The expressions for the number of sweets that Tony and Sue now have are:
Given:
Sue has 18 sweets
Sue = 18
Tony also has 18 sweets, that is:
Toney = 18
Sue gives Tony × sweets; that is
Sue = 18 - x; and
Tony = 18 + x
Sue then eats 5 of her sweets, Tony then eats half of his ⇒ Sweets:
that is ⇒
Sue = 18 - x - 5
Tony = (18 + x) / 2
Thus, simplifying the above, we have:
Sue = 13 - x
Tony = (18 + x) / 2
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How do you tell if something is a difference of squares?
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.
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Olivia tries to cut a piece of metal 45 inches long the piece of metal ends up being 43. 5 inches long what is the approximate orecent error in this situation
When Olivia tries to cut a piece of metal 45 inches long, the piece of metal ends up being 43.5 inches long, then there is an approximate percent error of 3.33% in this situation.
Therefore the answer is 3.33%.
To calculate the approximate percent error in this situation, we can use the formula:
Percent Error = (|Experimental Value - Theoretical Value| / Theoretical Value) x 100
In this case, the experimental value is 43.5 inches and the theoretical value is 45 inches. Plugging these values into the formula, we get:
Percent Error = (|43.5 - 45| / 45) x 100
= (1.5 / 45) x 100
= 0.033 x 100
= 3.33%
So the approximate percent error in this situation is 3.33%.
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The red line on this graph is y=-2x-1
The dotted line is y=x.
Write the equation of the inverse of this function
Answer:
Step-by-step explanation:
Find the value of x.
2x-8
6
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
3. Find the values of a and b. 36° 113° O
The measure of angles a and b is 144° and 67° respectively.
What is quadrilateral?There are four sides, four vertices, and four angles in a closed quadrilateral. It has a polygonal shape. It is produced by joining four non-collinear points. The total internal angle of a quadrilateral is always 360 degrees.
The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides. Each of a quadrilateral's four sides does not always have to be the same length.
Given a quadrilateral,
in which opposite sides are parallel,
so, When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional to 180°.
36° + a° = 180°
and 113° + b° = 180°
a° = 180° - 36° = 144°
and b° = 180° - 113°
b° = 67°
Hence the values of a° is 144° and b° is 67°.
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Find the value of x.
2x-8
6
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Constructing a line segment of length 2 and then finding the
midpoint
B. Drawing a perpendicular line segment through a given point on a
given segment
C. Drawing a line through a given point parallel to a given line
D. Drawing a perpendicular line segment from a given point to a
given segment
Answer: Constructions A, B, and D can be accomplished with paper folding.
Construction A involves constructing a line segment of length 2 and then finding the midpoint, which can be done by folding the paper in half.
Construction B involves drawing a perpendicular line segment through a given point on a given segment, which can also be done by folding the paper.
Construction D involves drawing a perpendicular line segment from a given point to a given segment, which can also be done by folding the paper.
Construction C, drawing a line through a given point parallel to a given line, cannot be accomplished with paper folding. To do this construction, you would need a straightedge, such as a ruler.
Step-by-step explanation:
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment. What is construction in mathematics?Constructions are accurate drawings of shapes, angles and lines in geometry. Some basic constructions -
Constructing bisectors of lines and angles.Constructing regular polygons inscribed in circles.Constructing circumcircles and incircles.Constructing a line tangent to a circle.Given is to find which of the following constructions can be accomplished with paper folding.
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.Therefore, the following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.To solve more questions on constructions, visit the link-
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Consider rigid-body physics in a higher or lower dimension than three. How many coordinates are required to specify the location and orientation of a rigid body:If the space is two-dimensional?a. 2b. 3c. 4d. 5
In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.
In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.
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Dave can clean pools at a constant rate of 3/5 pools/hour. How long does it take Dave to clean 15 pools?
9 hours will it take to clean the 15 pools.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Dave can clean pools at a constant rate of 3/5 pools per hour.
This also means that he cleans 3 pools in 5 hours
So, the time taken to clean 15 pools is
= 15×3/5
= 9 hours.
Hence, the time taken is 9 hours.
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Michael's pumpkin farm sold 75 pumpkins on October 24 that day they made $600. What did Michael charge for each pumpkin?
Answer:
$8.
Step-by-step explanation:
right!!
3) Camile offers you a challenge. Are the triangles below similar? Examine them and tell how
you know.
a) Use a flowchart to organize your explanation.
b) Camile says, "These triangles aren't just similar-they're congruent!" Is Camile
correct? What special value in your flowchart indicates that the triangles are
congruent?
a) The flowchart for the congruency of triangles is given below.
b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.
What is congruency?
The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.
In the given diagram, it can be seen that -
Line segment DQ = Line segment XZ.
Similarly, Line segment PQ = Line segment XY.
Since, the two sides of the triangle are equal, hence the third side must also be equal.
Line segment PD = Line segment ZY.
Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.
Therefore, the triangles PDQ and ZXY are equal and congruent.
The flowchart for the same is given below.
