1+3+5+7+9+11+13+15
=4+12+20+28
=16+48
=64
What value of k will result in the quadratic having one rational solution if 4x2+kx+4=0?
The value of 'k' in the quadratic Equation [tex]4x^{2}+kx+4=0[/tex] having one rational solution is k is 8.
What is a Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of the type [tex]f(x) = ax^{2} + bx + c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.The standard form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex] .Here, the given equation is [tex]4x^{2}+kx+4=0[/tex]
By comparing the given equation with the standard form of the quadratic equation we get,
a = 4
b = k
c = 4
The given quadratic is having one rational solution, which means [tex]b^{2} -4ac=0[/tex]
Therefore,
[tex]k^{2} -4 \times 4\times4=0\\k^{2} -64=0\\k^{2} =64\\k=\sqrt{64} \\k=8[/tex]
Therefore, the value of k is 8.
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Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
The statement that can be concluded from the triangle is A. RS/VU=ST/UT and ∠S≅∠U.
How to illustrate the information?The Side-Angle-Side Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
In this problem the included angle is ∠S≅∠U, therefore side RS must be proportional to side VU and side ST must be proportional to side UT
Hence, RS/VU=ST/UT.
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PLEASE HELP!! This graph shows the bird population of a large lake. Note that the
number of birds at the lake in the month of December is zero. What
does this extreme drop between November and December MOST
likely represent?
Select one:
O a. The beginning of duck hunting season.
O b. A reflection of the migratory nature of the birds at the lake.
O c. An inaccurate collection of data, and so, invalid results.
Od. A reflection of the hibernation patterns of the birds at the
lake.
The extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.
What is Bird Migration?Bird migration is a natural process which can be described as a the movement of different birds by flight across thousands of kilometers in search of ecological conditions and habitats that favors breeding, feeding, and raising of their young.
Migratory birds have well built physiology and morphology that make them better equip to fly fast and across long distances in search of the best ecological conditions, which is dependent on seasons.
Like in the graph given, like we see that at the beginning of January, number of birds were few in the lake until sudden increase occurred. It can be said that during those period of increase, the ecological conditions favored the survival of the bird until November and December. This extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.
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Find the vertex and axis of symmetry
Answer:
Below in bold.
Step-by-step explanation:
f(x) = 2x^2 - 12x + 24
Convert to vertex form:
f(x) = 2(x^2 - 6x) + 24
= 2[(x - 3)^2 - 9] + 24
= 2(x - 3)^2 - 18 + 24
= 2(x - 3)^2 + 6
So the vertex is at (3, 6) and the axis of symmetry is x = 3.
SOMEONE PLEASE HELP!!!!!!
Consider the functions graphed below. A curve a intersects a parabola b at (negative 1, 0 point 5) and a parabola c at (negative 2 point 4, 0 point 3). A diagonal curve d intersects the parabola b at (0 point 5, 0) and (2, 3) and parabola c at (negative 1 point 2, negative 1 point 2). Determine which function has the greatest rate of change over the interval [0, 2]. A. d B. b C. c D. a
The function with the greatest rate of change over the interval [0, 2] is: D. a.
How to determine function with the greatest rate of change?In Mathematics, the rate of change of a function over a given interval can be determined by calculating the slope of the straight line which connect its end points.
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]
For line a, we have:
Points (x, y) = (0, 1) and (2, 4)
Slope = (4 - 1)/(2 - 0)
Slope = 3/2 or 1.5.
For line b, we have:
Points (x, y) = (0, 0) and (2, 2)
Slope = (2 - 0)/(2 - 0)
Slope = 2/2 or 1.0.
For line c, we have:
Points (x, y) = (0, -1) and (2, 0)
Slope = (0 + 1)/(2 - 0)
Slope = 1/2 or 0.5.
For line d, we have:
Points (x, y) = (0, 0.5) and (2, 2.5)
Slope = (2.5 - 0.5)/(2 - 0)
Slope = 2/2 or 1.
In conclusion, we can logically deduce that "function a" has the greatest rate of change over the interval [0, 2].
