Divya should not check her answers for extraneous solution as it's not required in this case.
What is an extraneous solution?It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.
Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.
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Answer:
No, she shouldn't.
Solve the compound inequality for x and identify the graph of its solution.
x+7> 3 and x-5≤-1
OA. Solution: x<-4 or x ≥ 4
++
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
--
-5-4-3 -2 -1 0 1 2 3 4
OC. Solution: x>-4 and x≤ 4
+
H
-5 -4 -3 -2 -1 0 1
2
4 5
OD. Solution: x2-4 and x < 4
44
-5-4-3 -2 -1 0 1 2 3 4 5
3
5
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
Let's solve the compound inequality step by step:
x + 7 > 3
Subtract 7 from both sides to isolate x:
x > 3 - 7
x > -4
and, we have,
x - 5 ≤ -1
Add 5 to both sides to isolate x:
x ≤ -1 + 5
x ≤ 4
Now, we have two inequalities for x:
x > -4
x ≤ 4
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.
The correct representation is:
OC. Solution: x > -4 and x ≤ 4
Graph:
-5 -4 -3 -2 -1 0 1 2 3 4 5
+---|---|---|---|---|---|---|---|---|---+
-4 0 4
The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.
The shaded area between -4 and 4 represents the solution to the compound inequality.
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What are the more appropriate measures of center and spread for this data
set?
35 40 45
55
90
hi
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
select two choices: one for the center and one for the spread.
a. better measure of spread: the standard deviation
select two choices: one for the center and one for the spread
The more appropriate measure of center is mean.
The more appropriate measure of spread is standard deviation.
What is mean and standard deviation?Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.
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I’m still not sure how the answer would be D (CBA), couldn’t it also be ACB?
Answer: No it could not be ACB.
Step-by-step explanation:
Angles are named based on the vertex of the angle so this could be referred to as ∠B. The other way to name an angle is by saying the three points, However, when you say the three points the vertex must be in the middle. Hence, the answer is ∠CBA as the middle point of the angle is in the middle of the name.
The table shows the probability of how a certain score will
compare to a listed score on a popular video game. Use the
probability distribution to find the variance, o².
The variance of the probability distribution is 400
The Variables of X and their Probability Distribution.
To find Variance, first we should find out Mean and then Variance
The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)
The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.
Step – 1: Calculation of Mean Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)
Mean = X * P(X) Variance = Sum of (X – Mean)²*P(X)
X P(X) X*P(X)
-50 0.029 -1.45
-30 0.121 -3.63
-10 0.210 -2.1
10 0.485 4.85
30 0.145 4.35
50 0.010 0.5
Mean 2.52
X P(X) X - Mean (X – Mean)² (X – Mean)²*P(X)
-50 0.029 -52.52 2758.35 79.99216
-30 0.121 -32.52 1057.55 127.9636
-10 0.210 -12.52 156.7504 32.91758
10 0.485 7.48 55.950 27.13594
30 0.145 27.48 755.1504 109.4968
50 0.019 47.48 2254.35 22.5435
Variance=400.00
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Reflection across X=1
It should be noted that a reflection is known as a flip and it's a mirror image of the shape.
How to illustrate the reflection?An image will reflect through a line, known as the line of reflection.
Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.
In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.
The reflection is attached.
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If area of a circle is 49/64 pie cm square,then find the circumference of the circle?
Answer:
7/4 * pi
Step-by-step explanation:
Area of circle = pi * r^2
Find radius:
pi * 49/64 = pi * r^2
49/64 = r^2
7/8= r
Circumference of circle = 2pi * r
2 * pi * (7/8) = 7/4 * pi
Assuming that the answer is in terms of pi as the question is in terms of pi
On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). a point is at (negative 3, 1). what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)? y – 1=negative three-halves(x 3) y – 1=negative two-thirds(x 3) y – 1= two-thirds(x 3) y – 1= three-halves(x 3)
The equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
Equation of a lineA line is the distance between two points. The equation of a line in point-slope form is expressed as:
y - y0 = m(x-x0)
Given the coordinates (-2, -4) and (2, 2) on the line, the slope is expressed as:
Slope = 2-(-4)/2-(-2)
Slope = (6)/4
Slope = 3/2
Find the equation of the line
y -(1) = 3/2(x-(-3))
y - 1 = 3/2(x+3)
Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
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Answer:
d
Step-by-step explanation:
A,B and C are points in the cartesian plane. the coordinates of A are (3,-2),BA=(4,-3)and AC=(4,9). Calculate
i. the coordinates of B and C
Could I get some help on this pls, and most importantly how you could solve it.
