The value of a and b for the given quadrilateral to be a parallelogram is a = 16 and b = 4.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.
We know that the opposite sides of a parallelogram are equal in length so we can equate the two sides as follows:
For a:
2a + 6 = 3a -10
Isolate the value of a by moving all the values having a to one side:
2a + 6 = 3a -10
3a - 2a = 6 + 10
a = 16
For b:
6b - 3 = 5b + 1
Isolate the value of b by moving all the values having b to one side:
6b - 3 = 5b + 1
6b - 5b = 1 + 3
b = 4
Hence, the value of a and b for the given quadrilateral to be a parallelogram is a = 16 and b = 4.
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Brian is a salesman for a wholesome computer parts company. He earn straight commission at a rate of 4% last month is total sales were 82,968. What was his gross income last month
Brian's gross income last month will be $3319.
How to calculate the income?The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, Brian is a salesman for a wholesome computer parts company. He earn straight commission at a rate of 4% last month is total sales were 82,968.
Brian's gross income last month will be:
= 4% × 82968
= $3319
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Which describes the correlation shown in the scatterplot? PLS HURRY
So on solving the provided question given scatter plot shows a negative correlation so correct option is (b).
What is a scatter plot?The values for two different numerical variables are represented by dots in a scatter plot. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, employ scatter plots.
The options given are the following:
A)There is a positive correlation in the data set.
B)There is a negative correlation in the data set.
C)There is no correlation in the data set.
D)More points are needed to determine the correlation.
Positive correlation
We say there is a positive correlation between the variables when the y variable tends to rise when the x variable rises.
Negative correlation
We say there is a negative correlation between the variables when the y variable tends to decrease as the x variable increases.
No correlation
We claim there is no correlation between the two variables when there is no obvious connection between them.
From observing the given graph, we can see that as x value increases, the y value decreases.
So the correlation shown in the scatter plot is a negative correlation.
Therefore the correct option is option(B).
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A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet 1.2 hours for the flight, and it takes the private airplane 1.8 hours. The speed of the commercial jet is 170 miles per hour faster than the speed of the private airplane. Find the speed, in miles per hour, of both airplanes.
Both planes have a speed of 340 miles per hour and 510 miles per hour, respectively.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Let tc be the time of commercial jet and tp be the time of private airplane.
Let vc be the speed of commercial jet and vp be the speed of private airplane.
Let dc be the distance of commercial jet and dp be the distance of private airplane.
now,
dc=dp
vc=vp+170
vc*tc=vp*tp
(vp+170)*1.2=vp*1.8
(vp+170)*2=vp*3
2vp+340=3vp
vp=340 miles/hour
vc=340+170
vc=510 miles/ hour
The speed, in miles per hour, of both airplanes is 340 miles per hour and 510 miles per hour.
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How to test the normality of regression ?
kite is flying 79 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 57º. Find the length of the string. Round your answer to
the nearest tenth.
Check the picture below.
Make sure your calculator is in Degree mode.
You are driving on a highway and are about 140 miles from a state border. You set your cruise control at 60 miles per hour
and plan to turn it off within 30 miles of the border on either side. Find the minimum and maximum numbers of hours you
will have cruise control on.
Using the absolute value function, we have that:
The minimum time is of 1.833 hours.
The maximum time is of 2.833 hours.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
It measures the distance of a point x to the origin, hence |2| = |-2| = 2.
here, we have,
In this problem, the minimum and maximum distances are within 30 miles of 140, hence:
|d - 140| = 30.
The minimum distance is of:
d - 140 = -30
d = 110.
Hence the minimum time(distance divided by velocity) is:
110/60 = 1.833 hours.
The maximum distance is of:
d - 140 = 30
d = 170.
Hence the maximum time(distance divided by velocity) is:
170/60 = 2.833 hours.
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Please help me someone
Answer:
6/8
Step-by-step explanation:
1/8+1/4+3/8
1/8+2/8+3/8
1 If we want to find the volume of the child's toy shown below, we will need to find the volumes of which 3D solids? (Mark all that apply)
A Sphere/Hemisphere
B Prism
C Cylinder
D Pyramid
E Cone
F Cube
The solution is Option C , Option E.
