a) The list with all the possible outcomes is given as follows:
Heads, Heads, Heads.Heads, Heads, Tails.Heads, Tails, Heads.Heads, Tails, Tails.Tails, Heads, Heads.Tails, Heads, Tails.Tails, Tails, Heads.Tails, Tails, Tails.b) The probabilities are given as follows:
P(all three heads) = 1/8.P(at least one tail) = 7/8.How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Of the 2³ = 8 outcomes, only one result in three heads, hence the probability is given as follows:
p = 1/8.
At least one tail is complementary to three heads, hence it's probability is given as follows:
p = 1 - 1/8 = 8/8 - 1/8 = 7/8.
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1) Classify each triangle by its angles and sides.
2) If ΔJKL is an equilateral triangle, JK=13x+5, KL=17x-19, and JL=8x+35, find x and the measure of each side.
1) The triangle classified according to their sides is given as follows:
a) Isosceles triangle - It has two equal sides
b) Scalene Right Angled Triangle.
c) obtuse scalene triangle -Has an angle that is over 90 degrees, as well as three unequal sides
d) Equilateral Triangle - Three equal sides and three equal angles
e) Isosceles Right Angled Triangle - Right angle with two equal sides and two equal angles
f) Scalene Triangle - Three unequal sides and three unequal angles.
g) Equilateral Triangle - Three equal sides and three equal angles
h) Obtuse Isosceles Triangle - has two equal sides with an angle measuring above 90 degrees.
2) Note that the value of x is 6, JK is 83, KL is 83 and JL is 83.
What is is an Equilateral Triangle?As indicated above, an Equilateral Triangle is one whose sides are equal. Thus,
JK = KL = JL
That means 13x + 5 = 17x -19 ..............1
Simplifying 1 by collecting like terms:
17x - 13x = 19 + 5
4x = 24
x = 24/4
x = 6
We can proceed to find the sides now
JK = 13x + 5
13 x 6 + 5
= 78 + 5
= 83
JK = 83
KL = 17x - 19
= 17 x 6 - 19
= 102 - 19
= 83
KL = 83
JL= 8x + 35
= 8 x 6 + 35
= 48 + 35
= 83
JL = 83
Therefore, the value of x is 6, JK is 83, KL is 83 and JL is 83.
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Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Carla is getting her golf bag prepared for a golf tournament and decides to do a quick experiment with the three brands of golf balls she
has stored in her bag.
She randomly draws 20 golf balls to determine the frequency of occurrence for each brand, returning the drawn ball after each trial.
The data from her experiment is displayed in the table below. Determine the correct values to complete the rest of the table, and
complete the accompanying statement. For this item, any answers that are not whole numbers should be entered as a decimal,
rounded to the hundredths place.
Brand
Best Flight
Distance King
High Loft
Frequency
3
Reset
6
11
Experimental
Probability
0.30
If Carla performed another experiment using the same set of golf balls and drew 12 Best Flight golf balls, she would draw
approximately
Distance King golf balls.
on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
equation given is 3(x+2)=7x-48
value of x
[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]
value of x from the given equation comes out to be 13.5
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What is the domain of the function y=√x+6-7?
The domain of the function y=√x+6-7 is x>= -6.
What is domain of the function?The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
The set of inputs that a function will accept is known as the domain of the function in mathematics. It can also be written as dom (f) or dom f, where f stands for the function.
To put it more exactly, the domain of f is X given a function f: X - Y. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
Given data :
The given function is a radical function.
Note that a radical function is only defined for values that will make the radicand greater than or equal to zero.
Hence, the radicand of the given function must be greater than or equal to zero or:
x+6>=0
x + 6 - 6 0 - 6
x>= -6
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Alyssa is working two summer jobs, making $8 per hour walking dogs and making $10 per hour clearing tables. In a given week, she can work a maximum of 15 total hours and must earn at least $130. Also, she must work at most 3 hours walking dogs. If a represents the number of hours walking dogs and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Alyssa worked 1 hour walking dogs and 13 hours clearing tables. This solution satisfies all of the given conditions.
The first inequality represents the condition that Alyssa must work at most 3 hours walking dogs:
a ≤ 3
The second inequality represents the condition that Alyssa can work a maximum of 15 total hours:
a + y ≤ 15
The third inequality represents the condition that Alyssa must earn at least $130 in a given week:
8a + 10y ≥ 130
We can graph these inequalities on the same coordinate plane to find the region of possible solutions. The solution to the system of inequalities is the region of the plane that satisfies all of the inequalities.
