The statement that "if you took a true "if-then' statement and reversed the clauses, the new statement would also be true" is False.
Why is this false ?By reversing the clauses within an accurate "if-then", one will manifest a new statement known as the "converse" of the initial formula. Though, it is not inevidably true.
For instance, if the original expression was "If it rains, then the ground gets wet", its converse is "If the ground gets wet, then it rains". Unfortunately, that specific converse has the potential to be incorrect since there are several other methodologies from which the land can gain moisture beside rain (e.g. sprinkler system, someone unintentionally pouring water, etc.).
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Triangle ABC is being enlarged using a scale factor of and centre (2,9) to
give triangle A'B'C'.
a) What are the coordinates of the vertex C'?
b) What is the length of the side A’B’
a) The coordinates of the vertex C' are C'(x, y) = (5, 5).
b) The length of the side A'B' is equal to 4.
In this problem we find the case of a right triangle, whose image must be found by a kind of rigid transformation known as dilation. The dilation formula for a vertex is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
k - Dilation factor
O(x, y) - Center of dilation
P(x, y) - Original vertex
P'(x, y) - Resulting vertex
And the dilation formula for a formula is:
L' = k · L
Where:
L - Original length.
L' - Resulting length.
Please notice that side lengths can be found by Pythagorean theorem.
we know that O(x, y) = (2, 9), k = 1 / 2, A(x, y) = (6, 7), B(x, y) = (10, 7) and C(x, y) = (6, 1), then the resulting vertices and sides are:
C'(x, y) = (2, 9) + (1 / 2) · [(6, 1) - (0, 9)]
C'(x, y) = (2, 9) + (1 / 2) · (6, - 8)
C'(x, y) = (2, 9) + (3, - 4)
C'(x, y) = (5, 5)
And the length of the side A'B' is:
AB = 8
A'B' = (1 / 2) · AB
A'B' = 4
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
Step-by-step explanation:
C (Wait for another defendant, check with him and write this answer)
Kyle is buying gifts for Megan's birthday and needs to stay in budget
Cake = half his money + 36.50
Decorations = half of what he had left + 36.50
Sweets = half of what he had left + 18.25
Now he is out of money, what did he start with?
Answer: Let's start by using algebra to represent the problem.
Let X be the amount of money that Kyle started with.
Then we can create the following equations:
Cake = 0.5X + 36.50Decorations = 0.5(X - Cake) + 36.50Sweets = 0.5(X - Cake - Decorations) + 18.25
And we know that he's out of money, so:
Cake + Decorations + Sweets = XWe can use substitution to solve for X.
Substitute the first equation into the second equation to get:
Decorations = 0.5(X - (0.5X + 36.50)) + 36.50Decorations = 0.25X + 9.25
Substitute the first two equations into the third equation to get:
Sweets = 0.5(X - (0.5X + 36.50) - (0.25X + 9.25)) + 18.25Sweets = 0.25X + 4.75
Substitute all three equations into the fourth equation to get:
(0.5X + 36.50) + (0.25X + 9.25) + (0.25X + 4.75) = X
Simplify and solve for X:
1X + 50.50 = X50.50 = 0.5XX = 101
Therefore, Kyle started with $101.
The cubic polynomial shown below has zeroes at x=-1and x= only and has a relative maximum at (3,8). Which of the following is its y-value when x=5?
The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.
Therefore the option C is correct.
What is polynomial?A polynomial expression is described as an algebraic expression with variables and coefficients.
If the zeroes of the polynomial are negative 4, 2, and 2.
Then the factors will be (x + 4), (x - 2), and (x - 2).
Then the cubic polynomial will be
→ (x + 4) (x - 2) (x - 2)→ (x + 4) (x² - 4x + 4)→ (x³ - 12x + 16)we can write the polynomial equation as:
y = C(x³ - 12x + 16)
Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.
y = 0.25 (x³ - 12x + 16)
y = 0.25 (6³ - 12 × 6 + 16)
y = 0.25 (216 - 72 + 16)
y = 0.25 (160)
y = 40
Note that there was no diagram provides, i solved a similar question
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5. Which box-and-whisker plot represents this set of data? (1 point)
90, 98, 75, 84, 89, 91, 70, 81, 93, 84, 100
I really need hel with this please
The resulting matrix after row 1 is multiplied by 2 is given as follows:
[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
The first row is given as follows:
7, -4 and 8.
