Two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm is 12.3cm and 19.3cm.
In space, a point is a precise position or location. It is possible to depict it in relation to a coordinate system and its origin. It has no length and is a zero-dimensional entity.
A line is made up of an unlimited number of points that form a straight line. One-dimensional objects like lines lack both thickness and width. It stretches forever in both directions. An endpoint and a beginning point define a line segment, which is a component of a line. A linear equation can be used to depict a line.
D is between C and E
_ _ _
C D E
CD =CE-DE
CD=15.8-3.5cm
CD=12.3 cm
E is between D and C
_ _ _
D E C
CD=CE+DE
CD=15.8+3.5cm
=19.3cm
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The figure to the right shows the graph y= 3^-x and three inscribed rectangles. What is the sum of the areas of the rectangles?
Based on the calculations, the sum of the areas of the rectangles is equal to: A. 0.25 square unit.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.By critically observing the figure (see attachment), we can logically deduce the following information:
Width of rectangle A = 2 units
Width of rectangle B = 2 units.
Width of rectangle C = 4 units.
Next, we would determine the length and area of each of the rectangle.
The length of the first rectangle is given by:
Length of rectangle, y = 3^-x
Length of rectangle, y(0) = 3⁻⁰ = 1 units.
Length of rectangle, y = 3^-x
Length of rectangle, y(2) = 3⁻² = 0.11 unit.
Area of first rectangle = 2(0.11)
Area of first rectangle = 0.22 square unit.
For the second rectangle, we have:
Length of second rectangle, y = 3^-x
Length of second rectangle, y(4) = 3⁻⁴ = 0.012 unit.
Area of second rectangle = 2(0.012)
Area of second rectangle = 0.025 square unit.
For the third rectangle, we have:
Length of third rectangle, y = 3^-x
Length of third rectangle, y(8) = 3⁻⁸ = 0.00015 unit.
Area of third rectangle = 4(0.00015)
Area of third rectangle = 0.0006 square unit.
Now, we can calculate the sum of the areas of the rectangles:
Total area = 0.22 square unit + 0.025 square unit + 0.0006 square unit.
Total area = 0.246 ≈ 0.25 square unit.
Total area of rectangle = 0.25 square unit.
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Complete Question:
Figure 3 shows the graph of y = 3^−x and three inscribed rectangles. What is the sum of the areas of the rectangles?
[a] 0.25
[b] 0.50
[c] 2.45
[d] 6.26
[e] 12.68
which term best describes the number of solutions that will maximize the function below given the constraints listed? (assume that and .) 3x 2y a. one optimal solution c. unbounded b. alternate optimal solutions d. infeasible please select the best answer from the choices provided a b c d
The best term that describes the number of solutions that will maximize the function is one optimal solution (a).
Number of Solutions in linear equations:
There are 3 possible types of solutions to the set of linear equations. They are:
Unique Solution - linear equation represents that there exists only one point, which on substitution, L.H.S becomes equal to R.H.S. In the case of simultaneous linear equations in two variables, the solution should be an ordered pair (x, y).
No Solution - linear equations are parallel, then the system of linear equations has no solution.
Infinitely Many Solutions - graph for the system of linear equations with infinitely many solutions is a graph of straight lines that overlaps each other.
Given,
Here we need to find the number of solutions that will maximize the function below given the constraints listed.
the constraints are 3x and 2y.
We know that, linear equations in two variables, the solution should be an ordered pair (x, y).
So, here we have exactly only one solution that is a unique solution.
Then the option (a) one optimal solution is correct
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ashley recently opened a store that uses only natural ingredients. she wants to advertise her products by distributing bags of samples in her neighborhood. it takes one person 2/3 of a minute to prepare one bag.
Ashley and her four friends will need 5 hours and 19.57 minutes to make 1575 bags if Ashley takes 2/3 of a minute and each friend takes 75% longer.
What is a minute?
The first sexagesimal fraction of an hour, or one-fifth of an hour, or 60 seconds, is known as the minute. On rare occasions, due to leap seconds, a minute in the UTC time zone has 61 seconds (A negative leap second might be inserted, producing a minute of 59 seconds; however, this has never occurred in more than 40 years under this system.) The minute can be used with SI units even if it isn't a SI unit. Minute or minutes is represented by the SI unit min (without a dot). Occasionally, people would slangy refer to minutes of time by the prime symbol.
Calculations:
For a bag, Ashley needs about 2/3 of a minute.