The red line represents the first inequality, a ≤ 3. The blue line represents the second inequality, a + y ≤ 15. The green line represents the third inequality, 8a + 10y ≥ 130.
The region of the plane that satisfies all three inequalities is the area above the red line and below the green line, and to the left of the blue line. This region is shaded in the graph above.
Thus, one possible solution is point (1,13), which is the intersection of the red and blue lines. This corresponds to Alyssa working 1-hour walking dogs and 13 hours clearing tables. This solution satisfies all of the given conditions.
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O f(x) = (x + 1)(x-2)(x - 3)
Of(x) = (x - 1)(x + 2)(x+3)
Of(x) = (x + 1)(x + 2)(x+3)
Of(x) = (x - 1)(x - 2)(x − 3)
Answer:
D) f(x) = (x - 1)(x - 2)(x - 3)-------------------------------------
The x-intercepts are the roots of the function and according to the graph the roots are:
1, 2 and 3Hence the function is:
f(x) = (x - 1)(x - 2)(x - 3)Answer:
D) f(x) = (x - 1)(x - 2)(x - 3)
Step-by-step explanation:
From inspection of the given graph, the points at which the curve intersects the x-axis are:
(1, 0)(2, 0)(3, 0)Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
According to the factor theorem, as f(x) = 0 when x = 1, x = 2 and x = 3 then (x - 1) and (x - 2) and (x - 3) are factors of the polynomial.
Therefore, the equation of the function is:
f(x) = (x - 1)(x - 2)(x - 3)Nachelle mixes 6 cups of melon and 1 cup of apple and Arturo mixes 10 cups of melon and 3 cups of apple. Use Nachelle and Arturo’s percent of melon to determine whose fruit salad will taste more melony.
The fruit salad that will taste more melody when the percent of melon in both Arturo and Nachelle are compared would be Nachelle's fruit salad.
What is percentage of a quantity?The percentage of a quantity is determined when we divide the value by the total value and then multiply the resultant by 100.
For Nachelle;
Quantity of melon = 6 cups
quantity of apple = 1
Total quantity = 7
The percentage of melon = 6/7× 100
= 600/7 = 85.7%
For Arturo;
Quantity of melon = 10 cups
quantity of apple = 3
Total quantity = 13
The percentage of melon = 10/13 ×100
= 1000/13= 76.9%
Therefore,the fruit salad that will be melony would be Nachelle's fruit salad with the percentage of 85.7 of melon making up the salad.
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Which expression is equivalent to (ab3rd power)4th power?
a4th power b 12th power
ab 12th power
a 5th power b 4th power
ab 7th power
The expression that is equivalent to (ab3rd power)4th power in the question is a4th power b 12th power.
Exponential expression.Exponential expression is the power to which a given term of mathematical expression is raised to. The value of the power to which a variable is raised is not limited. Sometimes, some laws are required to solve some exponential expressions. An example is the law of indices which can be applied to solve some expressions in a given question with large numbered powers. The law of indices is one of the major law to refer to when discussing power of numbers or variables.
Thus the expression that is equivalent to (ab3rd power)4th power is:
(ab3rd power)4th power = (ab^3)^4
expand the given bracket to have;
(ab^3)^4 = a^4 * b^(3*4)
= a^4b^12
Therefore the expression is equivalent to a^4b^12 i.e a4th power b 12th power.
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Please help!! I dont know what to do
The additional information needed to that triangle ADN is congruent to triangle DCO using SAS is
AN ≅ DO and < BAN ≅ CDNWhat do we mean by congruent triangles?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent
The SAS says that the corresponding sides and the included angle must be congruent
the angles and side used here include
AN - < BAN - BA
DO - < CDN - CD
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In construction, floor space must be planned for stair cases. If the vertical distance between the first and second floors it's 3.6 m and a contractor is using the standard step pattern of 28 cm wide for 18 cm high and how many steps are needed to get the first to the second floor and how much linear distance will be needed for the staircase? How long would a railing be that was parallel to the steps in the previous question? Use a calculator and round your answer to the nearest hundredth.
The length of the railing that was parallel to the steps is; 6.65 meters
How to use Pythagoras Theorem?Let us first of all convert the distance in meters to centimeters. From unit conversion, we know that 1 meter equals 100 centimeters. Thus;
3.6m * 100cm / 1m = 360cm
Now we calculate the number of steps as;
360 cm / 18 cm = 20 steps
Since each step measures 28 cm, it means that total measure of steps is;
20 * 28 = 560 cm
To calculate the length of the ladder, we must apply Pythagoras theorem: c² = a² + b²
From the question, we can say that;
a = 360; b = 560
Thus;
c² = 360² + 560²
c² = 443200
c = √443200
c = 665.73
Expressing 665.73 cm in meters would give us 6.65 meters.
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The mass of a wood is 19.5061g. When it was dropped in a cylinder, it had initial water volume of 8.75cm^3, the total volume was 9.76cm3. What is the density of the piece of metal in g/cm3
The density of the wood weighing 19.5061 grams is approximately 19.313 g/cm².
What is the density in wood?Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given the data in the question
Mass of wood m = 19.5061gInitial volume water in the cylinder = 8.75cm³Final volume of water in the cylinder = 9.76cm³Density of the wood = ?First, we determine the volume of the wood which is the change in the volume of volume in the cylinder.
Volume of the wood = Final volume of water - Initial volume water
Volume of the wood = 9.76cm³ - 8.75cm³
Volume of the wood = 1.01 cm³
Now, we determine the density of the wood.
p = m / v
p = 19.5061g / 1.01 cm³
p = 19.313 g/cm²
Therefore, the density of the wood is 19.313 g/cm².
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The following dot plot shows how far peter ran in each of his tennis matches this year. find the median distancethe following dot plot shows how far peter ran in each of his tennis matches this year.
a. the following dot plot shows how far peter ran in each of his tennis matches this year.
b. find the median distance.
c. find the median distance..
The median distance is 5km.
What is median distance?The median distance, symbolized by δM, is the median value of the distance among any two node pairs. This is measured over each network's largest linked component, and takes into account pairs including of the same node.
In this case, the dots in the picture (attached) represent the number of matches.
So, if we write it all down here, the data will be:
3, 4, 4, 5, 5, 5, 5, 7, 7
Since the total of values in the data is odd number, that is 9, then the formula for the median distance will be:
Median = (n + 1) / 2
with n = 9
Thus, the median distance in this case:
= (n + 1) / 2
= (9 + 1) / 2
= 10 / 2
= 5
Hence, the median distance is 5km.
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Question 3 of 11
What is the slope of the line given by the equation y = 9x?
Answer here
SUBMIT
Answer:
the slope is 9
Step-by-step explanation:
The slope is the number before the x.
Answer:
Slope = 9
Step-by-step explanation:
Now we have to,
→ find the slope of the equation.
Formula we use,
→ y = mx + b
→ m = Slope
Then the required slope will be,
→ y = mx + b
→ y = 9x + 0
→ y = 9x
→ [ m = 9 ]
Hence, the value of slope is 9.
Lines intersected by a transversal can never be parallel lines
true or false
Answer:
True.
Step-by-step explanation:
When two lines are crossed by a transversal, the interior angles between them will always add up to 180 degrees, which means they can never be parallel.
another algebraic expressions question
find the value of the following expression, when x= -1
(i) -x + 2
(ii) x²+ 2x + 1
(iii) 2x² - x - 2
The values of the expressions when x = -1 will be;
(i) 1
(ii) 0
(iii) 1
What are Algebraic Expressions?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra shows how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
when x = -1
(i) -x + 2
-1 + 2 = 1
(ii) x²+ 2x + 1
(-1)² + 2(-1) + 1
1 - 2 + 1 = 0
(iii) 2x² - x - 2
2(-1)² - (-1) - 2
2(1) + 1 - 2
2 + 1 - 2
3 - 2 = 1
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Devon made a small batch of cookies. He’s used 5/6 of a cup of sugar, and 3/4 of a cup of flour. Evaluate the following expression to determine how much more sugar he used then flour 5/6 - 3/4
To evaluate the expression 5/6 - 3/4, we need to first convert the fractions to a common denominator. The least common multiple of 6 and 4 is 12, so we can rewrite the fractions as follows:
5/6 - 3/4 = (5/6)(2/2) - (3/4)(3/3)
= 10/12 - 9/12
= 1/12
Therefore, Devon used 1/12 of a cup more sugar than flour.
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used. Complete the table with the ratios of the base areas, surface areas, and volumes of these two similar cones. Assume the ratios are written in the form cone A : cone B.
The ratio of the base areas and ratios of volume are respectively; 1/9 and 1/27
How to find the surface area of a cone?A) Base area of the cone has the formula;
A_b = 3V/h
where;
V is volume
h is the vertical height
Since the ratio of both heights is 5:15 = 1:3, then;
Ratio of base areas = 1²/3² = 1/9
B) Formula for the volume of a cone is;
V = ¹/₃πr²h
Thus;
Va = ¹/₃π(r²)5
Va = ⁵/₃π(r²)
Vb = ¹/₃π(R²)15
Thus;
Va/Vb = ⁵/₃π(r²)/¹/₃π(R²)15
Earlier, we saw that;
r²/R² = 1/9. Thus;
Va/Vb = (1/3) x (1/9)
Va/Vb = 1/27
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A bank loaned out $10,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $1000, how much was loaned at 7%
The amount of money loaned at a rate of 7% will be $7,000.