Multiplying the first row by two, we have that:
7 x 2 = 14.-4 x 8 = -8.8 x 2 = 16.(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).
Hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]
(the second row was kept constant, while the first row was multiplied by 2).
Missing InformationThe matrix is:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
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PLSSS HELP ITS DUE TOMMROW I WILL GIVE U MORE POINTS WHEN I GET MORE PLSSS
Answer:
[tex]A_{\text{red}} = 1766.25 \text{ in}^2[/tex]
Step-by-step explanation:
We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:
[tex]r_1 = \dfrac{1}{4} \cdot 30 = 7.5\\[/tex]
[tex]r_2 = \dfrac{2}{4} \cdot 30 = 15\\[/tex]
[tex]r_3 = \dfrac{3}{4} \cdot 30 = 22.5\\[/tex]
[tex]r_4 = 30[/tex]
We can now find the area of each red band by subtracting:
the area of the circle within the white band just inward of the red band
-- from --
the area of the circle within the red band.
Finding the area of the outer red band:
[tex]A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})[/tex]
[tex]A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)[/tex]
↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])
[tex]A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)[/tex]
↓ using 3.14 for [tex]\pi[/tex]
[tex]A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)[/tex]
↓ evaluating the right side
[tex]A_{\text{outer red}} = 2826 - 1589.625[/tex]
[tex]A_{\text{outer red}} = 1236.375 \text{ in}^2[/tex]
Finding the area of the inner red band:
[tex]A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})[/tex]
[tex]A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)[/tex]
↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])
[tex]A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)[/tex]
↓ using 3.14 for π
[tex]A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)[/tex]
↓ evaluating the right side
[tex]A_{\text{inner red}} = 706.5 - 176.625[/tex]
[tex]A_{\text{inner red}} = 529.875 \text{ in}^2[/tex]
Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.
[tex]A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}[/tex]
[tex]A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2[/tex]
[tex]\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}[/tex]
!! will give brainlist !!
Use trigonometric ratios to find the value of each variable. Round answers to the nearest tenth.
Answer:
Set your calculator to degree mode.
2) tan(43°) = x/8.2
x = 8.2tan(43°) = 7.6
3) sin(29°) = 3.5/x
x sin(29°) = 3.5
x = 3.5/sin(29°) = 7.2
help pls i dont understand this
The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.
The cost in dollars of the admission ticket is $ 37.50.
How to find the cost of the tickets ?Let x be the cost, in dollars, of each admission ticket, including tax.
The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.
The total cost of 4 admission tickets and parking is given as $175.00, so we can write:
4x + $25.00 = $175.00
Simplifying the equation, we can solve for x:
4x = $175.00 - $25.00
4x = $150.00
x = $37.50
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37. When making biscuits, a baker
mixes flour and sugar in the ratio
4:1. If he uses 6kg of sugar when
making some biscuits, how much
flour should he use?
(a) 30kg
(b) 24kg
C 10kg
D 8kg
E 1.5kg
The baker should use 24kg amount of flour when making the biscuits. The correct answer is (b) 24kg.
To determine the amount of flour the baker should use when making biscuits, we can use the given ratio of flour to sugar, which is 4:1.
Since the ratio is 4:1, for every 4 parts of flour, there is 1 part of sugar. Therefore, the ratio of flour to sugar can be expressed as 4/1.
If the baker uses 6kg of sugar, we can set up a proportion to find the corresponding amount of flour:
4/1 = x/6
Cross-multiplying, we get:
4 * 6 = 1 * x
24 = x
Therefore, the baker should use 24kg of flour when making the biscuits.
In summary, the correct answer is (b) 24kg.
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A decorative tile is in the shape of a square. It is made up of a smaller square of side length 4 centimeters which is surrounded by a border of width b centimeters. Find an expression for the total area (in square centimeters) of the decorative tile in terms of . Simplify the result.
