Answer:
The figure PEST is a rhombus
Step-by-step explanation:
* Lets talk about the difference between all these shapes
- At first to prove the shape is a parallelogram you must have one
of these conditions
# Each two opposite sides are parallel OR
# Each two opposite sides are equal in length OR
# Its two diagonals bisect each other
- After that to prove the parallelogram is:
* A rectangle you must have one of these conditions
# Two adjacent sides are perpendicular to each other OR
# Its two diagonals are equal in length
* A rhombus you must have one of these conditions
# Two adjacent sides are equal in length OR
# Its two diagonals perpendicular to each other OR
# Its diagonals bisect its vertices angles
* A square you must have two of these conditions
# Its diagonals are equal and perpendicular OR
# Two adjacent sides are equal and perpendicular
* Now lets solve the problem
∵ The vertices of the quadrilateral PEST are
P (-1 , -5) , E (8 , 2) , S (11 , 13) , T (2 , 6)
- Lets find the slope from each two points using this rule :
m = (y2 - y1)/(x2 - x1), where m is the slope and (x1 , y1) , (x2 , y2)
are two points on the line
- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)
∴ m of PE = (2 - -5)/(8 - -1) = 7/9
- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)
∴ m of ES = (13 - 2)/(11 - 8) = 11/3
- Let (x1 , y1) is (11 , 13) and (x2 , y2) is (2 , 6)
∴ m of ST = (6 - 13)/(2 - 11) = -7/-9 = 7/9
- Let (x1 , y1) is (2 , 6) and (x2 , y2) is (-1 , -5)
∴ m of TP = (-5 - 6)/(-1 - 2) = -11/-3 = 11/3
∵ m PE = m ST = 7/9
∴ PE // ST ⇒ opposite sides
∵ m ES = m TP = 11/3
∴ ES // TP ⇒ opposite sides
- Each two opposite sides are parallel
∴ PEST is a parallelogram
- Lets check if the parallelogram can be rectangle or rhombus or
square by one of the condition above
∵ If two line perpendicular , then the product of their slops = -1
- Lets check the slopes of two adjacent sides (PE an ES)
∵ m PE = 7/9
∵ m ES = 11/3
∵ m PE × m ES = 7/9 × 11/3 = 77/27 ≠ -1
∴ PE and ES are not perpendicular
∴ PEST not a rectangle or a square (the sides of the rectangle and
the square are perpendicular to each other)
- Now lets check the length of two adjacent side by using the rule
of distance between two points (x1 , y1) and (x2 , y2)
d = √[(x2 - x1)² + (y2 - y1)²]
- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)
∴ PE = √[(8 - -1)² + (2 - -5)²] = √[9² + 7²] = √[81 + 49] = √130 units
- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)
∴ ES = √[(11 - 8)² + (13 - 2)²] = √[3² + 11²] = √[9 + 121] = √130 units
∴ PE = ES ⇒ two adjacent sides in parallelogram
∴ The four sides are equal
* The figure PEST is a rhombus
#18 please help me thank you
Answer:
The solutions of the equation is 0 , π , 2π
Step-by-step explanation:
* Lets revise some identities in the trigonometry
- tan²x + 1 = sec²x
- tan²x = sec²x - 1
* Now lets solve the equation
∵ tan²x sec²x + 2sec²x - tan²x = 2
* Lets replace tan²x by sec²x - 1
∴ (sec²x - 1) sec²x + 2sec²x - (sec²x - 1) = 2 ⇒ open the brackets
∴ sec^4 x - sec²x + 2sec²x - sec²x + 1 = 2 ⇒ add the like terms
∴ sec^4 x -2sec²x + 2sec²x + 1 = 2 ⇒ cancel -2sec²x with +2sec²x
∴ sec^4 x + 1 = 2 ⇒ subtract 1 from both sides
∴ sec^4 x = 1 ⇒ take root four to both sides
∴ sec x = ± 1 ⇒ x is on the axes
∵ sec x = 1/cos x
∵ sec x = 1 , then cos x = 1
∵ sec x = -1 , then cos x = -1
∵ 0 ≤ x ≤ 2π
∵ x = cos^-1 (1)
∴ x = 0 , 2π ⇒ x is on the positive part of x-axis
∵ x = cos^-1 (-1)
∴ x = π ⇒ x is on the negative part of x-axis
* The solutions of the equation is 0 , π , 2π
Which of the following is not a property of the sample standard deviation s?
