The value of A in the 4-digit number, 3A5A is 5.
What is the value of A?The 4-digit number provided in the question has to be a multiple of 15 given the information in the question. A multiple of a number is divisible by that number. A multiple of 10 is 100 because when 100 is divided by 10 , the value gotten is 10.
A multiple of a number is the product of an integer and that number. For example, a multiple of 2 is 100. This is because 2 multiplied by 50 is equal to 100.
The multiplies of 15 either have a unit value of 5 or 0.
If A is 5, the number becomes 3555.
3555 / 15 = 237
If A is 0, the number becomes 3050
3050 / 15 = 203.33
Thus, the value of A is 5 because 3555 is divisible by 15.
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Simplify the expression 36 + 63 ÷ 9.
A 90 -inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece.
Answer:
30 inches
Step-by-step explanation:
We know that the total length of the board is 90 inches and we know that the shorter piece is two times smaller than the other so we have two pieces divided into three sections 90 divided by three is 30 and since we realize that 30x2=60 and 60+30=90 it means the longer board is 60 inches and smaller one is 30 I hope this helps.
Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)... 13/5, a₆, a₇, a₈, 37/5, . . . . . .
The missing term in the sequence is A5 = 5 .
Let's assume for the sake of simplicity that the third term they provided you was >3, and the twenty-fifth is >25. As a result, you put 3 as A sub-one rather than specifying that A sub-3 is 3 and A sub-25 is 25. Here's where things become tough. Set A sub-23 to 25. (why? because 1 to 23 and 3 to 25 are equally distant.
A3=3, A25=25 } A1=3, A23=25
Apply the equation An = A1 + (n-1)D.
(Read: A-sub n = A sub 1 - the nth term - D)
A23(A sub-23)= 3 Plus (23-1)
D 25 = 3 + 22D \s-3 -3
22 = 22D
D = 1
Once more, An = A1 + (n-1)D.
A3 = A1 + (3-1) X 1
3 = A1 + 2
-2 -2
A1 = 1
An = 1 + (n-1) X 1
An = 1 + 1n - 1
An = 1n + 0
So you are left with the general formula An = 1n. You can use this formula to find any term in the sequence, all you got to do is plug in (An) the number you want. In this case, plug in A sub-5 if you want to find the fifth term. You get
An = 1n
A5 = 1X5
A5 = 5
The fifth term in the sequence is 5. (it goes 1,2,3,4,,5,..)
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Find the coordinates of M if N(1.5,2.5) is the midpoint of \overline{M P} and P has coordinates (6,9)
Applying the midpoint formula, the coordinates of point M are: (-3, -4).
How to Apply the Midpoint Formula?The midpoint formula is given as, (x, y) = [(x2 + x1)/2, (y2 + y1)/2].
Given the following:
N(x, y) = (1.5, 2.5)
P(x1, y1) = (6, 9)
M(x2, y2) = (?, ?)
Plug in the values into the midpoint formula
N(1.5, 2.5) = [(x2 + 6)/2, (y2 + 9)/2]
Isolate each coordinate
1.5 = (x2 + 6)/2
2(1.5) = x2 + 6
3 = x2 + 6
3 - 6 = x2
x2 = -3
2.5 = (y2 + 9)/2
5 = y2 + 9
5 - 9 = y2
y2 = -4
Therefore, applying the midpoint formula, the coordinates of point M are: (-3, -4).
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Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.
parallelogram
A rectangle as the only parallelogram that can be inscribed in a circle.
What shapes can be inscribed in a circle?Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.
The only parallelogram that can be inscribed in a circle is a rectangle. Because every rectangle can be inscribed in a (unique circle), the important point is that the radius of the circle is R. (I think). One of the properties of a rectangle is that the diagonals bisect in the 'center,' which is also the center of the circumscribing circle.
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Can someone help me with my geometry hw?
Answer:
Step-by-step explanation:
Write an explicit and a recursive formula for each arithmetic sequence. -2,-13,-24, . . . . .