Area = 4b² + 16b + 16 square centimeters
How to solve the expressionThe side length of the larger square, L, is equal to the side length of the smaller square plus twice the width of the border:
L = 4 + 2b
Now, we want to find the total area of the decorative tile, which is the area of the larger square. The area of a square is given by the side length squared:
Area = L²
Substitute the expression for L from above:
Area = (4 + 2b)²
Now, we can expand this expression:
Area = (4 + 2b)(4 + 2b)
Area = 16 + 8b + 8b + 4b²
Area = 16 + 16b + 4b²
So, the total area of the decorative tile in terms of b is:
Area = 4b² + 16b + 16 square centimeters
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HELP ME PLEASE!
Whoever answers right gets brainliest!
Step-by-step explanation:
The 'x's ' ( the domain) are mapped into two values of 'y' (the range)
Range = 1,6
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C
What are algebraic expressions?Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.
Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;
BracketDivisionSubtractionMultiplicationParenthesesAdditionFrom the information given, we have that;
24 is the constant
Let the number be represented as n
Then, the expression is given as;
24 = 31.4(n) - 8.4
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mrs. gordon bought a stove which cost $850. no down payment was required. mrs. gordon has to pay $160 for the next six months. what is the average amount she pays in interest each month?
Answer:
the average amount Mrs. Gordon pays in interest each month, we need to determine the total interest paid over the six-month period and divide it by the number of months.
The total interest paid can be found by subtracting the cost of the stove from the total amount paid over six months:
Total interest paid = Total amount paid - Cost of the stove
The total amount paid over six months is calculated by adding the monthly payments:
Total amount paid = $160/month * 6 months
Let's perform the calculations:
Total amount paid = $160/month * 6 months = $960
Total interest paid = Total amount paid - Cost of the stove
= $960 - $850
= $110
Now, to find the average amount Mrs. Gordon pays in interest each month, we divide the total interest paid by the number of months:
The average amount paid in interest each month = Total interest paid / Number of months
= $110 / 6 months
≈ $18.33
Therefore, Mrs. Gordon pays an average of approximately $18.33 in interest each month.
write the equation of a circle with center (-4,3) and radius 9 ?
Step-by-step explanation:
Standard form of circle with center (h.k) and radius r :
( x-h)^2 + (y-k)^2 = r^2
FOr the data given:
(x + 4)^2 + ( y-3)^2 = 81 (81 is the radius, 9, squared)
Select all the correct answers.
If the measure of angle 0 is 2n/3, which statements are true?
Can someone help me with this please
Answer:
36 °
Step-by-step explanation:
The markings imply equal sides*
So both of the angles are 27° there
To find angle a we do 180 - (27+27) and obtain 126°
Then to find angle y, we do 180-angle a which is 180-126 and we get 54°
We now have reached the triangle where you're supposed to find x right?
So x is equal to 180 - both other angles, which is 180 - (90 and angle y) = 180- (90+54) = 180 - 144 = 36 which is your final answer
The point R(1,– 2) is translated 2 units down. What are the coordinates of the resulting point, R'?
The coordinates of the resulting point, R', are (1,-4).
What are the coordinates of the resulting point, R'?A translation is a type of transformation in geometry that moves a point or an object from one place to another without changing its size, shape, or orientation.
To translate a point, you need to specify the direction and distance of the movement.
Given that:
The point R(1,-2) is being translated 2 units down, which means that it will move vertically downwards by a distance of 2 units.
The x-coordinate will remain the same, as the movement is only in the y-direction.
So, to find the coordinates of the resulting point, R', we subtract 2 from the y-coordinate of the original point R:
R' = (1, -2 - 2)
R' = (1, -4)
Therefore, resulting coordinates of R' are (1,-4).
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Add: -8x8 + (-3x8 + 3)
Enter the correct answer.
Please solve
1.) 4(v + 1) = 16
Answer:
it's an easy one
Step-by-step explanation:
1. combine those -->4v+4=16
2. subtract the like terms--> 4v=16-4--> 4v=12
3. divide--> v=12/4-->3
4. Answer--> v=3
A tunnel is shaped in the form of a semi-ellipse. The width of the tunnel is 20 feet and the height of the tunnel is 12 feet. A train is 10 feet wide and centered in the tunnel. Determine whether a 10-foot high train would have clearance to pass through. If so, by how much? If not, by how much? (Nearest inch.)
