A national organization sets out to investigate the change in prevalence of HIV since the last census in 2010. A total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive. Assume that the data from the census indicated that the prevalence of HIV in the particular population was 7. 5%. A) Write out the null and alternative hypotheses for a formal test of significance. B) Interpret your results at 95% confidence
Answers
A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census
B) At a 95% confidence level, the critical value for a two-tailed test is ±1.96.
A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is still 7.5%. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is different from 7.5%.
B) To test the hypothesis, we can use a z-test for proportions. The test statistic can be calculated as:
z = (p - p0) / \(\sqrt{(p0(1-p0)/n)}\)
where p is the sample proportion of HIV positive cases, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.
In this case, p = 468 / 4706 = 0.099, p0 = 0.075, and n = 4706. Plugging these values into the formula, we get:
z = (0.099 - 0.075) / \(\sqrt{0.075(1-0.075)/4706}\) = 8.80
At a 95% confidence level, the critical value for a two-tailed test is ±1.96. Since the calculated z-value (8.80) is much larger than the critical value, we can reject the null hypothesis and conclude that there is strong evidence to suggest that the prevalence of HIV has changed since the last census. In other words, the prevalence of HIV is different from 7.5%.
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Related Questions
determine the quotient of 1 2/3 divided by 4/5
Answers
First turn any mixed numbers into improper fractions. 1 3/4 would be 7/4. Becuase you multiply the whole number by the denominator and then add the numerator.
So now you have 7/4 divided by 2/5. Whenever you divide, you flip the 2nd fraction upside down... known as the reciprocal. And after that you multiply the first number by the upside down 2nd number.
So now you have 7/4 X 5/2. When multiplying, just multiply the numerators across and the denominators across. As your answer, you get 35/8 or 4 3/8.
The quotient obtained by dividing two given fractions is 25/12.
The given fractions are \(1\frac{2}{3}\) and 4/5.
What is a quotient of numbers?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, the mixed fraction \(1\frac{2}{3}\) can be written as 5/3.
Now, 5/3 ÷ 4/5
= 5/3 × 5/4
= 25/12
Hence, the quotient obtained by dividing two given fractions is 25/12.
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y
5t
dy+(5lny+3)dt=0
Answers
The given differential equation is a first-order linear homogeneous equation.
The given differential equation is of the form:
dy/dt + (5ln(y) + 3) = 0
This is a first-order linear homogeneous equation because it can be written in the form dy/dt + P(t)y = 0, where P(t) = 5ln(y) + 3. In this equation, y represents the dependent variable and t represents the independent variable.
To solve this type of equation, we can use an integrating factor. By multiplying both sides of the equation by the integrating factor, which is e^(integral of P(t) dt), we can simplify the equation and solve for y.
After multiplying by the integrating factor, the equation becomes:
e^(integral of P(t) dt) * dy/dt + (e^(integral of P(t) dt) * (5ln(y) + 3)) = 0
Simplifying further, we obtain:
d/dt (e^(integral of P(t) dt) * y) = 0
Integrating both sides with respect to t, we get:
e^(integral of P(t) dt) * y = C
Where C is the constant of integration.
Finally, solving for y, we have:
y = Ce^(-integral of P(t) dt)
This is the general solution to the given differential equation. By specifying initial conditions or additional information, we can determine the particular solution that satisfies the given conditions.
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Graph y=-5x I am not sure how to plot this?
Answers
Okay, here we have this:
Considering that this is a linear equation if we get two points, we can draw a line that will correspond to the function, so let's find it:
We are going to replace x with 1 and with 2:
x=1:
y=-5x
y=-5(1)
y=-5
We obtain (1,-5).
x=2:
y=-5(2)
y=-10
We obtain here (2,-10)
Now, let's graph this:
two friends are playing with water balloons. they each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. joy walked 12 steps forward, and shaunte walked 8 steps backwards. which expression correctly represents the distance between the friends?
Answers
The correct expression that represents the distance between the friends is 4 steps.
To calculate this
Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:
12 + (-8) = 12 - 8 = 4
So the correct expression that represents the distance between the friends is 4 steps.
Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.
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Quadratic Graphs Investigation
Answers
The functions in relation to the Quadratic graphs investigation are tabularized and attached accordingly.
