If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Option (d) is the correct choice.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
A parallelogram has the following qualities:
The opposing sides are equally spaced and parallel.
Angles on either side are equal.
The following or neighboring angles are supplemental.
All of the angles will be at right angles if any one of them is a right angle.
The two diagonals cut across one another.
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18. Solve for b:
3 (23-2b) + 3b = 48
A. 10
B. 13
C. 7
D. -10
Answer:
Step-by-step explanation:
3(23-2b) + 3b = 48
1. Use the distributive property and distribute the 3 before the parenthesis
3(23-2b) (make sure you read the (-) as part of the 2b so it's -2b
69 - 6b
2. 69 - 6b +3b = 48 (combine like terms...the bs: -6b + 3b)
69 -3b=48
3. 69 - 3b = 48 (subtract 69 from both sides)
-69 -69
4. -3b = -21 (divide both sides by negative three...we want the b to be +
/-3 /-3
Answer: b = 7
So, C is your answer
Christopher has 95 toy cars. He arranges his cars in 5 equal rows. Write numbers in the boxes to complete the partial quotient model and the equation to find the number of cars in each row. 95 + 5 = cars
The number of boxes to complete the partial quotient model is found to be as 19 cars .
On dividing 95 from 5 we will get 19 as the quotient.
95 / 5 = 19
The quotient is the number that is produced when two integers are divided. It is the outcome of the division process , when we divide a number from another the result is known as quotient.
In arithmetic division, four primary terms are used which are divisor, dividend, quotient, and remainder. In this post, each phrase will be defined and shown using examples.
Dividend = Divisor + Quotient + Remainder
If the divisor is not able to completely divide the dividend then it leaves a remainder.
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Find the rate of change for this linear function.
y = 5x - 1
Find the initial value of the linear function
Y=5x+2
rate of change for this linear equation, y = 5x - 1 is +5
the initial value of the linear equation, y = 5x + 2 is +2.
What is linear equation?A linear equation is an algebraic equation of the form y = mx+c, where m is the slope and c is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.
Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.
Given that,
y = 5x - 1 is a linear equation.
As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.
Therefore, for the given equation, rate of change is 5 and initial value is -1.
Given that,
y = 5x + 2
is a linear equation.
As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.
Therefore, for the given equation, rate of change is 5 and initial value is + 2.
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BOUNDS QUESTION GCSE MATHS - A race is measured to have distance of 10.6km, correct to the next0.1km. Sam runs the race in a time of 31 minutes 46seconds, correct to the nearest second.
Sam's average speed in this race is Vkm/hour.
By considering bounds, calculate the value of Vkm to a suitable degree of accuracy. You must show your work and get reasons for your answer. [5 MARKS]
The average speed of Sam's race car is equal to 20 kilometers per hour.
How to determine the average speed of a race car
In this question we find the case of a race car being displaced in a race whose length (s) is 10.6 kilometers, a distance traveled in a time (t) of 31 minutes and 46 seconds (1906 seconds). The average speed (v), in kilometers per hour, is described by the following formula that assumes an hypothetical constant speed:
v = s / t
Where:
s - Distance, in kilometers.t - Time, in hours.First, convert time into hours:
t = (31 min) · (1 hour / 60 min) + (46 s) · (1 hour / 3600 s)
t = 0.529 h
Second, calculate the average speed:
v = (10.6 km) / (0.529 h)
v = 20.038 km / h
v = 20 km / h
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Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. -2 1 1 - 4 3 4 ; 2 = -1,4 -2 2 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. For P=___ D= 0 4 0 0 0 4 -1 0 0 O B. For Pa = ___ D = 0 -1 0 0 04 OC. O The matrix cannot be diagonalized.
The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.
To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.
The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.
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What are 5 ways to solve problems?
The 5 ways to solve problems are identifying the problem, generating different solutions, choosing one solution, implementing the chosen solution and evaluating the result.
A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.
There are 5 different steps to solving a problem
Step 1. Identify the Problem
Step 2. Generate potential solutions
Step 3. Choose one solution
Step 4. Implement the solution you’ve chosen
Step 5. Evaluate results
Sometimes it is required to start the process entirely over. To make the problem-solving process easier, it’s best to facilitate the solution as much as possible. Try to concentrate on the solution instead of the problem. Finally, be in the correct psyche to want to change. This contains having the right mindset language, both are positive and open-minded. With sufficient practice, any problem can be solved.
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Find the area of the polygon with the given vertices.
W(-1, 1)
-4
Z(-3,-2)
4
Ay
2
-4
2
X(4,1)
4 x
Y(2,-2)
The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.
What is polygon?A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.
The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,
where XW is the vector from W to X and ZY is the vector from Z to Y.
In this example,
XW = (3, -2) and ZY = (-2, -4).
Therefore, the area of triangle
WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.
The area of triangle XYA is calculated similarly,
where XY = (2, 3) and YA = (-2, -4).
Therefore, the area of triangle
XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.
The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.
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A hiker maintains an average speed of 3 3/4 km/h. How many kilometers will the hiker walk in:5hrs
help
multiple 5x 3 3/4 then change to an improper fraction
Find the equation of the line that goes through ( 0, 2 ) and ( 3, 4 ).
Select one:
a.
2x + y - 3 = 0
b.
- 2x + 3y - 6 = 0
c.
x + y - 2 = 0
d.
2x + 3y + 6 = 0
Answer:
Option b. -2x + 3y - 6 = 0
Step-by-step explanation:
Let's look for a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
Calculate the slope first. Slope is the Rise/Run of any two points on a straight line. Using the given points, (0,2) and (3,4) we find:
Rise = 4 - 2 = 2
Run = 3 - 0 = 3
Slope, m, Rise/Run = (2/3)
The equation becomes y = (2/3)x + b
To find b, enter either of the two given points.
y = (2/3)x + b
2 = (2/3)(0) + b : for point (0,2)
b = 2
The equation becomes: y = (2/3)x + 2
Reformat this to match the format of the answer options.
y = (2/3)x + 2
3y = 2x + 6 [Multiplied by 3]
3y - 2x - 6 = 0
-2x + 3y - 6 = 0 [rearrange]
This matches option b.
Darius has a cylindrical can that is completely full of sparkling water. He also has an empty cone-shaped paper cup. The height and radius of the can and cup are shown.
Darius pours sparkling water from the can into the paper cup until it is completely full. Approximately, how many centimeters high is the sparkling water left in the can?
Answer: 6.2
Step-by-step explanation:
What is translation in coordinate geometry?
In the coordinate geometry the translation represents one type of transformation to change the location without changing the shape, size.
As given in the question,
In the coordinate geometry,
The translation is one type of transformation.Translation represent the change in the location of the given geometrical figure in the coordinate plane.No change in the shape and size of the geometrical figure.Change in the location vertical and horizontal direction.Right and left direction represents the horizontal direction.Up and down represents the vertical direction.Therefore, in the coordinate geometry the translation represents one type of transformation to change the location of the geometrical figure.
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You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work
There are 8 half dollars and 9 quarters inside the cup.
We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.
Let h be the number of half dollars and q be the number of quarters.
The first equation represents the total number of coins in the cup:
h + q = 17The second equation represents the total value of the coins:
0.5h + 0.25q = 5.50To solve for h and q, we can use either the substitution or elimination method.
By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.
So, q = 17 - h
then substitute it into the second equation:
0.5h + 0.25(17 - h) = 5.50
By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9
So, there are 8 half dollars and 9 quarters inside the cup.
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Please help me, find the area to figure around to the nearest hundredth necessary.
A submarine must descend at an average rate of at least 12 feet per minute for 5 minutes. The table shows how many feet the submarine descends
in the first 4 minutes. How many feet must the submarine descend in the fifth minute?
Submarine must descend 17 feet in the 5th minute.
What is the average of the data?
Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.
Let the distance descended by submarine in 5th minute = x feet
Average distance descended by the submarine
= (Total distance distended/ Duration or time)
= (6 + 8 + 14 + 15 + x) / 5
= (43 + x) / 5
Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"
So the inequality for the statement will be,
(43 + x) / 5 ≥ 12
43 + x ≥ 60
x ≥ 17
Therefore, submarine must descend 17 feet in the 5th minute.
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Felix hasa bucket of golf bals, The table shows the number of golf balls of each color in the bucket. Golf Balls in a Bucket Color Pnk White Orange Green Number 11 8 18 (A)e Felix selects a golf ball at random. Based on the Information in the table, which statement is true? A The golf ball is more likely to be green than all other colors combined. B The golf ball is equally likely to be pink, white, orange, or green. C The golf ball is 2 times as likely to be orange as it is to be pink. D The golf ball is 7 times as likely to be green as it is to be white.