The radius of a cylindrical water tank is 6 ft, and its height is 16 ft. Helpppppp I’m running out of time
What is the volume of the tank?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
6 ft
16 ft
0
ft
Answer:
V ≈ 1809 ft^3
Step-by-step explanation:
Given:
r (radius) = 6ft
h (height) = 16ft
π = 3,14
Find: V (volume) - ?
[tex]v = \pi {r }^{2} \times h[/tex]
[tex]v = 3.14 \times {6}^{2} \times 16 ≈1809 \: {ft}^{3} [/tex]
HELPPPPPPPPPP... please help i don't get this whatsoever and my teacher doesn't really help. i dont get none of it at all. please help asap !
Answer:
I can tell
Step-by-step explanation:
Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)
What is an equation of the line that passes through the point (5,-5)(5,−5) and is parallel to the line x+5y=20?
Answer:
[tex]y = -x/5 -4.[/tex]
Step-by-step explanation:
To simplify the line x + 5y = 20 into y = mx + b form:
x + 5y = 20.
5y = -x + 20.
y = -x/5 + 4.
The line parallel to the line y = -x/5 + 4 will have the same slope of -1/5.
We get the equation:
y = -x/5 + b.
To find b, we plug in the point (5, -5).
-5 = -5/5 + b.
-5 = -1 + b.
b = -4.
[tex]y = -x/5 -4.[/tex]
Solve the following equation by completing square 15x^2-2ax=a^2
Answer:
Step-by-step explanation:
Answer: x=a/3 x=a/5
Step-by-step explanation:
15x²-2ax = a² subtract a² from both sides
15x²- 2ax - a² = 0
You would solve this like you would any quadratic. Factor.
Start my multiplying the first and last coefficients
15(-a²) = -15a² =>find 2 numbers that multiply to this but add to middle
term (-2a)
-5a and +3a multiply to -15a² and adds to -2a
Substitute the middle term with the numbers we just found, keeping the x
15x²- 2ax - a² = 0
15x²- 5ax+3ax - a² = 0 > group the first 2 terms and last 2
(15x²- 5ax)(+3ax - a²)= 0 > this is not your factors, you need to take
GCF out of each grouping
5x(3x-a)+a(3x-a)=0 >if the parenthesis is same, you did good
now the parenthesis is your GCF and one of
your factors, whatever is left is your other
factor
(3x-a)(5x-a)=0 > set each factor = 0 and solve for x
(3x-a)=0 and (5x-a)=0
x=a/3 x=a/5
Choose the correct Set-builder form for
the following set written in Roster form:
{4, 5, 6, 7, 8}
The value of correct Set-builder form is,
⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }
We have to given that;
The set is,
⇒ {4, 5, 6, 7, 8}
Thus, We can write correct Set-builder form as,
⇒ {4, 5, 6, 7, 8}
⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }
So, The value of correct Set-builder form is,
⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }
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Simplify the polynomial expression. (x+7)^2
Answer:
x²+14x+49
Step-by-step explanation:
(a+b)²=a²+2ab+b²
(x+7)²=x²+2×7×x+7²=x²+14x+49
what is the slope of the line below?
Answer:
B. Y= 5x - 2
Step-by-step explanation:
The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.
Billy Bob wants to paint the outside wall of his circular pool. The circular
wall is 4 feet tall and has a radius of 15 feet. If paint cost $28 per gallon and
covers 225 square feet, how much will it cost to paint the wall. The paint is
only avaliable in gallon containers.
The amount it would cost to paint the wall, given the cost of paint and the area covered is $ 56 .
How to find the cost to paint ?The surface area of the circular wall would be :
A = 2 x π x r x h
The area is therefore:
= 2 x π x r x h
= 2 x 3. 14 x 15 x 4
= 376. 8 square feet
The number of gallons needed is therefore:
= 376. 8 / 225
= 1. 674
= 2 gallons
The cost of two gallons is:
= 2 x 28
= $ 56
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N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.
To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:
Time spent on videos = 10% of 40 hours = 4 hours
Time spent on homework = 15% of 40 hours = 6 hours
Time spent on games = 20% of 40 hours = 8 hours
Time spent on social media = 25% of 40 hours = 10 hours
Time spent on shopping online = 20% of 40 hours = 8 hours
Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.
The difference between these two amounts is:
6 hours - 8 hours = -2 hours
This means that Heracio spent 2 hours more on shopping online than on doing homework.
Step-by-step explanation:
