we conclude that the system of inequalities has more solutions than the system of equations.
What can we conclude about the two given systems?We have the system of equations:
y = (-1/2)*x + 1
y = x - 5
And the system of inequalities:
y > (-1/2)*x + 1
y < x - 5
First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.
Now let's look at the system of inequalities, we can get solutions like:
x = 10
y = 1
1 > (-1/2)*10 + 1 = -4
1 < 10 - 5 = 5
So both inequalities are true, which means that the point (10, 1) is a solution.
And also is the point (11, 1), and (12, 1), and infinite other points.
Then we conclude that the system of inequalities has more solutions than the system of equations.
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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3.
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length.
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function?
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
The given function for the difference in length is presented as follows;
[tex]f( \theta) = 2 \cdot cos( \theta) + \sqrt{3} [/tex]
When the pogo stick will be equal to its non compressed length, the difference is zero, therefore;
[tex]f( \theta) = 2 \cdot cos( \theta) + \sqrt{3} = 0[/tex]
[tex] 2 \cdot cos( \theta) = - \sqrt{3} [/tex]
[tex]\theta= arccos \left( \frac{ - \sqrt{3} }{2} \right) [/tex]
Which gives;
[tex] \theta = \frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{6} [/tex]
[tex] \theta = -\frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{6} [/tex]
Part B; If the angle was doubled, we have;
[tex]f( \theta) = 2 \cdot cos(2 \cdot \theta) + \sqrt{3} = 0[/tex]
Therefore;
[tex] 2 \cdot cos(2 \cdot \theta) = - \sqrt{3} [/tex]
Which gives;
[tex] \theta = \frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{12} [/tex]
[tex] \theta = -\frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{12} [/tex]
Between 0 and 2•π, we have;
[tex] \theta = \frac{5\cdot \pi}{12} [/tex]
[tex] \theta = \frac{ 17\cdot \pi}{12} [/tex]
Part C;
The toddler's pogo stick is presented as follows;
[tex]g( \theta) = 1- son^2( \theta) + \sqrt{3} [/tex]
Integrating the original function between 0 and theta gives;
[tex]2 \cdot sin( \theta) + \sqrt{3}\cdot \theta [/tex]
The original length =
Therefore, when the lengths are equal, we have;
[tex]1- son^2( \theta) + \sqrt{3} = 2 \cdot sin( \theta) + \sqrt{3}\cdot \theta [/tex]
To solve this system of equations using substitution, what could be substituted in place of y in the first equation? 4x = 5 − 2y y − 2x = 7
Answer:
y = [tex]-\frac{4x-5}{2}[/tex]
Step-by-step explanation:
Step 1: Switch sides
5 - 2y = 4x
Step 2: Subtract 5 from both sides
5 - 2y - 5 = 4x - 5
Step 3: Simplify
-2y = 4x - 5
Step 4: Divide both sides by -2
[tex]\frac{-2y}{-2} = \frac{4x}{-2} - \frac{5}{-2}[/tex]
Step 5: Simplify
y = [tex]-\frac{4x-5}{2}[/tex]
please help asap i am so confused
The table so fined below based on the information given about the function.
How to illustrate the information?The table based on the function given will be:
Plan A. Plan B
Monday. 10. 30
Tuesday. 20. 40
Wednesday. 40. 50
Thursday. 80. 60
Friday. 160. 70
A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.
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Quick algebra 1 question for 25 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Yes
It's inverse variationSee
3 contractors took 8hours
4 contractors took 6hours
We observe
No of contracter increases hence time decreasesSo it's inverse variation
Answer:
[tex]\fbox {Yes}[/tex]
Step-by-step explanation:
An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.
Here, as the number of contractors increase, the time taken to complete the work decreases.
∴ Hence, this represents an inverse variation.
The acting club two-act plays begins at 3:20 P.M. The first act is twice as long as the second act, and there is a 15-minute break between the two acts. The play ends at 4:50 P.M. How long is Act 1?
Answer:
50 minutes
Step-by-step explanation:
3:20 pm - 4:50 = 90 minutes
90 = 2a + 15 + a
90-15= 75
75= 2a + a
75 = 3a
75/3 = 25
25 x 2 = 50 minutes
Help please!!!!
Will give brainliest
The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.
How to interpret features of trigonometric Graphs?
3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.
c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.
4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.
c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.
