The area and perimeter of a polygon with vertices (1,-2) , (1,5) , (7,-2)
A=23.27644 units^2
What are the area and perimeter of a polygon with vertices (1,-2) , (1,5) , (7,-2)?Let
A= (1,-2) ,
B=(1,5) ,
C=(7,-2)
Therefore, the equation for distance is mathematically given as
d=\sqrt {(x^2-x^1)^2+(y^2-y^1)^2}
Therefore For AB
[tex]d=\sqrt {(-2-1)^2+(5-1)^2}[/tex]
d=5
For BC
[tex]d=\sqrt {(5-1)^2+(-2-7)^2}[/tex]
d=9.84
for CA
[tex]\sqrt {(5-1)^2+(-2-7)^2}[/tex]
9.486
Hence, Perimeter
P=9.486+9.84 +5
P=24.326
In conclusion, the Area of a triangle
A = √s(s−a)(s−b)
Where
s=24.326/2
Therefore
[tex]A=\sqrt{24.326/2((24.326/2)-5)((24.326/2)-9.486 )((24.326/2)-9.84 )}[/tex]
A=23.27644 units^2
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Amys weight this year is 50 pounds lessthan twice her weight from last year. if she weighs 120 pounds this year, what equation can be used to find her weight from last year?
Answer:
190
Step-by-step explanation:
(120*2) - 10 = 190
hope this helped !!
A stack of 9 cups measures 194 mm. Another stack of 22 of the same cups measures 272 mm.
1.) Find the height of one cup.
2.) How tall would a stack of n cups measure?
The result for the stack of cups are shown below;
The height of the one cup is found to be 6 mm,The height formed by the stack of n cups is 6n.What is defined as unitary method?The term unitary refers to a single or unique unit. As a result, the goal of this method is to determine values are related to a single unit.
The Unitary Method is the method in which we first find the value of one unit and then calculate the value of the necessary number of units.For example, if a car travels 44 kilometres on two litres of gasoline, we can employ the unitary method to calculate how far it will travel on one litre of gasoline.Now, as per the given question.
Part 1: The height of one cup;
The stack of 9 cups form the height 194 mm.
Similarly, the height of the 22 of the same cups measures 272 mm.
For the calculation of height of one cup;
Difference in the total height = 272 - 194 = 78.
Difference in the number of cups = 22 - 9 = 13.
Thus, the height of one cup = 78/13 = 6
The height of the one cup is found to be 6 mm.
Part 2: The height of n stack of cups;
The height of one cup is estimated as 6 mm.
There are total n number of cups.
Thus, the height of the n cups will be 6×n mm.
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finding the rise and the run on the graph
Answer:
rise = 4, run = 5. The slope would be 4/5
Step-by-step explanation:
You go up by four then right by 5
Subtract (5.3 x 108) − (8.2 x 106).
2.9 x 102
5.218 x 102
2.9 x 108
5.218 x 108
Answer: 5.218*10^8 ==> Option 4
Step-by-step explanation:
(5.3 x 10^8) − (8.2 x 10^6)=
(5.3*10^2 x 10^6) − (8.2 x 10^6)=
(5.3*100*10^6)-(8.2*10^6)=
(530*10^6)-(8.2*10^6)=
(530-8.2)*10^6=
(530.0-8.2)*10^6=
521.8*10^6=5.218*10^8 ==> Option 4
Tallie wants to buy a new iPhone. The iPhone costs
$850. She has saved $325 to put down as an initial
payment and will pay another $75 each month until
the phone is paid off. How many months will it take
for Tallie to pay for her new iPhone?
Answer:
7 months to pay it off.
Step-by-step explanation:
see attached for details.
3/2(8w-6)
can I get the answer in simplest form
Answer: 12w-9
Step-by-step explanation:
Which of the following is equivalent to (7y + 5x) + 8x?
35xy + 8y
7y + 13x
8x(7y + 5x)
7y + 40x
Answer:
7y + 13x
Step-by-step explanation:
Let's simplify step-by-step.
