Answer:
It may
Step-by-step explanation:
Vertically shift the graph of f(x) up 7 units.
By:-"||Ziddiboy||"
Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown. –15 –5 –3 3 5
Answer: To solve the inequality x^2 - 8x + 15 < 0, we first want to find the critical points, which are the points where the quadratic function changes direction (from increasing to decreasing or vice versa). To find the critical points, we need to set the quadratic equal to zero and solve for x. In this case, we have:
x^2 - 8x + 15 = 0
To solve this equation we should factor it or use the quadratic formula.
(x - 5)(x - 3) = 0
x = 5, x = 3
This means that the critical points for the inequality are x = 5 and x = 3. To find the solution set of the inequality, we test the signs of the function at the critical points and in the intervals between them.
The solution of the inequality is x < 3 or x > 5.
Step-by-step explanation:
The range of the function f (x) =√x^2−4
is (−∞, −1) ∪ (1, ∞). To explain
why this is true, you have to do two things:
(a) Show that if f (x) = y for some x, then either y > 1 or y < −1.
(b) Show that if y < −1 or y > 1, then the equation f (x) = y has a solution in x.
The solutions for the given function are (-2, 0) and (2, 0).
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
The given function is f(x)=√(x²-4).
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,−2]∪[2,∞),{x|x≤−2,x≥2}
Range: [0,∞),{y|y≥0}
Therefore, the solutions for the given function are (-2, 0) and (2, 0).
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The area of the regular octagon is 10.15 cm².
1.45 cm
What is the measure of the apothem, rounded to the
nearest hundredth of a centimeter
The measure of the apothem is 1.75cm.
What is a regular octagon?
Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.
Here, we have
Given: The area of the regular octagon is 10.15 cm².
We have to find the measure of the apothem.
The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.
Area (triangle AOB) = 10.15/8 = 1.27cm².
Area(triangle AOB) is also 1/2*MO*AB
1.27 = 1/2*MO*1.45
MO = 1.75cm
Hence, the measure of the apothem is 1.75cm.
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Please help, I’ll mark brainlest
g(x) = 2(x+3)^2 - 1
Value of g(x) with given values of x:
x -5 -4 -3 -2 -1
g(x) 7 1 -1 1 7
Given: the functional equation:
g(x) = 2(x + 3)^2 – 1
Solution:
Value of g(x), when x= -5
g(x) = 2 (-5 +3)^2 – 1
= 2 (-2)^2 – 1
= 2* (-2)* (-2) – 1
= 8 – 1
= 7
Value of g(x), when x= -4
g(x) = 2 (-4 +3)^2 – 1
= 2 (-1)^2 – 1
= 2* (-1)* (-1) – 1
= 2 – 1
= 1
Value of g(x), when x= -3
g(x) = 2 (-3 +3)^2 – 1
= 2 (0)^2 – 1
= 2* 0 – 1
= 0 – 1
= - 1
Value of g(x), when x= -2
g(x) = 2 (-2 +3)^2 – 1
= 2 (1)^2 – 1
= 2* (1)* (1) – 1
= 2 – 1
= 1
Value of g(x), when x= -1
g(x) = 2 (-1 +3)^2 – 1
= 2 (2)^2 – 1
= 2* (2)* (2) – 1
= 8 – 1
= 7
Arianys invests money in an account paying a simple interest of 3% per year. If m
represents the amount of money she invests, which expression represents her balance
after a year, assuming she makes no additional withdrawals or deposits?
Answer:
Step-by-step explanation:
The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:
Balance = Principal + Interest
where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.
Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:
Interest = Principal * Interest Rate * Time
Substituting the given values:
Interest = m * 0.03 * 1
So the expression that represents Arianys balance after a year is:
Balance = m + (m*0.03)
= m + 0.03m
= 1.03m
This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.
Please answer:
The fraction 1/7 is equal to the repeating decimal 0.142857 . Which digit occurs in the 2023rd place after the decimal point?
The digit that occurs in the 2023rd place after the decimal point is; 1
How to Interpret Repeating Decimals?A repeating decimal has another name called a recurring decimal, and it is defined as a number whose decimal representation eventually becomes periodic
Now, we are given the fraction as 1/7 which is a repeating decimal because its decimal representation is periodic for every 6 decimal units as shown below; 1/7 = 0.142857142857...
Now, the digits are repeated after every 6 digits and as such to get the digit in the 2023rd place;
2023/7 = 337 remainder 1
Thus, the sequence 142857 would be repeated 337 times after which the next digit which is the 2023rd digit will be 1.
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The sides of MNPQ are represented by the expressions below. Find the perimeter of MNPQ.
