The length of G’J’ is 3.5 units
Hence, the correct option is 3.5 units.
What is dilation?
In mathematics, dilation is a geometric transformation that changes the size of an object, but not its shape. Dilation involves stretching or shrinking an object by a certain scale factor while maintaining its proportions.
To find the length of G’J’, we first need to find the coordinates of G’, I’, and J’, which are the images of G, I, and J after dilation with a scale factor of 1/2.
The coordinates of G’ can be found by multiplying the x-coordinate and y-coordinate of G by 1/2:
G'(-41/2, 21/2) = (-2, 1)
Similarly, the coordinates of I' and J' can be found by multiplying the x-coordinate and y-coordinate of I and J by 1/2:
I'(61/2, 31/2) = (3, 1.5)
J'(31/2, 21/2) = (1.5, 1)
Now we can find the length of G’J’ by using the distance formula between G’ and J’:
d(G’J’) = √[(x2 - x1)² + (y2 - y1)²]
= √[(1.5 - (-2))² + (1 - 1)²]
= √[3.5²]
= √12.25
= 3.5
Therefore, the length of G’J’ is 3.5 units
Hence, the correct option is 3.5 units.
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GIVING BRAINLIEST!!!
Show that(Factor it) 4x^4-12x^3+22x^2-24x+26
=(x-1)^2[(2x-1)^2+9]
Answer:
See belowStep-by-step explanation:
Given equation:
4x⁴ - 12x³ + 22x² - 24x + 26 = (x-1)²[(2x-1)² + 9]Expand the right side and compare with left side:
(x - 1)²[(2x - 1)² + 9] = (x² - 2x + 1)(4x² - 4x + 1 + 9) = (x² - 2x + 1)(4x² - 4x + 10) = x²(4x² - 4x + 10) - 2x(4x² - 4x + 10) + (4x² - 4x + 10) = 4x⁴ - 4x³ + 10x² - 8x³ + 8x² - 20x + 4x² - 4x + 10 = 4x⁴ - 12x³ + 22x² - 24x + 10As we see LHS is different from RHS and the difference is 26 ≠ 10, all the other terms are equal
What is the slope no games please i will report!
at top cruising speed, a mako shark can swim 4 kilometers in 1/10. a blue whale can swim 5 kilometers in 1/4 hour. which animal swims faster at top cruising speed? how much faster?
Answer:Blue whale
Step-by-step explanation:
The blue whale goes an extra kilometer faster
The Mako shark faster at top cruising speed and by 20km/h.
Given that,
The mamo shark should swim 4 km in one-fourth.While on the other hand, Blue whales should swim 5 km in one-fourth hour.Based on the above information, the calculation is as follows:
We know that
\(Speed = \frac{Distance}{Time}\)
For Mako shark,
\(= \frac{4}{\frac{1}{10} }\)
= 40 km/h
For Blue whales
\(= \frac{5}{\frac{1}{4} }\)
= 20 km/h
Based on the above calculations we can say that the Mako shark should be faster and by 20 km/h.
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Which equation accurately represents this statement? Select three options.
Negative 3 less than 4.9 times a number, x, is the same as 12.8.
Negative 3 minus 4.9 x = 12.8
4.9 x minus (negative 3) = 12.8
3 + 4.9 x = 12.8
(4.9 minus 3) x = 12.8
12.8 = 4.9 x + 3
The equations that represents the problem statement are equation (i), (ii) and (v)
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
In the given problem, we have a problem statement and we need to find an equation that represents the statement.
The equations that accurately represent the statement "Negative 3 less than 4.9 times a number, x, is the same as 12.8" are:
1. Negative 3 minus 4.9 x = 12.8
2. 4.9 x minus (negative 3) = 12.8
3. 12.8 = 4.9 x + 3
So, the correct options are:
- Negative 3 minus 4.9 x = 12.8
- 4.9 x minus (negative 3) = 12.8
- 12.8 = 4.9 x + 3
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The table represents a linear function.
X
y
-4
-16
17
-2
-6
0
4
2
14
4
24
What is the slope of the function?