A. Sensitive to changes in the distribution
B. Calculated based on the mean
C. Larger than the population standard deviation o D. Resistant to extreme data values
E. All of the above.
The property of the sample standard deviation that is not accurate is 'D. Resistant to extreme data values'. The sample standard deviation is indeed sensitive to extreme data values. The other properties listed are true about the sample standard deviation.
Explanation:The property of the sample standard deviation (s) that is not accurate from the given options is 'D. Resistant to extreme data values'. The sample standard deviation is sensitive to extreme values, not resistant. In other words, if there are outliers or extreme values in the data, the sample standard deviation will tend to be larger, reflecting the increased variability.
Let's quickly review the other options for clarity. 'A. Sensitive to changes in the distribution' and 'B. Calculated based on the mean' are true properties of the sample standard deviation. The standard deviation, whether for a sample or a population, measures the spread or dispersion of the data points about the mean. Therefore, it changes with the distribution and is calculated based on the mean. 'C. Larger than the population standard deviation σ' is typically true, unless the sample perfectly represents the population.
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The sample standard deviation is C. larger than the population standard deviation o.
Explanation:The sample standard deviation, denoted as s, is a measure of spread that quantifies how much the data values deviate from the mean. It is calculated based on the mean. However, it is not necessarily larger than the population standard deviation, o, as it depends on the specific data set.
The other options are not correct:
A. The sample standard deviation is sensitive to changes in the distribution, as it considers the individual data values and their deviations from the mean.B. The sample standard deviation is calculated based on the mean, as it involves calculating the deviations of individual data values from the mean.D. The sample standard deviation is not resistant to extreme data values, as it considers each data value and its deviation from the mean.E. All of the above is not the correct answer, as the correct answer is C.
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Find the angle between vector u=2i+sqrt(11)j and v=-3i-2j to the nearest degree
Answer: Last option 155°
Step-by-step explanation:
We have the components of the vectors u and v.
Then, to find the angle between them, perform the following steps:
1) Calculate the scalar product u * v
If [tex]u = 2i + \sqrt{11}j[/tex] and [tex]v = -3i-2j[/tex]
Then, the product scalar u * v is:
[tex]u * v = (2)(-3) + (\sqrt{11})(-2)[/tex]
[tex]u * v = -6-2\sqrt{11}[/tex]
[tex]u * v = -12.633[/tex]
2) Calculation of the magnitude of both vectors.
[tex]| u | = \sqrt{(2) ^ 2 + (\sqrt{11})^2}\\\\| u | = \sqrt{4+11}\\\\| u | = \sqrt{15}[/tex]
[tex]| v | = \sqrt{(- 3) ^ 2 + (- 2) ^ 2}\\\\| v | = \sqrt{9 +4}\\\\| v | = \sqrt{13}[/tex]
3) Now that you know the product point between the two vectors and the magnitude of each, then use the following formula to find an angle
[tex]u * v = | u || v |cos(\alpha)[/tex]
[tex]-12.633 = \sqrt{15}\sqrt{13}*cos(\alpha)\\\\cos(\alpha) = \frac{-12.633}{\sqrt{15}\sqrt{13}}\\\\arcos(\frac{-12.633}{\sqrt{15}\sqrt{13}}) = \alpha\\\\\alpha =155\°[/tex]
origami is the Japanese art of paper folding the diagram below represents an unfolded paper kabuto a samuri warriors helmet which of the following are pairs of congruen segments? check all that apply
Answer: FR and NR
NO and NM
RC and RO
Step-by-step explanation: just did it on apex. good luck!
Answer:
The correct options are A, C and D.
Step-by-step explanation:
The given figure shows an unfolded paper. It is a square sheet.
Here the line of symmetry are diagonals FN, AK and midline CM, OI. All of these lines are intersecting at point R.
Diagonals of square bisect each other, therefore R is midpoint of FN.
[tex]FR\cong NR[/tex]
[tex]AO\cong ON[/tex] (OI is line of symmetry)
[tex]PO\neq ON[/tex]
[tex]RC\cong RO[/tex] (AK is line of symmetry)
[tex]NO\cong NM[/tex] (FN is line of symmetry)
[tex]DV\cong HV[/tex] (FN is line of symmetry)
[tex]DV\neq EW[/tex]
Therefore the correct options are A, C and D.
