The transformation that relates the two functions:
f(x) = y = -√(-4x)
g(x) = y = √(-4x)
Is a reflection across the x-axis.
What is the transformation applied?
We define a reflection across the x-axis as a transformation that does a "vertical reflection" along the line y = 0 (which is the x-axis).
For a function f(x), a reflection across the x-axis generaste the new function g(x) that can be written as:
g(x) = -f(x).
In this case the original function is:
f(x) = y = -√(-4x)
And the transformed function is:
g(x) = y = √(-4x)
You can see that the only difference is the sign, such that we can write:
g(x) = -f(x) = -(-√(-4x)) = √(-4x)
So we conclude that the transformation is a reflection across the x-axis.
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A circle passes through (-2, 6) , (2, 8) , and (5, -1) Using the general form of a circle and the points above, fill in missing numbers to create the system of equations. (-2, 6) creates D + E + 1F = (2, 8) creates D + E + 1F = (5, -1) creates D + E + 1F = Solve the system of equations that you created, and write the equation for the circle by filling in the values for D, E, and F.
The equation of the circle passing through points (-2, 6) , (2, 8) , and (5, -1) is given as follows:
(x - 2)² + (y - 3)² = 25.
Equation of a circleThe equation of a circle with center (x*, y*) and radius r is given according to the following rule:
(x - x*)² + (y - y*)² = r².
The circle passes through point (-2,6), hence the first equation of the system is given as follows:
(-2 - x*) + (6 - y*)² = r².
r² = x*² + 4x* + 4 + y*² - 12y* + 36.
The circle also passes through point (2,8), hence the second equation of the system is given as follows:
(2 - x*) + (8 - y*)² = r².
r² = x*² - 4x* + 4 + y*² - 16y* + 64.
The final point is point (5,-1), meaning that the third equation is:
(5 - x*) + (-1 - y*)² = r².
r² = x*² - 10x* + 25 + y*² + 2y* + 1.
The system of equations to find the coordinates of the center and the radius is given as follows:
x*² + y*² + 4x* - 12y* + 40 - r² = 0.x*² + y*² - 4x* - 16y* + 68 - r² = 0.x*² + y*² - 10x* + 2y* + 26 - r² = 0.The solution to the system is given as follows:
x* = 2, y* = 3, r² = 25.
Hence the equation of the circle is:
(x - 2)² + (y - 3)² = 25.
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A secant line intersects the curve g(x)=-x² +8 at x = 1 and x = 1+h. What expression is equal to the slope of this secant?
The slope of the line secant to the curve g(x) = - x² + 8 is equal to m = - (2 + h).
How to derive the equation of the slope of a line secant to a curve
A secant line is a line that passes through a curve in two places, the formula for the slope of the secant line is described below:
m = [f(a + h) - f(a)] / [(a + h) - a]
m = [f(a + h) - f(a)] / h
If we know that f(x) = - x² + 8 and a = 1, then the equation for the slope of the secant line is:
m = {[- (1 + h)² + 8] - (-1² + 8)} / h
m = (- 1² - 2 · h - h² + 8 + 1² - 8) / h
m = (- 2 · h - h²) / h
m = - 2 - h
m = - (2 + h)
The slope of the line is equal to m = - (2 + h).
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In the diagram shown, lines MN and PQ intersect at R. If ZNRS is a right angle and the measure of ZMRQ is 1420, then what is the measure of ZPRS? Show or explain how you arrive at your answer.
The measure of the angle PRS is given as follows:
m<PRS = 45º.
Measure of angle PRSAs stated in this problem, these following angles are given:
<MRQ = 142º.m<NRS = 90º.MRQ and and QRN form a ray, hence they are supplementary angles.
For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:
142 + x = 180
x = 180 - 142
x = 38º.
The entire diagram forms an angle of 360º, hence:
142 + 38 + 90 + m<MRS = 360º.
270 + m<MRS = 360º
m<MRS = 90º.
The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:
The diagram is given by the image at the end of the answer.
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Use the information provided to answer questions 2 - 5. Leah would like to earn at least $ 120 per month. She babysits for $ 5 per hour and works at an ice cream shop for $ 8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;
[tex]\begin{gathered} 5x+8y\ge120---(1) \\ x+y\leq20---(2) \\ Solve\text{ these on a graph and you'll have;} \end{gathered}[/tex]The red graph represents x + y =<20
The blue graph represents 5x +8y =>120
Observe that the region where the blue and red are "mixed" together represent the solution region.
Option A (4, 15)
Option B (5, 12) and
Option C (10, 9) are possible solutions
535(-8) ??? What is the answer
Answer: the answer is -4280
Step-by-step explanation:
A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total.What do x and y represent?