O-10
456
O-5
O 10
Answer:
Step-by-step explanation:
0, 10
Julia and her children went into a movie theater and where
they sell drinks for $5.50 each and pretzels for $4 each. Julia
has $90 to spend and must buy at least 18 drinks and pretzels
altogether. If Julia decided to buy 5 drinks, determine the
maximum number of pretzels that she could buy. If there are
no possible solutions, submit an empty answer.
Answer:
15 pretzels
Step-by-step explanation:
5.50x 5=27.50
90-27.50=62.50
62/4=15.50 --- you can only buy a whole pretzel
hope it helps....
please mark brainliest...
thx
College Readiness M... Overview Plans Resources Follow-up and reports Partici Equation 1: f(x) = x2 + 2x - 3 Equation 2: f(x) = -x2 + 2x + 3 Equation 4: f(x) = -x2 + 2x - 3 Equation 3: f(x) = x2 + 2x + 3 Using the above set of equations, answer the following question: What is different between equations 1 and 3? Your answer: The graph of equation 1 is narrower than the graph of equation 3. The "a" value is greater in equation 3 than in equation 1. The graph of equation 3 is 6 units above the graph of equation 1 as the y-intercepts are 6 units apart. The y-intercept of equation 1 is at (0,3); the y-intercept of equation 3 is at (0, -3). The "c" value is +3 in equation 1 and -3 in equation 3 The graph of equation 3 is 6 units above the graph of equation 1 as the y-intercepts are 6 units apart. The y-intercept of equation 1 is at (0,-3); the y-intercept of equation 3 is at (0,3). The "C" value is -3 in equation 1 and +3 in equation 3. The graph of equation 3 is concave up, the graph of equation 4 is concave down. Equation 3 has a y-intercept at -3 while equation 4 has a y-intercept at 3. The "a" value is positive in equation 3 and negative in equation 4. The "c" value is -3 in equation 3 and +3 in equation 4.
Answer:
so a sset of oervie 74=4948
Step-by-step explanation:
79:07
please help.. honestly, i just need part a answered!
A plane can fly 640 miles in the same time as it takes a car to go 240 miles. If the car travels 100 mph slower than the plane, find the speed (in mph) of the plane.
Answer:
Let s be the speed of the plane. Then s - 100 is the speed of the car.
640/s = 240/(s - 100)
640(s - 100) = 240s
8(s - 100) = 3s
8s - 800 = 3s
5s = 800, so s = 160 mph
The speed of the plane is 160 mph, and the speed of the car is 60 mph.
Solve for x.
5x - 4 = -3x+ 12
X = 2
X=6
X=-4
Answer:
x = 2
Step-by-step explanation:
Given
5x - 4 = - 3x + 12 ( add 3x to both sides )
8x - 4 = 12 ( add 4 to both sides )
8x = 16 ( divide both sides by 8 )
x = 2
State the most specific name for each figure
PLS HELP
1.) parallelogram
2.) trapezoid
3.) kite
4.) parallelogram
What are the qualities of a parallelogram?The parallelogram is a type of quadrilateral that has the following unique properties such as:
The opposite sides are parallel and equal.The opposite angles are equal.The consecutive or adjacent angles are supplementary.If any one of the angles is a right angle, then all the other angles will be at right angle.The two diagonals bisect each other.The kite is also a type of quadrilateral that has two pairs of adjacent equal sides with a pair of opposite angles that are equal.
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Need help here! ( Thank You )!
Answer: 1st box
Step-by-step explanation:
It’s at its safest atm
Leeza is making labels in the shape of parallelograms each label has an area of 18 square centimeters and a base of 6 centimeters. What is the height of each labe
Answer:
3cm
Step-by-step explanation:
A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area of a parallelogram = base x height
18cm² = 6cm x height
height = 18cm² / 6cm = 3cm
Frank wants to find the area enclosed by the figure at the right the figure on each side has semicircles of a 40 meter by 40 meter square. Find the area by the figure use 3. 14 for pi
The area enclosed by the figure at the right is 2856 square meters.