In rabbits. brown fur B is dominant to white fur (b) and short fur (H) is dominant to long fur (h).
A brown. long-furred rabbit (Bbhh) is crossed with a white, short-furred rabbit (bbHh). Both the Band H traits
assort independently from one another
What percentage of the offspring will be brown with long fur?
The cross between Bbhh and bbHh yields genotypic frequencies
1/4 BbHh1/4 Bbhh1/4 bbHh1/4 bbhhso that 1/4 of the offspring should be expected to be brown with long fur (genotype Bbhh)
Answer:
1/4
Step-by-step explanation:
ADE and ABC are similar which best explains why the spike of the line between point A and D is the same as the slope between points A and B
The same slope between line AD and line AB results from the property of similar triangles. This property states that corresponding sides are proportional, which also applies to the slopes of these sides. Hence, the slopes are equivalent.
Explanation:The reason the slope of the line between point A and D is the same as the slope between points A and B derives from the concept of similar triangles in geometric math. In similar triangles, corresponding sides are proportional. This proportionality is carried over to the slopes of the lines that form these sides. Slope is defined by the change in y (vertical change) over the change in x (horizontal change). In similar triangles, these changes are proportional meaning the division, or the slope will be the same.
Consider this using Figure A1 Slope and the Algebra of straight lines where they indicate that the slope is the same all along a straight line. This also applies to the lines of similar triangles. Therefore, if triangles ADE and ABC are similar, then the slope of line AD will be the same as the slope of line AB because the ratios of their changes in y over changes in x are equal.
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if 5lb of cheese cost 18.50, how much would 1 lb cost
Answer:
3.70
Step-by-step explanation:
18.50 ÷ 5 = 3.70
fairly simple math but can be confusing depending upon how its asked, you just have to find the words that describe what you have to do and check your math to make sure
Someone please answer this
The two lines with the equations are the same length.
Set the two equations to equal and solve:
3x +3 = 6x - 57
Add 57 to each side:
3x +60 = 6x
Subtract 3x from each side:
60 = 3x
Divide both sides by 3:
x = 20
Answer:
x= 20
Step-by-step explanation:
The width of a rectangle is fifteen feet less than its length. If the area of the rectangle is 54 square feet, find the width.
Answer:
3 ft
Step-by-step explanation:
It is because 3 times 18 is 54 and 3 is 15 less than 18
The width of a rectangle is 3 feet .
What is area of rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.)
According to the question
Let length of rectangle = x
The width of a rectangle is fifteen feet less than its length.
i.e,
Width of a rectangle = x - 15
Now,
Area of the rectangle = 54 square feet .
Length * Width = 54
x (x - 15 ) = 54
[tex]x^{2}[/tex] - 15x - 54 = 0
[tex]x^{2}[/tex] - (18-3)x - 54 = 0
[tex]x^{2}[/tex] - 18x + 3x - 54 = 0
x(x-18) +3(x-18) = 0
(x-18) (x+3) = 0
x= 18 , -3
length of rectangle = 18 feet
Width of a rectangle = 18 - 15
= 3 feet
Hence, The width of a rectangle is 3 feet .
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What is the tangent ratio for B
Answer:
C [tex]\frac{2}{1}[/tex]
Step-by-step explanation:
Recall the mnemonics SOH-CAH-TOA
The tangent ratio is the ratio of the opposite side of the right triangle to the adjacent side.
From the diagram, the side opposite to <B is 2 units and the adjacent side is 1 unit.
This implies that;
[tex]\tan \angle B=\frac{2}{1}[/tex]
The correct choice is C
So what am I supposed to be looking for?
Answer:
C. 2.5
Step-by-step explanation:
If the number is -2.5
Basically the opposite in a summary
Answer:
C
Step-by-step explanation:
The additive inverse is what you add to a number to get zero.
That is, the negative of a number
Here A is positioned at - 2.5
The additive inverse is 2.5 → C
Since - 2.5 + 2.5 = 0
John wants to deposit $1000 as a principle amount, with an interest of 4% compounded quarterly. Cayden wants to deposit $1000 as the principle amount, with an interest of 3% compounded monthly. Explain which method results in more money after 5 years. Show all work.
Answer:
John will get more money after 5 years.