Thank you.
Using your choice of technology, find the line of best fit using the data below for the women’s 100-meter Olympic records. Interpret the y-intercept, and explain the significance of the slope.
The equation of the line of best fit is y = -0.03x + 69.94
How to determine the line of best fit?The column headers are given as:
Year Time(s)
To enter the data values in a graphing calculator, we use the following representations:
x ⇒ Year
y ⇒ Time (s)
Using the above representations, we have the following calculation summary from a graphing calculator:
Sum of X = 72209Sum of Y = 432.95Mean X = 1951.5946Mean Y = 11.7014Sum of squares (SSX) = 17242.9189Sum of products (SP) = -514.5997The equation of the line of best fit is:
y = bx + a
Where
b = SP/SSX = -514.6/17242.92 = -0.02984 ≈ -0.03
a = MY - bMX = 11.7 - (-0.03*1951.59) = 69.94497 ≈ 69.94
So, we have:
y = -0.03x + 69.94
A linear equation is represented as:
y = Slope * x + y intercept
So, we have:
Slope = -0.03
y intercept = 69.94
The y-intercept implies that the initial time is 69.94 seconds, while the slope implies that the time decreases by 0.03 seconds each year
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A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
Answer:
The ratio of decay rates is 3:4. So, option D is correct.
Step-by-step explanation:
Concept: The Decay rate for any function can be calculated by the formula Decay rate = Difference in y values / Difference in x values in given interval
Decay Rate for the exponential function in the interval -2 ≤ x ≤ 0 is (4-1) / (-2-0) = 3/2.
Decay rate for quadratic function in same interval = [(4-0) ÷ -(-2-0)] = 2.
Ratio of decay rates = (3/2) : (2) = 3:4
Option D, the exponential function decays at three-fourths the rate of the quadratic function is the correct answer.
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A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation
to estimate the number of packages that would need to be randomly selected to find a package that was not
delivered on time. The student assigns the digits to the outcomes.Beginning at line 1, and starting each new trial right after the previou
trial, carry out 5 trials of this simulation.
Based on the 5 trials, what is the average number of packages the
led to be selected in order to find a package
that was not delivered on time?
The average number of packages the led to be selected in order to find a package that was not delivered on time is 2.2 option first is correct.
What is simple random sampling?With simple random sampling, each component of the population has an equal chance of being selected for the sample.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A shipping company claims that 95% of packages are delivered on time.
From the table:
00- 04 is the package not delivered on time.
05-99 - package delivered on time.
The first simulation's third number, 31, 64, 04, is where you can locate an item that wasn't delivered on time.
The second simulation's second number, 34, 02, is the location of a late-delivered delivery.
The third simulation is equal to 96,00 - the second number, which is the location of a late package.
The second number where to find a shipment not delivered on time in the fourth simulation is 31,04
Where to find a box that wasn't delivered on time in the fifth simulation: 98, 01, second number
The average number = (3 + 2 + 2 + 2 + 2)/5
= 11/5
= 2.2
Thus, the average number of packages the led to be selected in order to find a package that was not delivered on time is 2.2 option first is correct.
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cosA/secA+sinA/cosecA=1
Step-by-step explanation:
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If the diagonal of the rectangle is 10.5 inches and the length of the rectangle is 7.25, what is the width of the rectangle?
Answer:
w≈7.6in
Step-by-step explanation:
L= 7.25
D= 10.5
Using the formula [tex]d=\sqrt{w^{2} + l^{2} } \\[/tex]Solving for w [tex]w=\sqrt{d^{2} -l^{2} }[/tex] [tex]\sqrt{10.52^{2}-7.25^{2} } = 7.59523in[/tex]Answer:-
The width of this rectangle is = 7.59
Given:-
In this question, it is given that -
The diagonal of this rectangle is = 10.5
the length of this rectangle is = 7.25
To find:-
We have to find the width of this rectangle.
