
3. To find the total distance traveled by the fly, we need to find out how long it takes for the turtles to meet.
The combined rate of the turtles is 10 + 20 = 30 m/s, so it will take them 150/30 = 5 seconds to meet.
The fly travels at a constant rate of 100 m/s, so in 5 seconds it will have traveled 100*5 = 500 meters.
Therefore, the total distance traveled by the fly is 500 meters.
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t Marie's Beading Boutique, 32 out of the 32 beads on clearance are plastic. What percentage of beads on clearance are plastic?
Write your answer using a percent sign (%).
Answer:
100%
Step-by-step explanation:
If all 32 the beads were plastic it would be 100%
solve asap
q3)in a production chain, 20% of the items are exceptionally good. If 10 items are inspected by a quality assurer, find the probability that exactly 2 of them are exceptionally good.
0.50
0.68
0.30
0.57
q2)A student answers randomly three True (T) or False (F) questions.
(a) Make the list of all possible outcomes (sample space).
(b) Make the list of outcomes corresponding to the following event: The student answered True at least two times
(c) Evaluate the probability that the student answered True at least two times
Q3) The correct answer is 0.30.
Q2) (a) The sample space for three True or False questions is:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF
Q2) The outcomes corresponding to the event "The student answered True at least two times" are:
TTT, TTF, TFT, FTT
Q2) The probability of the student answering True at least two times is:
P(X >= 2) = 4/8 = 0.50
The probability of an item being exceptionally good is 0.20, and the probability of an item not being exceptionally good is 0.80. We can use the binomial probability formula to find the probability of exactly 2 of the 10 inspected items being exceptionally good:
P(X = 2) = (10 choose 2) * (0.20)^2 * (0.80)^8 = 45 * 0.04 * 0.16777 = 0.30
Therefore, the correct answer is 0.30.
(a) The sample space for three True or False questions is:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF
(b) The outcomes corresponding to the event "The student answered True at least two times" are:
TTT, TTF, TFT, FTT
(c) The probability of the student answering True at least two times is:
P(X >= 2) = 4/8 = 0.50
Therefore, the correct answer is 0.50.
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ind all solutions of the system of equations algebraically. oordinate points. y=-3x^(2)+12x 3x+y=12
The given system of equations can be written as: y=-3x^2+12x 3x+y=12
To solve this system, we can use the substitution method. We will solve the first equation for y and substitute this value in the second equation to solve for x. From the first equation, we have y=-3x^2+12x. Substituting this in the second equation, we get 3x+(-3x^2+12x)=12. Simplifying, we get -3x^2+15x=12.
Now, we can solve this equation for x. To do this, we can divide both sides of the equation by -3 to get x^2+5x/3=4/3. Factoring the left side, we get (x+5/3)(x-4/3)=0. From here, we can find the two solutions for x: x=-5/3 and x=4/3. Substituting these values in the first equation, we get the two solutions for y: y=-17/3 and y=20/3. Therefore, the two solutions for the system of equations are (x=-5/3, y=-17/3) and (x=4/3, y=20/3).
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Big ideas 7.5 question (image)
Answer:
Option three
Step-by-step explanation:
The first two are incorrect reasonings so they are not even options to consider. The bottom two are correct reasonings. But, the third option would be best because it is most specific. With it being an isosceles trapizoid.
In 1846 the depth of the river was 5 feet deep.
In 1847 it dropped to 3.6 feet.
This year, 1848, it rose to 5.7 feet.
Find the percent change in river depth & complete the
table.
The percentage change of the depth from 1846 to 1847 is 28%.
The percentage change of the depth from 1846 to 1848 is 14%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Percentage change formula:
= [ (Final percentage - Initial percentage) / Initial percentage ] x 100
Percentage change of the depth from 1846 to 1847.
= [ (3.6 - 5) / 5 ] x 100
= 1.4/5 x 100
= 1.4 x 20
= 28
Percentage change of the depth from 1846 to 1848.