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I dont know this. pls help
Answer:
28, 4 or 4, 28 (order doesn't matter, both are true answers)
Step-by-step explanation:
l + w = 32
l*w = 112
l = 112/w
112/w + w = 32
w = 28 or 4
l = 28 or 4
Answer:
4,28
Step-by-step explanation:
So let's look at the sentence to take any necessary information out. It says the length of a rectangle plus it's width is 32. Since we do not know what the length and width are, let's just represent them as L (length) and W (width). Using this information we get the equation: [tex]L + W = 32[/tex] and since we're given the area of the rectangle, we can also define another equation which is: [tex]LW = 112[/tex] since the length * width = area.
So now all we have is a systems of equations. We can solve for L or W in the area equation and plug it into the addition equation. We can also solve for L or W in the addition equation and then plug it into the area equation, either should work, but in this example I'll solve for L in the addition equation:
Original Equation:
[tex]L + W = 32[/tex]
Subtract 32 from both sides
[tex]L = 32-W[/tex]
Now let's use this definition of L to plug into the second equation:
[tex]LW = 112 \implies (32-W)W = 112[/tex]
Distribute the W
[tex]-W^2+32W=112[/tex]
Now if you notice, we simply have a quadratic equation and we can subtract 112 from both sides and then use the quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Subtract 112 from both sides
[tex]-W^2+32W-112=0[/tex]
Use quadratic formula
[tex]W = \frac{-32\pm\sqrt{32^2-4(-1)(-112)}}{2(-1)}[/tex]
Simplify stuff in radical
[tex]W = \frac{-32\pm\sqrt{576}}{-2}[/tex]
Calculate the square root
[tex]W=\frac{-32\pm24}{-2}[/tex]
Use positive sign:
[tex]W=\frac{-32+24}{-2}[/tex]
Simplify numerator
[tex]W = \frac{-8}{-2}[/tex]
Simplify fraction
[tex]W=4[/tex]
Take negative sign
[tex]W = \frac{-32-24}{-2}[/tex]
Simplify numerator
[tex]W=\frac{-56}{-2}[/tex]
W = [tex]28[/tex]
So we have two solutions, and the reason for this is because had we solved for W in the original equation and substituted that into here, there would be no different, it's not bound by some variable name. So these are actually the two sides of the rectangles
4 + 28 = 32
4 * 28 = 112
4, 28
Find the volume of the pyramid. Round to the nearest tenth if necessary. hurry!!
Answer:
Step-by-step explanation:
All pyramids have a volume as one-third of a prism with the same base area and the same height.
This will make the formula for the volume [tex]\frac{1}{3}(base*height)[/tex]. We already know the height of the pyramid is 10, but the area of the base for this rectangle would be its length and its width. Let's calculate this:
[tex]7*2.3=16.1\hspace{0.1cm}in^2[/tex]
Let's put these values back into the formula:
[tex]V=\frac{1}{3}(16.1*10)\\ V=\frac{1}{3}(161)\\ V= 53.7\hspace{0.1cm}in^3[/tex]
In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as:
In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.
Leitmotiv, from the German "leading motive," is a recurrent musical motif that typically appears in operas but can also be found in symphonic poems.Overture to a concert. Romantic-era concert piece for orchestra in one movement, frequently based on a literary program.What is serious opera called?
Opera seria, or "serious opera," is an Italian operatic genre that was popular in 18th-century Europe. The genre is commonly referred to as Neapolitan opera since it first appeared in the late 17th century, particularly in the works of Alessandro Scarlatti and other composers based in Naples.What is Wagnerian leitmotif?
A theme of easily recognizable melodic, rhythmic, or harmonic identity, first used in connection with a certain character of incident, and which returns time and time again, always with a recollection of the original association. The term was coined by the Wagnerian scholar Hans von Wolzogen.Learn more about leitmotif
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PLEASE ANSWERERRREEERRR
the operation:
[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]
Gives a square number.
How to get a perfect square?
A perfect square is the product of a number and itself.
As you can see in the example, 16 is a square number. Then let's try to get 16.
To get 16 we can use the difference:
20 - 4
So the first therm needs to be equal to 20, and the second equal to 4.
To write 20 in scientific notation we have:
[tex]2*10^1[/tex]
To write 4 in in scientific notation:
[tex]4*10^0[/tex]
Then the operation:
[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]
Gives a square number.
