The options that are true as a result of doubling the rectangle dimensions are;
p → q represents the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
What are conditional statements?We are told that;
Doubling the dimensions of a rectangle increases the area by a factor of 4.
Now, p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.
Thus, using conditional statements notation, we can say that;
p → q represents the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
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55. a rubber ball is dropped from a height of 60 feet. if it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.
The required total distance the ball travels, approximately, is 180 feet.
Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).
The first fall distance (a) is 60 feet.
The first rebound distance (r) is (2/3) * 60 feet.
The total distance covered during the first fall and rebound cycle is:
60 + (2/3) * 60 = 60 + 40 = 100 feet.
Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:
Second fall distance = r * a
= (2/3) * 60
= 40 feet.
Second rebound distance = r*(2/3) * 60
= (2/3) * 40
= 80/3 feet.
The total distance covered during the second fall and rebound cycle is:
40 + (80/3) ≈ 66.67 feet.
The pattern will continue for the subsequent cycles.
To represent this as an infinite geometric series, we can write:
Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]
Where:
a = 60 feet (height of the first fall)
r = 2/3 (rebound factor)
Using the formula for the sum of an infinite geometric series:
Total distance = a / (1 - r)
Total distance = 60 / (1 - 2/3)
Total distance = 60 / (1/3)
Total distance = 60 * 3
Total distance = 180 feet.
Therefore, the total distance the ball travels, approximately, is 180 feet.
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MATHHH!!! area stuff
Answer:
112
Step-by-step explanation:
▪︎ Volume of pyramid = (1/3) * base area * height
▪︎ Base area = 8 * 7
▪︎ Height = 6
▪︎ Volume = 8 * 7 * 6 / 3 = 112
Graph the solution to this system of inequalities in the coordinate plane.
For the system of equations, we need to plot a straight line passing through the intercepts.
Inequality GraphsInequalities are equations separated by an equal sign. Given the following system of inequality
3y >2x + 12
2x + y ≤ -5
For the system of equations, we need to plot a straight line passing through the intercepts.
For the inequality 3y >2x + 12, the upper part of the graph will be shaded and the line dashed.
For the inequality 3y >2x + 12, the lower part of the graph will be shaded and the line solid.
The graph of the system of equations is graphed below
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_____cups flour is equivalent to 1 pound.
i dont now what it is
Answer:
Its option C
As,
x+8=3x
8= 3x-x
8=2x
8/2=x
4=x
#x=4
Select the correct statement about the function represented by the table
The correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values
The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
Given a table on which there are two column in which one column represents x values while other column represent the y values
We have to find whether the relationship between x value and y value is linear or exponential
From given table let,
y₁ = 34; y₂ = 41; y₃ = 48; y₄ = 55
x₁ = 1; x₂ = 2; x₃ = 3; x₄ = 4
If the relationship between the x value and y value is linear then the difference between two consecutive value of x value and y value would be equal
So y₂-y₁ = y₄-y₃ and x₂-x₁ = x₄-x₃
Putting the value we get difference of y value 7 and x value as 1 since it is same we can say that the relation ship between x value and y value is linear
Hence the correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values
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HELP PLS I'LL MARK U BRAINLIST
Answer:
this answer is of 2nd question
Step-by-step explanation:
since it is an isosceles triangle
3y-1=y+11
3y-1=y+113y-y=11+1
2y=12
y=6
now putting the value of y in 3y-1,y+11,4y-9
we get,
3y-1=3*6-1=17
y+11=6+11=17
4y-9=4*6-9=15
the answer is 17,17,15I'm confused I got an answer but got it wrong help please.
Answer:
[tex]y = \frac{2}{3}x -6[/tex]
Step-by-step explanation:
I'm just gonna assume you want the equation of the line
Standard slope-intercept form is [tex]y=mx+b[/tex] with [tex]m[/tex] being the slope [tex]\frac{rise}{run}[/tex] (aka [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]) and [tex]b[/tex] being the y-intercept (the point where the line crosses the y-axis)
First we will find the slope using the 2 points on the line.