7y+5x+8x
Combine Like Terms:
=7y+5x+8x
=(5x+8x)+(7y)
=13x+7y
The expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x which is correct answer would be option (B).
What is algebra?Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.
What is the algebraic expression?
Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.
⇒ (7y + 5x) + 8x
Open parenthesis and combine like terms to get the solution,
⇒ 7y + 5x + 8x
⇒ (5x + 8x) + (7y)
⇒ 13x + 7y or
⇒ 7y + 13x
Therefore, the expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x.
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researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. the researchers attend political debates and record how frequently each candidate displays positive facial expressions. which research method are the researchers using? a. random sample b. case study c. naturalistic observation d. survey
researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. c. naturalistic observation
What is naturalistic observation?A study technique called naturalistic observation includes watching participants in their natural settings. Many psychologists and other social scientists employ this strategy. It is an approach to qualitative research that emphasizes gathering, analyzing, and describing non-numerical data.
When performing lab research would be impractical, expensive, or would adversely influence the subject's behavior, it may be helpful. Naturalistic observation is to capture behavior as it happens in its natural environment without intervention or efforts to change any of the factors. In a lab context, people frequently act differently than they would in the wild. Sometimes, researchers wish to watch their subject's behavior "in the wild".
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what are corresponding angles
I need help ASAPPPPPPPPP
Answer:
C) 3/8 < 1/2 good luck
Step-by-step explanation:
brainliest please
Mrs. Figueroa made a spaghetti dinner for the cheerleaders after practice. She purchased four and three fourths pounds of beef for $3.99 per pound. How much money did she spend on the beef for the spaghetti?
$7.25
$8.87
$9.98
$18.95
Answer:
$18.95
Step-by-step explanation:
Find the surface area of a cylinder with a height of 8 inches and base diameyer of 6 inches i need help badly
The surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
How to find the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches?The given parameters are
Height, h = 8 inches
Diameter, d = 6 inches
The radius is calculated as
r = d/2
So, we have
r = 6/2
r = 3
The surface area of a cylinder is calculated as
S = 2πr(r + h)
So, we have
S = 2 * 3.14 * 3 * (3 + 8)
Evaluate
S = 207.24
Hence, the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
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What is the slope of the line that passes through the points (10, 8) and (7, 14)?
Write your answer in simplest form.
Answer:
-0.2667
Step-by-step explanation:
m =y2 - y1
x2 - x1
=14 - (10)
-7 - (8)
=14 - 10
-7 - 8
=4
-15
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30
The system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30
How to determine the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?The given parameters are
Length = Not more than 12 inches
Perimeter = Less than 30 inches
"Not more than" means less than or equal to
So, we have
l ≤ 12
The perimeter of a rectangle is
P = 2l + 2w
So, we have
2l + 2w = Less than 30 inches
"Less than" is represented with <
So, we have
2l + 2w < 30
Hence, the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30
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Answer:
a. I ≤ 12
2l + 2w < 30
Step-by-step explanation:
i got it right on edge.
Given: B is midpoint if AC
C is the midpoint if BD
Prove: AB is congruent to CD
Answer:
See proof below
Step-by-step explanation:
If B is the midpoint of AC, then AB = BC
If C is the midpoint of BD then BC = CD
Using the transitive property of equality, if a = b and b = c then a =c
We apply this to the above line segments and get
If AB = BC and BC = CD then AB=CD
For two line segments to be congruent they must have the same length
So AB is congruent to CD
How many boxes of cereal can you buy with $42 if one box costs $5.25? As Equation Review
Answer:
8
Step-by-step explanation:
$ 42 / 5.25 $ / box = x = 8 boxes
7. Vernon filled his gas tank with 16 gallons of
gas. The table shows the linear relationship
between the amount of gas remaining in his
tank and the miles driven. What is the rate of
change of gallons of gas per mile driven?