MW=-2+37
QP= y+14
NP= x-5
MN=4y+5
perimeter: ? units
Answer:
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all its sides. To find the perimeter of MNPQ, we need to add up the lengths of MN, NP, PQ and PM.
Given that:
MW=-2+37 = 35
QP= y+14
NP= x-5
MN=4y+5
The perimeter can be calculated by adding up the above expressions:
Perimeter = MN + NP + QP + MW
= (4y + 5) + (x - 5) + (y + 14) + 35
= 4y + x + y + 54
= (4y + y) + (x + 54)
= 5y + x + 54
So the perimeter of MNPQ is 5y + x + 54 units.
3. Line DG is the perpendicular bisector of chord El.
EF = 7, EI = 9.5, and DG = 1.8.
What is the diameter of the circle? Show your work.
The diameter of the circle would be given as = 10
What is a diameter?Diameter is defined as the length of a line through the center that touches two points on the edge of the circle.
The diameter of the circle can be found through finding first the radius of the circle.
The radius of the circle is half of the diameter. it is the line DI which is also the longer line of the triangle DGI.
Using the Pythagorean formula c² = a² + b²
The lines that represents ;
a= DG
b= EI/2 = 4.8
C= DI = ?
C² = DI
a² = 1.8²
b² = (9.5/2)² = 4.8²
c² = 2.24 + 23.04 = 25.28
C =√25.28
C = 5
Therefore the diameter of the circle = 5×2 = 10
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0.15 | 0.3 | 1 | 2 | 2.7 | 5.4 | 6.4 | ? | ?
A 12.2, 12.9
B 9.5, 13.6
C 7.1, 8.6
D 6.8, 7.5
The next two numbers on the number pattern will be 12.2, 12.9 the correct option is A
How to obtain the next two points on the number pattern?To obtain the next two points on the number pattern, first we must identify what is the meaning of pattern.
The pattern is given as follows;
The double of an amount is calculated.
Now 0.7 is increased to double the amount, and we return to step 1, doubling the value.
The final term is 6.1, which is obtained after the addition of 0.7 to 5.4. Double 6.1 is obtained multiplying the number by 2, as follows;
2 x 6.1 = 12.2.
Then the number obtained after 0.7 is added to 12.2 is given as follows;
0.7 + 12.2 = 12.9.
It implies that the correct answer of the given number pattern is 12.2, 12.9
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It is estimated that wireless soil monitors could save up to 6 trillion gallons of
water per year by reporting precise information needed to irrigate crops
properly. Using this data, express the number of gallons of water saved in two
years, in scientific notation.
Hint:
1Million=6 zeros
1billion=9 zeros
1trillion=12 zeros
____x10____
Using scientific notation, the number of gallons of water saved in two years by the wireless soil monitors is 1.2 x 10^12.
What is scientific notation?Scientific notation is a shorthand way of writing very large numbers or very small numbers in a simpler form.
The parts of a scientific notation are coefficient, base, and exponent.
We state that a number is written in standard notation when the number is between 1 and 10 and it is multiplied by a power of 10.
The number of gallons of water per year saved by wireless soil monitors = 6 trillion
The number of gallons of water saved by wireless soil monitors in 2 years = 12 trillion
In scientific notation, 12 trillion = 1.2 x 10^12.
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Jeremy analyses one of his parachute jumps.
He draws a graph showing his velocity up to the opening of his parachute.
The acccceleration will be 1m/s² and the average speed is 47m/s.
How to calculate the acceleration?For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.
Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.
Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.
If we estimate the speed at 5 seconds intervals, then we have
Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7
Average speed = 331/7 = 47.29 m/s
Average speed = 47 m/s
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Erica earned a total of 67,160 last year from her two jobs. The amount she earned from her job at the store was 1,550 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college
Answer:
Let's call the amount Erica earned from her job at the college "x". We know that:
Total income = $67,160
Income from store = 3x + 1,550
Total income = Income from store + Income from college
67,160 = 3x + 1,550 + x
67,160 = 4x + 1,550
Now we can solve for x:
67,160 - 1,550 = 4x
65,610 = 4x
x = 16,402.5
Erica earned $16,402.50 from her job at the college.
Gershon Smudgenick had 4 pounds of broccoli sprouts. He
went to Joe's Discount Bonanza and got some more. He ended up
with 11 pounds of broccoli sprouts. What is the fractional increase
in Gershon's broccoli sprouts? What is the percent increase in
Gershon's broccoli sprouts?
Answer: The fractional increase in Gershon's broccoli sprouts is 7/4 and the percent increase in Gershon's broccoli sprouts is 175%.