Step-by-step explanation:
To calculate compound interest we use the formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A = Amount
P = Principal
r = Rate of interest ( in decimal )
n = number of compounding period (quarterly = 4) (monthly = 12)
t = time in years
John wants to deposit $1000 with an interest of 4% compounded quarterly for 5 years.
[tex]A=1,000(1+\frac{0.04}{4})^{(4)(5)}[/tex]
[tex]A=1,000(1.01)^{20}[/tex]
A = 1000 ( 1.22019 )
A = $1220.19
John will get $220.19 as interest after 5 years.
Cayden wants to deposit $1,000 with an interest of 3% compounded monthly for 5 years.
[tex]A=1,000(1+\frac{0.03}{12})^{(12)(5)}[/tex]
[tex]A=1,000(1.0025)^{60}[/tex]
A = 1,000 ( 1.161617 )
A = 1161.62
Cayden will get $161.62 as interest after 5 years.
Therefore, John will get more money after 5 years.
Write a recursive formula for the sequence –2, 4, –8, 16, ...
please help and thank you
Answer:
see explanation
Step-by-step explanation:
A recursive formula allows us to calculate any term in the sequence from the previous term.
These are the terms of a geometric sequence with r being the common ratio between consecutive terms.
r = 4 ÷ - 2 = - 8 ÷ 4 = 16 ÷ - 8 = - 2
Multiplying a particular term by - 2 gives the next term in the sequence.
Hence recursive formula is
[tex]a_{n+1}[/tex] = - 2 [tex]a_{n}[/tex] with a₁ = - 2
-2,4,-8,16,...
a₁ = -2
a₂ = -2a₁
a₃ = -2a₂
..................
=> aₙ₊₁ = -2•aₙ, with a₁ = -2
30 points and brainliest!! \Part A: A number is increased by 54. The sum is then divided by 9. The result is 21.
Write an equation to represent the description above. Use n for the number.
Equation: _____________________________
Part B: Find the value of n. Show your work.
n = __________________________________
Part C: Choose two numbers and use them to do the following:
Write an equation that shows your first number added to n equal to your second number. Solve your equation for n.
Equation: _____________________________
Solution: ______________
Answer:
Part A) The equation that represent the situation is [tex]\frac{n+54}{9}=21[/tex]
Part B) The value of n is [tex]n=135[/tex]
Part C) The equation is [tex]35+n=60[/tex] and the solution is [tex]n=25[/tex]
Step-by-step explanation:
Part A) A number is increased by 54. The sum is then divided by 9. The result is 21. Write an equation to represent the description above. Use n for the number
Let
n-----> the number
we know that
The linear equation that represent this situation is equal to
[tex]\frac{n+54}{9}=21[/tex]
Part B) Find the value of n
we have
[tex]\frac{n+54}{9}=21[/tex]
solve for n
Multiply by 9 both sides
[tex]n+54=21*9[/tex]
[tex]n+54=189[/tex]
Subtract 54 both sides
[tex]n=189-54[/tex]
[tex]n=135[/tex]
Part C) Choose two numbers and use them to do the following:
Write an equation that shows your first number added to n equal to your second number. Solve your equation for n
I choose 35 and 60
[tex]35+n=60[/tex]
Solve for n
Subtract 35 both sides
[tex]n=60-35[/tex]
[tex]n=25[/tex]
What is the expanded form of the series represented below?
A. -3 + 2 + 7 + 12 + 17
B. -3 + 3 + 8 + 13 + 18
C. 2 + 7 + 12 + 17 + 22
D. 5 + 2 + (-1) + (-4) + (-7)
Answer:
See below
Step.-by-step explanation:
Choice A has first term -3 and common difference 5. The formula for the kth term is -3 + (k - 1)5. It is an arithmetic series.
The required expanded form for the Sum is:
5
S5 = ∑ [-3 + (k - )5)]
k = 1
Answer:
Expanded form of the series is:
A. -3 + 2 + 7 + 12 + 17
Step-by-step explanation:
when k=1 -3+(k-1)5= -3
when k=2 -3+(k-1)5= -3+5=2
when k=3 -3+(k-1)5= -3+10=7
when k=4 -3+(k-1)5= -3+15=12
when k=5 -3+(k-1)5= -3+20=17
Hence, value of [tex]S_{5}= -3+2+7+12+17[/tex]
Hence, expanded form of the series is:
A. -3 + 2 + 7 + 12 + 17
Please help with this question!!!!