Solution:-
We can easily solve this problem using the Pythagorean theorem.
In this problem, it is given that the length of this rectangle is = 7.25 and the diagonal is =10.5
so by the Pythagorean theorem, we can get-
(length)² + (width)² = (diagonal)²
or, (7.25)² + (width)² = (10.5)²
or, (width)² = (10.5)² - (7.25)²
= 17.75 × 3.25
= 57.6875
or, width = 7.59
So, the width of the rectangle is 7.59.
The graph below shows the solution to which system of inequalities?
Answer:
C
Step-by-step explanation:
The horizontal line, y=2, is solid and shaded above, so it represents
[tex]y \geqslant 2[/tex]
The slanted line, y=x is dashed and shaded below, so it represents y<x.
Answer
Answer is A
Step-by-step explanation:
22*90 what 2+2 3 +3 3+3
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{ASSUMING: }\\\mathsf{22\times90}\\\mathsf{= 90 \times 22}\\\mathsf{= 1,980}[/tex]
[tex]\mathsf{ASSUMING: }\\\mathsf{2 + 2 + 3 + 3 + 3 + 3}\\\mathsf{= 2\times 2 + 3\times4}\\\mathsf{= 4 + 12}\\\mathsf{= 16}[/tex]
[tex]\huge\textsf{Answer \#1. 1,980 }\huge\checkmark\\\\\\\huge\textsf{Answer \#2. 16 }\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Simplify this radical
[tex]\sqrt{84} \\\\A: 2\sqrt{21} \\B: 2\sqrt{42} \\C: 4\sqrt{21} \\D: 4\sqrt{42} \\[/tex]
The given radical root 84, the simplification is option B; [tex]2\sqrt{21}[/tex].
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given radical;
[tex]\sqrt{84} \\\\\sqrt{42 \times 2} \\\\\sqrt{7\times3\times 2 \times 2} \\\\2\sqrt{21} \\[/tex]
Thus, the correct option is B; [tex]2\sqrt{21}[/tex].
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I need help on this question
pls help yes
The arc length of the semicircle is 5π units
Calculating length of an arcFrom the question, we are to calculate the arc length of the semicircle
Arc length of a semicircle = 1/2 the circumference of the circle
∴ Arc length of a semicircle = 1/2 × 2πr
Arc length of a semicircle = πr
Where r is the radius
From the given information,
r = 5
∴ Arc length of the semicircle = 5 × π
Arc length of the semicircle = 5π units
Hence, the arc length of the semicircle is 5π units
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David can you 25/6 meters per hour manually, but using a digging machine he can dig 3 times as fast. how many meters would david be able to dig with the machine in an hour?
Answer:
12.5 meters
Step-by-step explanation:
1 hour manually = 25/6 meters
1 hour using machine = 25/6 × 3 meters
1 hour using machine = 12.5 meters
Hope this helped and have a good day
Which expression is equivalent to 2 (14x-37+28x+12.2-5y-17.5)?
A. 84x-16y-10.6
B. 28x-6y-10.6
C. 42x-8y-5.3
D 84x-16y-5.3
Answer:
A. 84x - 16y - 10.6
Explanation:
[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]
[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]
[tex]\sf \rightarrow 84x -16y-10.6[/tex]
A plant grows at a constant rate . daniel records the height of the plant each week . the unit reat is meausred in inches per week . what is the constant of proportionality ?
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
How to find a constant of proportionality in direct proportional equation
Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:
k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
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NOTE: I DO NOT NEED A LONG ANSWER
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Answer:
Scale factor is 3
0.738×0.28 is 0.20664 but is rounded to 0.21. which rule or rules are applied to this calculation? select all that apply.