To find the area enclosed by the figure at the right, we first need to find the area of the square and the two semicircles on each side. The square has sides of 40 meters, so its area is 40 x 40 = 1600 square meters. Each semicircle has a radius of 20 meters (half the side length of the square), so its area is 1/2 x pi x r^2 = 1/2 x 3.14 x 20^2 = 628 square meters. Since there are two semicircles on each side, the total area of all four semicircles is 2 x 628 = 1256 square meters.
To find the total area enclosed by the figure, we add the area of the square and the area of the four semicircles:
1600 + 1256 = 2856 square meters
Therefore, the area enclosed by the figure at the right is 2856 square meters.
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Which equations are in standard form? Check all that apply
□ y = 2x+5
2x + 3y = -6
-4x + 3y = 12
Dy=2x-9
1x +3=6
□ x-y=5
Practice writing and graphing linear equations in standard
form.
5x + 3y = //
Intro
✔Done
The equations that are in standard forms are;
2x + 3y = -6
-4x + 3y = 12
Options B and C
How to determine the formsAn equation is simply defined in standard forms as;
Ax + By = C
Such that the parameters are expressed as;
A, B, and C are all constants and x and y are factors.
The condition is set out so that the constant term is on one side and the variable terms (x and y) are on the cleared out.
The coefficients A, B, and C are integers
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what is ur favorite character from boondocks mine is Riley freeman and also Huey freeman
Answer:lol
Step-by-step explanation:
Determine the solution to the equation. 8+4x=2x+8+2x A Infinite B One Solution C No Solution
After solving the given equations the answer is an Infinite solution. Hence, option A is correct
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
8 + 4x = 2x + 8 + 2x
Firstly, let's write the given equation in a simplified manner,
8 + 4x = 8 + 4x
As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.
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if bobby was born in 05 how old would he be
Answer:
the answer is 15
Step-by-step explanation:
find the value of y.
Answer:
B.) 40°
Step-by-step explanation:
because the sum of all the interior angles should be 180°, so 50°+90°+y=180°
y must equal 40°
h 10 yd.
L 14 yd.
W 3 yd.
Volume=
Answer:
10yd x 14 yd x 3yd = 420yd ^3
Step-by-step explanation:
When calculating for the volume you multiply all three numbers. That’s why when you write your answer you cube it.
I don’t know the answer helppp
Answer:
(1, -2)
Step-by-step explanation:
equate the two answers (make them equal to each other). Then solve.
7x + 11 = -3x + 1
7x + 3x = 1 - 11
10x = -10
x = 1
Plug "x" in to one of the equations to find "y" (I'm using equation 2)
y = -3(1) + 1
y = -3 + 1
y = -2
final answer: (1, -2)
The number of calories burned y after x minutes of kayaking is represented by the linear function y=4.5x. The graph shows the calories burned by hiking.
Answer:
22.5 more calories are burned
Hiking:
y=255
kayak
y=202.5
Two angels of a quadrilateral measures 260 and 30. The other two angels are in a ratio of 3:4. What are the measures of those two angels?
Given,Two angles of a quadrilateral measures 260 and 30.The other two angles are in a ratio of 3:4.
Let the measures of other two angles be 3x and 4x (in degrees).Since the sum of all angles in a quadrilateral is 360°, we can write the equation as follows;
Sum of all the angles of the quadrilateral = 260 + 30 + 3x + 4x =360
= 290 + 7x = 360
= 70x = 10°
= x = 7°
Now, measure of other two angles = 3x and 4x = 3(10°) and 4(10°)= 30° and 40°
Hence, the measures of those two angles are 30° and 40°.
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Find the area of this trapezoid. Be sure to include the correct unit in your answer.
i’ll make you brainliest
Answer:
117yd^2
Step-by-step explanation:
First find area of rectangle = length times width = 63(7*9)
Then find area of triangle = 1/2 length times width = 54(1/2*12*9)
The 12 is from 19 minus 7
solve 3^x = 81
Please answer, not a lot of time left.