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Why is triangle always 180 degrees?
Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.
1. A triangle is a three-sided polygon with three angles.
2. The sum of the three angles in any triangle must be 180 degrees.
3. This is known as the Triangle Angle Sum Theorem.
4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.
5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.
6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.
7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.
8. The sum of the three angles will always equal 180 degrees.
9. Therefore, triangle is always 180 degrees.
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3) Breanna thought of a number, subtracted 4 from it, and then multiplied her answer by 3. She got
a final number of 24. What was her starting number?
x^2=Σ(o-e)^2/e
17. A candidate for mayor is discussing the crime rate in the city. She asks the police department to provide some statistics on how many people out of a group of 500
people were victims of four specific crimes. She expects that she can verify this information by doing her own survey. She then asks a group of 500 people to identify
whether they were victims of the same crimes. Her results are the observed quantities, and the police data are the expected quantities. The following is a table of the
results.
Category: observed/ expected
Robbery
24/18
Assault
15/21
Discrimination
79/56
Theft
124/138
Calculate the chi-square value for her survey. Remember, to calculate the chi-square value, use the formula shown.
A. 12.68
B. 8.56
C. 8.15
D. 14.58
On solving the provided question we cans ay that - the value of the following exponent is
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
here,
= [tex]10^2 X 10^-3[/tex] X 32
= 100 X 1/1000 X 32
=1/10 X 32
=3.2
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Please help ASAP this is for a final test
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answer: I'm sorry bro i don't know
Step-by-step explanation:
Figure ABCD is a parallelogram if point C lies on the line y=-1 what is the x vale of point C
The value of x of point C is 4. The coordinate of C is (4,-1).
What is the coordinate of a point?
The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.
The distance between points A and B is 4 units.
The opposite sides of a parallelogram are equal and parallel.
To make parallelogram, the point C lies on the left side of point D.
The distance between point C and D must be 4 unit.
The coordinates of C is (4,-1).
The x value of point C is 4.
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To the nearest pound, Tim has £8
To the nearest 50p, Sue has £4. 50
Work out the maximum possible total amount of money.
Give your answer in pounds (£).
The maximum possible total amount of money would be = 13.23 £
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one.
Given,
To the nearest pound, tim has £8
To the nearest 50p, sue has £4.50
so, to the nearest pound, tim has £8
=> 7.5 ≤ Tim has < 8.5
sue has £4.50
to the nearest 50 p
=> 4.25 ≤ Sue < 4.75
=> possible total amount of money
= 7. 5 + 4.25 ≤ Amount < 8.5 + 4.75
=> 11.75 ≤ Amount < 13.25
maximum possible total amount of money would be less than 13.25
and in term of paisa maximum < 4.75 = 4.74
and maximum less than < 8.5 = 8.49
Hence maximum possible total amount of money would be = 13.23 £
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Select the correct answer.
Which phrase best describes the relationship indicated by the scatter plot?
A. constant correlation
B. negative correlation
C. positive correlation
D. no correlation
Answer: B
Step-by-step explanation:
Correlation tells us the relationship of 2 variables. Looking at the graph, the data appears to going down, as we read graphs from left to right. We can automatically eliminate C and D, since we have determined going down. We know it's also not A because if the correlation is constant, then all the dots would be lined up, and not scattered around. Since the dots are going down, this tells us that it is a negative correlation. Hence, B is the answer.
Answer:
B. negative correlation
Step-by-step explanation:
Find the general solution of the given differential equation. (x + 1) dy + (x + 2)y = 8xe^-x y(x) = __
Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) ___
Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
______
The general solution of the given differential equation is y(x) = C₁e^-x + 4xe^-x. The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution.
The differential equation given can be rearranged into the form dy/dx + (x + 2)/(x + 1)y = 8xe^-x, which is a linear first order differential equation. Using the integrating factor method, an integrating factor of e^(x + 1) can be used to obtain the general solution y(x) = C₁e^-x + 4xe^-x.
The integration constant C₁ can be determined by supplying the appropriate initial conditions. As the equation is a linear first order differential equation, the general solution is valid over the entire domain of x, which is (-∞, ∞). As the equation does not involve any terms that provide a particular value for y at any point in the domain, there are no transient terms in the general solution.
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Find the values of x and y in parallelogram PQRS.
PT =y. TR = 3x + 1, QT = 3y. TS = 5x + 11
x=
y=
PLEASE HELPPP!!!!
In the parallelogram PQRS, x = 2 and y=7
Parallelogram:
A parallelogram is a quadrilateral with two pairs of parallel sides. A parallelogram has opposite sides of equal length and opposite angles of equal length. Also, the interior angles on the same side of the horizontal line are supplementary angles. The sum of all interior angles is 360 degrees. A three-dimensional shape whose faces are parallelograms is called a parallelepiped. The area of a parallelogram depends on its base (one of its parallel sides) and its height (height drawn from top to bottom). The perimeter of a parallelogram depends on the length of its four sides.