What is the explanation of the attached table?The table lists 10 different equations, each representing a different quadratic function in the form of "y = ax² + bx + c." For each equation, the table provides the following information:
Concavity: This refers to the shape of the parabola, which can be either concave up (opening upwards) or concave down (opening downwards).Vertex: This is the point on the parabola where it changes direction, and is represented as (h,k) in the form "y = a(x-h)² + k."x-intercepts(s): These are the point(s) where the parabola intersects the x-axis, and are represented as (x,0).y-intercept(s): This is the point where the parabola intersects the y-axis, and is represented as (0,y).Axis of Symmetry: This is the vertical line of symmetry that divides the parabola into two mirror images. It passes through the vertex and is represented as "x = h."Stretch or Compression: This refers to how the parabola has been vertically stretched or compressed, and is represented as a coefficient before the x² term. A value greater than 1 indicates a vertical stretch, while a value between 0 and 1 indicates a compression.By examining these characteristics for each equation, we can gain a better understanding of how each parabola is shaped and where it is located on the coordinate plane.
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The quantity z varies directly with w and inversely with x. When w = 12 and x = 4, z = -42. Find z when w = 11 and x = 7.
PLEASE HELP ME!!!!!!!
Answers
Given the joint variation and the constant of variation, the value of z when w = 11 and x = 7 is -22
How to solve variation?z =( k × w) / x
where,
z = -42 w = 12x = 4k = constant of variation-42 = (k × 12) / 4
cross product
4 × -42 = 12k
-168 = 12k
k = -168 /12
k = -14
Find z when w = 11 and x = 7z =( k × w) / x
z = (-14 × 11) / 7
= -154 / 7
z = -22
Therefore, the value of z when w = 11 and x = 7 is -22
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give it to me an example for Primary and secondary Data Collection
Answers
Answer:
Primary data when the researcher collect the information like census by government . And secondary data means when like an entrepreneur take the census data from the government and collect more information .
Which of the equations below represent exponential decay? Select all that apply. •y= (0.01)^x •y= 500(1-0.35)^x •y= (5.45)^x •y= (1/2)^x •y= (4/5) 3^x
Answers
The exponential decay equation is of the form:
\(y\text{ = a(}1-b)^x\)where a = the original amount
b = decay factor
x = time
For the equation to represent an exponential decay, 1-b must be less than 1. That is, b > 0
The options that represent this equation are:
\(\begin{gathered} y=(0.01)^x \\ \text{y = 500(1-0.35)}^x \\ y\text{ = (}\frac{1}{2})^x \end{gathered}\)let ppnq be the statement that a postage of n cents can be formed using only 3-cent stamps and 5-cent stamps. ppnq can be proved by strong induction. what is the correct basis step?
Answers
The correct basis step for proving the statement P(n) using strong induction is to show that P(8) is true
Strong induction is a method of proving that a statement is true for all values of n by demonstrating that it is true for a base case and that if it is true for all values up to n, then it must also be true for n+1. It can be used to prove the statement P(n) that a postage of n cents can be formed using only 3-cent stamps and 5-cent stamps.
To demonstrate that P(8) is true is to do the proper basis step for strong induction. This is so that we may create an 8 cent postage using a 3-cent and a 5-cent stamp.
The following argument can be used to demonstrate that the basic step is P(8) being true:
A postage of 8 cents can be made with one 3-cent stamp and one 5-cent stamp.
Thus, P(8) must be true.
We don't need to check any other values for the base step because P(n) only depends on the values of P(k), where k n.
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1) Find the solution set of the quadratic inequality -x²+x+6≥0 on the set of all i) N = natural numbers. ii) Z = integers. (5pts) iii) R = real numbers.
2) Someone bought 16 two types of books in birr 1560. He bought one mathematics book in birr 120 and one biology book in birr 80. How many mathematics and biology books did he buy?
3) Show the following relations f≤ NX N and g = R XR are functions or not. a) f = {(ab, a + b): a,b € N} b) g = {(labl, a + b): a, b = R} x
4) Let f(x) = 2 and g(x)=be functions. The find x²-5x+6 a) Dom (f) and Dom (g) b) Dom (f±g) and Dom (fg) c) Dom() d) Dom (fog) e) Dom(gof)
5) Find all roots (zeros) of the polynomial x4 -x³-5x² - x - 6.
Answers
i) N: The quadratic inequality -x²+x+6≥0 can be factored as -(x-3)(x+2)≥0. Thus, the solution set is {1,2,3,4,5,...}. ii) Z: The quadratic inequality can be factored as -(x-3)(x+2)≥0.
The values of x that satisfy the inequality are x ≤ -2 and x ≥ 3. Thus, the solution set is {...,-3,-2,-1,0,1,2,3,...}. iii) R: The quadratic inequality can be factored as -(x-3)(x+2)≥0. The values of x that satisfy the inequality are x ≤ -2 and x ≥ 3. Thus, the solution set is (-∞,-2] ∪ [3,∞).
Let the number of mathematics books be x and the number of biology books be y. Then, x+y=16 and 120x + 80y = 1560. Solving for x and y, we get x=9 and y=7. Thus, the person bought 9 mathematics books and 7 biology books.
a) f is a function because for each value of a and b in N, there is a unique value of a+b. b) g is not a function because for a given value of |ab|, there can be multiple values of a+b, since a and b can take on any real values.
a) Dom(f) = R and Dom(g) = R. b) Dom(f+g) = R and Dom(fg) = R. c) Dom(1/f) = {x | x ≠ 0} and Dom(√f) = {x | x ≥ 0}. d) Dom(fog) = Dom(g) = R. e) Dom(gof) = Dom(f) = R.
To find the roots of the polynomial x^4 - x^3 - 5x^2 - x - 6, we can use the rational root theorem to test possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. Testing these values, we find that x=-1 and x=2 are roots of the polynomial.
Using long division, we can factor the polynomial as (x-2)(x+1)(x^2-3x-2), which has additional roots of x=3+√11 and x=3-√11. Thus, the roots of the polynomial are x=-1, x=2, x=3+√11, and x=3-√11.
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Answer:
Step-by-step explanation:
c (3,5)
A project has five activities with the durations (days) listed
below:
Activity
Precedes
Expected
Duration
Variance
Start
A, B
-
-
A
C
40
0.31
B
E
32
0.25
C
D
21
0.35
Answers
The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.
To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.
Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.
The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.
Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.
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During hurricanes Irma and Maria in 2017, some lizards on Pine Cay in the southern Bahamas got blown out of the trees and off the island, while others managed to hang on and survive. As shown in the histograms to the right, the lizards remaining on the island after the storms had larger toepads, on average, than the lizards that were on the island before the storms (see the black triangles). The researchers determined that lizards with larger toepads are better able to hang on to trees in extreme wind.two of the three requirements for evolution by natural selection are strongly supported by the data. which two, and how are they demonstrated?The pre-storm distribution of toepad size across multiple values demonstrates _____, while the change in that distribution from before to after the storm, toward larger toepad sizes, demonstrates __________. The other requirement has not been demonstrated by this data set, but could be supported by other data.
Answers
The pre-storm distribution of toepad size across multiple values demonstrates variation, while the change in that distribution from before to after the storm, toward larger toepad sizes, demonstrates heritability.
During hurricanes Irma and Maria in 2017, some lizards on Pine Cay in the southern Bahamas got blown out of the trees and off the island, while others managed to hang on and survive.
Two of the three requirements for evolution by natural selection are strongly supported by the data. These two requirements are variation and natural selection.
The pre-storm distribution of toepad size across multiple values demonstrates variation, as there is a range of toepad sizes present in the population before the storm.
The change in that distribution from before to after the storm, toward larger toepad sizes, demonstrates natural selection, as the lizards with larger toepads were more likely to survive the storm and pass on their genes to the next generation.
The other requirement, heritability, has not been demonstrated by this data set, but could be supported by other data showing that toepad size is a genetically inherited trait.
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100 Points
How many solutions does this system of equations have?
Answers
Answer:
A) No real solutions--------------------
Given system:
y = x² + x + 3y = - 2x - 5Equate the right sides to get a quadratic equation:
x² + x + 3 = - 2x - 5x² + 3x + 8 = 0The discriminant of ax² + bx + c = 0 is D = b² - 4ac.
Substitute a = 1, b = 3, c = 8 and find the value of D:
D = 3² - 4*1*8 = 9 - 32 = - 23Since D < 0, there is no real solution, hence the correct choice is A.
Q.1 Write the equivalent MATLAB statements for the following equations : a. A=e
ax
tan
−1
(y)
b. 7ysin
−1
(x)+x
3
cos
−1
(y) c. 25
6.5
+10.5
2.5
d. 77x
3
1
+0.5π e.