Miles Driven
Gas (gal)
0,16
84,12
105,11
336,0
* coordinates is a chart x representing miles driven y representing gas(gal)
Vernon put 16 liters of gas in his tank. 21 miles per gallons of gas are consumed each mile that is driven.
Given that,
Vernon put 16 liters of gas in his tank.
The table depicts the linear relationship between the mileage driven and the amount of gas in his tank.
We have to find how many gallons of gas are consumed each mile that is driven.
From the table we can say
The total Distance is 336
The total gallons of gas is 16
Rate= Total distance/Total gallons
Rate=336/16
Rate=21 miles per gallons
Therefore, 21 miles per gallons of gas are consumed each mile that is driven.
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If the length of a certain rectangle is increased by 1, then the area of the rectangle is increased by 12. If instead, the width is increased by 2, then the area of the rectangle is increased by 42. What is the area of the original rectangle?
Answer: Let the length and breadth of a rectangle are x and y units , its area is x.y units^2
Step-by-step explanation: sorry no explanation
Solve the inequality 34q−23q<512q−112 and write the solution in interval notation.
Answer: [tex]q=\frac{112}{501}[/tex]
Step-by-step explanation:
1) Add similar elements: 11q < 512q - 112
2) Subtract 512q from both sides: 11q - 512q < 512q - 112 - 512q
3) Simplify: -501q < -112
4) Multiply both sides by -1 to reverse the inequality: (-501q)(-1) > (-112)(-1)
5) Simplify: 501q > 112
6) Divide both sides by 501: [tex]\frac{501q}{501} > \frac{112}{501}[/tex]
7) Simplify: [tex]q=\frac{112}{501}[/tex]
At Cheng's Bike Rentals, it costs $46 to rent a bike for 9 hours. How many hours of bike use does a customer get per dollar? Answer each part. If necessary, round your answers to the nearest hundredth.
Answer:
0.20 hours
Step-by-step explanation:
Bike rental is $46 for 9 hours.
We want to find hours per dollar, so divide time by cost:
9 hours / 46 dollars = 0.19565217... hours/dollar
Rounded to nearest hundredth:
0.20 hours
the limit of f(x) as xa describes what happens to f(x) when x is near, but not equal to, the value a.
If x is near but not equal to, the value an is that f(a) then the function will not continue.
What is the limit?Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.
In another word, limit is a mathematical concept in which we find out the value of any function at a point by its adjacent very close point.
If a function f(x) is defined near to x = a but not a then there will be no continuity of that function at that point.
To exist a limit at x = a
LHL = RHL
But for continuity
LHL = RHL = f(a)
Hence "If x is near but not equal to, the value an is that f(a) then the function will not continue".
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The list of ingredients for chocolate
brownies given at right will make 16
brownies.
Use the list to decide how much of
each ingredient is needed to make 6
brownies.
2
3
5 ounces unsweetened chocolate
1/2 cups sugar
cup butter
2 teaspoons vanilla
2 eggs
1 cup flour
www
cup(s) of butter is needed.
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
ounce(s) of chocolate are needed
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
The following ingredients are needed to make 6 brownies:
Cups of butter needed is 1/4 cups
Ounces of chocolate needed is 1 7/8
Cups of sugar needed is 9/16
Ounces of vanilla needed is 3/4
How much ingredients are needed?
Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero. An example of an integer is -1.
A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator.
Cups of butter needed = (2/3 x 6) / 16
4 / 16 = 1/4 cups
Ounces of chocolate needed = (5 x 6) / 16
= 30 / 16 = 1 14/16 = 1 7/8
Cups of sugar needed = ( 1 1/2 x 6) / 16
(3/2 x 6) / 16 = 9/16
Ounces of vanilla needed = ( 2 x 6) / 16
= 12 / 16 = 3/4
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What is the measure of x?
What is an undefined term?
Answer : Undefined terms are those terms that don’t require a formal definition. The four terms are point line plane and set
Step-by-step explanation:
Help with all answers
The value of m∠1 is 158° as the two line x and y are parallel.
