12) (2, 3) over the x - axis becomes, (2, -3).
13) (7, -2) over the y - axis becomes, (-7, -2).
14) (4, 5) 90° about the origin becomes, (-5, 4).
15) (-3, -2) 270° about the origin becomes, (-2, 3).
16) (17, -23) over the line y = x becomes, (-23, 17).
What is transformation of points?
The reflection is the type of alteration that takes place when each point in the shape is reflected over a line. The picture is on the opposite side of the line from the pre-image when the points are reflected across a line, but it is still at the same distance from the line as the pre-image. The reflection of each point (p, q) onto an image point (q, p).
12) Reflect (2, 3) over the x axis:
Since, the x-coordinate of a point that is reflected across the x-axis stays constant, but the y-coordinate is assumed to be the additive inverse.
The x-axis' reflection of point (x, y) is (x, -y).
So, (2, 3) becomes, (2, -3).
13) Reflect (7, -2) over the y axis:
Since, the y-coordinate of a point that is reflected across the y-axis stays constant, but the x-coordinate is assumed to be the additive inverse.
So, (7, -2) becomes, (-7, -2).
14) Rotate (4, 5) 90° about the origin:
(x, y) → (-y, x) is the formula for a 90° rotation about the origin.
So, (4, 5) becomes, (-5, 4).
15) Rotate (-3, -2) 270° about the origin:
(x, y) → (y, -x) is the formula for a 270° rotation of the origin.
So, (-3, -2) becomes, (-2, 3).
16) Reflect (17, -23) over the line y=x.
The angle at which the point (x, y) is reflected across the line y = x is (y, x).
So, (17, -23) becomes, (-23, 17).
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f: x → x + 5 9: x→ 8x What is the value of fg(4.5)?
The mapping of the function f of g(x) will result to 41
What is a functionA function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.
By mapping of the functions f and g defined as;
f : x » x + 5 and g : x » 8x
then;
f of g(x) = f of 8(4.5)
f of g(x) = f of 36
f of g(x) = 36 + 5
f of g(x) = 41
Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.
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winner gets brainiest | Don't type in any bs Actually answer the question please
Find domain and range of this linear graph
Answer:
Domain: {0 \leq x} Range {0 \leq y}
Step-by-step explanation:
btw \leq means less than or equal to
A Starbucks gift card has a balance of $75. Assume that the person who owns the gift card only uses it to purchase Frappuccino drinks that cost $4.65 apiece.
Construct a 98% confidence interval based on the data. Assume the variable is normally distributed
The 98% confidence interval limits are given by 1.6 < μ < 33.7.
What is the confidence interval in statistics?
A confidence interval is the mean of your estimate plus and minus its variation. Within a certain confidence level, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.
Given data: 10, 32, 24, 0, 5, 27, 5, 50, 6.
Sample mean = ∑x/n = 159/9 = 17.66
Sample variance = s² = ∑(x - sample mean)²/n-1
= 2206/8
= 275.75
Sample standard deviation = s = [tex]\sqrt{s^2}[/tex]
= [tex]\sqrt{275.75}[/tex]
= 16.60
Significance level = α = 1 - 0.98 = 0.02
Degree of freedom (d.f.) = n - 1 = 9 - 1 = 8
Critical value = [tex]t_{{\frac{\alpha}{2}},d.f}[/tex]
= 2.896
Margin of error = E = critical value * [tex]\frac{s}{\sqrt{n} }[/tex]
= 16.03
Limits of 98% confidence level are given by:
Lower limit = sample mean - E = 17.66 - 16.03 ≈ 1.6
Upper limit = sample mean + E = 17.66 + 16.03 ≈ 33.7.
Hence, the 98% confidence interval limits are given by 1.6 < μ < 33.7.
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Mr. Carson drove 1,027 miles in April. He drove 988 miles in May. Mr. Carson used the expression below to find how many more miles he drove in April than in May -> 1,027 - 988. How many more miles did Mr. Carson drive in April than in May?
Answer:
Mr. Carson drove 39 more miles in April than in May
Step-by-step explanation:
1027-988=39
WILL GIVE BRAINLIEST PLEASE HELP!!!!
A cat runs 10 meters north, sees a dog and runs 2 meters back south. It then runs 6 meters west. What is the displacement of the cat and the total distance it ran?
Answer:
The cat is at at 8 north 6 west
Step-by-step explanation:
The cat ran a total of 14 meters
Please help me with these questions
The rate of change of the linear functions given in tabular form and equations are found as follows;
1. a. The rate of change of the function is 5
b. The rate of change of the function is 7
c. The rate of then function is 0.75
d. The function has a rate of change of -8
2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values
b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days
c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day
The rate of change of a function is a measure of how much the output changes per unit change in the input.