(Be
x
)
A
2
+tan(90)90 is in degree f. 5log(7)+9π Q.2 Explain the steps of the following CODE in MATLAB lambda =1; c
0
=10; t=[0:0.1:1]; f=c
0
∗exp(−lambda∗t) plot (t,f); grid
Answers
The exponential function with c0 and λ are defined in the variable f. Finally, the plot() function is used to plot the graph of the exponential function f against time interval t with the help of MATLAB.
Q.1 Write the equivalent MATLAB statements for the following equations :a. The MATLAB statements for the following equations A = e(ax tan −1(y)) is given by, syms a x y A A= exp(a*x*tan(asin(y)))b. The MATLAB statements for the following equations 7y*sin −1(x)+x3cos −1(y) is given by, syms x y A A = 7*y*sin(asin(x))+x/3*cos(acos(y))c. The MATLAB statements for the following equations 256.5+10.52.5 is given by, A= 25+6.5*(10.5/2.5)d. The MATLAB statements for the following equations 77x31+0.5π is given by, syms x A A= 77*x^3+0.5*pi e. The MATLAB statements for the following equations (Bex)A2+tan(90)90 is in degree is given by, syms A B x A = B^(x)*A^(2) + tan(90*(pi/180)) f. The MATLAB statements for the following equations 5log(7)+9π is given by, syms A A= 5*log(7)+9*piQ.2 The steps of the following CODE in MATLABThe following are the steps for the given MATLAB code λ = 1; c0= 10; t=[0:0.1:1]; f=c0*exp(-lambda*t) plot (t,f); gridThe given MATLAB code plots the graph of c0*exp(-λt) against time interval t, where c0 = 10 and λ = 1. The time interval values are given by t=[0:0.1:1]. The exponential function with c0 and λ are defined in the variable f. Finally, the plot() function is used to plot the graph of the exponential function f against time interval t with the help of MATLAB. The graph is then shown on the screen with a grid on it.
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What is an exponent? Because i am confused
Answers
An exponent is a number written above and to the right side of a value or number in math. The value or number is called the base, and the expression is read out as;
"Base raised to the power of exponent."
An example is given below;
\(10^3\)In this example, 10 is the base and 3 is the EXPONENT.
The expression is now read out as,
"10 raised to the power of 3"
Note that even unknown values (such x as we commonly use in math) can also be an exponent or base. For example, we can have;
\(\begin{gathered} 10^x \\ OR \\ 2x^3 \end{gathered}\)So basically, an exponent indicates the number of times a number is used to multiply itself.
The area of Australia/Oceania is approximately 7.69 × 106 square kilometers. Its population is approximately 3.11 × 107 people. What is the approximate population density (people per square kilometer) of Australia/Oceania? Write your answer in standard form. If necessary, round your answer to the nearest hundredth.
PLEASSSSEEEE HELPPPPPPPPPPP
Answers
Answer: 3.11*10^7/7.69*10^6
3110/769
4.04
Step-by-step explanation:
Find a value of the standard normal random variable z, call is z0, such that:a. P(z<=z0)=.05How would I solve this?
Answers
The question is:
\(P(z\le z_0)=0.05\)This means it is required to find the z-score for 0.05.
To do this, you have to refer to the Area Under Normal Distribution Table.
z-scores are given along the 1st column and 1st row.
The value 0.05 is the significance level. We have to find its corresponding confidence level. To do that, subtract from 0.5:
\(0.5-0.05=0.45\)The z-score for 0.45 is the same as the z-score for 0.05.
Check this or its approximate value in the table:
You'll see for 0.4495.
This falls on 1.6 under .04
Add them together to get 1.6+0.04=1.64
The z-score is 1.64.
Carla has a rectangular garden in her backyard. The width of the garden is 9 meters. The area of the garden is 360 square meters. What is the length of the garden? Show your work.
Answers
Answer:
l = 40 m
Step-by-step explanation:
The formula for area of a rectangle is
A = lw, where
A is the area in square units,l is the length,and w is the widthStep 1: Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):
360 = 9l
Step 2: Divide both sides by 9 to solve for l
(360 = 9l) / 9
40 m = l
Optional Step 3: We can check our answers by checking that the product of 40 and 9 is 360
40 * 9 = 360
360 = 360
what is 149x1007? because i am having troubles trying to figure out
Answers
Answer:
150043 Is the answer
2x + y = 3
3х - 2y = 8
Answers
..........................I'm just trying
this is right plz check ❤️
Michael says that 5(153)=5(53). Is his answer correct? Explain. A. Yes; Both expressions are equal to 625. B. Yes; Both expressions are equal to 125⋅ C. No; The first expression is equal to 125 and the second expression is equal to 625. D. No; The first expression is equal to 625 and the second expression is equal to 125.