Given that
PT=y, TR=3x+1, QT=3y, TS=5x+11
The diagonals of a parallelogram bisect each other
PT = TR and QT = TS
y = 3x+1 and 3y = 5x+11
Now,
We have a system of equations
Multiply the first equation by 3
3y = 9x+3 and 3y = 5x+11
Set them equal
9x + 3 = 5x + 11
⇒ 9x - 5x = 11 -3
⇒ 4x = 8
⇒ x =2
Now,
Putting the value of x =2 in equation :
y = 3x+1
=3(2)+1
=7
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Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leaves 1 hour before the faster and arrives at the opposite shore at the same time as the other ferry, what is the speed of the slower ferry
The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.
How to find the calculation?Let x represent the first ferry's speed.
The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)
First ferry time equals distance/speed equals
50/x
Time spent on the second ferry:
50 / x - 5
The difference in times is 1 hour because the second ferry departs an hour earlier.
50 / x - 5 - 50/x = 1
50x - 50(x - 5) = x (x - 5 )
250 = x² - 5x
x² - 5x - 250 = 0
(x - 10 )(x + 5) = 0
x = 18.5 - 13.5
Speed can never be detrimental.
Therefore, the first ferry's speed is 18.5 mph.
and the second ferry, which is slower, travels at 13.5 mph.
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Stacy wants to buy a tree to decorate her apartment. Her living room has 8 foot high ceilings. The height of each tree she is interested in buying is given below. Which tree(s) can she buy so that they fit in her living room? Choose all that apply
A. 108 inches
B. 114 inches
C. 94 inches
D. 79 inches
or other you can type what you got
Answer:
C And D
Step-by-step explanation:
94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall
Answer:
C and D
Step-by-step explanation:
You should start by changing the inches to feet
(there are 12 inches in foot [ 12 inch = 1 foot ])
A. 9 foot
B. 9.5
C. about 7 feet
D. about 6 feet
C and D are correct. Hope this helps!
Write two equations that can be solved using the double 7+7
Using doubles plus one fact the sum of 7 + 7 is equal to 15 it is done by simply adding 1 to the given number.
What is Doubles plus ?When we add two of the same number, we add using the “doubles fact”. For example, 1 + 1 and 2 + 2 are both doubles facts. Look at the example below: 4 + 4 = 8 is a doubles fact. Doubles fact can help us know other additional strategies like doubles plus one
A double is a number or an amount that is twice as large as the given number or amount. So, if we multiply a number by 2 or if we add a number to itself we say that the number is doubled
The sum of 7 + 7 can be determined by using doubles plus one fact as:
Simply add 1 in 7 + 7 to get the result required.
Therefore by using doubles plus one fact the sum of 7 + 7 is equal to 15.
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One of the legs of a right triangle measures 2 cm and its hypotenuse measures 5 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth."
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
what is Pythagoras theorem ?Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.
given
by Pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
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Which of the following chocies is not a function?
A {(0, 0), (1, 4), (2,8)}
B {(0, 0), (3, 16), (16, 49)}
C {(1, 1), (2, 2), (3, 3), (4,4)}
D {(7, 1), (6, 2), (5, 3), (5,4)}
E All of these choices are functions.
The manufacturer's price for a Jinko car is $x
Ben was given a 7% discount on the manufacturer's price when he bought a Jinko.
Ben paid $23 622 when he bought his Jinko.
(a) Calculate the value of x.
Answer:
x = $25,400 [the original price of the Junko car]
Step-by-step explanation:
The price Ben paid, $23,622, is after the 7% discount. Let x be the original price of the Jinko car. Ben's prices reflect a 7% discount:
x*(1-0.07) = $23,622 [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]
(0.93)x = $23,622
x = $25,400
Amrita divides a circular disc of radius 7 cm in two equal parts. What is the perimeter of each semicircular shape disc? (USE π=22/7 )
The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.
Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs
Step 1: Calculate the circumference of the original circle.
Circumference of a circle = 2πr
Circumference of the circle with a radius of
7 cm = 2πr = 2 × 22/7 × 7 = 44 cm
Step 2: Calculate the perimeter of each semicircular shape disc.
The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.
Perimeter of each semicircular shape disc
= 44 cm/2
= 22 cm
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expand this expression using the distributive property. 4(-2g+4-3t)
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
The quotient of 25 and 5 increased by 3
Answer: 8
Step-by-step explanation: Based on the given conditions, formulate 25/5+3 Reduce the sum or difference: to 8 therefore the answer is 8
Answer:
down below
Step-by-step explanation:
The quotient means the total amount that comes from dividing two things. In this case, the problem is asking for 25 and 5 to be divided. 25 divided by 5 is 5. You can check this by multiplying 5 and 5 to get 25. So, you know it's right. Now, take 5 and add 3 to it. 5 + 3 = 8. So, the answer is 8.
Hope this helps! :)
Using a number line, find both the intersection and the union of the following
intervals:
[1, 5] and (0,8]
pls help !
Answer:
The union of the intervals is (0,8]
The intersection of the intervals is [1,5]
Hope this helped!