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What is the coordinate point of the linear function 5x+3y=15
Answer: Y-intercept: (0,5) X-intercept: (3,0)
Step-by-step explanation: Set x and y equal to 0.
Mari works part time selling both hats and scarfs. One week she earns $114.00 by selling eight hats and 10 scarves. The following week she sold 12 hats and six scarves and earned $108.00. How much does she earn for each hat and scarf she sells?
Using a system of equations, it is found that she earns $5.5 for each hat and $7 for each scarf sold.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Cost of a hat.Variable y: Cost of a scarf.One week she earns $114.00 by selling eight hats and 10 scarves, hence:
8x + 10y = 114.
The following week she sold 12 hats and six scarves and earned $108.00, hence:
12x + 6y = 108
Simplifying by 6:
2x + y = 18
y = 18 - 2x.
Replacing in the first equation:
8x + 10y = 114.
8x + 10(18 - 2x) = 114
12x = 66
x = 66/12
x = 5.5
y = 18 - 2x = 18 - 2 x 5.5 = 7.
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Answers are 1/3, 1/2, and 1/4 (not respectively). But can someone tell me how to get there please?
The value of X is 1/3 and Y is 1/2 and Z is 1/4.
According to the statement we have given the equations which are
X + Y = 5XY -(1)
Y + Z = 6YZ -(2)
Z + X = 7XZ -(3)
and we have to find the value of X,Y,Z.
So, solve the equations for the X,Y,Z
From (1) equation
Y = X / (5X-1) -(4)
From (3) equation
Z = X / (7X-1) -(5)
Put (4) and (5) in (2) then
X / (5X-1) + X / (7X-1) = 6{[X / (5X-1)][X / (7X-1)]}
X(7X-1) + X(5X-1) = 6{[X / (5X-1)][X / (7X-1)]} / {[1 / (5X-1)][1 / (7X-1)]}
Then after solving
12(X)^2 -2X = 6(X)^2
6(X)^2 -2X = 0
X (6X-2) = 0
X = 0, X = 1/3
Here X = 0 is neglected.
So, X=1/3 -(6)
Put (6) in (4) and (5) then
From 4
Y = X / (5X-1)
Y = (1/3) / (5(1/3)-1)
Y = (1/3) / (2/3)
Y = 1/2.
From (5) equation
Z = X / (7X-1)
Z = (1/3) / (7(1/3)-1)
Z = (1/3) / (4/3)
Z = 1/4.
So, The value of X is 1/3 and Y is 1/2 and Z is 1/4.
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Geometric series
2 + 6 + 18 + 54 + ... , find tn
The function that gives the value of tn for the geometric series is presented as follows;
[tex]t_n = 2 \times 3^{(n - 1)} [/tex]
How can the expression that represents the geometric series be found?
The given geometric series is presented as follows;
2 + 6 + 18 + 54 +...
From the above series, we have;
First term, a = 2Common ratio, r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3The nth term of the geometric series is therefore;
[tex]t_n = a \cdot r^{(n - 1)} [/tex]
Which gives;
[tex]t_n = 2 \times 3^{(n - 1)} [/tex]
Where, tn is the nth term
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If the sum of three numbers is 200, and the smallest number is 25, could the largest number be 75?
Answer:
No largest no could be 100
Step-by-step explanation:
Yes, the sum of the three numbers is 200, and the largest number can indeed be 75.
Let's assume the three numbers are:
Smallest number = 25
Middle number = x (unknown)
Largest number = 75
The sum of the three numbers is 200, so we can set up the equation:
25 + x + 75 = 200
Now, let's solve for x:
x = 200 - 25 - 75
x = 100
So, the middle number is 100.
Now, we can check if the largest number (75) is correct:
25 + 100 + 75 = 200
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A streetlight is at the top of an 18ft tall pole. A woman 6 ft tall walks away from the pole at a speed of 4 ft/sec along a straight path. How fast (in ft/sec) is the tip of her shadow moving away from the pole when she is 45 ft from the base of the pole
The woman's shadow is moving away from the pole at the speed of 4 feet/sec.