Answers
Answer:
Michael's answer is not correct
5(153)≠ 5(53)
Step-by-step explanation:
Michael says that 5(153)=5(53)
Is his answer correct?
We solve for the left hand side
5(153) = 5 × 153
= 765
Solving for the right hand side
= 5(53) = 5 × 53
= 265
Therefore, from the above calculation,
5(153)≠ 5(53)
5(153) is not equal to 5(53)
Michael's answer is not correct
can you match the data types with the best graph for displaying that information? sort each data example to the graph type that would best represent it.
Answers
A combination of different graph types may be more appropriate to represent complex data relationships.
Certainly! Here are some common data types and the corresponding graph types that would best represent them:
Continuous Data (Quantitative):
Line Graph: Suitable for displaying trends and changes over time.
Scatter Plot: Useful for showing the relationship between two continuous variables.
Histogram: Effective for visualizing the distribution and frequency of continuous data.
Categorical Data:
Bar Graph: Ideal for comparing categorical variables and displaying their frequencies or proportions.
Pie Chart: Useful for illustrating the composition or relative proportions of different categories.
Stacked Bar Graph: Effective for comparing multiple categories and their subcategories.
Hierarchical Data:
Tree Diagram: Suitable for visualizing hierarchical relationships or organizational structures.
Sunburst Chart: Effective for displaying hierarchical data with multiple levels, often used for representing proportions.
Relationships between Variables:
Scatter Plot: Shows the correlation or relationship between two continuous variables.
Bubble Chart: Similar to a scatter plot, but with an additional dimension represented by the size of the bubbles.
Geographical Data:
Choropleth Map: Useful for representing data based on geographic regions, using colors or shading to indicate values.
Bubble Map: Similar to a choropleth map, but with bubbles of different sizes placed at specific locations to represent data.
Comparison:
Bar Graph: Suitable for comparing multiple categories or groups and their respective values.
Box Plot: Effective for comparing distributions and identifying outliers among different groups.
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What is the value of r of the geometric series?
Answers
Answer: The common ratio, r, is found by dividing any term after the first term by the term that directly precedes it. In the following examples, the common ratio is found by dividing the second term by the first term, a2 / a1 . When the common ratio of a geometric sequence is negative, the signs of the terms alternate.
Step-by-step explanation:
Answer:
\(r =0.8\)
Step-by-step explanation:
\(\text{By Comparing}~ 1.3(0.8)^{n-1}~ \text{with the nth term}~ ar^{n-1},\\\\\text{First term,}~a= 1.3\\\\\text{Common ratio,}~ r = 0.8\)
Which number represents the probability of an event that is impossible to
occur?
Answers
Answer:
An impossible event has a probability of 0. A certain event has a probability of 1.
36x + 31 = 535
A.
none of these
B.
1
C.
17
D.
12
Answers
Answer:
A
Step-by-step explanation:
36x = 535 - 31
36x = 504
36/36 x = 504/36
x = 14
\({ \green{ \boxed{ \red{ \sf{x = 14}}}}}\)
Step-by-step explanation:
\({ \purple{ \tt{36x + 31 = 535}}}\)
\({ \purple{ \tt36x = 535 - 31}}\)
\({ \purple{ \tt{36x = 504}}}\)
Divide both the sides by 36 then,
\({ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}\)
\({ \red{ \boxed{ \green{ \sf{x = 14}}}}}\)
Write a cosine function for each description. Assume that a>0 .
amplitude 3 , period 2π
Answers
To write a cosine function with an amplitude of 3 and a period of 2π, we can use the general form of the cosine function: f(x) = A * cos(Bx + C) + D
Here, A represents the amplitude, B determines the frequency (in this case, B = 2π/period), C represents any horizontal shift, and D represents any vertical shift. Given the amplitude of 3 and the period of 2π, we have:
A = 3
Period = 2π
Since the period is 2π, we can substitute this value into the formula for B:
B = 2π/period
B = 2π/(2π)
B = 1
Therefore, the cosine function with an amplitude of 3 and a period of 2π is: f(x) = 3 * cos(x) + D Since no vertical shift is mentioned in the description, we can assume D = 0.