Answer:
x = no of people in a small car
y = number of people in a van
Explanation:
The relevant information in the problem is that the total number of people is 27 and that the small car costs $10 and the large van $15.
If we call x the number of people in a small car, and y the number in the large van then the following equations can be obtained
[tex]\begin{gathered} x+y=27 \\ 10x+15y=80 \end{gathered}[/tex]The first equation simply says that the total number of people is 27 and the second equation says that the total cost of the trip is $80.
Hence,
x = no of people in a small car
y = number of people in a van
Solve 4(3m + 1) − 2m = −16. m = −0.83 m equals negative 20 over 12 m equals negative 17 over 10 m = −2.
The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2
How to determine the solution to the equation?The equation is given as
4(3m + 1) − 2m = −16
Open the brackets in the above equation
So, we have
12m + 4 − 2m = −16
Collect the like terms in the above equation
So, we have the following equation
12m − 2m = −16 -4
Evaluate the like terms in the above equation
So, we have the following equation
10m = −20
Divide both sides by 10
m = -2
Hence, the soluton is m = -2
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A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
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help me please
help me :>
Based on the graphs and equations given, the simultaneous equations can be solved to give x = 1.5 and y = 5.5.
How to solve the simultaneous equation?To solve the simultaneous equation, come up with the values of y using values of x in the given formulas:
For y = 3x + 1: the values of y will be:
When x = 1, then y will be:
= 3(1) + 1
= 4
When x = 2, then y will be:
= 3(2) + 1
= 7
When x = 3, then y will be:
= 3(3) + 1
= 9
For the equation, x + y = 7:
When x = 1, then y will be:
y = 7 - 1
= 6
When x = 2, then y will be:
= 7 - 2
= 5
When x = 3, then y will be:
= 7 - 3
= 4
When these are plotted on a graph, we find that the value of x is 1.5 and the value of y is 5.5. This is the point where the lines intersect.
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Shannon started a savings account by putting
in $25. On the 1st week she deposited $15
and plans to continue depositing $15 each
week.
Given the graph, description or sequence values create an explicit equation
solve 2/3x + 4 = 5/6x by eliminating the fraction.
The value of x in the given equation is 24.
Given equation:
(2/3)x + 4 = (5/6)x
We have to find the value of x by eliminating the fraction.
Fraction
Fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
LCM (3,6) = 6
Multiplying the whole equation by 6, we get:-
(2/3)x*6 + 4*6 = (5/6)x*6
4x + 24 = 5x
5x - 4x = 24
x = 24
Hence, the value of x is 24.
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Hi! So I am stuck on three problems right now, can you Please help me?number 1, says "What is the cosine ratio of
The cosine ratio is given by the following formula:
[tex]\cos (Z)=\frac{\text{adjacent leg}}{hypotenuse}[/tex]The adjacent leg of angle Z is side ZY=12 and the hypotenuse of the triangle is the side XZ=20, thus the cosine ratio of Z is:
[tex]\cos (Z)=\frac{12}{20}[/tex]what is the correct ascending order for these numbers1.525/848%
Given the set of numbers:
[tex]\text{ 1.52, 5/8 and 48\%}[/tex]To be able to determine their correct ascending order, we must first make all the numbers into similar forms.
Let's convert a
Find the mean and population standar deviation for each data set.
Hours slept
Mean of given set is 7.8
Define mean.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value." It is a statistical idea with significant financial implications.
Given,
Mean:
Formula:
Sum = 118.25
Total = 15
[tex]\frac{sum}{total}[/tex]
[tex]\frac{6.75 + 6.5 + 7 +8 +7+8.75+7.25+5.75+9.25+7.75+7+7.5+8+7.5+8+6.25}{15}[/tex]
= [tex]\frac{118.25}{15}[/tex]
= 7.8
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At a restaurant, Elena wants to leave a tip that is 15% of the bill B plus $1. Which linear model best describes the total T?
Answer:
The total T can be described as
[tex]T = (B+(B*.15))+1[/tex]
Evaluate: -6 × (-4)
= Enter your next step here
() TO
Answer:
24
Step-by-step explanation:
-6*(-4)
The negative signs cancel:
6*4
24
Please help asap
this is an assignment due today please help real quick
no fake answers
Answer:
where???????????????
Which angle pair is NOT an example of Corresponding Angles?
angle 2 and angle 10
angle 1 and angle 11
angle 13 and angle 15
angle 8 and angle 16
Answer:
Step-by-step explanation:
So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!
Convert 450 liters into fluid ounces. Round your answer to the nearest whole number.