1. The rate of change of the functions are as follows;
a. The first difference of the y-values is constant, therefore the function is a linear function
The formula for the rate of change of the linear function is presented as follows;
[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{-3 - (-8)}{1 - 0} = 5[/tex]b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]
The rate of change of the function is 7 unit changes in the y-value per unit change in the x-valuesc. The function is a linear function, as the first difference is constant and equal to 0.75
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]
The rate of change of the function is 0.75d. The first difference is constant and equal to -8
The rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]
The rate of change of the function is -82. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function
The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4
The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units
b. When the number of antibodies is 360, we have;
360 = 20·d + 100
20·d = 360 - 100 = 260
d = 260 ÷ 20 = 13
It would take 13 days for the patients blood to have 360 antibodiesc. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.
3. The function that gives the amount of antibodies in the body is a = 20·d + 100
d = The number of days
a = The number of antibodies
a. The table is completed as follows;
Data for Medicine A
d [tex]{}[/tex] a
0 [tex]{}[/tex] 100
1 [tex]{}[/tex] 120
2 [tex]{}[/tex] 140
3 [tex]{}[/tex] 160
4 [tex]{}[/tex] 180
5 [tex]{}[/tex] 200
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Plot the following numbers on the number line: -3 1/2 1 3/4
A number line which shows -3, 1/2, 3/4, and 1 correctly plotted on a graph is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical value -3 would be plotted on the left hand side of zero (0) while the numerical values 1/2, 3/4, and 1 would be plotted on the right hand side of zero (0) using a number line.
In conclusion, a number line has been used for the comparison of the given numerical values, and they are plotted on the number line shown in the image attached below.
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50. WATER HOSES A water hose can spray water at an
initial velocity of 40 feet per second. Use the formula
h(t) = vot – 16t², where h(t) is the height of the water
in feet, vo is the initial velocity in feet per second, and
t is the time in seconds.
-
a. How long will it take the water to hit the
nozzle on the way down?
b. Assuming the nozzle is 5 feet up, what is
the maximum height of the water?
It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.
a) Given equation
h(t) = v₀t - 16t^2
Substitute v₀ = 40, h(t) = 0 in the given equation
40t - 16t^2 = 0
Solve for t
⇒ 16t^2 = 40t
⇒ 16t = 40
⇒ t = 40/16
⇒ t = 2.5 seconds
Hence, water will take 2.5 seconds to hit the nozzle on the way down.
b) The function that represents the given condition
h(t) = -16t^2 + 40t + 5
The maximum value of the function is the y-coordinate of the vertex.
The x-coordinate of the vertex
= -40/2(-16) = 5/4
Find the y-coordinate of the vertex by substituting t = 5/4
⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5
⇒ h(5/4) = -25 + 50 + 5
⇒ h(5/4) = 30
Hence, the maximum height of the water is 30 ft.
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Pls help me, giving brainliest 50 POINTS!
Pls show your work and not only your answers pls
If you can’t answer it then don’t answer but if you can thank you
You will be reported if you put links
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]
[tex] \textsf{36 = 2 × 2 × 2 × 2 × 2 × 1} [/tex][tex] \textsf{3 = 3 × 1 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]
[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]
Similarly,
[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]
[tex] \textsf{6 = 2 × 3 } [/tex][tex] \textsf{54 = 2 × 3 × 3 × 3 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{GCD = 2 × 3 = 6 } [/tex]
[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]
[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]
[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]
[tex] \textsf{16 = 2 × 2 × 2 × 2} [/tex][tex] \textsf{8 = 2 × 2 × 2 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{GCD = 2 × 2 = 4 } [/tex]
[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]
Answer:
Numbers are : 36, 3, 12
36 = 2 × 2 × 2 × 2 × 2 × 1
3 = 3 × 1
12 = 2 × 2 × 3
HCF = product of total common factors of all three numbers, i.e : 2
LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96
Similarly,
2. Numbers are : 6, 54, 12
6 = 2 × 3
54 = 2 × 3 × 3 × 3
12 = 2 × 2 × 3
GCD = 2 × 3 = 6
[ 2 and 3 are the only ones common among all three ]
LCM = 2² × 3³ = 4 × 27 = 108
3. Numbers are : 16, 8, 12
16 = 2 × 2 × 2 × 2
8 = 2 × 2 × 2
12 = 2 × 2 × 3
GCD = 2 × 2 = 4
LCM = 2⁴ × 3 = 16 × 3 = 48
QUESTION 1
1 POINT
To study whether there is a correlation between regular exercise and sleep, a researcher randomly selected 100 people who
exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on
average.