= Ashley prepare bag in 1 minute = 3/2
Her friends takes 75% Longer to prepare a bag
time taken by her friends = 2/3 + (75/100)(2/3)
= (2/3)( 1 + 3/4)
= (2/3)(7/4)
= 7/6 Minutes
Her one friend prepare bag in 1 minute = 6/7
Bag prepared by Ashley & her 4 friend in 1 Minute
= 3/2 + 4*6/7
= (21 + 48)/14
= 69/14 Bag
69/14 Bag prepared in 1 minute
1 Bag prepared in 14/69 minutes
1575 bags prepared in 1575 * 14/69
= 319.57 minutes
= 5 hrs 19.57 Minutes
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Point L is the midpoint of JK . JK intersects MK at K . If MK ≅ JL , prove that LK ≅ MK
You can see that JL = LK and MK ≅ JL, hence according to the transitive property, we can conclude that LK ≅ MK
Midpoint of coordinateA midpoint is a point that divides a line of a segment into two equal parts. It also means that the point bisects the given line.
If the point L is the midpoint of JK, then;
JL + LK = JK and;
JL = LK .........1
Similarly, K intersects MK at K, then;
MK ≅ JL..........2
From equation 1 and 2, you can see that JL = LK and MK ≅ JL, hence according to the transitive property, we can conclude that LK ≅ MK
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Members of a baseball team raised $1128.75 to go to a tournament. They rented a bus
for $856.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Equation:
The baseball team can bring 11 players to the tournament based on their budget.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of players the team can bring to the tournament. They rented a bus for $856.50 and budgeted $24.75 per player for meals, hence:
24.75x + 856.5 = 1128.75
x = 11
The baseball team can bring 11 players to the tournament based on their budget.
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A contaminat is found in solution at a level of 3/500%. What fraction of the solution isnthis?
The fraction of the solution present in the contaminant is 3/5.
What is defined by the term fraction?Fractions represent parts of a whole or group of objects. A fraction is made up of two parts. The number at the top of the line is made reference to as the numerator. It specifies the number of equal portions of the entire or collection that are taken. The denominator is the number just below line. It displays the total number of equal portions into which the whole is divided or the total number of identical objects in a collection.First, we convert 50% to fractions.
Changing a percentage to a fraction is equivalent to dividing a number by 100.
500% = 500/100
Taking this into account, we get 3/(500/100).
Then, when we divide a number by a fraction, we multiply the result by the inverse of the fraction.
= 3/(500/100)
= 3 x 100/500
Further simplifying;
= 300/500
= 3/5
Therefore, the value of the fraction of contaminant solution is 3/5.
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Simplify 1 3/4 and 2 1/2
Answer: 1 3/4=7/4
2 1/2=5/2
Step-by-step explanation:
1 3/4=
1 + 3/4=
4/4 + 3/4=
(4+3)/4=7/4
2 1/2=
2+1/2=
4/2+1/2=5/2
Bianca spent 1/2 of an hour playing on her phone . that used up 1/3 of her battery how long would she have to play on her phone to use the entire battery
Bianca should play with her phone for 1.5 hours to use the entire battery.
What exactly are fractions?A fraction is a portion of a whole or, to put it another way, any number of equal parts.A fraction in everyday English refers to the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.Bianca spent 1/2 of an hour playing on her phone which used up 1/3 of her phone's battery.
So, 1/3 × 3 = 3/3 = 1So, if she plays with her phone 3 times more she will use the entire battery of the phone.Then,
1/2 × 3 = 3/2 = 1.5 hoursTherefore, Bianca should play with her phone for 1.5 hours to use the entire battery.
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I’m thinking of a number when I add 1 and then take 2/3 of it I get 18 what is my number
Answer:
53/3
Step-by-step explanation:
[tex]x \: + 1 - \frac{2}{3} = 18 \\ x \: - \frac{2}{3} = 18 - 1 \\ x - \frac{2}{3} = 17 \\ x = \frac{17}{1} + \frac{2}{3} \\ x = \frac{51 + 2}{3} \\ x = \frac{53}{3} \\ check \\ \frac{53}{3} + \frac{1}{1} \\ = \frac{53 + 3}{3} \\ = \frac{56}{3} - \frac{2}{3} \\ = \frac{56 - 2}{3} \\ x = \frac{54}{3} \\ x \: = 18[/tex]
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please I want a beautiful and nice sentences in12 words:bedrock,robust,isolation,eliminate,ritual, endure, diagnose, outlive, relieve,ailment, relentless and mortality.and thanks
Answer:
Step-by-step explanation:
What is the formula for the sum of two whole numbers is 72. The difference is 48 what are the two numbers
Answer:
It works in both equations, so the two numbers are 60 and 12.
Step-by-step explanation:
Explain how to graph the function using transformations seen in the function. f(x)=3(x+7)^3 - 9
Answer:
Step-by-step explanation:
f(x)=3(x+7)³-9
1. Let's graph the function у=3х³
2. Shift the graph of the function to the left by 7 units along the х-axis
3. Slide the graph of the function down 9 units along the y-axis
Carter wants to ride his bicycle 28.7 miles this week. He has already ridden 17 miles. If he rides for 3 more days, write and solve an equation which can be used to determine mm, the average number of miles he would have to ride each day to meet his goal.