Step-by-step explanation:
The fractional increase in Gershon's broccoli sprouts is the difference between the final amount and the initial amount divided by the initial amount.
So in this case, it would be (11 - 4) / 4 = 7 / 4.
The percent increase in Gershon's broccoli sprouts is the fractional increase multiplied by 100.
So, it would be (7 / 4) * 100 = 175%.
It means Gershon's broccoli sprouts increased by 175% from 4 pounds to 11 pounds.
-
2 x
3
5
сл
6
The volume of a cuboid is 364cm³.
The length is 7cm and the width is 13cm.
Work out the height of the cuboid.
8
The height of the cuboid is 4 cm
What is a cuboid?
A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.
volume of a cuboid = l *w*h
where, l= length, w=width, h= height
=> 364 = 7*13*h
=> h=364/(7*13) = 364/91
=> h= 4 cm
Thus, the height of the cuboid is 4 cm
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There are 135 people in a sport centre.
73 people use the gym.
73 people use the swimming pool.
67 people use the track.
36 people use the gym and the pool.
35 people use the pool and the track.
32 people use the gym and the track.
14 people use all three facilities.
How many people use exactly one of these facilities?
The number of people that uses exactly one of gym, swimming pool and track is 49people
What is set?A set is the mathematical model for a collection of different things. A set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
The number of people that uses gym= 73- ( 32-14+ 36-14 + 14)
73-(18+22+14)
73 - (54) = 19 people
The number of people that use pool only = 73-(36-14+35-14+14)
= 73-(22+21+14)
= 73-(57)
= 16people
The number of people that use track only = 67-(32-14+35-14+14)
= 67-(18+21+14)
= 67-53
= 14people
therefore the number of people that use one of the facility is 19+16+14 = 49people
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What is the equation of this line? y>1/2x−3 y<1/2x−3 y>2x−3 y<2x−3
Answer:
The equation of this line is y>1/2x-3
Step-by-step explanation:
This is an inequality equation that represents a line that is greater than 1/2x-3. The inequality symbol ">" indicates that all the y-coordinates that are on the same side of the line as the y-axis are greater than 1/2x-3.
In other words, all the points that lie above the line will satisfy the inequality, while all the points that lie below the line will not.
It's worth noting that the line y<1/2x-3 represents the same line but the inequality symbol "<" indicates that all the y-coordinates that are on the same side of the line as the x-axis are less than 1/2x-3.
y>2x-3 and y<2x-3 represent different lines, the first one represents a line with a slope of 2 and the second one represents a line with a slope of -2.
If 7 more than twice a number is 5 less than three times the same number, what is the number?
Answer:
12
SolutionLet X be the unknown number we are supposed to find.
Given information from the question, we can form up an equation:
2X + 7 = 3X - 5
3X - 2X = 7 + 5
X = 12
Therefore the unknown number is 12
Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes
Point
Slopes
(1, 1)
(a) 3 (b) -3 (c) -5/2 (d) Undefined
The sketch for slope is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Point Slopes
(1, 1) (a) 3
_ (b) -3
_ (c) -5/2
_ (d) Undefined
a) Now, using slope intercept form
y - 1= 3 (x-1)
y- 1= 3x- 3
y= 3x - 2
(b) Equation of a line has a slope -3 is given by
y - 1= (-3) (x-1)
y-1 = 3- 3x
y = -3x + 4
(c) Equation of a line has a slope -5/2 is given by
y - 1= (-5/2) (x-1)
y-1 = -5/2x + 5/2
y= -5/2x + 7/2
(d) The line parallel to y axis and passes through given point : x=1
"undefined" means the line is vertical.
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In triangle ABC, M is the midpoint of AB and N divides CB such as NB:NC = 1:5. Find the area of triangle MNB, MNC and ABC
The area of triangle MNB, MNC and ABC 6 in.², 60 in.², and 30 in.² respectively
How to find the area of the triangle?The ratio of the base of the triangles ΔMNB and ΔCBM, that shares a common vertex, is the ratio of their areas.