The cosine function with an amplitude of 3 and a period of 2π is f(x) = 3 * cos(x). To write a cosine function with an amplitude of 3 and a period of 2π, we can use the general form of the cosine function:
f(x) = A * cos(Bx + C) + D. In this case, the amplitude is given as 3 and the period is given as 2π. The amplitude, represented by A, determines the maximum value of the function.
Since the amplitude is 3, the maximum value of the cosine function will be 3 and the minimum value will be -3. The period, represented by B, determines the length of one complete cycle of the function. In this case, the period is 2π, which means that one complete cycle of the cosine function occurs over an interval of 2π. By substituting the given values into the general form of the cosine function, we can write the specific function as f(x) = 3 * cos(x). This function represents a cosine curve with an amplitude of 3 and a period of 2π.
The cosine function with an amplitude of 3 and a period of 2π is f(x) = 3 * cos(x).
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At Mitchell's Arcade, 5/6 of the games are racing games. Among the racing games, 3/5 are motorcycle-racing games. What fraction of the games at Mitchell's Arcade are motorcycle-racing games?
Answers
Answer:
3 out of 5
Step-by-step explanation:
it says it in the question so say the max games is 6 one part 1 less as max witch is the motorcycle-racing games if it only has 3 then its really just 3 out of 5 so really that should be it. im not 100% sure so if im wrong please tell meme
I know it’s not 26 need help please
Answers
Answer:
x=11
Step-by-step explanation:
The angles are opposite interior angles and opposite interior angles are equal when the lines are parallel.
4x = 2x+22
Subtract 2x from each side
4x -2x = 2x+22-2x
2x = 22
Divide by 2
2x/2 =22/2
x = 11
Giselle stars with the two parallel line segments shown. She correctly reflects the segments across
the x-axis and then translates them following the rule (x,y) → (x-2, y + 5).
Line Segment AB has endpoints (2,4) and (-2,-1). Line Segment CD has end points (3,1) and (-1.-4).
(image attached)
Which statements about the reflection and translation of the line segments are true? Select all that
apply.
Answers
omg what is the......................
Really struggling with these problems please help!
Solve.
\( \sqrt{10y + 24} - 3 = y + 1\)
Answers
Answer:
\(y_1 = -2\) and \(y_2 = 4\)
Step-by-step explanation:
\( \sqrt{10y + 24} - 3 = y + 1\)
Move the constant to the right-hand side and change their sign.
\( \sqrt{10y + 24} = y + 1 + 3 \)
combine like terms
\( \sqrt{10y + 24} - 3 = y + 4\)
Square both side to remove square brackets.
10y + 24 - 3 = y²+ 8y + 16
Move the expression to the left-hand side and change its sign.
10y + 24 - y² - 8y - 16 = 0
Combine like terms
10y - 8y + 24 - 16 - y² = 0
2y + 8 - y² = 0
Use commutative property to reorder the terms.
-y² + 2y + 8 = 0
Change the sign of expression.
y² -2y -8 = 0
split -2y
y² + 2y - 4y - 8 = 0
Factor out y from the first pair and -4 from the second equation.
y ( y + 2 ) - 4 ( y + 2 ) = 0
Factor out y+2 from the expression.
( y + 2 ) ( y - 4)
When the products and factors equals 0, at least one factor is 0.
y + 2 = 0
y - 4 = 0
Solve for y
y = -2
y = 4
When we plug the both solution as y we found that both is true solution of this equation.
This equation has two solutions which are -2 and 4.
Answer:
Solution given:
\( \sqrt{10y + 24} - 3 = y + 1\)
keep the constant term in one side
\( \sqrt{10y + 24} =y+1+3\)
solve possible one
\(\sqrt{10y+24}=y+4\)
now
squaring both side
\((\sqrt{10y+24})²=(y+4)²\)
10y+24=y²+8y+16
taking all term on one side
10y+24-y²-8y-16=0
solve like terms
8+2y-y²=0
doing middle term factorisation
8+4y-2y-y²=0
4(2+y)-y(2+y)=0
(2+y)(4-y)=0
either
y=-2
or
y=4
y=-2,4