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Teboho has to sell a certain number of cars each month. For every car he sells over and above this number he earns 17% commission on the price of the car before VAT is added. He sold three cars on which he earned commission. The VAT included prices were R271 800,00; R316 800,00 and R99 300,00. Calculate:
1.1 The prices of the cars before VAT was added
1.2 The commission he earned on the cars.
The commission earned are R41123.17, R47931.67 and R15024.09
The prices of the cars before VAT was addedThe VAT included prices are given as:
R271 800,00; R316 800,00 and R99 300,00.
The VAT rate is 12.36%.
So, the price before VAT is calculated as:
VAT included = Price without VAT * (1 + 12.36%)
This gives
VAT included = Price without VAT * 1.1236
So, we have:
Price without VAT = VAT included/1.1236
For the three cars, we have:
Price without VAT = R271 800.00/1.1236 = R241901
Price without VAT = R316800.00 /1.1236 = R281951
Price without VAT = R99300.00/1.1236 = R88377
Hence, the prices of the cars before VAT was added are R241901, R281951 and R88377
The commission he earned on the cars.This is calculated as:
Commission = Price * 17%
So, we have:
Commission = R241901 * 17% = R41123.17
Commission = R281951 * 17% = R47931.67
Commission = R88377 * 17% = R15024.09
Hence, the commission earned are R41123.17, R47931.67 and R15024.09
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-2x+3
Step-by-step explanation:
Use the slope formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
According to the table, x=1 and y=1. There is another point x=2 and y=-1.
We can say that [tex]x_{1}=1[/tex] and [tex]y_{1} =1[/tex]. We can also say that [tex]x_{2}=2[/tex] and [tex]y_{2}=-1[/tex]. Plugging this into the equation we get:
[tex]m=\frac{-1-1}{2-1}=-2[/tex].
This means that the slope of your equation is -1/2
Point intercept form is y=mx+b
So plugging the slope in we have [tex]y=2x+b[/tex]
We can plug in one of the values from the value table for x and y, but to keep things simple, I’m going to just use x=1, and y=1, the first values on the table. Plugging these into the equation we get:
[tex]1=-2(1)+b\\ 1=-2 +b\\b=1+2 \\b=3[/tex]
So our equation is [tex]y=-2x+3[/tex]
Three consecutive positive prime numbers have a sum that is a multiple of . What is the least possible sum
Answer:
3, 7, 14
Step-by-step explanation:
small brain
Please Help me with this problem!!! ASAP
The average rate of change is -5 per month
How to determine the average rate of change?The interval is given as:
July to December
From the graph, we have:
July = 110
December = 30
The average rate of a function over the interval (a, b) is calculated as:
Rate = [f(b) - f(a)]/[b - a]
So, we have:
Rate = (30 - 110)/(December- July)
This gives
Rate = (30 - 110)/(12 - 7)
Evaluate
Rate = -16
Hence, the average rate of change is -5 per month
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Consider the sequence Three-fourths, four-fifths, StartFraction 5 Over 6 EndFraction, StartFraction 6 Over 7 EndFraction, ellipsis
Which statement describes the sequence? 3/4, 4/5, 5/6, 6/7,...
The sequence diverges.
The sequence converges to 1.
The sequence converges to ∞.
The sequence converges to –∞.
Using limits, it is found that the correct statement defining the sequence is:
The sequence converges to 1.
What is the rule that defines this sequence?The numerator starts at 3 and increases by 1, while the denominator starts at 4 and increases by 1, hence the rule is:
[tex]\sum_{n = 0}^{\infty} \frac{3 + n}{4 + n}[/tex]
To verify if it converges, we find the limit as n goes to infinity, hence:
[tex]\lim_{n \rightarrow \infty} \frac{3 + n}{4 + n} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]
Hence the sequence converges to 1.
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Answer:
B i took quiz
Step-by-step explanation:
Owen has enough materials to build up to 10 birdhouses in shop class. each birdhouse needs 12 square feet of wood. the function w(b) = 12b represents the total amount of wood that owen would need to build b birdhouses. what domain and range are reasonable for the function?
Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].
What is domain and range of a function?The range of values that we are permitted to enter into our function is known as the domain of a function.
A function's range is the collection of values it can take as input.
Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.
The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.
Therefore, the domain of the function is [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].
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Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin
Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.