Given an arithmetic sequence -2,-13,-24, . . . , the recursive formula is: a(n) = a(n-1) -11 and the explicit formula is a(n) = 9 - 11n
Suppose we are given an arithmetic sequence:
a(1), a(2), a(3), a(4), ....
Then, in an arithmetic sequence, the next term is obtained by adding a constant to the previous term. This constant is called a common difference.
Let d = common difference, then
a(2) = a(1) + d
a(3) = a(2) + d
and so on, until
a(n) = a(n-1) + d
This is a recursive formula. Here a(n) = nth term, and a(n-1) = (n-1)th term.
The sequence in the problem:
-2,-13,-24, . .
Notice that:
-13 = -2 + (-11)
-24 = -13 + ( -11)
Hence, d = -11, and therefore, the recursive formula for the nth term is:
a(n) = a(n-1) -11
To find the nth term, we can also use the explicit formula:
a(n) = a(1) + (n-1).d
In the given sequence, a(1) = -2, and d = -11. Substitute these parameters:
a(n) = -2 + (n-1) . (-11)
= -2 - 11n + 11
= 9 - 11n
Thus, the explicit formula is a(n) = 9 - 11n.
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Determine whether each sequence is arithmetic. If so, identify the common difference. 1,1,2,3,5,8, ...........
The sequence 1,1,2,3,5,8, ........... doesn't form an AP as they have the varying common difference.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between these two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few specific keywords in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be explained in expressed in the form of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' : d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the sequence given is; 1,1,2,3,5,8, ...........
The series contains of given 6 terms.
Let the initial term be 'a₁' = 1.
The second term be 'a₂' = 1.
The third term be 'a₃' = 2.
And, the fourth term is 'a₄' = 3.
For the sequence to form the AP, they must have the equal common difference. So,
d = a₃ - a₂
Substitute the values.
d₁ = 2 - 1
d₁ = 1
Thus, the calculated common difference is 1.
or d = a₅ - a₄ (Put the values)
d₂ = 5 - 3
d₂ = 2
Since, d₁ ≠ d₂
Thus, we can say that the given sequence is not forming an AP.
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In Δ A B C, ∠ B is a right angle and ∠A is 20° greater than ∠C . What is the measure of ∠C ?
A 30
B 35
C 40
D 45
E 70
The measure of ∠C in ΔABC is 35°.
Angle Sum Property of a triangle states that sum of all the interior angle of a triangle is 180°.
In the given Question
∠B=90° , ∠A=∠C+20°...(1)
By angle sum property of triangle for ΔABC
we get
∠A+∠B+∠C=180°
Substituting the values of ∠B and ∠C from equation (1) we get
∠C+20°+90°+∠C=180°
2∠C+110°=180°
2∠C=180°-110°
2∠C=70°
∠C=35°
Therefore , the value of ∠C in ΔABC is 35°.
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For the function f(x) = − 4x + 8, f( – 6) = _.
I need help
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=2 x-y-13
The given function y = 2x - y - 13² , is a linear function
where:
Its linear term is -12x Constant is -18What is a function?
A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.
The function we have is particular because it has two variables, and these two are "x" and "y", but the y is the image so we do not consider it a variable.
y = 2x - y - 13y + y = 2x - 13
2y = 2x - 13
y = (2x - 13)/2
y = x - 13/2
y = x - 6.5
Here we notice that we have a linear function
It has no quadratic term Its linear term is "x" Its constant is "-6.5".Learn more about functions at:
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Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of ice tea she can serve?
x minus y equals 44
44 plus y equals x
y minus x equals 44
x equals 44 minus y
The number of glasses of iced tea is x = 44 − y.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
She has only 44 glasses in which to serve the drinks.
x represents the number of glasses of iced tea
y represents the number of glasses of lemonade
According to given question we have
x is the number of glasses of iced tea, and y is the number of glasses of lemonade. The sum is 44,
x + y = 44
Solving for x:
x = 44 − y
Therefore, the number of glasses of iced tea is x = 44 − y.
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The product of 4 and a number plus 17 is 5.”
Answer:
5 - 17 = -12
-12/4 = -3
Answer:
number is - 3
Step-by-step explanation:
let the number be n then the product ( multiplication ) of n and 4 is 4n , so
4n + 17 = 5 ( subtract 17 from both sides )
4n = - 12 ( divide both sides by 4 )
n = - 3
the number n is - 3
Just give me an example for problem 3 please
The angles that has C as a vertex are:
13. ∠HVJ, ∠HVI, ∠JVI
14. ∠DVF, ∠DVE, ∠FVE
How to Name Angles Using Their Vertex?Angles that have letter V at their vertex can be named as an angle contain V as a point.
13. The angles that have V as vertex are:
∠HVJ
∠HVI
∠JVI
They all contain vertex V.
14. The angles that have V as vertex are:
∠DVF
∠DVE
∠FVE
They all contain vertex V.
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9/7 is greater than or less than 3/1
Answer: Less than. (9/7<3/1)
Step-by-step explanation: We know the answer is 9/7<3/1 because 3/1 as a whole number will be 3. If we convert 9/7 into a proper fraction with a whole number, it will be 1 2/7. 3 is greater than 1 and 2/7ths.
a) Urgen has 500 rupees. She spent 50 rupees to eat Mo:Mo and 100 rupees to buy exercise books. How much money did she have?
Answer:
650 Rupees
Step-by-step explanation:
Add all together
What is the solution of the equation √x+5=√2x-4?
Answer:
x=9
Step-by-step explanation:
[tex]\sqrt{x+5}=\sqrt{2x-4} \\ \\ x+5=2x-4 \\ \\ x=9 [/tex]
On substituting this back into the equation, we see x=9 satisfies it.
I need help with this problem please and thank you :)
The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².
What is the difference between the original function and the transformed function?
In this problem we find a quadratic equation, of which we must infer the series of rigid transformations to be used to obtain a resulting expression. Rigid transformations are transformations applied on functions such that Euclidean distance is not changed. The most used rigid transformations are listed below:
TranslationReflectionRotationDilationContractionAfter comparing the two expressions, we find that this procedure was applied in the following order:
Translation 8 units in the -x direction.Dilation by a factor of 3.Translation 4 units in the +y direction.Finally, we show the procedure to prove this manner:
y = x²
Step 1
y' = (x + 8)²
Step 2
y'' = 3 · (x + 8)²
Step 3
f(x) = 3 · (x + 8)² + 4
The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².
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need help solving please
Answer:
3 option
Step-by-step explanation:
To find the missing side (c) you need to do a^2 and b^2
Formula a^2 + a^2 = c^2
Solve 9x - 2y = 15 for y.
Y =
How to get the equation of a line
Answering the Question
There are a couple ways we can get the equation of a line, depending on what we're given.
The Equation FormMost linear equations are organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of a line can be calculated algebraically when we know two points that fall on the line:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the two pointsY-interceptThe y-intercept is the value of y when the line crosses the y-axis, or when x = 0. When given a graph, you can sometimes read the y-intercept directly from the graph.
For instance, if the line passes through the point (0,5), then the y-intercept is 5.
You can also find the y-intercept algebraically if you know the slope and one point that falls on the line. You plug in that point as (x,y) and isolate b.
Summary
For most cases, you can use the following method to find the equation of a line:
Find the slope of the line (using the slope equation) and plug it into y=mx+bFind the y-intercept of the line algebraically and plug it into y=mx+bPaulina has completed 24 of 42 problems she was assigned for homework. She plans to finish her homework by completing 9math problems each hour,h write an equation to find the number of hours it will take Paulina to complete her math homework assignment
Answer:
Step-by-step explanation:
42=24+9h
Determine whether the following statements are sometimes, always, or never true. Explain.
If possible, draw an isosceles triangle with base angles that are obtuse. If it is not possible, explain why not.
An isosceles triangle is a triangle with (at least) two equal sides. In the picture above, we have two equal side lengths and the remaining side length. .This property corresponds to two equal angles in a triangle.
verify the following equation:
Find the equation is possible or not?
Yes, it is possible to draw an isosceles obtuse triangle.
An isosceles obtuse triangle is a triangle in which one of its three angles is obtuse (between [tex]90[/tex] and [tex]180[/tex]degrees) and the other two are acute angles.
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Two rectangular prisms are similar. The height of the first prism is 6 yards and the height of the other prism is 9 feet. If the volume of the first prism is 810 cubic yards, what is the volume of the other prism?
The value of the volume of the other rectangular prism is V = 101.25 yd³.
What is a numerical ratio?A numerical ratio is a constant value that relates a system of two or more variables, it allows us to know how their variations will be as the values change.
First we must find the ratio between the heights of the rectangular prisms, for this we determine the height in the same unit:
1 yard = 3 ft9 ft x (1yd / 3ft) = 3ydWe express the following:
b/a = 3/6b/a = 1/2For volume
1/2³ = 1/8 = V/810
V = 101.25 yd³
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Find the value of 8 1/3
Answer: The answer is 25/3.
Step-by-step explanation: 8 1/3 = 8 x 3 + 1/3 = 24 + 1 = 25/3
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3 3
Evaluate each logarithm.
log₄ 64
Answer:
well done .... keep practicing....
Find the slope of the line that passes through (2,1) and (5,6). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the line that passes through the given points is equal to 3/5.
Given the following data:
Points on x-axis = (2, 5).
Points on y-axis = (1, 6).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (5 - 2)/6 - 1)
Slope = 3/5
In conclusion, the slope of the line that passes through the given points is equal to 3/5.
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Describe a different sequence of transformations in which the blue figure is the image of the red figure.
There are two different sequences of transformation.
What is sequence of transformation?
A sequence of transformation is an operator acting on a given space of sequences. Sequence transformations include linear mappings such as convolution with another sequence, and resummation.
What is origin?
A graph in the two-dimensional coordinate plane has the point (0,0) as its origin. The origin is located at the intersection of the vertical and horizontal axes, and the distance to all points can be measured from this point.
Given figure is in which the blue figure is the image of the red figure
The above figure can be transformed in two sequences
a) We could first rotate clockwise 90 degrees from the origin, and then reflect on the x axis. And translate two units right side.
b) We could rotate counter clockwise 90 degrees and then reflect on the y axis. And translate two units upwards.
By these sequence of transformation, blue figure is the image of red figure.
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Select the correct answer.
The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true?
OA The mean of data set XIs greater than the mean of data set Y.
OB. The median of data set X is less than the median of data set Y.
OC. The standard deviation of data set Xis greater than the standard deviation of data set Y.
OD. The range of data set X is less than the range of data set Y.
O E.
The mode of data set X is greater than the mode of data set Y.
Answer:
C
Step-by-step explanation:
Just the spread of normally distributed data tells us nothing about the mean, mode or median, so answers A, B, and E are out of question.
The range is based on the difference between the highest and lowest elements. As there can be big outliers, we have no idea if D is true, although we expect distributions with bigger spread to generally exhibit bigger ranges.
We're left with answer C. Standard deviation is a measure of "how much the data can deviate from the mean". It's also one of the measures of spread. We expect data that's more spread out (higher spread) to have a higher standard deviation.
To estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree's shadow end at the same point. Dave is 6 feet 4 inches tall and his shadow is 15 feet long. If he is standing 66 feet away from the tree, what is the height of the tree?
The height of the tree, which Dave is standing 66 feet away from, is 34 feet and 2.4 inches.
If Dave's and the tree's shadows end at the same point, then the length of the shadow of the tree must be the sum of Dave's shadow and his distance from the tree.
tree's shadow = Dave's shadow + distance from the tree
tree's shadow = 15 feet + 66 feet
tree's shadow = 81 feet
Using ratio and proportion, we can solve for the height of the tree.
Dave's height : height of tree = Dave's shadow : tree's shadow
let x = height of the tree
6 feet 4 inches : x = 15 feet : 81 feet
converting feet to inches (1 feet = 12 inches)
76 : x = 180 : 972
Solving for x by evaluating the proportion:
180 x = 76 (972)
x = 410.4 inches
x = 34 feet and 2.4 inches
Hence, the height of the tree is 34 feet and 2.4 inches.
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