The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.
What is an interior angle?Interior angles are those that lie inside a polygon.
To calculate an interior angle of a hexagon, we use the formula below.
Formula:
a = 360-(b+c+d+e+f)............ Equation 1Where:
a = The sixth exterior angleb = 55°c = 60°d = 69°e = 57°f = 57°Substitute these values into equation 1
a = 360-(55+60+69+57+57)a = 360-298a = 62°Recall that, the sum of an interior and exterior angle is 180°
a'+a = 180............... Equation 2Where:
a = Interior angle of the sixth exterior angle.Substitute the value of a into equation 2
a' = 180-62a' = 118°Hence, the value of the interior angle is 118°.
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If it' 50c outide and the temperature will drop 70c in next 3 hour, how cold will it get?
The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.
Given:
If it' 50 c outside and the temperature will drop 70 c in next 3 hour.
Temperature (cold) = present temperature - temperature in next 3 hour.
= 50 - 70
= -20 c.
Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.
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Solve the system of inequalities by graphing.
y < -2x - 5
y > 6x + 5
Answer:
Take a look at the attachment...
Hope this helps! :)
Find the equation of a line that passes through the point (0,-1) and has a gradient of -3. Leave your answer in the form y = m x + c
The equation of a line that passes through the point (0,-1) and has a gradient of -3 is y = -3x - 1
How to determine the equation of the line?From the question, we have the following points that can be used in our computation:
(x, y) = (0, 1)
Also, we have the slope to be
gradient = -3
Rewrite as
m = -3
The equation of the line is then calculated using the following equation
y = m(x - x₁) + y₁
Where
(x, y) = (0, -1)
m = -3
Substitute the known values in the above equation, so, we have the following representation
y = -3 * (x - 0) - 1
Evaluate
y = -3 * x - 1
So, we have
y = -3x - 1
Hence, the line equation is y = -3x - 1
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one antifreeze solution is 26% alcohol and another is 20% alcohol. how much of each mixture should be added to make 45 l of a solution that is 24% alcohol?
30 L of 26% and 15L of 20% of each mixture should be added to make 45 l of a solution that is 24% alcohol.
What is concentration?The quantity of a substance, like salt, that is present in a specific volume of tissue or liquid, like blood, according to science. When there is less water present, the substance becomes more concentrated. You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution.
Here,
26x + 20(45-x) = 45(24)
26x -20x = 45(24) -(20(45)
6x = 4(45) = 180 x = 180/6 = 30 L of 26%
45-x = 45-30 = 15L of 20%
To make 45 l of a 24% alcohol solution, combine 30 l of 26% and 15 l of each mixture.
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The points (0, –10) and (15, 6) fall on a particular line. What is its equation in slope-intercept form?
Answer:
slope: (6+10)/(15-0)
M: 16/15
B = -10
y = 16/15x -10
You are in an elevator in a mine shaft preparing to descend into the mine. As you begin, you are nine feet above ground level. You then begin to descend. Your elevation changes at the rate of negative one foot per second. Treat elevations above ground level as positive and elevations below ground level as negative.
What will your elevation be in five minutes?
The elevation is represented by y = -t + 9, and after 5 minutes would be 4 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the height of the elevator above the ground after t seconds.
As you begin, you are nine feet above ground level. Your elevation changes at the rate of negative one foot per second. Hence:
y = -t + 9
In 5 minutes:
y = -(5) + 9 = 4
The elevation in 5 minutes would be 4 feet.
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-2.2f + 0.4f - 16 - 8
The volume of a sphere is decreasing at a constant rate of 55 cubic feet per minute. At the instant when the radius of the sphere is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V= 3 4 πr 3 . Round your answer to three decimal places.
If the volume of a sphere is decreasing at a constant rate of 55 cubic feet per minute. The volume of a sphere is 0.036.
How to find the volume of a sphere?Using this formula to find the volume of a sphere
V = 4/3 π r³
Taking the derivative with respect to time:
dV/dt = 4π r² dr/dt
Let plug in the formula
55 = 4π (11)² dr/dt
dr/dt = 55/ (484π)
dr/dt = 55/1,520.5308
dr/dt = 0.036
Therefore the volume of a sphere is 0.036.
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Please helpp 20 points
Show all your work and steps please
Solve for W
P = 2L + 2W
The equation to solve for W is W = (P-2L)/2.
According to the question,
We have the following information:
P = 2L + 2W
Now, we have to solve this equation for W.
Subtracting 2L from both sides of the equation will give us the following expression:
P-2L = 2W
Now, we will divide both sides of the equation by 2. And we will have the following expression:
(P-2L)/2 = W
(More to know: now, in this equation, if the value of P and L are given then we can use this equation to find the value of W.)
Hence, the equation to solve for W is W = (P-2L)/2.
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Is this relation a function?
(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)
The given relation is not function, because 15 is repeating twice. In domain 15 is with 8 and 2.