Calculating the value of shadow speedThe height of a pole-mounted street light = 18 ft
The height of a lady = 6 ft
The woman is moving quickly and directly away from the pole. Her speed = 4ft/sec.
The woman's distance from the pole at the precise moment question want to know the speed of the woman's shadow's leading edge = 45ft
A woman standing 6 feet tall moves away from the pole in a straight route at a pace of 4 feet per second. If we assume that t is the passing time in seconds and that x is the distance in feet between the pole and the lady, we are informed that dx/dt=4 ft/sec.
Therefore, it is concluded that the final answer is 4 ft/sec.
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A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
show all work
insert picture of the tree diagram pls
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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PLS SOLVEEEEEEEE!!! This is urgent :(
Answer:
B) 16
Step-by-step explanation:
12/3 = x/4
48 = 3x Divide both sides by 3
16 = x
Can anyone tell me how to solve this with step by step and show work
Also apparently the answers are A and C but I need to know how to get to the answer
Simplify 4/9 + 1/3
A 5/12
B 7/9
C 1 1/9
D 15/9
Answer:
B) 7/9
Step-by-step explanation:
Fraction addition: If the denominators are not same, find the LCM of the denominators.LCM of 3 and 9 is 9.
Now, find equivalent fractions with denominator as 9.[tex]\sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\[/tex]
[tex]\sf =\dfrac{3}{9}[/tex]
Now add.[tex]\sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\[/tex]
[tex]\sf =\dfrac{7}{9}[/tex]
Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surveyed, 13 said the test was easy, 11 rated it as moderate, and 3 found it difficult. Assuming that all students took the same test, how many of the 162 total students in Christian’s grade would probably rate the test something other than easy?
Answer:
84
Step-by-step explanation:
Total students he surveyed: 27
Amount that found it something OTHER than easy: 14 (11 moderate + 3 difficult)
This means that [tex]\frac{14}{27}[/tex] found it something other than easy
Multiply that by 162 to find the proportion for the larger population:
162 * (14/27), and we get 84.
Find the missing side length of the triangle.
SOLUTION :
c² = 5² + 5²
c² = 25 + 25
c² = 50
c = √50 ft
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5th grade algebra. Pls help with these am offering brainliest + bonus points! :D
Answer:
3. 6 5. 3
Step-by-step explanation:
PEMDAS
3. 0.5 x (24) / 3 + 2
12/3 +2
4 + 2
6
5. (4 + 6/3) x 0.5
(4 + 2) x 0.5
6 x 0.5
3
Answer: number 3. is 6 and number 5. is 3
hope it helped
Please help
The area of a circle is 354 cm². Find in degrees and minutes, the angle subtended at the centre of the circle by a 2.9cm arc.
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
What is the measure of the central angle of a circular section?
In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:
r = √ (A / π) (1)
r = √ (354 / π)
r ≈ 10.615 cm
Then, the measure of the central angle in radians is found by the equation of circular arc:
θ = s/r
θ = 2.9 cm / 10.615 cm
θ = 0.273 radians
Finally, we convert the angle into DMS system:
θ = 0.273 rad × 180°/π
θ = 15.641°
Degrees: 15°
Minutes and seconds: 0.641° (38.46')
Minutes: 38'
Seconds: (0.46' = 27.6'')
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
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How to represent 5 rational numbers on line. the numbers should be of form p/q where p or q should be a taxicab number. the fraction can be then reduced to its standard form. write about the taxicab numbers in brief.
The five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.
According to the question,
To represent 5 rational numbers on line, the numbers should be of form p/q where p or q should be a taxicab number.
A taxicab number is a smallest integer can be expressed as a sum of two positive integer cube.
The most famous taxicab number is 1729. Thus,
1729 = 1³ + 12³
1729 = 9³+ 10³
Now, 2 = 1³ + 1³ so, 2 is the first taxicab number. Therefore, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1.
In 1/1729 -> 1729 is taxicab number
In 1/2 -> 2 is taxicab number
In 3/2 -> 2 is taxicab number
In 1/1729 -> 2 is taxicab number
In 1729/1 -> 1729 is taxicab number
Hence, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.
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PLEASE HELP QUICK!!