According to the statement
We have given that the two rectangles EFGH and ABCD and we have show that the these rectangles Are dilation at origin or not.
So, According to the given diagram
Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation of rectangle at the origin.
Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.
The scale factor could be calculated by the ratio of the sides of the image to the pre-image rectangle.
According to the diagram In Rectangle ABCD:
Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).
Now consider rectangle EFGH:
Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).
Hence the scale factor is becomes from these values is:
EF/AB = EH/AD = FG/BC = HG/DC = 4/3.
Hence the scale factor becomes 4/3.
Also
∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°
( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).
So, Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.
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The median for the samples from the school math contest are:
The median of Sample 1 from Grades 9 and 10 is 79.
The median of Sample 2 from Grades 11 and 12 is 86.
What conclusions can you derive from the random samples?
The students performed equally between all the grades.
The students in grades 11 and 12 scored higher than the students in grades 9 and 10.
The students in grades 11 and 12 are likely to do well in college.
The students in grades 9 and 10 were not allowed enough time in the school math contest.
The sample size was too small to derive a valid conclusion
A conclusion which can be derived from these random samples is that: B. the students in grades 11 and 12 scored higher than the students in grades 9 and 10.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Based on the information provided for these samples, we can logically conclude that the students in grades 11 and 12 scored higher than the students in grades 9 and 10 because a median score of 86 is greater than a median score of 79.
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Through how many radians does the minute hand of a clock turn during a 3-minute period?
pi/5.
Think of a clock as a circle. The minute hand when it moves around the clock will have traveled 360 degrees or 2*pi radians, traveling 2*pi radians in 60 minutes. So3 minutes out of 60 minutes is 1/10. So the minute hand travels 1/10 of 2*pi radians (multiply 1/10 and 2*pi to get your answer).
Therefore your answer is pi/5 which is the letter a.
Well, a Radian, simply put, is a unit of measure for angles that is based on the radius of a circle. What this means is that if we imagine taking the length of the radius and wrapping it around a circle, the angle that is formed at the center of the circle by this arc is equal to 1 Radian.
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You are in a hot air balloon looking down at two ponds. Pond A which is in front of your balloon, is at an angle of depression that is your birth month (October), in degrees. (October = 10 degrees). Pond B, which is behind the balloon, is at angle of depression that is your Birth Day in degrees. (October 8 = 8 degrees). The balloon is 875 m in the air.
a. Draw and label a diagram
b. Find the distance from the hot air balloon to both Pond A and B
c. FInd the distance between the two ponds.
a. See attachment for the labelled diagram
b. Using the sine ratio, distance from the hot air to pond A is 5,038.9 m, while distance from the hot air to pond B is 6,287.1 m.
c. Distance between the two ponds is 1,263.5 m.
What is the Sine and Tangent Ratios?Sine ratio, is: sin ∅ = opposite side/hypotenuse length
Tangent ratio is: tan ∅ = opposite side/adjacent length.
a. The diagram with the appropriate labels is shown in the image attached below.
b. Use the sine ratio to find the distance from the hot air to pond A (CA) and to pond B (CB):
CA = hypotenuse
∅ = 10°
Opposite = 875 m
sin 10 = 875/CA
CA = 875/sin 10
CA ≈ 5,038.9 m (distance from the hot air to pond A)
CB = hypotenuse
∅ = 8°
Opposite = 875 m
sin 8 = 875/CB
CB = 875/sin 8
CB ≈ 6,287.1 m (distance from the hot air to pond B)
c. Distance between the two ponds, BA = BD + DA.
Apply the tangent ratio to find BD and DA
tan 8 = 875/BD
BD = 875/tan 8
BD = 6,225.9 m
tan 10 = 875/DA
DA = 875/tan 10
DA = 4,962.4 m
Distance between the two ponds = 6,225.9 - 4,962.4 = 1,263.5 m.
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Suppose 60% of the freshmen at msu take a course in outdoor survival skills. the probability that a freshman selected at random who did not get lost during a hike is 90%. the probability that a freshman selected at random who took the course and did not get lost is 50%.
Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
According to the question,
Probability of freshmen who took course at MSU in outdoor survival skills is 0.6.
Probability that a freshmen selected at random who did not get lost during a hike is 0.9.