The total volume of the toy is the sum of volumes of cone and cylinder
What is a Cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Surface area of the cone = πrl
where l = √ ( b² + r² )
Given data ,
Let the total volume of the child's toy be represented as V
Now , the value of V is
Let the cone be represented as C
The volume of Cone C = ( 1/3 ) πr²h
The radius of the cone r = 5 cm
The height of the cone h = 13 cm
So , the volume of Cone = ( 1/3 ) π ( 5 )² x 13
The volume of Cone = ( 325/3 )π cm³
Now , the volume of cylinder = πr²h
The height of cylinder = 2 cm
The volume of cylinder = π ( 5 )² x 2
The volume of cylinder = 50π cm³
So , the volume of toy = volume of cylinder + the volume of Cone
The volume of toy = ( 325/3 )π cm³ + 50π cm³
The volume of toy = ( 475/3 )π cm³
Hence , the volume of toy is ( 475/3 )π cm³
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Someone please help me I need to pass this before 5 o clock
By the property of parallelograms that diagonals are equal in length and they bisect each other we have determined the values of x and y.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know the diagonals of a parallelogram are equal and they bisect each other, From this property, we can write,
OA = OC.
x + 23 = 31.
x = 31 - 23.
x = 8 units.
XZ = 2(OX).
26 = 2(- 44 + x).
26 = - 88 + 2x.
2x = 114.
x = 57 units.
OL = OJ
8x - 56 = 24.
8x = 80.
x = 10.
OM = OK.
36 = 4y + 20.
4y = 16.
y = 4.
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Julie ordered data collected on a survey and identified one student's answer of 74 as the median. Thirteen answers were below the median. How many people did she question on her survey?
13students;it had already said it.
A farmer has sufficient grains to feed 30 hens for four days. How long will the grains last for 40 hens?
Answer:
Below
Step-by-step explanation:
30 hens x 40 days = 120 hen days of food
120 hen days / 40 hens = 30 days of food for 40 hens
Hurry!
The following is a function, true or false?
Answer:
Step-by-step explanation: true
Solve 2 log x = log 64.
x= 1.8
x=8
x= 32
x=128
x=8.
Step-by-step explanation:1. Write the expression.[tex]2log(x)=log(64)[/tex]
2. Divide both sides of the equation by "2".[tex]\frac{2log(x)}{2} =\frac{log(64)}{2}\\ \\log(x)=\frac{log(64)}{2}[/tex]
3. Apply number "10" as the base of an exponent of each side of the equation.When a logarithm doesn't have it's base expressed (base is tipically written as a subscript) we can assume it'sbase is 10. Therefore, to solve this equation, take the following step:
[tex]10^{log(x)} =10^{\frac{log(64)}{2}} \\ \\x=10^{\frac{log(64)}{2}}\\ \\x=8[/tex]
4. Verify the answer.If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "x" by it's calculated value, 8.
[tex]2log(8)=log(64)\\ \\1.806179974=1.806179974[/tex]
As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!
Answer:
x = 8
Step-by-step explanation:
Given expression:
[tex]2\log x=\log 64[/tex]
[tex]\textsf{Apply the log power law}: \quad n\log x=\log x^n[/tex]
[tex]\implies \log x^2=\log 64[/tex]
Rewrite 64 as 8²:
[tex]\implies \log x^2=\log 8^2[/tex]
[tex]\textsf{Apply the log equality law}: \quad \textsf{If\;\;$\log x=\log y$\;\;then\;\;$x=y$}[/tex]
[tex]\implies x^2=8^2[/tex]
Square root both sides:
[tex]\implies x=8[/tex]
At the ruins of Caesarea, archaeologists discovered a huge hydraulic concreate block with a
volume of 945 cubic meters. The block's dimensions are x meters high by 12x-15 meters
long by 12x-21 meters wide. Find the dimensions of the block.
Dimension is a term used to describe the length, width, and height of an item, such as a box, in common usage.
What is mean by dimension ?In mathematics, a dimension is a way of describing the length or width of an area, a space, or an object as viewed from one particular angle. The measurement of anything's length, width, and height can be put more simply. Typical ways to express dimensions include: Length.
There are three dimensions in everything around us, including the buildings we live in and the items we use on a daily basis.
something's height, length, or width measured in a specific direction: 26 feet by 15 feet is the room's size.
In everyday speech, a dimension is the sum of an object's length, width, and height that describes the size of an object, like a box. A line is one dimension, a plane is two dimensions, and space is three dimensions. In mathematics, the concept of dimension is an extension of these ideas.
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Without changing the order of the numbers, write an equivalent expression for 8 + (-9)
Answer:
-1
Step-by-step explanation:
Step-by-step explanation:
8 + (-9) is an expression that represents the mathematical operation of adding 8 and -9.
An equivalent expression for 8 + (-9) is 8-9 which is the same as 8 + (-9)
Both expressions are equivalent and have the same value, which is -1.
So, 8 + (-9) and 8-9 are equivalent expressions.
7. Use substitution to write an equivalent quadratic equation for the polynomial below. Then solve
for the roots by factoring.
Find the Real Roots and Imaginary Roots.
Quadratic Equation:
Real Roots:
Imaginary Roots:
x4 + 9x²-10 = 0
There are four real roots for the quadratic-like equation x⁴ + 9 · x² - 10 = 0: x₁ = + √(- 9 / 2 + 11 / 2), x₂ = + √(- 9 / 2 - 11 / 2), x₃ = - √(- 9 / 2 + 11 / 2) and x₄ = - √(- 9 / 2 - 11 / 2)
How to solve a quadratic-like equation by factoring
In this problem we find a quadratic-like equation of the form a · x²ⁿ + b · xⁿ + c = 0, where a, b, c are real coefficients and whose roots must be found. This can be done by completing the square and clear variable x. First, write the polynomial:
x⁴ + 9 · x² - 10 = 0
Second, use the following substitution: u = x²
u² + 9 · u - 10 = 0
Third, complete the square:
u² + 9 · u + 81 / 4 = 10 + 81 / 4
u² + 9 · u + 81 / 4 = 121 / 4
Fourth, factor the expression and clear variable u:
(u + 9 / 2)² = 121 / 4
u + 9 / 2 = ± 11 / 2
u = - 9 / 2 ± 11 / 2
Fifth, reverse the substitution and clear variable x:
x² = - 9 / 2 ± 11 / 2
x = ±√(- 9 / 2 ± 11 / 2)
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Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube (I)6655
Answer:
Step-by-step explanation:
yooyyo
differentiate f(x) =5√x using first principle
Answer: To differentiate a function using the first principle, we first need to know the function and it's original value. Given that the function is f(x) = 5√x .
The first principle of differentiation states that the derivative of a function f(x) at a point x is approximately equal to the change in f(x) for an infinitesimal change in x. We can use this principle to find the derivative of a function f(x) at a point x by calculating the limit of the ratio (f(x+dx)-f(x))/dx as dx approaches zero.
To differentiate f(x) = 5√x with respect to x using the first principle, we take the following steps:
Find the change in f(x) as x changes by dx, which is f(x + dx) - f(x)
Divide that change by dx to find the slope of the function at that point
Take the limit of that slope as dx approaches zero
So:
f(x + dx) = 5√(x + dx)
f(x) = 5√x
change in f(x) = f(x + dx) - f(x) = 5√(x + dx) - 5√x
slope = change in f(x) / dx
= (5√(x + dx) - 5√x) / dx
The limit as dx approaches zero is the derivative of the function,
lim (dx->0) [(5√(x + dx) - 5√x) / dx]
= lim (dx->0) [(5(x+dx)^1/2 - 5x^1/2) / dx]
= 5 * lim (dx->0) [(x+dx)^1/2 - x^1/2] / dx
= 5 * (1/2)x^(-1/2)
So the derivative of the function f(x) = 5√x is (5/2)x^(-1/2)
This is the slope of the function at a point x, which is the rate of change of the function at that point x.
Step-by-step explanation:
A pair of fair dice is tossed. Find the probability ofgetting;
a.) a total of 8.
b.) at most a total of 5.
Please solve and show layout and explain work..thx
The probability of total of 8 is 0.1389, the probability of at most a total of 5 is 0.2778.
A pair of fair dice is tossed.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen
P(E) = Number of favourable outcomes [tex]/[/tex] Total Number of outcomes(a)) A total of 8 can be obtained with the following outcomes,
The sample space S contains n(S) = 36 elements when a pair of dice is tossed.
⇒{(2,6),(3,5),(4,4),(5,3),(6,2)} i.e. 5 outcomes.
⇒Required probability = [tex]\frac{5}{36}[/tex] = 0.1389
The probability of a total of 8 is 0.1389.
(b).
At most a total of 5 can be obtained with the following outcomes:
⇒{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)} i.e. 10 outcomes.
⇒Required probability =[tex]\frac{10}{36}[/tex] =0.2778
The probability of at most a total of 5 is 0.2778.
Therefore, the probability of total of 8 is 0.1389, the probability of at most a total of 5 is 0.2778.
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WILL MARK BRAINLIEST (CORRECT ANSWER)
There are 3 students to 1 adult on a field trip. You need to find the number of adults needed for 24 students. What would the second ratio of the proportion look like if the first proportion is as follows?
3 students/ 1 adult
A. 1/3
B. 24 students/x
C. x/24 students
D. 3/1
Answer:
24 studens
3 students and 1 adult - [tex] \frac{3}{1}
24 students and x adults - [tex]\frac{24}{x}
After solving the answer is 8 adults to 24 kids
Step-by-step explanation:
According to a recent survey of 37 million citizens in the United States, 5 million were planning to start a new degree program or continue their education in the next year.
According to this data, what is the probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year? (Round to four decimal places.)
The probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year is; 0.8649
How to solve probability of selection?Probability of selection defines the probability that a population unit is included in a sample generated by probability sampling.
It simply means that the probability of selection.
For example, at a school board meeting there are 9 parents and 5 teachers. Two teachers and 5 parents are female. If a person at the school board meeting is selected at random, we can use the concept of probability selection to find the probability that the person is a parent or a female.
Now, we are told that a recent survey of 37 million citizens in the United States, 5 million were planning to start a new degree program or continue their education in the next year. Thus, we can say that;
Total number of people in survey = 37 million
Number of people planning to start a new degree program or continue their education in the next year = 5 million
Thus;
P(People starting new program) = 5 million/37 million
= 5/37
Thus;
P(People NOT starting new program) = 37/37 - 5/37
= 32/37 = 0.8649
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First one to answer gets brainlest
Square root of 42.25
Answer:
Square root of 42.25 is 6.5
The square root of 42.25 is 6.5.
To find the square root of 42.25, we need to determine the number that, when multiplied by itself, equals 42.25. In this case, the square root of 42.25 is 6.5 because 6.5 multiplied by itself (6.5 x 6.5) equals 42.25.
Mathematically, it can be represented as:
√42.25
= 6.5
The square root (√) is the inverse operation of squaring a number.
When we square a number, we multiply it by itself.
In this case, squaring 6.5 (6.5 x 6.5) gives us the original value of 42.25.
Therefore, the square root of 42.25 is 6.5.
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Type the correct answer in each box. Use numerals instead of words.
You reflect triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1), across the x-axis, across the y-axis, and across the x-axis again to form triangle P′Q′R′.
After these reflections, the coordinates of P′ will be ( ____ , ____ ).
After these reflections, the coordinates of P′ will be ( __4__ , __-4__ ).
What are coordinates?
Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. Any point's location on a plane can be described by an ordered pair of values (x, y), which are referred to as coordinates.
Step by step Explaination:
* Let's update a few changes.
If x-axis reflection at position (x, y)
∴ Seeing it is (x , -y)
If the y-axis at position (x, y) was reflected
∴ Seeing it is (-x , y)
* Let's deal with the issue.
The triangle PQR, which is defined by the points P(-4, -4), Q(-1, -3), and R. (-3, -1)
Across the x-axis, the triangle is reflected.
PQR is visible along the x-axis.
All y-coordinates of the vertices P, Q, and R have their signs reversed.
∴ The new points are going to be (-4, 4), (-1, 3), and (-3 , 1)
A reflection of the new vertices along the y-axis will occur.
All of the new vertices' x-coordinates had their signs reversed.
The new points are (4, 4), (1, 3), and (3 , 1).
The updated vertex positions will reflect along the x-axis to produce the letters P'Q'R.
∴ The new vertices' y-coordinates all had their signs flipped.
∴ P' = (4 , -4) , Q' = (1 , -3) , R' = (3 , -1) (3 , -1)
The coordinates of P′ following these reflections will be (4 , -4).
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Combine as indicated by the signs.
4/y^2-9 + 5/y+3
The combined expression for the given expression will be ( 5y -11 ) / ( y² - 9 ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is ( 4 / y² - 9 ) + ( 5 / y + 3 ).
The expression will be solved as below,
E = ( 4 / y² - 9 ) + ( 5 / y + 3 ).