The correct statement regarding the probabilities from the table is given as follows:
C The golf ball is 2 times as likely to be orange as it is to be pink.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of balls for this problem is given as follows:
4 + 11 + 8 + 18 = 41.
Hence the probability of selecting each ball is obtained as follows:
Pink: 4/41.White: 11/41.Orange: 8/41.Green: 18/41.Hence statement C is correct, as:
2 x 4/41 = 8/41.
(which is the probability of orange, obtained multiplying the probability of pink by two).
Missing InformationThe number of pink balls is of 4.
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
The odds against exactly 5 cars passing over the bridge in that time are given as follows:
5.25:1.
What is the relation between probabilities and odds?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.
The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:
0.16 : (1 - 0.16) = 0.16 : 0.84.
To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:
0:84 : 0.16.
As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:
5.25 : 1.
Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.
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The Fudd family is attending a family reunion. They plan to rent a
car from the ABC Car Rental Company. Let m represent the number
of miles the family will drive. Let c represent the cost for renting a
car. Complete problems
The complete problem equation will be c = k*m + b
The cost equation for renting a car from the ABC Car Rental Company in terms of the number of miles driven, m, and the cost, c, would likely take the form of:
c = k*m + b where k is the rate of cost per mile and b is the fixed cost for renting the car independent of the miles driven.
It is important to note that this is a general equation and the specific cost equation of the ABC Car Rental Company is not provided. Also, this equation assumes that the cost of renting a car is linear to the miles driven, which may not be the case in practice. Other factors such as the type of car and duration of the rental period could also be included in the cost equation.
Therefore, the problem equation will be c = k*m + b
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PLS HELP
using factorisation solve
E=(a+1)(a-1)-3(a+1)²
Answer:
Step-by-step explanation:
factoring
e =
(a+1)(a-1-3(a+1))
= (a+1)(a-1-3a-3)
= (a+1)(-2a-4)
= -2(a+1)(a+2)
Solve this problem
Step by step
Answer:
√259 or 16.09
Step-by-step explanation:
Hello!
I'll be labeling the vertices so that it is easier to understand the sides.
These are both right triangles, and we can find the measures of right triangles (given two other sides) by using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
a = legb = legc = hypotenuse (leg opposite to 90°)In Triangle BCD, we have the measures of the hypotenuse and a leg. We can use that to find the missing side: CB
Since DB is the hypotenuse, it would be side c, and we can say that CD can be side a.
Solve for CB:[tex]a^2 + b^2 = c^2[/tex][tex]10^2 + b^2 = 25^2[/tex][tex]100 + b^2 = 625[/tex][tex]b^2 = 525[/tex][tex]b = 5\sqrt21[/tex]CB in simplest radical form is 5√21.
We can now solve for x, because now in triangle ABC, we have the measures of two sides: hypotenuse AC and leg CB.
Solve for AB:[tex]a^2 + b^2 = c^2[/tex][tex](5\sqrt{21})^2 + b^2 = 28^2[/tex][tex]525 + b^2 = 784[/tex][tex]b^2 = 259[/tex][tex]b = \sqrt{259}[/tex]AB in simplest radical form is √259, which is approximately 16.09.
The solution for x is √259 or 16.09.
The scale on a map of Florida is 2 inches = 50 miles. What is the distance in miles
represented by a length on the map of 7 inches?
The distance in miles represented by a length on the map of 7 inches is 0.28
What is scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Given;
The scale of a map says that 2 inches represents 50 miles.
2 inches = 50 miles
1 Mile = 2/50 inches
Hence, 7 Mile = 7 * 2/50 inches
7 Mile = 14/50 inches
7 Mile = 0.28 inches
Therefore, the scale factor of 7miles in the map will be 0.28inches
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Lia bought 4 3/5 pound of trail mix. She gave 3/5 of it to her iter. How much did give away?
Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.
Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.
To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.
3. 3/5 multiplied by 9/5 is equal to 27/25.
To simplify this fraction, we can divide both the numerator and denominator by 3.
27/25 can be simplified to 9/5 or 2 2/5 pounds.
Therefore, Lia gave away 2 2/5 pounds of the trail mix.
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Coroline runs 3 1/2 miles in 22 1/4 minutes how many miles does she run per minute
Answer:
To determine the number of miles Coroline runs per minute, we need to first convert the distance she runs to a fraction of a mile and the time it takes her to run that distance to a fraction of an hour.
3 1/2 miles is equivalent to 3 + 1/2 = 3 + 1/(2*1) = 7/2 miles.
22 1/4 minutes is equivalent to 22 + 1/4 = 22 + 1/(4*1) = 23/4 minutes.
To convert the time to hours, we can divide the number of minutes by the number of minutes per hour. There are 60 minutes per hour, so we have:
23/4 minutes / (60 minutes/hour) = (23/4) / (60/4) = 23/60 hours
To determine the number of miles Coroline runs per minute, we can divide the distance she runs by the time it takes her to run that distance:
(7/2 miles) / (23/60 hours) = (7/2) / (23/60) = (760) / (223) = 420/46
Simplifying, we have:
420/46 = 9 1/23
Therefore, Coroline runs approximately 9 1/23 miles per minute.
Step-by-step explanation:
Answer:
she runs 0.078 miles per minute.
Step-by-step explanation:
A. To wash the first window, Roger extends the
ladder to 20 feet long. He places the base of
the ladder 6 feet from the side of the house.
Sketch a labeled picture of this to the right.
B. How far up the house will the 20-foot ladder
reach, to the nearest tenth of a foot? Show your
work in the space to the right.
lines are and s are parallel. what is m1
Answer:
30 degrees
Step-by-step explanation:
How do you find the parent function of a line?
The parent function of a line (usually of the form y = ax + b) is y = x.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
Linear FunctionLinear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.
These functions represent relationships between two objects that are linearly proportional to each other.
Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.
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What is the domain of the function y=5√6−2x
The domain is all values of x that makes the expression defined.
Set-Builder Notation: {x| x ≤ 3 }
Interval Notation: (-∞,3]
What is the domain of the given function?Given the function in the question;
y = 5√(6−2x)
To find the domain, set the radicand greater than or equal zero and solve for x.
6 - 2x ≥ 0
Subtract 6 from both sides
6 - 6- 2x ≥ 0 - 6
-2x ≥ -6
Divide both sides by -2
-2x/-2 ≤ -6/-2
x ≤ -6/-2
x ≤ 3
Therefore, the domain is;
Set-Builder Notation: {x| x ≤ 3 }
Interval Notation: (-∞,3]
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What is the sum of 1.3 and –1.8?
Answer in explanation:
although there's an addition sign, you subtract the two because a
(+) + (-) = (-) subtract
[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]
subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)
1.3 + (-1.8) =
-0.5
-0.5 is your answer
Hope this is clear!
I don't get this question can some one please help me solve it
Answer:
3, 2
Step-by-step explanation:
In order for the equation to be equal to zero, the following must be true:
x-3 = 0 or,
x-2 = 0
Therefore the 2 solutions are x=3, x=2
a paint roller has a width of 12 inches and a radius of 3 inches, what is the surface area that can be painted with one complete rotation of the roller
The surface area that can be painted with one complete rotation of the roller is 226.19 inches².
Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.
A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.
SA = 2πrh
where SA = surface area
r = radius of the base = 3 inches
h = height of the cylinder = width = 12 inches
Plug in the values and solve for the surface area.
SA = 2πrh
SA = 2π(3 inches)(12 inches)
SA = 226.19 inches²
Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².
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The goal for the size of the Santa on a Christmas Santa cup is 3. 5 cm with an acceptable tolerance of ± 0. 9 cm. The grand mean of the size of the Santa from the samples that were taken is 3. 4 cm and the standard deviation is 0. 28 cm. What is CP? (rounded to three decimals)
The processing capability for the size of the Santa rounded to three decimal places is 1.07.
CP (Process Capability) is a statistical measure that compares the performance of a process to the specifications of that process. It can be calculated using the formula:
CP = (USL - LSL) / (6 * standard deviation)
Where:
USL = Upper Specification Limit (3.5 + 0.9) = 4.4 cm
LSL = Lower Specification Limit (3.5 - 0.9) = 2.6 cm
Standard deviation = 0.28 cm
Substituting these values into the formula:
CP = (4.4 - 2.6) / (6 * 0.28) = 1.8 / 1.68 = 1.07
So, CP rounded to three decimal places is 1.07
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