= [ (5.1 - 5) / 5 ] x 100
= 0.7/5 x 100
= 0.7 x 20
= 14
Now,
Year 1847 1848
Depth 3.6 feet 5.7 feet
Percentage change 28% 14%
Thus,
The percentage change of the depth from 1846 to 1847 and 1846 to 1848 is 28% and 14%
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3 mi. and 10,000 ft.
is the same equal or different
Answer:
3 Miles
Step-by-step explanation:
3 mi = 15,840ft.
15,840 is greater than 10,000, so 3 miles is more
What is the product of -2x^3+x-5 and x^3-3x-4?
(A) Show your work.
(B) Is the product equal to (x^3-3x-4)*(-2x^3+x-5)? Explain your answer.
Answer:(A) Show your work.
Step-by-step explanation:(A) Show your work.
Answer: holy math sucks but check the explanation i gotchu
Step-by-step explanation: A) -2x^6 + 3x^5 - 2x^4 - 15x^3 + 4x^2 -20x - 20
B) No, the product is not equal to (x^3-3x-4)*(-2x^3+x-5). This is because the order of the terms in the product is different than the order of the terms in the expression. The product takes the form of -2x^6 + 3x^5 - 2x^4 - 15x^3 + 4x^2 -20x - 20, whereas the expression has the form of (-2x^3+x-5)*(x^3-3x-4).
Chad will drive 672 more miles. He continues to drive at the same rate. How many hours will it take Chad to drive the 672 miles?
The time needed for Chad to drive the 672 miles is given as follows:
t = 672/v.
In which v is his current rate.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
For a distance of 672 miles, we have that the parameter d is given as follows:
d = 672.
Hence the time is obtained as follows:
v = 672/t
t = 672/v.
(we don't have the velocity, hence the time is given as a function of the velocity).
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The graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses. What is the domain of this graph?

The answer of the given question based on the graph shows number of birdhouses Penn and his father can build, if they have enough time to build not more than 10 birdhouses, the correct option is A).
What is Graph?
In mathematics, a graph is a collection of points (called vertices or nodes) and the lines or arcs (called edges) that connect them. Graphs are used to model and analyze a variety of real-world situations, such as social networks, transportation systems, and electrical circuits.
Based on the given graph, the horizontal axis represents the number of birdhouses Penn's father can build and the vertical axis represents the number of birdhouses Penn can build. The graph is bounded by the line x + y = 10, which means that the sum of number of the birdhouses Penn and his father can build cannot be exceed more than10.
Therefore, the domain of this graph is the set of possible values for the number of birdhouses Penn's father can build, subject to the constraint that the sum of the number of the birdhouses Penn and his father can build cannot be exceed more than 10. This domain is the set of non-negative integers less than or equal to 10, inclusive. In interval notation, this can be written as [0, 10].
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Complete question:-The graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses. What is the domain of this graph?
The number 52m is a perfect cube. Find the smallest positive integer value of m.
The smallest positive integer value of m is 676.
To find the smallest positive integer value of m, we need to factor 52m into its prime factors and find the smallest value of m that makes 52m a perfect cube.
First, let's factor 52m into its prime factors:
52m = 2 * 2 * 13 * m
A perfect cube has all of its prime factors raised to the power of 3. So, in order for 52m to be a perfect cube, we need to have two more 2's, two more 13's, and two more m's.
This means that m must be equal to 2 * 2 * 13 * 13 = 676.
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A widget manufacturer's expense function is
E = 6.00 q + 11,000
What are the variable costs to produce one widget?
The variable costs to produce one widget is 6.00
How to determine the variable costsFrom the question, we have the following parameters that can be used in our computation:
E = 6.00 q + 11,000
The variable cost is the slope of the relation
Using the above as a guide, we have the following:
Fixed cost = 11000
Variable cost = 6.00
The above parameters mean that
The variable cost is 6.00
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I NEED HELP PLS I NEED THIS BY FRIDAY
The required measure of the angle S in the isosceles trapezoid is ∠S = 115°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
For isosceles trapezoid,
The sum of the opposite angle is equal to 180°.