Answer:
D) The number line with a solid dot and the arrow going to the right of 3.
Step-by-step explanation:
x - 5 >/= -2
x >/= 3
x is greater than or equal to 3.
For this case we must find the solution of the following inequality:
[tex]x-5\geq-2[/tex]
So:
If we add 5 to both sides of the inequality we have:
[tex]x-5 + 5\geq - 2 + 5\\x\geq - 2 + 5\\x\geq 3[/tex]
Thus, the solution is given by all values of x greater than or equal to 3.
Answer:
Option D
How do I solve this?
Answer:
[tex]\large\boxed{4\sqrt{-81}+\sqrt{-25}=41i}[/tex]
Step-by-step explanation:
[tex]i=\sqrt{-1}\\\\\sqrt{-81}=\sqrt{(81)(-1)}=\sqrt{81}\cdot\sqrt{-1}=9i\\\\\sqrt{-25}=\sqrt{(25)(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\4\sqrt{-81}+\sqrt{-25}=4(9i)+5i=36i+5i=41i[/tex]
what is the value of g(3)?
a. 2
b. 3
c. 9
d. 14
The answer is 3 because you need to use the last equation which is x is greater than or equal to 3.it doesn't make sense to use any of the other two equations because it asked what is the value of g(3).hope this helps if it does please mark brainliest
The answer is 3 you’re welcome
Jane had R Beanie Babies. She gave 8 of them to her friend. Later her grandma bought her 5 more Beanie Babies than she had in the beginning. How many Beanie Babies did Jane have in the beginning, if now she has 27 of them?
Jane had 10 Beanie Babies in the beginning.
The number of Beanie Babies Jane had in the beginning.
- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.
- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.
- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.
- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.
Jane had 20 Beanie Babies in the beginning.
To calculate:
1. Let's denote the number of Beanie Babies Jane had in the beginning as [tex]\( x \).[/tex]
2. She gave 8 of them to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.
3. Her grandma bought her 5 more Beanie Babies than she had in the beginning, so she now has [tex]\( x + 5 \)[/tex] Beanie Babies.
4. Given that she now has 27 Beanie Babies, we can set up the equation:
[tex]\[ x - 8 + (x + 5) = 27 \][/tex]
Now, let's solve for [tex]\( x \):[/tex]
[tex]\[ 2x - 3 = 27 \][/tex]
[tex]\[ 2x = 30 \][/tex]
[tex]\[ x = 15 \][/tex]
However, this is the number of Beanie Babies Jane had after her grandma bought her 5 more. To find out how many she had in the beginning, we need to subtract 5 from [tex]\( x \):[/tex]
[tex]\[ x = 15 - 5 = 10 \][/tex]
So, Jane had 10 Beanie Babies in the beginning.
- Let [tex]\( x \)[/tex] be the number of Beanie Babies Jane had in the beginning.
- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.
- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.
- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.
- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.
Complete question
Jane had R Beanie Babies. She gave 8 of them to her friend. Later her grandma bought her 5 more Beanie Babies than she had in the beginning. How many Beanie Babies did Jane have in the beginning, if now she has 27 of them?
The table below shows the three-day rain forecast
for Friday, Saturday and Sunday in Aberystwyth.
Day Probability of rain
Friday
70%
Saturday
70%
Sunday
70%
a) Work out the probability that it will rain on all three days.
b) Work out the probability that it will rain on exactly two consecutive days.
Answer:
a=0.343
Step-by-step explanation:
70/100=0.7
0.7x0.7x0.7=0.343
Find the total surface area of this object.
Answer:
60
Step-by-step explanation:
Use the formula for the surface area and plug in the given numbers. See work for more.
Simplify ( 2 + sqrt-3 / 2) (2 - sqrt-3 / 2)
Answer:
[tex]2.5[/tex]
Step-by-step explanation:
The given radical expression is
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })[/tex]
Observe that, the given expression can be written as difference of two squares.