What is the solution to the equation?
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A bank loaned out $10,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $1000.
Let 'x' be the amount of money loaned at a rate of 7%. Then the amount of money loaned at a rate of 17% will be ($10,000 - x). Then the equation is given as,
0.07x + 0.17($10,000 - x) = $1,000
0.07x - 0.17x + $1,700 = $1,000
0.10x = $700
x = $7,000
The amount of money loaned at a rate of 7% will be $7,000.
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2. If all of the partridges eat at this same rate, how many
pears will they eat in 1 hour and 45 minutes? (Assume the
birds eat at a constant rate.)
The total number of pears consumed by all the 6 partridges is given by the equation A = 84 pears
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of pears be represented as A
Let the number of partridges be n = 6
Now , Pete the partridge eats 4 pears in 30 minutes
So , the number of pears in 1 hour = 2 x 4
The number of pears in 1 hour = 8 pears
The number of pears in 1 hour 30 minutes = 8 + 4 pears
The number of pears in 1 hour 30 minutes = 12 pears
The number of pears in 1 hour 45 minutes = 12 + 2 pears
The number of pears in 1 hour 45 minutes = 14 pears
So ,
The total number of pears by all 6 partridges A = 6 x number of pears in 1 hour 45 minutes
Substituting the values in the equation , we get
The total number of pears by all 6 partridges A = 6 x 14
On simplifying the equation , we get
The total number of pears by all 6 partridges A = 84 partridges
Therefore , the value of A is 84 partridges
Hence , the number of partridges is 84
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Consider the table that includes the input and output values of a function.
An answer which classifies the function using finite differences is: B. the function is linear with a constant first difference of 3.
How to classify a function using finite differences?Based on the data points in the table, we have the following input and output values;
x f(x)
-16 -13.5
-12 -10.5
-8 -7.5
-4 -4.5
0 -1.5
Next, we would determine the slope of this function for data points 1 and 3 as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-7.5 - (-13.5))/(-8 - (-16))
Slope, m = 3/4
For data points 1 and 5, the slope is given by;
Slope, m = (-1.5 - (-13.5))/(0 - (-16))
Slope, m = 3/4
For the common difference, we have:
Common difference = -10.5 - (-13.5) = 3
Common difference = -7.5 - (-13.5) = 3
Common difference = -4.5 - (-7.5) = 3
Common difference = -1.5 - (-4.5) = 3
Therefore, this function is linear because the slope is constant and the common difference is constant between successive data points.
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Complete Question:
Consider the table that includes the input and output values of a function.
-16 -13.5
-12 -10.5
-8 -7.5
-4 -4.5
0 -1.5
Which answer classifies the function using finite differences?
The function is linear with a constant first difference of –3.
The function is linear with a constant first difference of 3.
The function is quadratic with a constant second difference of –3.
The function is quadratic with a constant second difference of 3.
26.
circle
triangle
hexagon
rectangle
pentagon
Two-dimensional cross-sections could be obtained from a right rectangular prism a Rectangles. Option D
What is a right rectangular prism?Generally, A right rectangular prism may give rise to three distinct varieties of two-dimensional cross-sections, and they are as follows:
A rectangle may be created by cutting the right rectangular prism along either of its faces to create a parallelogram, which can then be folded in half.
Obtaining a parallelogram requires cutting the correct rectangular prism at an angle that is not perpendicular to any of its faces. This will result in the formation of a parallelogram.
You may acquire a trapezoid by cutting the right rectangular prism at an angle that is not parallel to any of its faces. This will result in the formation of a trapezoid.
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Overview
Question Progress
"
9°℃
Homework Progress
14/31 Marks
A square of area 36 cm² is cut to make two rectangles, A and B.
U
Width:
A
Area = 36 cm²
The ratio of area A to area B is 2:1
Work out the dimensions of rectangles A and B.
Rectangle A
Length:
B
cm
Rectangle B
Length:
cm Width:
cm
cm
65%
10
11
12
13
Rectangle measures 6 by 4 whereas rectangle b measures 6 by 2. A rectangle has two dimensions: a length and a width that are both perpendicular to it.