Is the study observational or experimental? If it is an experiment, what is the controlled factor?
Select the correct answer below:
The study is an experiment. The controlled factor is the amount of sleep.
O The study is an experiment. The controlled factor is the amount of exercise.
The study is an observational study.
O The study is an experiment. The controlled factor is the survey.
Since the researcher randomly selected 100 people who exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on average: C. the study is an observational study.
What is an observational study?An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating, altering, or changing those who are or aren't exposed to it (controlled conditions).
In Science, a controlled variable must always be held constant and unchanged in an experiment in order to prevent it from affecting or influencing the result, which is not applicable to this research.
In conclusion, we can logically deduce that this research is an observational study because people (participants) were chosen through an appropriate process, however, no attempt was made to control any aspect of the people (participants), even though the variable of interest (exercise) was recorded for one of the group.
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For what value of x is g(x) = 2
Answer:
x = 2
Step-by-step explanation:
For the function g(x) to have to equal only 2, that would have to be for the input, x, to be 2 itself considering there's no equation given.
Hope this helps!
PLEASE HELP ME ON THIS!!!!!!!!!!!!!!
A student would like to show their teacher that they have practiced long enough for the day. Which measure of center should the student give to their teacher? Explain your answer.
Answer: hours
Step-by-step explanation:
minutes would be way too many
seconds - just self explanatory
days- would be less than one
hours is the only possible solution
Let f(x) = 4 + 2x and g(x) = 1/2x + 2 . Find f(g(x)) . Simplify the expression.
f(g(x)) = ___
Answer: x + 8
Step-by-step explanation:
[tex]f(g(x))=f(\frac{1}{2}x+2) = 4+2(\frac{1}{2}x+2) = 4+x+4 =x +8[/tex]
What is 4/5 ÷ 1/3? The quotient is 2 and
Answer:4/5 : 1/3=4/5 x 3/1=12/5
Step-by-step explanation:
Answer:
12/5
Step-by-step explanation:
If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5
was it helpful?
what is 20 x4 please i need a answer quickly
In 2012, 1,664,479 students took the SAT exam. The distribution
of scores in the verbal section of the SAT had a mean μ = 496 and a
standard deviation of o= 114.
Let X = a SAT exam verbal score section for 2012.
Then X-N (496, 114)
Find the z-scores for x1 = 325 and x2= 366.21.
Interpret each z-score.
What can you say about the x1= 325 and the x2= 366.21?
By using normal distribution of probability, it can be inferred that
For [tex]x_1 = 325[/tex], z = -1.5
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex], z = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-
[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]
where [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
For [tex]x_1 = 325[/tex]
[tex]z = \frac{325 - 496}{114} = -1.5[/tex]
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex]
[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
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Please help asap!! Please please please
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
What is the similarity test of two triangles?
If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.
In the given figures, the length of side AB is equal to the length of side DE.
Side AB = Side DE ----------(I)
Similarly, the length of side BC is equal to the length of side EF.
Side BC = Side EF ----------(II)
And the measure of angle ABC is equal to the measure of angle DEF.
∠ ABC = ∠ DEF -------(III)
From (I), (II), and (III), and by using the SAS test we can say that
ΔABC ~ ΔDEF ----------- SAS test
Hence,
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
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Adela paid $64.25 for 5 tickets at the skating rink. Calculate the unit rate per ticket.
Answer:
12.85
Step-by-step explanation:
hope it helps, pls lmk if it is wrong in comments!
Answer:
12.85
Step-by-step explanation:
64.25÷5
In a football game, Team A defeated Team B by a score of 31 to 14. The total points scored came from a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3
points, respectively. The numbers of touchdowns and extra-point kicks were equal. There were six times as many touchdowns as field goals. Find the number of touchdowns, extra-point
kicks, and field goals scored.
The number of touchdowns is 4.
The number of extra-point kicks is 4.
and the number of field goals is 2.
What are linear equations in three variables?
If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.
How to solve the system of linear equations in three variables?
Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.
Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".
Total points scored in game = 20+14 =34
Now,
According to the given question,
6x + y + 3z = 34 -----------(I)
x = y ----------(II)
x = 2z
z = [tex]\frac{x}{2}[/tex] -----------(III)
Putting the values of "y" and "z" in equation (I), we get
6x + x + 3×[tex]\frac{x}{2}[/tex] = 34
[tex]\frac{17x}{2}[/tex] = 34
x = 4
Now, putting the value of "x" in equations (II) and (III), we get
y = 4.
z = 2.
Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.
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What is the reason for each step in the solution of the equation?
−6x=−2(x+12)
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Distributive Property
Addition Property of Equality
Division Property of Equality
Step-by-step explanation:
Frist you distribute the -2 by multiplying it to everything in the parentheses. Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4
4. Angle X in the triangle below is a right angle.
W
15
X
T
h
-25-
2
20
R
9²4625
9+ 25²..
= 20²
400
-625-625
19² √225
15
(a) What is the measure of angle W?
450
(b) What is the height, h, of the triangle?
15.
/2 pts)
a ) The required measure of x = 90°
b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]
Given is a triangle with measure 15, 20 and 25
a ) Since a perpendicular is dropped from above
the two angles of x are equal because the angle is bisected by an angle bisector
So to check whether the angle x is a right angled or not
we can use the pythagoras theorem and check if the LHS = RHS or not
LHS = 15² + 20² = 225 + 400 = 625
and RHS = 25² = 625
Since LHS = RHS thus the angle is 90 degrees
b ) The height of the right triangle ;
by using the Pythagoras theorem again
12.5² + h² = 20² { side 25 is bisected = 12.5 }
h² = 400 - 156.25
h = [tex]\sqrt{244}[/tex]
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The slide at the playground has a height of 9 feet. The base of the slide measured onthe ground is 12 feet. What is the length of the slide?
O 15 feet
O 45 feet
21 feet
36 feet
Step-by-step explanation:
this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
length² = 9² + 12² = 81 + 144 = 225
length = sqrt(225) = 15 ft
The price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per
meter.
The table compares the total distance of a trip (in meters) and the price of the trip (in dollars).
Distance (meters)
80
110
140
How far can you climb for $131?
to be honest ion even know
Answer: 200 Meters
Step-by-step explanation:
For which value of x is line n parallel to line m?
Answer:
x is 70°
hopefully this will help u
What is the sale price including tax to the nearest cent? $595 refrigerator, 20% discount; 9.25% tax
The sale price including tax for the refrigerator is $520.
How to calculate the price?From the information, the following can be deduced:
Refrigerator = $595
Discount = 20%
Tax = 9.25%
The sales price will be:
= Refrigerator price + Tax - Discount
= $595 + (9.25% × $595) - (20% × 650)
= $595 + $55 - $130
= $520
The price is $520.
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George invest $500 in his friend's startup company. his friend agrees to give him 8% of the original investment each year for the next 3 years. write a linear function for this situation.
The linear function for the situation is :-
Amount at the end of 3 years = Original investment + original investment*Rate*Time/100
It is given in the question that:-
Investment of George's friend in startup company = $ 500.
Interest percent = 8 %
Time period of investment = 3 years
We have to find the linear function for this situation.
As this interest is on original investment, the interest will be simple.
Hence,
The linear function for the situation will be :-
Amount at the end of 3 years= Original investment + original investment*Rate*Time/100
Amount at the end of 3 years = 500 + 500*8*3/100 = 500 + 120 = $ 620
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quotient of 2÷ 3/7 iready
Answer:
6/7
Step-by-step explanation:
2÷3/7=2*3/7
6/7
Given that €1 = £0.75
a) How much is €530 in £?
b) What is the £ to €-exchange rate?
Answer: a.) 397.5 b.) 1.3333
Step-by-step explanation:
1 cent = £0.75
530 x 0.75 = 397.5
530 / 397.5 = 1.3333
Hope this helped please thank and rate!!
write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
The 10 forms 1/8 can be written is as follows;
1/81 ÷ 81/2³1/√64[tex]{8}^{ - 1} [/tex][tex]{√64}^{ - 1} [/tex]1 : 8[tex]{2}^{ - 3} [/tex]2/164 : 32How to write 1/8 in different forms?A fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction.
A denominator is the lower value of a fraction.
1 over 8 can be written in the following ways;
1/8
1 ÷ 8
1/2³
= 1 / 2×2×2
= 1/8
1/√64
= 1/8
[tex]{8}^{ - 1} [/tex]
= 1/8
1 : 8
= 1/8
[tex]{√64}^{ - 1} [/tex]
= 1/√64
= 1/8
[tex]{2}^{ - 3} [/tex]
= 1/2³
= 1/8
2/16
= 1/8
4 : 32
= 4/32
= 1/8
In conclusion, 1/8 can be written in different forms including using square root and ratios.
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