Answer:15216.31 Fluid Ounces
Step-by-step explanation:
Find the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.−10, −16, −21, −24, −4, −30, −32 range ________standard deviation __________variance __________
From the given values, we can see that the lowest values is -32 and the highest value ie -4. Since the range is the difference betwwwn the highest and the lowest value, the range is
[tex]\begin{gathered} \text{Range}=-4-(-32) \\ \text{Range}=28 \end{gathered}[/tex]On the other hand, the sample variance formula is
[tex]S^2=\sqrt[]{\frac{\sum ^7_{n\mathop=1}(x-\bar{x})^2}{n-1}}[/tex]where x^bar is the mean and n is the total number of sample elements. In our case, n=7 and the mean is
[tex]\begin{gathered} \bar{x}=\frac{-10-16-21-24-4-30-32}{7} \\ \bar{x}=-\frac{137}{7} \\ \bar{x}=-19.5714 \end{gathered}[/tex]Then, the sample variance is given by
[tex]\begin{gathered} S^2=\frac{(-10-19.57)^2+(-16-19.57)^2+(-21-19.57)^2+\cdot\cdot\cdot+(-32-19.57)^2}{6} \\ S^2=105.2857 \end{gathered}[/tex]Since the standard deviation is the square root of the sample variance, we have
[tex]\begin{gathered} S=\sqrt[]{105.2857} \\ S=10.26088 \end{gathered}[/tex]By rounding the solutions to the nearest tenth, the answers are:
[tex]\begin{gathered} \text{Range}=28 \\ \text{Variance}=105.3 \\ \text{ Standard deviation = 10.3} \end{gathered}[/tex]Please help!
2|x-1| >2
5
Answer: 6, -4
Step-by-step explanation:
[tex]\frac{2}{5}|x-1| \geq 2\\\\|x-1| \geq 5\\\\x-1 \leq -5, x-1 \geq 5\\\\x \leq -4, x \geq 6[/tex]
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
Drag the choices into the boxes to correctly complete the statements.
Considering the equation of a circle, it is found that:
The equation of the circle that represents the dartboard is [tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex], where the origin is the lower left corner of the room and the unit of the radius is in inches;The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In the context of this problem, we have that:
The radius of the circle is of 9 inches, as the diameter is of 18 inches and the radius is half the diameter.The height is of 5 feet 8 inches = 5 feet and 2/3 feet = 17/3 feet, which is the y-coordinate of the center.The bull's-eye is 12 feet from a wall to its left, hence the x-coordinate of the center is of 12.Hence the equation of the circle is given by:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex]
Brian's dart lands at the following position:
(11.5, 5)
All the points that land on the dartboard respect the following equation:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 \leq 81[/tex]
For the coordinate where the dart landed, we have that:
(11.5 - 12)² + (5 - 17/3)² = 0.7 < 81, meaning that Brian's dart lands on the dartboard.
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Select the correct answer.
Which of the following represents a function?
A. The first graph
B. The second graph
C. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
D.
x -5 -1 9 8 -1
y 1 7 23 17 1
Answer:
The answer is to the question A
Answer:
Its B 100%
i took the test and got it right
k bye :):):):):):):)
Step-by-step explanation:
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011$5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year (d) Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of P0 and d to the nearest dollar.Pt= (e) Using the regression model, predict the cost of insurance in 2030.$ (f) According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year
Part (a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).