That is; [tex](x+y)(x-y)=x^2-y^2[/tex]
We apply this property to obtain:
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=2^2-(\sqrt{-\frac{3}{2} })^2[/tex]
We now simplify to get:
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=4-\frac{3}{2}[/tex]
This simplifies to:
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=\frac{5}{2}=2.5[/tex]
LOOK AT PHOTO PLEASE
The slope of the line in the graph is ____
The y-intercept is______
The equation of the line is y=_____ x=_____
The slope of the graph is 3
The y-intercept is -4
The equation of the line is y=3x-4 it shouldn’t be y= then x=
Answer:
The slope is 3
The y-intercept is -4
The equation of the line is y=3 x=-4
Step-by-step explanation:
:)
Write a rule for the function represented in the table
Answer:
i think that it is y=5n
Step-by-step explanation:
Identify the vertex of the graph. Tell whether it is a minimum or maximum A. (-1, -2); maximum B. (-2,- 1); maximum C. (-2, -1); minimum D. (-1, -2); minimum
Answer:
D
Step-by-step explanation:
The vertex is the turning point of the graph.
This is at (- 1, - 2)
The graph changes from decreasing to increasing at (- 1, - 2)
Hence is a minimum at (- 1, - 2)
The graph of the parabola is minimum at (-2, -1).
Parabola
The path of an object that is thrown in the air and falls back to the earth.
GivenA graph of the parabola is given.
How to find maximum and minimum?
a. At ( -1, -2 ), the parabola is minimum.
b. At ( -2, -1 ), point does not satisfy.
c. At ( 2, 1 ), the point does not satisfy.
d. At ( 1, 2 ), the point does not satisfy.
Thus, the graph of the parabola is minimum at (-2, -1).
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Given: ABCD is a rectangle, < ABX is congruent to < XBC
PROVE: ABCD is a square
Figure is labeled ABCD clockwise with A starting in the upper left hand corner. Diagnosis AC and BD intersect at X
Answer:
im not sure were you got this but are there any pictures?
Step-by-step explanation:
The figure ABCD represents a square
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the figure be represented as ABCD
Now , the coordinates of ABCD are noted clockwise
And , the diagonals of the quadrilateral are AC and BD
Now , the diagonals AC and BD intersect at X
where the measure of angle ∠ABX = measure of ∠XBC
So , the diagonals are equal and the angles are equal
And , the figure represents a square
where the sides AB = BC = CD = AC
Hence , the figure is a square by SAS congruency
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Give the scale factor, perimeter ratio, and area ratio of figure A to figure B
Answer:
Scale factor: 4/7
perimeter ratio: 4:7
area: I don't know the height of the two
Step-by-step explanation:
Which of the following shows 27⁄54 written in prime factored form to help in reducing the fraction to simplest form?
A. 1⁄2
B. 9×3 ⁄9×6
C. 27×1 ⁄27×2
D. 3×3×3⁄3×3×3×2
Answer:
3×3×3⁄3×3×3×2
Step-by-step explanation:
27 = 3×3×3
54 = 3×3×3×2
The prime factored form of 27⁄54 is thus;
3×3×3⁄3×3×3×2
Answer:
D= 3×3×3/2×3×3×3
Step-by-step explanation:
A prime factored form breaks the number into prime numbers that give the same value when multiplied
27= 3×3×3
54=2×3×3×3
To get the simplest form of a fraction you proceed with division.
=3×3×3 / 2×3×3×3.............................cancel 3 in the numerator and denominator
= 1/2
LM has the endpoints L at –5 and M at 9. To find the point x so that x divides the directed line segment LM in a 2:3 ratio, use the formula x = (x2 – x1) + x1.
x = (9 – (–5)) + (–5)
x =
Answer:
3/5
Step-by-step explanation:
Bruh i gotchu Simple
The angles of a pentagon are x, x − 5
, x + 10
, 2x + 15and 2x + 30
. Find all the angles.
Answer:
65°, 70°, 80°, 155°, 170°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 ( pentagon )
sum = 180° × 3 = 540°
Sum the given angles and equate to 540
x + x - 5 + x + 10 + 2x + 15 + 2x + 30 = 540
7x + 50 = 540 ( subtract 50 from both sides )
7x = 490 ( divide both sides by 7 )
x = 70
Hence angles are
x = 70°
x - 5 = 70 - 5 = 65°
x + 10 = 7 0 + 10 = 80°
2x + 15 = (2 × 70) + 15 = 140 + 15 = 155°
2x + 30 = (2 × 70) + 30 = 140 + 30 = 170°