Two lines are said to be parallel if they do not meet at any point and the perpendicular distance between them is always the same.
A straight line intersecting both the parallel lines is called a transversal.The alternate interior or exterior angles formed are always equal.The corresponding angles are equal.The co-interior angles are supplementary.In the given figure it is given that x║y and m∠2 = 22°.
Now let us use the above principles to solve the value of the other angles.
m∠2+m∠1 = 180°(linear pair)
or, m∠1= 180°-22°
or, m∠1=158°
m∠2+m∠3 = 180°(co-interior angles are supplementary)
or,m∠3=158°
m∠2=m∠4(Corresponding angles are equal)
or, m∠4=22°
m∠2=m∠5 (vertically opposite angles are equal)
or, m∠5=22°
m∠6=m∠1 (vertically opposite angles are equal)
or, m∠6=158°
m∠2=m∠7(alternate angles are equal)
or, m∠7=22°
m∠3=m∠8 (vertically opposite angles are equal)
or, m∠8=158°
Hence all the above angles are calculated using the properties of parallel lines.
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for #13-14 determine if the lines are parallel, perpendicular or neither 10x +5y=-5 and y=-2x+6
Answer:
48
because. Of the time
of the 35 flavors of ice cream at an ice cream parlor, 25 flavors contain some sort of nuts, 12 are fat-free, and 8 both fat-free and contain nuts. how many of the flavors at the ice cream parlor neither are fat-free nor contain nuts?
The number of ice creams according to the probability, Neither contain nuts nor are fat free is 6.
According to the statement
We have to find that the ice creams that neither are fat-free nor contain nuts.
So, For this purpose, we know that the
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.
From the given information:
There are 35 flavors of ice cream at an ice cream parlor, 25 flavors contained ice creams.
Contain nuts = 25
Are fat free = 12
Are both = 8
Then
Contain nuts or are fat free = 25+12-8 = 29
Total = 35
Neither contain nuts nor are fat free = 35-29 = 6.
So, The number of ice creams according to the probability, Neither contain nuts nor are fat free is 6.
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is james scored a 40 on a test with a mean of 38 and the standard deviation was for whataburger z-score be
The value of z-score for James is 0.2
Step-by-step explanation:
From the formula of z-score we know that
z-score = individual score - mean / standard deviation
Given
James score = 40
Mean = 38
Standard deviation = 10 (missing in question)
To find
z-score =?
Let's put the values in the formula
z-score = 40-38/ 10
z-score = 0.2
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Calculate the electric potential energy in a capacitor that stores 1.0 x 10^-10 C
of charge at 100.0 V. Use PE = 1/2QAV.
OA. 1.0 x 10-8 J
OB. 1.0 x 102 J
O C. 5.0 × 10¹ J
OD. 5.0 × 10-9 J
The electric potential energy is 5.0 × 10^(-9) J
How to calculate the electric potential energy?
The formula to calculate the electric potential energy in a capacitor is;
E = 1/2 * C * V²
Where;
E = electric potential energy
C = capacitance = charge
V = voltage applied
We are given;
Voltage applied; V = 100 V
Capacitance (Charge) = 1 × 10⁻¹⁰ C
Plugging in the relevant values gives
E = 1/2 * 1 × 10⁻¹⁰ * 100
E = 1/2 * 1 × 10⁻⁸
E = 0.5 × 0⁻⁸ volts
E = 5.0 × 10^(-9) J
Thus, we conclude that the electric potential energy is 5.0 × 10^(-9) J
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Given f(x) = 2(3 - x) - 2x, what is the value of f(x) = -10?
The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.
To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.
Given:
f(x) = 2(3 - x) - 2x, we have:
-10 = 2(3 - x) - 2x
Let's simplify the equation step by step:
-10 = 6 - 2x - 2x
-10 = 6 - 4x
-10 - 6 = -4x
-16 = -4x
To solve for x, divide both sides by -4:
x = (-16) / (-4)
x = 4
Therefore, when f(x) = -10, the value of x is 4.
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