∠Q + ∠S = 180
Substitute the value in the above expression,
65 + ∠S = 180
∠S = 180 - 65
∠S = 115°
Thus, the required measure of the angle S in the isosceles trapezoid is ∠S = 115°.
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Show that when \( n \) is a positive integer, so also is \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \). Verify that the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians
The sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.
When \( n \) is a positive integer, we can use mathematical induction to prove that \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \) is also a positive integer.
Base case: \( n = 1 \), then \( \left(1^{3}+6 \cdot 1^{2}+2 \cdot 1\right) / 3 = \frac{9}{3} = 3 \) which is a positive integer.
Induction step: Assume \( \left(k^{3}+6 k^{2}+2 k\right) / 3 \) is a positive integer for some positive integer \( k \). Then:
\[ \left( \left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 = \frac{k^{3}+18 k^{2}+22 k+9}{3} \]
\[ = \frac{k^{3}+6 k^{2}+2 k + 6 k^{2}+16 k + 9}{3} \]
\[ = \frac{k^{3}+6 k^{2}+2 k}{3} + \frac{6 k^{2}+16 k + 9}{3} \]
\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \frac{\left(6 k^{2}+16 k + 9\right)}{3} \]
\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \left(2 k + 3\right) \]
Since the first term is a positive integer and the second term is a positive integer, it follows that \( \left(\left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 \) is a positive integer as well.
Therefore, it has been shown that when \( n \) is a positive integer, so also is \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \).
To verify that the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians, consider the following: the sum of the interior angles of any polygon is equal to \( (n-2) \pi \) radians, where \( n \) is the number of sides in the polygon. This is true for any type of polygon, whether it is a triangle, quadrilateral, pentagon, etc.
Therefore, the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.
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Find the exact value of each of the remaining trigonometric functions of \( \theta \). Rationalize denominators when applicable. \( \cot \theta=-\frac{\sqrt{3}}{7} \), given that \( \theta \) is in qu
The exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).
We can find the exact value of the remaining trigonometric functions of \( \theta \) by using the Pythagorean identity and the definition of the trigonometric functions. The Pythagorean identity states that \( \sin^2 \theta + \cos^2 \theta = 1 \). The definition of the trigonometric functions are \( \sin \theta = \frac{y}{r} \), \( \cos \theta = \frac{x}{r} \), \( \tan \theta = \frac{y}{x} \), \( \cot \theta = \frac{x}{y} \), \( \sec \theta = \frac{r}{x} \), and \( \csc \theta = \frac{r}{y} \).
Given that \( \cot \theta=-\frac{\sqrt{3}}{7} \), we can use the definition of the cotangent function to find the values of x and y. Let x = -\( \sqrt{3} \) and y = 7. Then, we can use the Pythagorean identity to find the value of r.
\( \sin^2 \theta + \cos^2 \theta = 1 \)
\( \frac{y^2}{r^2} + \frac{x^2}{r^2} = 1 \)
\( \frac{7^2}{r^2} + \frac{(-\sqrt{3})^2}{r^2} = 1 \)
\( \frac{49 + 3}{r^2} = 1 \)
\( \frac{52}{r^2} = 1 \)
\( r^2 = 52 \)
\( r = \sqrt{52} \)
Now, we can use the definition of the trigonometric functions to find the exact value of the remaining trigonometric functions of \( \theta \).
\( \sin \theta = \frac{y}{r} = \frac{7}{\sqrt{52}} = \frac{7\sqrt{52}}{52} \)
\( \cos \theta = \frac{x}{r} = \frac{-\sqrt{3}}{\sqrt{52}} = \frac{-\sqrt{3}\sqrt{52}}{52} \)
\( \tan \theta = \frac{y}{x} = \frac{7}{-\sqrt{3}} = \frac{-7\sqrt{3}}{3} \)
\( \sec \theta = \frac{r}{x} = \frac{\sqrt{52}}{-\sqrt{3}} = \frac{-\sqrt{52}\sqrt{3}}{3} \)
\( \csc \theta = \frac{r}{y} = \frac{\sqrt{52}}{7} = \frac{\sqrt{52}}{7} \)
Therefore, the exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).
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Math part 4 question 8
The function is decreasing in the interval (3, ∞).
Explain about the decreasing function?You must first compute the derivative, then make it equal to 0, and then determine whether zero values your function is negative between in order to determine whether a function is decreasing. In order to determine once the function is negative and, consequently, decreasing, test values from all sides of these.f(x) = -x² + 6x - 4
Differentiate the equation with respect to 'x'.
f'(x) = -2x + 6
Put f'(x) = 0
-2x + 6 = 0
x = 6/2
x = 3 (critical point)
Now, write the function as:
f(x) = -x² + 6x - 4
-(x² - 6x + 4) (negative form)
Thus, the function is decreasing in the interval (3, ∞)
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Determine all values that cause the expression to be undefined. (2z)/((z+1)(z-3))
The values that cause the expression to be undefined are z = 3 and z = -1.
The expression (2z)/((z+1)(z-3)) is undefined when the denominator is equal to zero. To find all values that cause the expression to be undefined, we need to solve the equation (z+1)(z-3) = 0.
Use the distributive property to expand the equation:
z^2 - 2z - 3 = 0
Use the quadratic formula to solve for z:
z = (-b ± √(b^2 - 4ac))/(2a)
where a = 1, b = -2, and c = -3
Plug in the values and simplify:
z = (-(-2) ± √((-2)^2 - 4(1)(-3)))/(2(1))
z = (2 ± √(4 + 12))/2
z = (2 ± √16)/2
z = (2 ± 4)/2
Solve for the two possible values of z:
z = (2 + 4)/2 = 3
z = (2 - 4)/2 = -1
Therefore, the values that cause the expression to be undefined are z = 3 and z = -1.
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FRACTIONS Additive property of equality with fractions and mixed numbers Solve for u. u-(3)/(4)=5(1)/(3) u
The solution for u-(3)/(4)=5(1)/(3) u is 2(5)/(12).
The additive property of equality states that if the same amount is added to both sides of an equation, the equation remains true. In this case, we can use the additive property of equality to solve for u by isolating the variable on one side of the equation.
Step 1: Add (3)/(4) to both sides of the equation to cancel out the subtraction on the left side of the equation.
u-(3)/(4)+(3)/(4)=5(1)/(3)+(3)/(4)
Step 2: Simplify the left side of the equation.
u=5(1)/(3)+(3)/(4)
Step 3: Find a common denominator for the fractions on the right side of the equation and combine them.
u=20(1)/(12)+(9)/(12)
Step 4: Simplify the right side of the equation.
u=29/(12)
Step 5: Convert the improper fraction to a mixed number.
u=2(5)/(12)
Therefore, the solution for u is 2(5)/(12).
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Nicole spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7225 feet. Nicole initially measures an angle of elevation of 15 ∘ ∘ to the plane at point � A. At some later time, she measures an angle of elevation of 33 ∘ ∘ to the plane at point � B. Find the distance the plane traveled from point � A to point � B. Round your answer to the nearest tenth of a foot if necessary.
Answer: The plane traveled 15838.5 feet from point A to point B.
Now the area can be calculated as: [(7)/(3)t^((3)/(2))-(1)/(5)t^((5)/(2))]_(0)^(7)
The area is 893/15.