M is the midpoint of side AB in ΔABC
NB:CB = 1:5
Area of ΔCAM = 30 in.²
The area of ΔMNB and ΔABC
Area = 1/2 * base * height
Height of ΔCAM = Height of ΔCBM = Altitude of point C above line AB
MA = MB by definition of midpoint
MA is the base of ΔCAM, and MB is the base of ΔCBM
Therefore; Area of ΔCAM = 1/2 AM * Height of ΔCAM
= 1/2 * AM* height of ΔCAM
Which gives;
Area of ΔCAM = Area of ΔCBM = 30 in.²
Area of ΔABC = Area of ΔCAM + Area of ΔCBM = 30 + 30 = 60
Area of ΔABC = 60 in.²
Taking CB as the base of ΔCBM, we have;
Height of ΔMNB = Height of ΔCBM from line CB
Base length of ΔCBM = 5 × Base length of ΔMNB
Therefore; Area of ΔMNB = 30/5 = 6 in²
Area of ΔCBM = 30 in.² = 5 × The area of ΔMNB
Conclusively, the Area of ΔMNB = 6 in.²
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Correct question:
In a triangle ABC, M is the mid point of the side AB and N is the mid point of the side AC. Find the lenght of the segment MN if AB =18, BC = 10 and AC = 20
GEOMETRY HELPPPP PLS
The new equation is y=-1/2x+5. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
What is mathematical equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2. The smallest equivalent fraction of the number is considered to be its simplest form. What to do to discover the simplest form? Investigate the numerator and denominator for shared factors. To see if a fractional number is a prime number, check it.Our first line in this equation is y=2x-1. By applying the equation y=mx+b, where "m" stands for the slope, we can see that our "m" in this instance is 2. then negate 2. It turns into -2.
Change the denominator and numerator after that. Since -2 is actually -2/1, let's change it to -1/2. The perpendicular line's slope is that.
We must now make it pass through (-2,6). We just have a line like this to work with at the moment: y=-1/2x
Plugging in the x-coordinate of our target location, -2, yields y=-1/2(-2), or 1. But hold on, because the y-coordinate we were given is 6, shouldn't y be equal to 6 as well? Yes! The only thing left to do is to add 5 to get from 1 to 6!
The complete question is,
Write an equation for a line perpendicular to y = 2 x − 1 and passing through the point (-2,6)
Write an equation for a line perpendicular to y=2x−1 and passing through the point (-2,6)
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Match the image to the scale factor from FG to F'G'.
Image 1
F
F
Image 2
F'
F
Image 3
F'
F
F
Image 4
F
F
Image 5
F'
12
12
8
6
18
12
12
12
12
24
G'
G
G
G'
G
G'
G
F
The scale factor for each of the dilation is given as -
K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2What is scale factor?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y}, greater than {x}.
Given is a line segment and its dilated image.
The scale factor is given by -
K = y/x
[1] -
K₁ = 18/12 = 3/2
[2] -
K₂ = 8/12 = 2/3
[3] -
K₃ = 12/12 = 1
[4] -
K₄ = 6/12 = 1/2
Therefore, the scale factor for each of the dilation is given as -
K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2To solve more questions on direct variation, visit the link below -
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HELP I NEED TO KNOW ANSWER! Determine if triangle QRS and triangle TUV are or are not similar and if they are state how you know
The given triangles are not similar because the sides given are not proportional.
What are Similar Triangles?Similar triangles are those triangles which has the same shape but different size.
The length of sides and angles are proportional in similar triangles.
Given are two triangles QRS and TUV.
Also given the measure of two sides of each triangle and an included angle of these sides of each triangle.
From the figure, given angles are equal.
If we prove that the sides including these angles are proportional, we can say the given triangles are similar by SAS similarity theorem.
7 / 35 = 1/5
But 13/55 ≠ 1/5
So they are not proportional.
Hence the given triangles are not similar.
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Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{5}{x}[/tex] - [tex]\frac{2}{x^2}[/tex] = 2
multiply through by x² ( x ≠ 0 ) to clear the fractions
5x - 2 = 2x² , that is
2x² = 5x - 2 ( subtract 5x - 2 from both sides )
2x² - 5x + 2 = 0 ← in standard form
(2x - 1)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]
x - 2 = 0 ⇒ x = 2
since x₁ < x₂ , then
x₁ = [tex]\frac{1}{2}[/tex] and x₂ = 2
Then
3x₁ + x₂
= 3 × [tex]\frac{1}{2}[/tex] + 2
= [tex]\frac{3}{2}[/tex] + 2
= [tex]\frac{3}{2}[/tex] + [tex]\frac{4}{2}[/tex]
= [tex]\frac{7}{2}[/tex]
How does the use of internal rhyme affect the poem? A. It adds suspense by means of the steady repetition of similar sounds. B. It makes the speaker seem more sympathetic since he is so clever at rhyming. C. It helps create and maintain the poem's playful tone. D. It creates more emotional impact for the poem by emphasizing emotional words.
The use of internal rhyme affect the poem by: C. It helps create and maintain the poem's playful tone
What is internal rhymeInternal rhyme tend to occurs when words that are in the same line of a poem rhyme with one another.