Javier will evaluate the expression 2a(to the power of 3) - 1 for a = 2. Once he submitted 2 for a in the expression, what is the next step Javier needs to take in order to evaluate the expression?
The next step Javier needs to take in order to evaluate the expression is to simplify it to it's lowest term. Details below
Data obtained from the questionExpression = 2a³ - 1Evaluation =?How to evaluate the expressionFrom the question given, we were told that Javier submitted 2 for a
Thus, the new expression becomes
2 × 2³ - 1
Recall
Aⁿ × Aᵐ = Aⁿ⁺ᵐ
Thus,
2 × 2³ = 2¹⁺³ = 2⁴
Therefore,
2 × 2³ - 1 = 2⁴ - 1
But
2⁴ = 16
Thus,
2⁴ - 1 = 16 - 1
2⁴ - 1 = 15
Therefore,
2 × 2³ - 1 = 15
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Georgie buys a pack of chocolate which has 18 small chocolate bars. She ate three bars in the morning, Later in the
day, Georgie's brother ate three fifth of the chocolates bar that were left, what fraction of the chocolate bars is left in
the packet?
Step 4: By the definition of similar polygons, the lengths of corresponding sides are __________. This means that OKNL = KMLM OKNL = KMLM . Substituting in the lengths, we get 128 = 20 + xx 128 = 20 + xx . Cross multiply and solve the proportion for x.
By the definition of similar polygons, the lengths of corresponding sides are proportional.
The proportion for [tex]x=40[/tex].
What are similar polygons?Similar polygons are two polygons that have the same shape but are not always the same size. Similar polygons have congruent angles and proportional sides. Consider identical polygons as enlarging or contracting the same shape. The similarity is represented by the symbol.As it is given in the definition, similar polygons have congruent angles and proportional sides.
Therefore, by the definition of similar polygons, the lengths of corresponding sides are proportional.
Cross multiply and solve the proportion [tex]x[/tex] as follows:
The blank should be proportional.
[tex]\frac{12}{8} =\frac{20+x}{x}\\ 12x=160+8x\\4x=160\\x=40[/tex]
Therefore, the proportion for [tex]x=40[/tex].
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What's the correct equation?
Answer:
C
Step-by-step explanation:
y=mx+b where m is the slope or weekly payments and b is the y-intercept or initial fee.
300 = 30w + 60 fits this
Which ordered pairs are in the solution set of the system of linear inequalities?
y > Negative one-halfx
y < One-halfx + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.
(5, –2), (3, 1), (–4, 2)
(5, –2), (3, –1), (4, –3)
(5, –2), (3, 1), (4, 2)
(5, –2), (–3, 1), (4, 2)
The ordered pairs (5 , -2) , (3 , 1) , (4 , 2) are in the set of the solution (Option C)
What is an ordered pair?An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order.
It aids visual comprehension by locating a point on the Cartesian plane.
How do we arrive at the solution?The first line has negative slope and passing through points (0 , 0) and (4 , -2)
That is y > (-1/2)x
The second line has positive slope and passing through points (-2 , 0) and (2 , 2)
That is: y < (1/2)x + 1.
- Refer to the accompanying diagram to discover the common component of the solutions.
- The inequity is shown by the red shading.
- The inequity is shown by the blue shading.
- The two-colored shaded area reflects the common solutions to the two inequalities.
- Let's discover the ordered pairs in the system of linear inequalities' solution set.
- Points (-4, 2), (-3, 1), (4, -3) define the common shaded area.
- Points (5, -2), (3, 1), (3, -1) (4 , 2)
As a result, Point (5, -2) is in the darkened region.
As a result, Point (3, 1) is in the darkened area.
As a result, Point (4, 2) is in the darkened area.
As a result, the ordered pairings (5, -2), (3, 1), (4, 2) are in the solution set.
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What is the missing letter in the pattern below?
t, s, r, q, _, o, n, m,...
A. u
B. p
C. l
D. v
The missing letter is p. The correct option is B. p
Letter patternFrom the question, we are to determine the missing letter in the given pattern
The given pattern is
t, s, r, q, _, o, n, m,...
Consider the English alphabet
a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z.
If we study the pattern, we will realize that the alphabets are in the reverse order.
Hence, the missing letter is p. The correct option is B. p
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