[tex]\frac{-2 - (-4)}{6-3} = \frac{2}{3}[/tex]
This means our slope ([tex]m[/tex]) is [tex]\frac{2}{3}[/tex].
Next we can find our y-intercept. The line crosses the y-axis at [tex](0, -6)[/tex] meaning the y-intercept ([tex]b[/tex]) is -6.
Finally we can plug in our values and find the equation of the line.
[tex]y = \frac{2}{3}x -6[/tex]
That might be the answer (i don't know the question)
- Kan Academy Advance
Review the graph of 2x – 7 – 3 ≥ y.
On a coordinate plane, a curve goes through (0, negative 3) and increases up through (8.5, 0) and (10, 5). Everything below the line is shaded and is labeled 2 Superscript x minus 7 Baseline minus 3 greater-than-or-equal-to y.
What is the least integer value that satisfies the inequality 2x – 7 ≥ 3?
7
8
9
10
The least integer value that satisfies the inequality [tex]2^{x-7} - 3[/tex] ≥ y is 7.
What is Exponential function?
Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round.
Here, In the given function
Least possible value of 2ˣ⁻⁷ is 1
2ˣ⁻⁷ = 2⁰
On comparing both sides, we get
x-7 = 0
x = 7
Thus, The least integer value that satisfies the inequality 2ˣ⁻⁷-3≥ y is 7.
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Answer:
7
Step-by-step explanation:
edg 2022
Can somebody please help answer this word problem using grass method? And showing how u get the answer thanks!!!
WILL MARK BRAINLIEST FOR WHOEVER ANSWERS THIS !!! :DD
Answer:
0.25m or 1/4m
Step-by-step explanation:
Given Height of Dorsal Fin = 1/6 of Length of whale Sculpture,
and given length of whale sculpture = 1.5m or [tex]1\frac{1}{2} m\\[/tex]
Height of Dorsal fin on scuplture = [tex](\frac{1}{6})(1\frac{1}{2} )\\[/tex]
= [tex](\frac{1}{6} )(\frac{3}{2}) \\= \frac{3}{12} \\= \frac{1}{4}m or 0.25m[/tex]
Point RR lies on the directed line segment from L\left(-8,-10\right)L(−8,−10) to M\left(4,-2\right)M(4,−2) and partitions the segment in the ratio 33 to 55. What are the coordinates of point RR?
The coordinates of point R of the given line segment are (-3.5, -7)
How to partition a line segment?
We are given the coordinates;
L (-8,-10) to M (4,-2)
We are told that they are partitioned in the ratio 3 to 5.
Thus;
The coordinates of R divide directed line segment from L (-8,-10) to M (4,-2) in ratio 3:5will be :
x = [3(4) + 5(-8)]/(3 + 5)
x = -3.5
y = [3(-2) + 5(-10)]/(3 + 5)
y = -7
Thus, the coordinates of point R are (-3.5, -7)
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solution for -2 1/3 divided by 4 2/3
Answer:
-0.5
Step-by-step explanation:
Omg I can't work this one out, help!!
You can also check whether I did wrong on the other ones but help me on the last question
Answer:
a) 26 tickets
b) £5
c) chips, pastie and a soft drink
Step-by-step explanation:
Given:
Price of one ticket = £7.50Total available to spend = £200Part (a)
Greatest number of tickets = total available to spend ÷ cost of one ticket
= 200 ÷ 7.5
= 26.66666...
= 26 tickets
(We can't round up, as 27 tickets would cost £202.50)
Part (b)
Money left = Total available spend - cost of 26 tickets
= 200 - (26 × 7.50)
= 200 - 195
= £5
Part (c)
Cost of 3 items = £10 - change
= £10 - £4.70
= £5.30
One of the items can't be a burger, as £5.30 - £3.50 = £1.80
and £1.80 is not enough to buy 2 items.
If he buys chips, he has: £5.30 - £2.40 = £2.90 left to spend on the other 2 items.
Pastie + Soft Drink = £1.60 + £1.30 = £2.90
So he can buy: chips, pastie and a soft drink
i need some help doing this
Translate the shape A three squares right and one square up
What are the coordinates of the vertices of the image?