E = 4 / ( y +3 ) ( y - 3 ) + 5 / ( y + 3 )
E = 1 / ( y + 3 ) [ ( 4 / ( y- 3 ) + 5 ]
E = 1 / ( y +3 ) [ ( 4 + 5y - 15 ) / ( y - 3 ) ]
E = ( 5y - 11 ) / ( y² - 9 )
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Find the slope of the line that passes through (3, 14) and (7, 7).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the given line that passes through (3, 14) and (7, 7) is m = - 7/4.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is a straight line that passes through points (3, 14) and (7, 7).
It is given that the line passes through (3, 14) and (7, 7). We can write the slope as -
m = (7 - 14)(7 - 3)
m = - 7/4
Therefore, the slope of the given line that passes through (3, 14) and (7, 7) is m = - 7/4.
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If a number has a factor, then both 2 and 4 are factors?
Answer:
Step-by-step explanation:
when 2 and 4 are factors of a number then 8 will also be factor of that number. Example: let's take the number 8 here 2,4 and 8 are factors of the number.
Which of the following is the equation that represents the graph?
Graph of a line the passes through the points negative 6 comma 0 and 0 comma negative 4.
y equals negative two thirds times x minus 6
y equals negative three halves times x minus 6
y equals negative two thirds times x minus 4
y equals negative three halves times x minus 4
The equation of line is y = -2/3x - 4, option C is correct.
What is slope of a line?
A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Given coordinates
(-6, 0) and (0, -4)
equation of line is y = mx + c
m = (y₂ - y₁)/(x₂ - x₁)
m = (-4 - 0)/(0 + 6)
m = -2/3
and c is y-intercept = -4
equation is y = mx + c
y = -2/3x - 4
Hence option C is correct.
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Answer:
The equation of line is y = -2/3x - 4, option C is correct.
Step-by-step explanation:
[tex]\frac{5}{x} -\frac{10}{x^{2}+2x }[/tex]
The factorized form of the given expression is [tex]\frac{ \textbf5}{( \textbf{x + 2})}[/tex].
What is factorisation form?In mathematics, factorisation or factoring is defined as the breaking or decomposition of an entity (for example, a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or matrix, etc. This concept will be emphasised heavily in your lower secondary classes from grades 6 to 8.
It is simply the division of an integer or polynomial into factors that, when multiplied together, result in the original or initial integer or polynomial. The factorisation method simplifies any algebraic or quadratic equation by representing it as the product of factors rather than expanding the brackets.
Given to simply the expression
⇒ [tex]$ \frac{5}{x} - \frac{10}{x^2 + 2x}[/tex]
[tex]$ \Rightarrow \frac{5}{x} - \frac{10}{x(x + 2)}[/tex]
[tex]$ \Rightarrow \frac{5(x + 2)}{x(x + 2)} - \frac{10}{x(x + 2)}[/tex]
[tex]$ \Rightarrow \frac{5(x + 2) - 10}{x(x + 2)}[/tex]
[tex]$ \Rightarrow \frac{5x + 10 - 10}{x(x + 2)}[/tex]
[tex]$ \Rightarrow \frac{5x}{ x(x + 2)}[/tex]
[tex]$ \Rightarrow \frac{ \textbf5}{( \textbf{x + 2})}[/tex]
Thus, the factorized form of the given expression is [tex]\frac{ \textbf5}{( \textbf{x + 2})}[/tex].
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Divisibility rules for 2, 5, and 10
Answer: not sure if this is what you want but a number is divisible by 2 if it ends in 2, 4, 6, 8 or 0 a number is divisible by 5 if it ends in 5 or 0 a number is divisible by 10 if it ends in a 0
Step-by-step explanation:
.
In the accompanying diagram, isosceles trapezoid has bases DC and AB with measures of 6 meters
and 18 meters respectively. If altitude CE is drawn and AC has a measure of 14 meters, find the length
of altitude CE to the nearest meter.
The length of the isosceles trapezoid height CE is 14 meters.
How do you calculate the length?To find the length of the height CE of the isosceles trapezoid, we can use the Pythagorean theorem.
The isosceles trapezoid CE is the hypotenuse of the right triangle formed by height CE and distance AC. CE is also the height of the trapezoid. Let the length of CE be 'x'
The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle (CE) is equal to the sum of the squares of the lengths of the other two sides (AC and CE).
x² = AC² + CE²
We know that AC = 14 meters and CE = x.
So x² = 14² + x²
x² = 196 + x²
x² = x² + 196
0 = 196
x = √196 = 14
Therefore, the length of height CE is 14 meters.
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