Probability that a freshman selected at random who took the course and did not get lost is 0.50
Conditional probability = P(A and B)/ P(A)
P(did not get lost/took the course) = P( freshmen did not get lost who took the course and freshmen took the course)/P(freshmen did not get lost)
= 0.5/0.6
= 0.8333
Hence, Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
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Gerri purchases a coupon book with discounts for her favorite coffee shop. every coupon for the coffee shop offers the same discount. the table shows her total savings, y, based on the number of coupons, x, used from the book. a table showing coffee shop coupon savings with 2 columns and 6 rows. the first column, x, has the entries, 0, 5, 10, 15, 20. the second column, y, has the entries. negative 20, negative 10, 0, 10, 20.
Slope 2 and y intercept is 10
The question seems to be incomplete and complete and the complete question is shown in the image
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases.
When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.
Y-intercept is the point at which the line intersects the y axis- meaning x = 0
From the table y = -20 when x= 0
y-intercept: -20
To find the slope
m = ΔY/ΔX
m = -20+10/0-5 = 2
Hence the slope is 2 and y intercept is 10
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please help me im stuck on this
Answer:
Step-by-step explanation:
dddfykb
Which of the following formulas, when evaluated using rational values for the variables, will result in an irrational number?
A shopkeeper has $680 in the denominations of $50, $20, $10 and $5 notes. The number of notes of each denomination is equal. What is the total number of notes?
The total number of notes is 32
The number of notes
Let the number of notes be x
$50 = x
$20 = x
$10 = x
$5 = x
Total number of notes = 4x
Let's find 'x'
50x + 20x + 10x + 5x = 680
85x = 680
x = 680/ 85
x = 8
We know that;
Total number of notes = 4x = 4 × 8 = 32 notes
Thus, the total number of notes is 32
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PLS BRAINLIST ANSWER ONLY
Answer:
y= -1/3x + 1
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y= -1/3x + 1
_____ is a quantitative statistical analysis that compares and combines the results of individual but similar studies.
"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.
What is meta analysis?A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.
Some characteristics of meta analysis are-
The statistical method for merging data from various studies is called meta-analysis. Meta-analysis can be used to pinpoint this common impact when the treatment effect (or effect size) is constant from one trial to the next. Meta-analysis can be performed to determine the cause of variance in the effect when it differs between studies.Regulatory agencies occasionally demand a meta-analysis as part of the approval process, which pharmaceutical companies employ to obtain clearance for new medications. Meta-analysis is used by clinicians and applied researchers in a variety of sectors, including medicine, education, psychology, criminal justice, and many more, to identify which therapies are most effective.To know more about Meta-analysis, here
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Calculate the slope of a line that goes through (3,3) and (8,1).
Answer:
slope formula= y2-y1/x2-x1
=1-3/8-3
= -2/5
pls mark as brainliest thanks!
Quick Please
(order from least to greatest)
please and thank you
Answer:
√(3 , √(π , 2
Step-by-step explanation:
ascending order
Answer 1/4 + 3/5-3/10 =
Answer:
11/20
Step-by-step explanation:
1/4= 10/40
3/5=24/40
3/10=12/40
10/40+24/40= 34/40
34/40 - 12/40= 22/40
simplifies to 11/20
the eccentricity of the conic section below is
Hi! ❄
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The eccentricity of the conic section below is 1, since the given conic section is a parabola, and any parabola's eccentricity is 1.
Hope that made sense !!
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[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]
A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66?
If x represents the number of 13 cent stamps and y the 18 cent stamps, which system represents the problem?
The system of equation which represent the scenario is;
x + y = 42
x + y = 420.13x + 0.18y = 6.66
Simultaneous equationlet
number of 13 cent stamps = xnumber of 18 cent stamps = yTotal cost of the stamps = $6.66Total number of stamps = 42x + y = 42
x + y = 420.13x + 0.18y = 6.66
Therefore, the equation which represent the problem is;
x + y = 42
0.13x + 0.18y = 6.66
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The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse
Answer:
Step-by-step explanation:
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse
What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66
The root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
How to determine the roots of the equation?The graph that completes the question is added as an attachment
The polynomial function is given as:
x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
From the attached graph, we have the following highlight:
The curves of both equations intersect at
x = -3, x = -2 and x = 3
This means that the root of the polynomial function is -3, -2 and 3
Hence, the root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
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Complete question
Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
What are the roots of the polynomial equation?
A) –3, –2, 3
B) –3, 2
C) 18, 32
D) 18, 32, 66