The rules of the calculation are:
Round the result to the same number of significant figures as the value with the least number of significant figuresRound up if the digit to be dropped is 5 or greater.How to determine the rule?The complete question is added as an attachment
The equation is given as:
0.738 × 0.28 = 0.20664
When approximated, we have:
0.738 × 0.28 ≈ 0.21
The above approximation can mean any of the following:
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What is the inverse of f(x)=5x/3+5
Answer:
f^-1(x)=8x/5
Step-by-step explanation:
The inverse of f(x)=5x/3+5 is 8x/5
The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
How to determine the inverse?We have:
f(x)=5x/3+5
Rewrite as:
y=5x/3+5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
5y/3 = x - 5
Multiply through by 3
5y = 3x - 15
Divide through by 5
y = 3x/5 - 15
Rewrite as:
f-1(x) = 3x/5 - 15
Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
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Which quadratic inequality does the graph below represent?
The quadratic inequality represented by the graph is:
y ≤ 2x² - 8x + 3
Which quadratic inequality does the graph below represent?
First, we can see that the shaded region is below the parabola, and the line of the parabola is solid, which means that the points on the parabola are solutions, then the inequality is:
y ≤ quadratic equation.
Now we need to get the quadratic equation.
Now, if you look at the y-intercept, you can see that it happens at y = 3. Then the constant term of the quadratic equation is 3.
The only one that has that (and the ≤ symbol) y-intercept is the first option:
y ≤ 2x² - 8x + 3
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given f(x)=2x+2 and g(x) =-5x-3 find (f-g)(x)
Answer:
(f-g)(x) = 7x+5
Step-by-step explanation:
Given that,
f(x)=2x+2 and g(x) =-5x-3
To Find:
(f-g)(x)Solution:
[tex](f - g)(x)[/tex]
Re-write as:
[tex]f(x) - g(x)[/tex]Now substitute the values on the polynomial/function:
Simplify using this order:BPEMDAS
[tex]2x + 2 - ( - 5x - 3)[/tex][tex]2x + 2 + 5x + 3[/tex][tex]2x + 5x + 2 + 3[/tex][tex] \boxed{ ( f - g)(x) = 7x + 5}[/tex]Hence,(f-g)(x) = 7x+5.
If anyone could help me, it would be greatly appreciated!
Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]
Step-by-step explanation:
All radii of a circle are congruent, so by the base angles theorem
z = y = (180-50)/2 = 65.Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.
1 2 3 4 5 6 7 8 9 10 11 12 13
Mark this and return
If a new data point at 12 is added to the graph, which will
be true?
O The mean will increase, and the median will stay the
same.
O The median will increase, and the mean will stay the
same.
O The mean will increase more than the median, but
both will increase.
O The median will increase more than the mean, but
both will increase.
Answer:
The mean will increase more than the median, but both will increase.
[third option listed]
Step-by-step explanation:
the median of a data set is the number in the middle [when listed from lowest to highest in value]
1 2 3 4 5 6 7 8 9 10 11 12 13
is the current median
let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)
1 2 3 4 5 6 7 8 9 10 11 12 12 13
[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]
so, 7.5 is the current median
(this is an increase of 0.5)
--
the mean of a data set is what we commonly refer to as the "average"
[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]
1 2 3 4 5 6 7 8 9 10 11 12 13
mean of original data set:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]
_______________________________________
13
[91 ÷ 13 = 7]
because our number is greater than our original mean [12 > 7], we know that the mean must increase:
[91 + 12 = 103]
[103 ÷ 14 ≈ 9.36]
[we had an increase of 2.36]
so, median increased by 0.5, mean increased by 2.36
so, both values increased, whilst the mean increased by more than the median [as to be expected]
you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]
hope this helps!! :)
find y in terms with z. help me please :)
Answer:
y = 5z
Step-by-step explanation:
added in the picture
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow y = 5z [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[ let the point at which line segments SV and RT intersects be O ]
[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]
[ linear pair ]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]
[ Exterior angle = sum of opposite interior angles ]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]
( let it be equation 1 )
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]
[ Sum of angles of Triangle ]
[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]
( let it be equation 2 )
____________________________________
By comparing both equations :
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]
[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]
( Add 180° on both sides )
[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]
[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]
[tex]\qquad \tt \rightarrow \: y = 5z[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
hi can some one help me
-5≥
so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)
Answer:
x> -6
Step-by-step explanation:
Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6
PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