The area can be calculated by evaluating the given expression at the limits of integration and subtracting the two values.
we will evaluate the expression at the upper limit of integration, t = 7:
[(7)/(3)(7)^((3)/(2))-(1)/(5)(7)^((5)/(2))] = [(7)/(3)(7^(3/2))-(1)/(5)(7^(5/2))] = [(7)/(3)(49)-(1)/(5)(16807/49)] = [(343/3)-(33614/245)] = [(343/3)-(274/5)] = [(1715/15)-(822/15)] = 893/15
we will evaluate the expression at the lower limit of integration, t = 0:
[(7)/(3)(0)^((3)/(2))-(1)/(5)(0)^((5)/(2))] = [(7)/(3)(0)-(1)/(5)(0)] = 0
we will subtract the two values to find the area:
893/15 - 0 = 893/15
Therefore, the area is 893/15.
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Evaluate. Write your answer as a fraction or whole number without exponents.
2^–2 =
Answer:
1/4
Step-by-step explanation:
you can plug it into a calculator
1/4
First rewrite the - as 1/2^2 , then 2^2=4 so answer is 1/4
Solve the following linear programming problem. Restrict x ≥ 0
and y ≥ 0. Minimize g = 44x + 13y subject to the following. x + y ≥
100 −x + y ≤ 20 −2x + 3y ≥ 30
The optimal solution for the given linear programming problem is x = 20 and y = 80
The given linear programming problem is:
Minimize g = 44x + 13y
Subject to:
x + y ≥ 100
-x + y ≤ 20
-2x + 3y ≥ 30
Where x, y ≥ 0
To solve this problem, we need to determine the feasible region for x and y. The first constraint is x + y ≥ 100, which gives the inequality x + y - 100 ≥ 0.
The second constraint is -x + y ≤ 20, which gives the inequality x - y + 20 ≥ 0.
The third constraint is -2x + 3y ≥ 30, which gives the inequality 2x - 3y + 30 ≥ 0. The feasible region for x and y can be represented by the three inequalities x + y - 100 ≥ 0, x - y + 20 ≥ 0 and 2x - 3y + 30 ≥ 0.
To minimize g = 44x + 13y, we need to use the graphical method. First, draw the feasible region. Then, we draw the line corresponding to the objective function g = 44x + 13y. We will be looking for the point where the line intersects the feasible region with the lowest possible value of g. The intersection point is the optimal solution.
In conclusion, the optimal solution for the given linear programming problem is x = 20 and y = 80, with the minimum value of g being g = 44*20 + 13*80 = 3200.
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36 flowers in 3 bouquets
This is called the unit rate.
Answer: Yes, you are correct.
Step-by-step explanation:
The relationship between the number of flowers and the number of bouquets is an example of a unit rate.
Answer:
yes
Step-by-step explanation:
it is a unit rate
8 Enrique has a container of 32 fl oz of orange juice. He is filling glasses with 1 cup of juice. The point on the graph shows the ratio of fluid ounces to cups. Based on this ratio, how many glasses can Enrique fill from the container? Plot a point on the graph to show the number of cups in 32 fl oz. Show your work
Using the graph, we can find that Enrique can fill 4 glasses from the container.
What are graphs?A structured representation of the data is all that the graph is. It assists us in comprehending the info. Data are the numerical details gathered by observation.
Data is a derivative of the Latin term datum, which means "something provided." Data is continuously gathered through observation once a research question has been formulated. After that, it is arranged, condensed, and categorised before being graphically portrayed.
Here,
We can see that the point on the graph suggests that for filling one glass,
8 fl oz of juice is required.
So, let the no. of glasses that will be filled be = x.
Now, x = Total amount of juice/ Amount of juice per glass
= 32/8
= 4 glasses.
Therefore, 4 glasses will be filled from the container.
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The complete question is:
8 Enrique has a container of 32 fl oz of orange juice. He is filling glasses with 1 cup of juice. The point on the graph shows the ratio of fluid ounces to cups. Based on this ratio, how many glasses can Enrique fill from the container? Plot a point on the graph to show the number of cups in 32 fl oz. Show your work.
Whatt is the answer?