The use of internal rhyme can tend to add more musical quality to a poem and it as well help to create cohesion within a line or stanza. Internal rhyme also help to a sense of playfulness in the poem.
Therefore we can conclude that the correct option is C.
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1. The sum of two three-digit numbers is a four-digit number.
Answer:
Step-by-step explanation:
What are the possible combinations of three-digit numbers that could add up to a four-digit number?
There are many possible combinations of three-digit numbers that can add up to a four-digit number. Here are some examples:
1. 100 + 900 = 1000
2. 200 + 800 = 1000
3. 300 + 700 = 1000
4. 400 + 600 = 1000
5. 500 + 500 = 1000
6. 600 + 400 = 1000
7. 700 + 300 = 1000
8. 800 + 200 = 1000
9. 900 + 100 = 1000
10. 111 + 889 = 1000
11. 222 + 778 = 1000
12. 333 + 667 = 1000
13. 444 + 556 = 1000
14. 555 + 445 = 1000
15. 666 + 334 = 1000
16. 777 + 223 = 1000
17. 888 + 112 = 1000
18. 999 + 001 = 1000
19. 123 + 877 = 1000
20. 234 + 766 = 1000
Recall that during the 2013-2014 academic year, the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities. A committee of community members was formed to explore various options for a bond proposal to pay for the plan¹. The committee presented three options to the board of trustees
Plan A has the majority of votes.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given this, the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities.
There is a total of 3 + 3 +1 = 7 votesthus we can say the total number of members who voted is 7.
For the majority, more than 50% of votes are required. In this case, 50% of 7 = 3.5Therefore, 4 votes are required for the majority.
Here, no plan received 4 Ist choice votes.Therefore, there is no plan that receives a majority of votes.
In the instant run-off method, the candidate with the lowest 1st choice votes is eliminated and his votes are transferred to the candidate of the next choice. This process continues till a majority winner is found. In the initial table:1st choice votes to A=3
1 choice votes to B=3 1st choice votes to C=1
So, C is to be eliminated and his 1 vote is to be transferred to A (as A is the next choice after C in column 3 of the table)
First choice vote to A = 3 + 1 = 4
First choice vote to B = 3
Since A gets the majority of votes A is the winner
Thus, Plan A has the majority of votes.
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Complete question:
What is the correct solution set for the following graph?
{ } or empty set
{point in Quadrant II}
{point in Quadrant IV}
{infinite set of points on the line}
The correct solution set for the given graph include the following: D. {infinite set of points on the line}.
What is a quadrant?In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.
This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:
Quadrant IQuadrant IIQuadrant IIIQuadrant IVGenerally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.
In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].
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Answer and explain please
The coordinates of the triangle before and after dilation is
preimage image
R (6, 9) R' (2, 3)
S (3, -9) S' (1, -3)
T (-6, -3) T' (-2, -1)
The rule that best describes the transformation is
(x, y) → (1/3 x, 1/3 y)How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
preimage image
R (6, 9) → (1/3 * 6, 1/3 * 9) → R' (2, 3)
S (3, -9) → (1/3 * 3, 1/3 * -9) → S' (1, -3)
T (-6, -3) → (1/3 * -6, 1/3 * -3) → T' (-2, -1)
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factor: x^2 -x -2
plssss
Answer:
(x+1)(x-2)
Step-by-step explanation:
[tex](x+1)(x-2)=x^{2} -x-2[/tex]
Hope this helps
Quick Help please
I don’t understand please answer all four.
Answer:
To find f(-3), substitute -3 for x in the equation for f(x):
f(-3) = 2(-3) + 5 = -6 + 5 = -1
Answer:
f(-3) = -1
To find g(x) - h(x), first substitute x into both g(x) and h(x) and then subtract h(x) from g(x):
g(x) - h(x) = -3x^2 + 2x - 6 - (-4 - x) = -3x^2 + 3x - 2
Answer:
g(x) - h(x) = -3x^2 + 3x - 2
To solve for x when f(x) = h(x), first substitute x into both f(x) and h(x), and then solve for x:
2x + 5 = -4 - x
3x = -9
x = -3
Answer:
x = -3
To determine which of the functions are linear, we need to look at the degree of the polynomials in each function. Linear functions have a degree of 1, while non-linear functions have a degree greater than 1.
f(x) = 2x + 5 is linear because it has a degree of 1
g(x) = -3x^2 + 2x - 6 is non-linear because it has a degree of 2
h(x) = -4 - x is linear because it has a degree of 1
Answer:
f(x) and h(x) are linear, while g(x) is non-linear.