The equation which can be used to solve the the average number of miles he would have to ride to meet his target is 28.7 = 17 + 3x.
The solve equation is x = 3.9 miles.
How to find the number of miles he will ride each day with an equation?He wants to ride his bicycle 28.7 miles this week.
He has already ridden 17 miles.
He rides for 3 more days.
The equation which can be used to determine the average number of miles he would have to ride to meet his target can be calculated as follows:
The total distance to ride is 28.7 miles.
Therefore,
28.7 = 17 + 3x
where
x = number of miles he will travel for the remaining 3 daysTherefore,
28.7 = 17 + 3x
subtract 17 from both sides of the equation
28.7 = 17 + 3x
28.7 - 17 = 17 - 17 + 3x
11.7 = 3x
divide both sides by 3
3x / 3 = 11.7 / 3
x = 11.7 /3
x = 3.9
Therefore, he needs to travels 3.9 miles daily for 3 days.
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What is the sum of the following numbers?
-7, 5, -3, 6, -4, 7, -5, 3, -1, 4
Answer:
5
Tips to Add Negative and Positive Numbers:
1.) Adding a negative number to a positive number is subtracting it.
example: 5 + (-3) = 5 - 3
2.) Adding a positive number to a smaller negative number is subtracting the smaller number by the larger one.
example: -3 + 5 = 5 - 3
3.) Adding a positive number to a larger negative number is having the positive number subtracted by the larger negative.
example: -5 + 3 = 3 - 5 (but the final answer needs a negative sign)
4.) Adding a negative number to another negative number is adding the numbers together, but with a negative sign in the final calculation.
example: -3 + (-2) = 3 + 2 (but the final answer needs a negative sign)
5.) I think you know how to add two positive numbers
(I know the wording of the tips can be confusing, so make sure to look at the examples if you don't understand)
because of the rainy season, the depth in a pond increase 3% each week. before the rainy season started, the pond was 10 feet deep. what is the equation that best represents the depth of the pond each week? hint: use the formula y
The equation that best represents the depth of the pond each week is,
[tex]y=10(1.03)^{x}[/tex]
What is an equation?
A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation.
Given:
The given equation is,
[tex]y=P(1+r)^{x} \;\;\;\;\;-------equation(1)[/tex]
Depth of the pond, P = 10 feet deep
Rate of pond increase, r = 3% = 0.03
Substitute the value of P and r in the equation (1),
[tex]y=10(1+0.03)^{x}[/tex]
Therefore, The equation that best represents the depth of the pond each week is,
[tex]y=10(1.03)^{x}[/tex]
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BOOKWORK Code: L82
allowed
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-
angled triangle.
Give your answer in centimetres (cm) to 1 d.p.
8 cm
3.9 cm
Not drawn accurately
The length of the hypotenuse in this right-angled triangle = 6.98 cm².
What exactly is the Pythagorean Theorem?The Pythagorean theorem states that the total of the squares on the legs of a right triangle equals the square upon that hypotenuse (the side opposite the right angle)—or, in popular algebraic notation, a2 + b2 = c2.
What is the triangle's formula?The basic formula for calculating the area of a triangle is the half square product of its base as well as height, i.e., A = 1/2 b h. This formula applies to all triangles, whether they are scalene triangles, isosceles triangles, or equilateral triangles.
According to the information:Hypotenuse (c) = 8 cm
Base (b) = 3.9 cm
Length =
C² = (a² + b³)
a² = C² - b²
a = √((8)² - (3.9)²)
= 6.98 cm²
The length of the hypotenuse in this right-angled triangle = 6.98 cm².
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3(-4x-2)=-6
X=???????
every student in a homeroom class takes a biology course or a spanish course or both. if 18 take biology, 13 take spanish and 5 take both, how many students are in the homeroom classroom?
=====================================================
Work Shown:
A = 18 take bio
B = 13 take Spanish
C = 5 take both
A+B-C = 18+13 - 5 = 26 students total
------------------------------
Another approach:
18 take bio and 5 take both, so 18-5 = 13 take bio only
13 take Spanish and 5 take both, so 13-5 = 8 take Spanish only
We then have 13+8+5 = 26 students
Both methods only work when each student is in either bio, Spanish, or both. We cannot have a student who is in neither class.
Pls pls help whoever gets it right gets a crown
Answer its the first one
Step-by-step explanation:
Is it possible to draw a triangle with angles 150˚, 20˚ and 20˚ and explain answer
Answer: False; the sum of the angles is not equal to 180
Answer:
No
Step-by-step explanation:
The sum of angles in a trigngle has tp be 180.
150+20+20 is 190, there fore you cant
Class work help Algebra 2
Answer:Algebra 2 is the third math course in high school and will guide you through among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.
A circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top. Calculate the pressure in N/m2 to 4sf.
The pressure of the circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top = 287.23 N/m².
The force defined as:A force seems to be an influence that could also cause an object's motion to change. A force can cause a mass item's velocity or acceleration to alter. The force can be expressed intuitively as a push or perhaps a pull. Because it has both magnitude and direction a force is a vector quantity.
What exactly do you mean by pressure?The force applied against the surface of an item per unit area across which that force is spread is referred to as pressure (symbol: p or P).
According to the given data:Force = 810N
Radius of the circular table = 90cm.
Pressures = force /area
Finding the area of circular table = πr²
= π x 90 x 10⁻² (1 cm = 10⁻²)
= 2.82 m²
substituting the value in the formula.
Pressures = force /area
= 810/2.82
= 287.23 N/m²
The pressure of the circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top = 287.23 N/m²
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can you solve this for me
The answer to the problem of logical reasoning will be:
8 + 9 × 4 = 8 + 36 = 44
By hit and trial method, we get that:
The value of bag will be 4.
The value of book will be 9
The value of pencil will be 5.
We get that:
4 + 9 × 4 = 4 + 36 = 40
Which is true
2(8) + 8 × 4 = 16 + 32 = 48
Which is true
9 + 8 + 2(8) = 9 + 8 + 16 = 33
Which is true
So, we get that:
8 + 9 × 4 = 8 + 36 = 44
Therefore, the answer to the problem of logical reasoning will be:
8 + 9 × 4 = 8 + 36 = 44
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A line passes through the point (-1,-2) and has a slope of
-5.
Write an equation in slope intercept form for this line.
Answer:
y = - 5x - 7
Step-by-step explanation:
A line has a function:
y = ax + b
Because the line has a slope of - 5
=> a = - 5
=> y = - 5x + b
Because the line goes through point (- 1; - 2)
=> - 2 = (- 5).(- 1) + b
=> 5 + b = - 2
=> b = - 7
=> The slope intercept from of the line:
y = - 5x - 7
Sam says that both 0.0032 and 0.0302 have 2 significant digits
because zeros are not significant. Do you agree?
Answer:
ask his mom she probobaly weighs more
Step-by-step explanation:
Nina has $40 in the bank. She writes a check for $63, deposits $80 and writes another check for $140. What is her balance?
Answer:
-$83
Step-by-step explanation:
Create an equation to model Nina's balance.
[tex]40-63+80-140=-83[/tex]
34 - 2x = 3x + 4 what is the answer with the work
A quantity increases from 225 to 250. what is the percentage increase? round your answer to the nearest tenth of a percent.
The percentage increase for given quantity is 11.1%
In this question,
A quantity increases from 225 to 250.
So, the absolute change in the quantity would be,
|225 - 250| = 25
The relative increase of the quantity would be,
R = [tex]\frac{|225 - 250|}{225}[/tex]
R = 25 / 225
R = 0.111
We know that, the percentage increase of the quantity is the relative increase multiplied by 100.
So, the percentage increase of given quantity would be,
P = 0.111 × 100
P = 11.1%
Therefore, the percentage increase for given quantity is 11.1%
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(2, 6) and (-1, 3) is this a negative slope
The slope associated with points (2, 6) and (-1, 3) is 1 so it is not a negative slope.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
Given the points,
(2, 6) and (-1, 3)
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
So,
Slope = (3 - 6)/(-1 - 2)
Slope = (-3)/(-3) = 1
Hence "Slope of the given points is +1 so it is positive".
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The boiling point of a liquid is the temperature at which the liquid starts to boil. The boiling point of water is 212°F. Propane gas is used for cooking in gas grills. Liquid propane has a boiling point of
–
44°F.
How much warmer is the boiling point of water than the boiling point of liquid propane?
The boiling point of water is 256 °F warmer than the boiling point of liquid propane.
In the question, we are given that the boiling point of a liquid is the temperature at which the liquid starts to boil. The boiling point of water is 212°F. Propane gas is used for cooking in gas grills. Liquid propane has a boiling point of -44°F.
We are asked to find how much warmer the boiling point of water is than the boiling point of liquid propane.
To find the warmth of the boiling point of water in comparison to the boiling point of liquid propane, we subtract the boiling of liquid propane from the boiling point of the water.
Thus, The warmer the boiling point of water is in comparison to the boiling point of liquid propane = The boiling point of water - The boiling point of liquid propane,
or, The warmer the boiling point of water is in comparison to the boiling point of liquid propane = 212 °F - ( -44 °F),
or, The warmer the boiling point of water is in comparison to the boiling point of liquid propane = 212 °F + 44 °F = 256 °F.
Thus, the boiling point of water is 256 °F warmer than the boiling point of liquid propane.
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