How do you determine a rectangle's dimensions?How to calculate a rectangle's dimensions: The perimeter equation can be expressed in terms of one of the following dimensions as follows: P = 2(a+b) b = P/2−a The equation for the area (A) plus the following one is as follows: The equation for area is A = ab.
We are given a square of 36 square centimeters.
The square's size will be 6 cm as a result.
Two rectangles are created by dividing the square into two equal-sized pieces.
Let the rectangles' measurements be 6*a and 6*b. Consequently, we can establish the ratio.
Moreover, we can set the combined area of rectangles equal to the area of square to form another equation:
Using substitution method, we can solve for 'a' and 'b' as shown below:
And
Therefore, dimensions of the two rectangles are 6x4 and 6x2, respectively.
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(0.95x -0.04)-(0.99x -0.13)
Answer: -0.04x + 0.09
Step-by-step explanation:
(0.95x - 0.04) - (0.99x - 0.13) = 0.95x - 0.04 - 0.99x + 0.13
= 0.95x - 0.99x + 0.13 - 0.04
= (0.95 - 0.99)x + (0.13 - 0.04)
= -0.04x + 0.09
Need help with this :'( Look at attachment below please.
The matching statements and reasons:
1. Triangle RAS is isosceles, AM is a median Given2. AR = AS Definition of isosceles3. MR = MS Definition of median4. AM = AM Reflexive property5. ΔRAM ≅ ΔSAM SSSSimplify -10x - 2x + 3x. 11 x 9 x -9 x
Answer:
x=16
Step-by-step explanation:
right!!
Find the value of k given that both points lie on a line passing through the orgin (k,7) and (-81,-9)
The value of k for the point on the line is 63
How to determine the value of k?We can find the value of k by using the slope formula. The slope of a line can is given by:
Slope = (y2-y1)/(x2-x1)
Since the pass through the origin (0,0), (k,7) and (-81,-9). we can write:
x1 = 0, y1 = 0 and x2 = -81, y2 = -9
Slope = (-9-0)/(-81-0) = 1/9
Also, we can write:
x1 = k, y1 = 7 and x2 = -81, y2 = -9. And the slope is still the same
1/9 = (-9-7)/(-81-k)
1/9 = -16/(-81-k)
1/9(-81-k) = -16
-9 - k/9 = -16
-k/9 = -16 + 9
-k/9 = -7
-k = -7 × 9
-k = -63
k = 63
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Please, i need help.
The opposite sides are parallel to each other if diagonals of the quadrilateral bisect each other.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
AC and BD bisect each other.
We know that in a quadrilateral if the diagonal of the quadrilateral bisect each other then the opposite sides are parallel to each other.
AC = BD (Equal diagonal)
Then the side AB and CD are parallel to each other. And similarly, the sides BC and AD are also parallel to each other.
AB || CD or BC || AD
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What is the answer to this question
Answer:
Do you have answer choices?
The possible answers are Plane PLN, Plane LNR, Plane NRP, and Plane RPL.
Please Answer and Explain
Answer:
x = 12
Step-by-step explanation:
3/9 = 4/x
3x = 36
x = 12
Answer:
The quadrilateral ABCD was dilated with a scale factor of 1.8
Take the value of x before the dilation (4), and multiply that by 1.8
The result should be 7.2
Hope this helps.
Emma is going to invest $3,300 and leave it in an account for 12 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Emma to end up with $7,200?
The required interest rate in order for Emma to end up with $7,200 is given as follows:
6.5%.
What is the continuous compounding formula?The balance of an account, using continuous compounding, after t years, is presented by the equation given as follows:
[tex]A(t) = A(0)e^{rt}[/tex]
In which the parameters are given as follows:
A(0) is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.The values of the parameters in the context of this problem are given as follows:
A(t) = 7200, A(0) = 3300, t = 12.
Hence the interest rate can be obtained solving the exponential equation as follows:
7200 = 3300e^(12r)
e^(12r) = 7200/3300
e^(12r) = 2.181818
ln(e^(12r)) = ln(2.181818).
(as exponential and ln are inverse operations)
12r = ln(2.181818).
r = ln(2.181818)/12
r = 0.065.
As a percentage, the interest rate is given as follows:
6.5%.
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Given the proportional relationship in the table below, write an equation to represent the relationship.
The equation that represent the proportional relationship is y = 11k.
How to write equation to represent relationships?Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.
Therefore, proportional relationship can be represented as follows:
y ∝ x
y = kx
where
k = constant of proportionalityHence,
x = 2
y = 22
Therefore,
22 = 2k
k = 22 / 2
k = 11
Therefore, the equation is y = 11k
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