The circle has center C. Suppose that m∠EDF = 38 and that DF is tangent to the circle at D.
a) mDE = 52°
b) m∠DCE = 14°
What is the tangent to the circle?A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called the point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects.
Since DF is tangent to the circle at D, we know that ∠DFC = 90 degrees (tangent and radius are perpendicular).
a) Since ∠EDF is an external angle to triangle CDF, we have:
m∠EDF = m∠CDF + m∠DFC
Substituting the given values, we get:
38 = m∠CDF + 90
m∠CDF = 38 - 90 = -52
However, angles cannot have negative measures, so we need to add 180 degrees to get a positive angle that is coterminal with -52 degrees:
m∠CDF = -52 + 180 = 128 degrees
Now, using the fact that the angles in a triangle add up to 180 degrees, we can find m∠CDE:
m∠CDE = 180 - m∠CDF - m∠EDF
m∠CDE = 180 - 128 - 38
m∠CDE = 14 degrees
Finally, since CD is a radius of the circle, we know that m∠CDE = m∠DCE, so:
m∠DCE = 14 degrees
Therefore, the answers are:
a) mDE = 180 - m∠CDF = 180 - 128 = 52°
b) m∠DCE = 14°
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Determine which point from the specified set satisfies the system of equations.
y =-1/3x + 3
y = -3/4x + 8
Select Choice
(12,-1)
(9,0)
(8,14)
Answer:
y= -1/3x+3
Step-by-step explanation:
we only need to look at the gradient as the gradient of both equations is not the same.
gradient= -1-0/12-9
= -1/3
hence, the answer is y= -1/3x+3
Factor the following polynomial given that it has a zero at 10 with multiplicity 2 (x^(4)-7x^(3)-118x^(2)+460x+4200)
The factorization of the polynomial is (x-10)² (x² + 13x + 42).
To factor the given polynomial, we can use the fact that it has a zero at 10 with multiplicity 2. This means that (x-10)² is a factor of the polynomial. We can divide the polynomial by (x-10)² using long division to find the other factor.
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2x+3y=18 how do we make that into a substitution
ASAP
The solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).
What is the linear equations?
A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
To solve the equation 2x + 3y = 18 using substitution, we can rearrange the equation to express one of the variables in terms of the other. For example, we can solve for x as follows:
2x + 3y = 18
2x = 18 - 3y
x = (18 - 3y)/2
Now we have an expression for x in terms of y. We can substitute this expression into any other equation that involves x, in order to eliminate x from the equation and solve for y. For example, if we have the equation:
x + y = 7
We can substitute (18 - 3y)/2 for x, to get:
(18 - 3y)/2 + y = 7
Now we can solve for y:
18 - 3y + 2y = 14
-y = -4
y = 4
Once we have solved for y, we can substitute this value back into one of the original equations to solve for x. For example, using the equation 2x + 3y = 18:
2x + 3(4) = 18
2x + 12 = 18
2x = 6
x = 3
Therefore, the solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).
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Lisa is 12(4)/(5) years old. Bill is 1(1)/(6) years older than Lisa and Jane is 1(1)/(3) years older than BilL How old is Jane?
The final answer of Jane is 13(9)/(30) years old.
To find out how old Jane is, we need to first calculate Bill's age and then add 1(1)/(3) years to it.
Here are the steps:
1. Calculate Bill's age:
- Start with Lisa's age: 12(4)/(5) years
- Add 1(1)/(6) years to it: 12(4)/(5) + 1(1)/(6) = 12(24)/(30) + 1(5)/(30) = 12(29)/(30) = 12 + 29/30 = 12(29)/(30) years
2. Calculate Jane's age:
- Start with Bill's age: 12(29)/(30) years
- Add 1(1)/(3) years to it: 12(29)/(30) + 1(1)/(3) = 12(29)/(30) + 1(10)/(30) = 12(39)/(30) = 12 + 39/30 = 12 + 1(9)/(30) = 13(9)/(30) years
So, Jane is 13(9)/(30) years old.
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