To better give a visual, I drew it out instead.
The attachment is the solution.
Answer:
(4, 5)
(4, 2)
(6, 2)
Step-by-step explanation:
add 3 in "x" and 1 in "y"
(1, 4) ⇒ (1+3, 4+1) = (4, 5)
(1 , 1) ⇒ (1+3 , 1+1) = (4, 2)
(3, 1) ⇒ (3+3, 1+1) = (6, 2 )
Hope this helps
what does permimeter mean
Total distance around a shape
1 pound is equivalent to ____ grams.
Answer:
453.592 grams or 454 grams if you round up
Answer:
1 pound = 454 grams
Step-by-step explanation:
Multiply 454 into the value.
The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?
O 3+3√2 ft
O 3+3√√3 ft
O 6+3-√√2 ft
O 6+3√√3 ft
Check the picture below.
The perimeter of the triangle with the given dimension of leg is 6+3√2.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Using Pythagoras theorem
c² = a² + b²
where c is the hypotenuse.
Here, c² = 3² + 3²
c = 3√2
So, the perimeter of triangle is
= 3 + 3 + 3√2
= 6 + 3√2
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George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.
Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.
A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.
How many feet of fencing will George need for the dog run?
Answer:
width is 30-22 = 8 feet
George would need 76 feet of fencing for the dog run
Step-by-step explanation:
30 x (30-x) = 240
30-x = 8
-x = -22
x = 22
Therefore width is 30-22 = 8 feet
8+8+30+30 = 76
Thus, George would need 76 feet of fencing for the dog run
is the statement 15=|-15| true
Answer:
Yes! |-15| = 15
Step-by-step explanation:
Many people think of absolute value (the two bars symbol around the -15) as ALWAYS POSITIVE.
You can also think of absolute value as a distance. If you move 15 units, it doesn't matter in what direction you go. 15 units travelled is 15 units.
Lastly, absolute value has a V-shaped graph, that is because its always positive.
A group of middle and high school students are surveyed as to their breakfast preferences. The results are shown below.
Eat Breakfast
Skip Breakfast
Middle Schooler
40
14
High Schooler
12
24
Total
52
38
What is the probability a randomly selected student eats breakfast?
What is the probability a randomly selected student is a middle schooler?
What is the probability a randomly selected student is either a high schooler OR eats breakfast?
What is the probability a randomly selected student is a high schooler AND eats breakfast?
What is the probability a randomly selected student is a high schooler, given that they eat breakfast?
What is the probability a randomly selected student eats breakfast given the student is a high schooler?
Total
54
36
90
The probability a randomly selected student eats breakfast is 0.58.
The probability a randomly selected student is a middle schooler is 0.60.
The probability a randomly selected student is either a high schooler OR eats breakfast is 0.98.
The probability a randomly selected student is a high schooler AND eats breakfast is 0.23.
The probability a randomly selected student is a high schooler, given that they eat breakfast is 0.33.
The probability a randomly selected student eats breakfast given the student is a high schooler is 0.23.
What are the probabilities?
The probability a randomly selected student eats breakfast = number of students that eat breakfast / total number of students
52 / (52 + 38) = 0.58.
The probability a randomly selected student is a middle schooler = total number of middle schoolers / total number of students = (40 + 14) / 90 = 0.60.
The probability a randomly selected student is either a high schooler OR eats breakfast = (total number of high schoolers / total number of students) + (number of students that eat breakfast / total number of students) = 36 / 90 + 52 / 90 = 0.98.
The probability a randomly selected student is a high schooler AND eats breakfast = (total number of high schoolers / total number of students) x (number of students that eat breakfast / total number of students) = 36 / 90 x 52 / 90 = 0.23.
The probability a randomly selected student is a high schooler, given that they eat breakfast = high schooler that eats breakfast / total number of students that eat breakfast
12 / 52 = 0.33.
The probability a randomly selected student eats breakfast given the student is a high schooler = high schooler that eats breakfast / total number of high schoolers = 12 / 36 = 0.23.