we have the ordered pairs
(1999, 2,196) -------> (0,2,196)
(2019,7,186) -------> (20,7,196)
Find out the slope
where
t -----> is the number of years since 1999
P ----> the cost
m=(7,196-2,196)/(20-0)
m=5,000/20
m=250
Find the equation of the linear model in slope-intercept form
P=mt+b
we have
m=250
point (0,2,196)
substitute and solve for b
2,196=250(0)+b
b=2,196
therefore
P=250t+2,196
Part b
Using this linear model, predict the cost of insurance in 2030
For t=2030=2030-1999=31 years
substitute
P=250(31)+2,196
P=$9,946
Part c
According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute in the linear model
12,000=250t+2,196
250t=12,000-2,196
250t=9,804
t=39 years
therefore
1999+39=year 2038
Part d
Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of
P0 and d to the nearest dollar
using a regression calculator
the equation is
ŷ = 239.15065X + 2406.39827
y=239x+2,406
Part e
Using the regression model, predict the cost of insurance in 2030
For t=2030-1999=31 years
P=239(31)+2,406
P=$9,815
Part f
According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute
12,000=239x+2,406
239x=12,000-2,406
239x=9,594
t=40 years
year=1999+40=2039
Given: angle CDE congruent to angle CED,
Angle A = angle B
Prove: DE || AB
Please explain the statement and reasoning
Ex: AB is congruent (the sign) to DE. Given
Ill reward brainliest to the one who explains it best ty
1) [tex]\angle CDE \cong \angle CED, \angle A \cong \angle B[/tex] (given)
2) [tex]m\angle CDE=m\angle CED, m\angle A=m\angle B[/tex] (definition of congruent angles)
3) [tex]m\angle C+m\angle CDE+m\angle CED=180^{\circ}, m\angle C+m\angle A+m\angle B=180^{\circ}[/tex] (sum of angles in a triangle)
4) [tex]m\angle C+2m\angle CDE=180^{\circ}, m\angle C+2m\angle A=180^{\circ}[/tex] (substitution)
5) [tex]m\angle C=180^{\circ}-2m \angle CDE, m\angle C=180^{\circ}-2m\angle A[/tex] (subtraction)
6) [tex]180^{\circ}-2m \angle CDE=180^{\circ}-2m \angle A[/tex] (transitive)
7) [tex]-2m\angle CDE=-2m\angle A[/tex] (subtraction)
8) [tex]m\angle CDE=m\angle A[/tex] (division)
9) [tex]\angle CDE \cong \angle A[/tex] (definition of congruent angles)
10) [tex]\overline{DE} \parallel \overline{AB}[/tex] (converse of corresponding angles theorem)
Simplify: 2.4 x 10−4 0.00024 0.000024 −0.000024 −2.4000
Answer:
0.00067
Step-by-step explanation:
You always want the period to the right of the first number meaning you’ll start from there counting backwards because it is negative.
12 is 150% of what number
To get 150% of a given number x, we multiply it by 1.5
This way, we'll have that:
[tex]1.5x=12[/tex]Solving for x,
[tex]1.5x=12\rightarrow x=\frac{12}{1.5}\rightarrow x=8[/tex]Therefore, we can conclude that 12 is 150% of 8
Past due I don't really understand, what's the answer??
Answer:
$50.16
Step-by-step explanation:
id.k if it's actually right but i believe the tip would be $8.36 if it's 20% so adding it together is $50.16
Write a verbal sentence to represent each equation.
9.3n-3579
10. 2(n³ + 3n²) = 4n
11.
5n
n+3
-=n-8
The expression's variables can be represented by a different symbol than the conventional x and y.
A mathematical assertion represented in English is known as a verbal expression.What does an algebraic verbal model mean?Talking Model is a formula utilizing the terms found in the problem. Labels matching variables or numerical values to the linguistic model Equational Expression Modification of the Verbal Model by the substitution of mathematical values and variables.How to Convert Algebraic Expressions to Verbal Expressions.
Step 1: Recognize the algebraic operations—such as addition, subtraction, multiplication, and division—used in the expression.Step 2: Write a statement in which a vocabulary word is combined with the numbers to represent each of these processes.Therefore, the expression's variables can be represented by a different symbol than the conventional x and y.
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Solve the trig equation on the interval [tex]0 \leqslant theta \: \ \textless \ 2\pi[/tex][tex]3 sec \: \: theta \: - 2 \sqrt{3 } = 0[/tex]
Answer:
pi/6 and 11pi/6
Explanation
Given the trigonometry equation:
[tex]\begin{gathered} 3\text{sec}\theta\text{ - 2}\sqrt[]{3}=0 \\ \end{gathered}[/tex]Add 2\sqrt[3] to both sides as shown;
[tex]\begin{gathered} 3\sec \theta-2\sqrt[]{3}=0+2\sqrt[]{3} \\ 3\sec \theta\text{ = 2}\sqrt[]{3} \\ \sec \text{ }\theta\text{ = }\frac{2\sqrt[]{3}}{3} \\ \frac{1}{\cos \theta}=\frac{2\sqrt[]{3}}{3} \\ \cos \theta\text{ =}\frac{3}{2\sqrt[]{3}} \\ \cos \text{ }\theta\text{ = }\frac{3\sqrt[]{3}}{2\cdot3} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the cos inverse of both sides
[tex]\begin{gathered} \cos ^{-1}(\cos \theta)=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=30^0 \end{gathered}[/tex]Since theta is between 0 and 2pi
theta = 360 - 30
theta = 330^0
Convert to radians
180^0 = pi rad
30^0 = x
180x = 30pi
x = 30pi/180
x = pi/6
Similarly;
180^0 = pi rad
330^0 = x
180x = 330pi
x = 330pi/180
x = 11pi/6
Hence the value of thets between 0 and 2pi are pi/6 and 11pi/6