Answer: x = 4.
Step-by-step explanation:
Taking the logarithm of both sides with base 3, we get:
x = log3(81)
x = log3(3^4) [Since 81 is equal to 3 raised to 4th power]
x = 4
Therefore, the solution is x = 4.
Answer:
Step-by-step explanatiON
X=81/3
X=4
What is the next step to inscribe a regular hexagon in Circle O below?
Answer:
draw diameter of the circle
The option second “with compass point at A, construct an arc of length OA intersecting the circle” is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
To construct a regular hexagon in Circle O first mark point A then, with compass point at A, construct an arc of length OA intersecting the circle.
Thus, the option second “with compass point at A, construct an arc of length OA intersecting the circle” is correct.
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Show your work for this please.
Answer:
that is the first one
I dunno if am correct.
find the area of the region bounded by the given curves. y = 6x2 ln(x), y = 24 ln(x)
The area of the region bounded by the given curves. y = 6x2 ln(x), y = 24 ln(x) is 2.85 sq.units.
In this question we need to find the area of the region bounded by the given curves. y = 6x^2 ln(x), y = 24 ln(x)
Equating both the equations of the curve,
6x^2 ln(x) = 24 ln(x)
24 ln(x) - 6x^2 ln(x) = 0
x = 1, 2
This means, the curves intersect at x = 1 and x = 2.
So, the required area would be,
A = ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx
First we find the indefinite integral ∫[24 ln(x) - 6x^2 ln(x)] dx
= -6 ∫[-4 ln(x) + x^2 ln(x)] dx
= -6 ∫ln(x) (x^2 - 4) dx
= -6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x
So, ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx
= [-6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x] _(x = 1 to x = 2)
= 32 ln(2) - 58/3
= 22.18 - 19.33
= 2.85 sq.units.
Therefore, the area of the region is 2.85 sq.units.
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Find the solutions to the following equation. Answers as ordered pairsx^2 + 6x + 5 = 0
x² + 6x + 5 = 0
To find the solution, we can use the quadratic formula.
\(\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-6\pm\sqrt[]{6^2-4(1)(5)}}{2(1)} \\ x_{1,2}=\frac{-6\pm\sqrt[]{36^{}-20}}{2} \\ x_{1,2}=\frac{-6\pm4}{2} \\ x_1=\frac{-6+4}{2}=-1 \\ x_2=\frac{-6-4}{2}=-5 \end{gathered}\)The solutions are (-1, 0) and (-5, 0)
public class BinarySearch \{ public static void main(Stringll args) f int [1]yl ist ={1,2,3,7,10,12,20}; int result = binarysearch ( inylist, 20); if (result =−1 ) System, out, println("Not found:"); else System.out.println("The index of the input key is " + result+ ". "): y public static int binarysearch(int]l List, int key) \{ int low =0; int high = iist. length −1 while (high >= low) \& int mid =( low + high )/2; if (key < List [mid] high = mid −1; else if (key =1 ist [ mid ] ) return inid; else low = mid +1; return −1; // Not found \} l TASK 4: Binary Search in descending order We have learned and practiced the implementation of the binary search approach that works on an array in ascending order. Now let's think about how to modify the above code to make it work on an array in descending order. Name your new binary search method as "binarysearch2". Implement your own code in Eclipse, and ensure it runs without errors. Submit your source code file (.java file) and your console output screenshot. Hint: In the ascending order case, our logic is as follows: int mid =( low + high )/2 if ( key < list [mid] ) else if (key = ist [mid]) return mid; In the descending order case; what should our logic be like? (Swap two lines in the above code.)
The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.
The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.
To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.
The modified code for binary search in descending order would look like this:
public static int binarysearch2(int[] list, int key) {
int low = 0;
int high = list.length - 1;
while (high >= low) {
int mid = (low + high) / 2;
if (key > list[mid])
high = mid - 1;
else if (key < list[mid])
low = mid + 1;
else
return mid;
}
return -1; // Not found
}
By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.
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