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Bob's living room floor is a rectangle that measures 9 feet by 12 feet. what is the diagonal distance, in feet, across the floor.
Answer:
15
Step-by-step explanation:
For this question you would need to do a squared + b squared so 9x9 is 91 + 12x12 which is 144. you add the two up then find the square root of that which should make your answer 15
Find the equation to the line below.
Answer:
y=-1/1x
Step-by-step explanation:
First, let's take the slope of a line equation:
y=mx+b
Now, all we have to do is find the slope(m) and the y-intercept(b).
The line intercepts the y axis at 0, so b=0.
Next, find the slope.
The equation to FIND slope is rise/run, so we can solve that:
1/1=1, but since the line goes down, it's negative.
The slope is 1, so m=1.
Now, put that into m.
y=-1x+0, but we don't need 0, so the answer is y=-1x.
Katherine is landscaping her home with juniper trees and pansies. She wants to arrange 15 pansies around each of 8 trees. Each tree costs $20.75 and a six-pack of pansies costs $2.50. Explain how to write an expression to find Katherine’s final cost
The expression that signifies Katherine’s final cost F= P + T= $466
Calculation of final costThe number of pansies to be arranged around each tree = 15 pansies
The cost of pansies(P) = 15 × 8 × 2.50 = $300
The number of juniper trees available = 8
The cost of the trees available(T) = 8 × 20.75= $166
Therefore Katherine's final cost(F)= $300 + $166 = $466
The expression to find Katherine’s final cost = F= P + T
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The complex numbers $z_1$ and $z_2$ are such that $|z_1| = 5,$ $|z_2| = 13,$ and
\[13z_1 - 5z_2 = 27 - 99i.\]find $z_1 z_2.$
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
How to determine two complex numbers based on their norms and a given operation
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
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Simplify (8z - 10) ÷ (-2) + 5(z - 1).
OZ
OZ-1
Oz-2
Answer:
A) z
Step-by-step explanation:
(8z - 10) ÷ (-2) + 5(z - 1)
1. Rewrite:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+5(z-1)$}[/tex]
2. Distribute 5
[tex]\large \textsf{$5(z-1)$}\\\\\large \textsf{$5(z)+5(-1)$}\\\\\large \textsf{$5z-5$}[/tex]
Now we have:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}[/tex]
3. Reduce the fraction:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}\\\\\large \textsf{$-4x+5+5z-5$}[/tex]
4. Combine like terms:
[tex]\large \textsf{$-4x+5+5z-5$}=\large \textsf{z}[/tex]
Final answer: z
Hope this helps!
Jamie is playing a card game. Jamie's score changes by -12 points for 8 turns in a row.
What is the total change in Jamie's score?
Answer:-96
Step-by-step explanation:The answer is -96
What is the exact value of x
Answer:
The value of x is 30 degrees.
Step-by-step explanation:
We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)
[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]
A cylindrical vase is 10 centimeters in height. When
filled to the very top, it holds 125 cubic centimeters of
water. What is the radius of the vase, rounded to the
nearest tenth? Explain or show your reasoning.
The measure of the radius of the cylinder to the nearest tenth is 1.7cm
Surface area of a cylinderThe formula for calculating the surface area of a cylinder is expressed as:
S = 2πr(r+h)
Given the following
S=. 125cm²
h = 10cm
Substitute
125 = 2πr(r+10)
Expand
125 = 2(3.14)r² + 20(3.14)r
6.28r² + 62.8r - 125 = 0
Factorize
On factorizing, the measure of the radius of the cylinder will be 1.7cm
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The function g(x) = -2x + 3. Compare the slopes and y-intercepts. A. Both the slopes and the y-intercepts are different. B. Both the slopes and the y-intercepts are the same. C. The slopes are the same but the y-intercepts are different. D. The slopes are different but the y-intercepts are the same.
Answer:
both the slopes and the y intercepts are the same for both of these functions because if you look at the graph you will notice that the y intercept is positive 3 just the function and to get its slope just use the formula y2-y1/x2-x1 to get the slope of also a -2 so answer is b