What is a Function in math ?Function is a mathematical phrase, rule, or law that establishes the connection between two variables. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.Most frequently, the letters f, g, and h are used to represent functions. The value of a function f at an element x in its domain is represented by the symbol f. (x)The collection of all pairings (x, f (x)), also known as the function graph, serves as the sole representation of a function.To learn more about Function refer :
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STRUCTURE Find the slope of the line that passes through the pair of points.
ty
O
(0, 1)
(1,-2)
X
The slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.
First, let us understand the slope of a line:
A slope of a line is defined in mathematics as the change in the y coordinate with regard to the change in the x coordinate.
We are given the points:
(0, 1) and (1, -2)
We will calculate the slope of the line using the following formula:
m = (y_2 - y_1) / (x_2 - x_1)
Let x_1 = 0, x_2 = 1, y_1 = 1 and y_2 = -2.
Substitute the given values in the above formula, we will get:
m = (-2 - 1) / (1 - 0) = -3 / 1 = -3
So, the slope of the line is -3.
Thus, the slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.
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A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 12-inch pieces can the dressmaker cut from 5 of these rolls of ribbon?.
45 pieces can the dressmaker cut from 5 of these rolls of ribbon.
Mathematical expression:
When we validly combine numbers and variables, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.
Here we have to find the number of 12-inch pieces can the dressmaker cut from 5 of these rolls of ribbon.
We are provided the length of the ribbon, which is 9 feet.
As we know that
1 feet = 12 inches
So rolls of 9 feet can make 9 pieces of 12 inches.
So 5 of these rolls of ribbon can make = 5 × 9 = 45 pieces.
Therefore we get 45 pieces.
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For the 4th & 5th grade end-of-year field trip, the PTA raised $7,985 to take students to Dominion. There will be 112students and 13 teachers. How much will the tickets cost for everyone?
The cost of the ticket for everyone, given the amount raised by the PTA, can be found to be $63.88
How to find the cost of the tickets?The cost of the tickets to each individual person, or to everyone, can be found by the formula:
= Amount raised by PTA / Number of students and teachers going on the trip
Amount raised by PTA = $7, 985
The number of students and teachers going on the trip:
= 112 + 13
= 125 people
The cost of the tickets are:
= 7, 985 / 125
= $63.88
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Can someone pls help me
Answer:
Total surface area of the cone = 208.81 sq cm
explanation
Diameter of the cone (d) = 7 cm
Slant height (L) = 15.5 cm
1) The radius of the cone= Half of the diameter
= 7/2 cm = 3.5 cm
⇒ r = 3.5 cm
Now, Total surface area of the cone =
taking π = 3.14
We get
and πrl = 3.14 x 3.5 + 15.5 = 170.345
So, Total surface area of the cone = 38.465 + 170.345 = 208.81 sq cm
HELP ASAP PLEASE PLEASE ILL DO THE BRAINLIST PLS PLS PLS
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate
the simple interest using /= prt.
O $69
O $90
O $420
O$1,080
Answer:
$90
Step-by-step explanation:
The amount Oliver borrowed = 1,500
The interest rate applied to the loan = 12%
Required: To calculate the simple interest using the formula, I = P•R•T
Where;
I = The simple interest
P = The principal borrowed = $1,500
T = The time or loan duration = 6 months = 1/2 year
R = The rate at which the loan is applied = 12% = 0.12
Therefore;
I = $1,500 × 0.12/year × 6/12 year = $90
The correct option for the interest paid on the loan is therefore;
$90
2^30 ? 30^2 which is bigger
Answer:
2³⁰ > 30²
Step-by-step explanation:
Now the values of,
→ 2³⁰ = 1073741824
→ 30² = 900
Then the expression will be,
→ 2³⁰ ? 30²
→ 1073741824 > 900
→ 2³⁰ > 30²
Hence, answer is 2³⁰ > 30².
In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree. What was the researchers’ solution?.
In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.
The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.
There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:
Use math to avoid constructing improbable trees
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What is the solution?
Answer:
x = - 1/2
Step-by-step explanation:
3x - 6 = -7.5
3x = -7.5 + 6
3x = - 1.5
3/3 x = -1.5 / 3
x = - 0.5
x = - 1/2
Answer:
x = -1/2
Step-by-step explanation:
Given equation,
→ 3(x - 2) = -7 1/2
Now the value of x will be,
→ 3(x - 2) = -7 1/2
→ 3x - 6 = -15/2
→ 3x = -7.5 + 6
→ x = -1.5/3
→ [ x = -1/2 ]
Hence, value of x is -1/2.
the mixed number 1 2/5 and the decimal number 1.4 can be used to represent the same data. true or false
Answer:
True
Step-by-step explanation:
True.
1 and 2/5 can be rewritten as 1 and 4/10, and thus is equal to 1.4.
y - 3x = 7 What is the y-intercept of the equation above?
a.7
b.9
c.-7
d.-7/3
Answer:
A: 7
Since the slope is 3 and passes down (1, 10), the answer will be 7
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
Answer: Simplify your answer and write it as a proper fraction, improper fraction, or whole number
Step-by-step explanation:
great to least -3/5, -2/3, 0.7, 0
Answer:
Step-by-step explanation:
Least to greatest :
-3/5,-2/3,0,0.7
For a project in his Geometry class, Levi uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.05 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 2 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
The measured distance of 1.15 meters from Levi's eyes to to the ground indicates that the height of the goalpost located 12.05 meters from the mirror when Levi is 2 meters from the mirror, found using similar triangles is approximately 6.93 meters.
What are similar triangles?Two triangles are similar if two angles in one triangle are congruent to two angles in the other triangle.
According the laws of reflection, the angle made by the incident ray with the normal is the same as the angle made by the reflected ray and the normal
Both the angle made by Levi and the angle made by the goalpost with the ground are perpendicular or 90°.
Therefore, the triangle formed by the line of site to the mirror and the reflected ray to the top of the goal post are similar triangles by Angle-Angle similarity postulate.
The ratio of corresponding sides is the same in similar triangles, therefore;
[tex]\dfrac{Levi's \, distance \, from \, the \, mirror}{Goalpost \, distance \, from \ the \ mirror }=\dfrac{Levi's \,height}{Height\, of \, the \, goalpost, H}[/tex]
[tex]\dfrac{2}{12.05} =\dfrac{1.15}{H}[/tex]
[tex]H =\dfrac{1.15\times 12.05}{2} \approx 6.93[/tex]
The height of the goalpost is approximately 6.93 meters
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principle is ___ ??????????????????????
- the original amount invested
- the total amount earned
- interest plus original amount invested
- interest on a loan
4x + 2 – (3 + 3x) = 7
The answer to the question is: x = 8
Answer:
x = 8
Step-by-step explanation:
4x + 2 - 3 - 3x = 7
x -1 = 7
x = 7 + 1
x = 8
Mrs. Becker wants to get family portraits taken and is comparing prices between two different photography studios. Murray Photography charges $25 per portrait sheet, plus $30 for the session fee. Lasting Memories Company charges $50 for the session fee and $15 per portrait sheet. If Mrs. Becker plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. What would the total cost be?
Write a system of equations, graph them, and type the solution.
A system of equations to describe this situation is:
c(n) = 25n + 30
c(n) = 15n + 50
The total cost is equal to $80.
The solution to this system of equations is 2.
How to write a system of equations?In order to write a system of equations to describe this situation, we would assign variables to the number of portrait sheets and cost of a photography session respectively, and then translate the word problem into algebraic equation as follows:
Let the variable n represent the number of portrait sheets.Let the variable c represent the cost of a photography session.The cost for Murray Photography is given by:
c(n) = 25n + 30
The cost for Lasting Memories Company is given by:
c(n) = 15n + 50
Next, we would solve the system of equations as follows:
25n + 30 = 15n + 50
25n - 15n = 50 - 30
10n = 20
n = 20/10
n = 2.
Now, we can calculate the total cost:
c(n) = 25n + 30
c(2) = 25(2) + 30
c(2) = $80.
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monica tiene una heladeria pago 210.000 por la compra de los ingredientes, recibio 550.000 y al final del mes pago 105.000 para el mantenimiento de equipos
que numero entero representa el balance de Monica al final del mes?
The number that represents Monica's balance at the end of the month, given the amount paid for the ingredients and the amount received, is 235, 000
How to find the end of month balance?The balance at the end of the month to Monica's ice cream parlor can be found by the simple formula:
= Amount received - Amount spent
The amount received is 550, 000.
The amount spent is:
= Purchase of ingredients + Equipment maintenance
= 210, 000 + 105, 000
= 315, 000
Monica's balance is therefore:
= 550, 000 - 315, 000
= 235, 000
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y=2(x+1)^2 has how many real roots
The answer will be:
The equation has one real root. And the root is -1/2.
The equation y= 2[tex](x+1)^2[/tex] has one real root and that is x=-1.
What is real roots of the equation?
We are aware that when we resolve a linear or quadratic equation, we always arrive at the value variable of the equation, or, to put it another way, we always locate the equation's solution. This "solution" is what we refer to as the real roots. For instance, when the equation [tex]X^2[/tex]-7x+12=0 is solved, the actual roots are 3 and 4.
Here given,
=> y = 2[tex](x+1)^2[/tex]
Take y=0 then,
=> 2[tex](x+1)^2[/tex]=0
=> [tex](x+1)^2[/tex]=0
=>(x+1)=0
=> x=-1
Hence the given equation has one real root and that is x=-1.
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find 3x+4y when x is 6 and y is -3
Answer:
Step-by-step explanation:
3x + 4y when x = 6 and y = -3
Put in values of x and y:
3(6) + 4(-3) = 18 + (-12) = 6
What is the 3 geometric means between 5 and 3125?.
The 3 geometric means between 5 and 3125 is 5, 25, 125, 625, 3125 using Geometric progression.
What is geometric mean?The geometric mean is a mean or average used in mathematics that uses the product of the values of a collection of numbers to show the central tendency of that set of numbers. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. An average that multiplies all values and determines the number's root is known as the geometric mean. You locate the nth root of their product for a collection of n integers. This descriptive statistic can be used to sum up your data.
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