We have a square with sides (s-4).
The perimeter of a square is 4 times the length of the side, so we can write:
[tex]P=4\cdot(s-4)=4s-16[/tex]If P is no more than 80 ft, we can find the maximum value for s as:
[tex]\begin{gathered} P<80 \\ 4s-16<80 \\ 4s<80+16 \\ 4s<96 \\ s<\frac{96}{4} \\ s<24 \end{gathered}[/tex]Answer:
1) The perimeter is P = 4s-16
2) The maximum value for s, if the perimeter is no more than 80 ft, is 24 ft.
Enter the value of b when the expression 1/2x + b is equivalent to 1/4(2x+3)
Answer:
b = 3/4
Step-by-step explanation:
[tex]\frac{1}{2}x + b=\frac{1}{4} (2x+3)[/tex]
Distribute.
[tex]\frac{1}{2}x + b=\frac{1}{2} x+\frac{3}{4}[/tex]
Subtract 1/2x from both sides to isolate the b.
[tex]b=\frac{1}{2} x+\frac{3}{4}-\frac{1}{2}x[/tex]
1/2x and -1/2x cancel each other out.
[tex]b=\frac{3}{4}[/tex]
So b = 3/4
What are the six trigonometric ratios, and how are some of them related to each other(which are reciprocals of which)?
Consider the following right triangle:
In this triangle
x = adjacent side to the angle theta.
y = opposite side to the angle theta.
h= hypotenuse.
Now, by definition, we have the following trigonometric ratios:
[tex]\cos(\theta)=\frac{adjacent\text{ side to the angle }\theta}{hypotenuse}\text{ =}\frac{x}{h}[/tex][tex]\sin(\theta)=\frac{opposite\text{ side to the angle }\theta}{hypotenuse}=\frac{y}{h}[/tex][tex]tan(\theta)=\frac{opposite\text{ side to the angle }\theta}{adjacent\text{ side to the angle }\theta}=\text{ }\frac{y}{x}=\frac{y\text{ /h}}{x\text{ /h}}\text{ =}\frac{\sin(\theta)}{\cos(\theta)}[/tex]and according to the above trigonometric ratio, we get:
[tex]cotan(\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]On the other hand, we get the following reciprocals:
[tex]csc(\theta)=\frac{1}{\sin(\theta)}[/tex]and
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]we can conclude that the correct answer is:
Answer:The six trigonometric ratios:
[tex]\cos(\theta)=\frac{adjacent\text{ side to the angle }\theta}{hypotenuse}\text{ }[/tex][tex]\sin(\theta)=\frac{opposite\text{ side to the angle }\theta}{hypotenuse}[/tex][tex]tan(\theta)=\frac{opposite\text{ side to the angle }\theta}{adjacent\text{ side to the angle }\theta}=\text{ }\frac{\sin(\theta)}{\cos(\theta)}[/tex][tex]csc(\theta)=\frac{1}{\sin(\theta)}[/tex][tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex][tex]cotan(\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]someone help please
Answer:
Angle 3 = 95° (vertically opposite angles)
Angle 2 and 4 = 180 - 95
= 85° (adjacent angles on straight line)
Angle 5 = 180 - 144
= 36° (adjacent angles on straight line)
Angle 6 = 180 - angle 3 - angle 5
= 180 - 95 - 36
= 49° (sum of angles in triangle=180)
Angle 1 = 180 - 90 - angle 6
= 180 - 90 - 49
= 41° (sum of angles in triangle=180)
Angle 7 = 180 - 38 - angle 5
= 180 - 38 - 36
= 106° (sum of angles in triangle=180)
given:m<6=m<8b l l cprove:a l l b
1) From the data, we can see that
[tex]\angle6=\angle8[/tex]is given.
2) Next,
[tex]\angle6=\angle7[/tex]since they are alternate angles.
3) By substitution, these means that
[tex]\angle7=\angle8[/tex]4) Finally, a || b since
[tex]\angle7=\angle8[/tex]this is because, angle 7 and angle 8 are corresponding angles.
Corresponding angles are angles that are on the same corner at each intersection. For instance, 2 and 6
4 and 8, 1 and 5, 3 and 7
In our case, 7 and 8 are corresponding angles
let f(x) =(4x"3+20)"2 and g(x) =4x"3+20.given that f(x)=(h°g)(x), find h(x)
Here, we want to find the function h(x)
From the question, we can see that the function f(x) is a composite function that was obtained by fitting g(x) into h(x)
What can we notice about g(x) and f(x)?
What we can see is that f(x) is the square of g(x)
Thus, what this mean is that h(x) = x^2
12 is 58% of what number?
Also can you explain how to solve these problems?
Answer:
20.68976
Step-by-step explanation:
Convert the percentage into decimal :
58% = 0.58
0.58 × x = 12
Divide both sides by 0.58 :
x = 12÷0.58
x = 20.689655...
x = 20.68976
So the method to these types of question is to make the question into an equation by converting the percentage into a decimal, rearrange to make the unknown number the subject and solve .
Hope you understood and have a good day
I got -52.7 degrees but I want to make sure. thank you
The given vector is
[tex]m=\langle16,-21\rangle[/tex]The formula to find the direction angle is
[tex]\theta=\tan ^{-1}|\frac{y}{x}|[/tex]Replacing each coordinate, we have
[tex]\theta=\tan ^{-1}|\frac{-21}{16}|=52.7[/tex]Therefore, the direction angle is 52.7°, approximately.v=LMH for L
thankssssss .
Tamarisk Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck (not the least of which is that it runs). The new truck would cost $56,619. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,100. At the end of eight years, the company will sell the truck for an estimated $28,500. Traditionally, the company has used a general rule that it should not accept a proposal unless it has a payback period that is less than 50% of the asset's estimated useful life. Thomas Anderson, a new manager, has suggested that the company should not rely only on the payback approach but should also use the net present value method when evaluating new projects. The company's cost of capital is 8%.
The cash Payback period is 6.66 years and the Net present value of the proposed investment is $5,329 (to see the calculation please refer the attached image.)
Computation of Payback Period
Cash Payback Period = Cost of truck/Annual cost savings.
Given that-
Cost of truck = $56,619
Annual cost savings = $8,100
Putting values, we get-
Cash payback period = ($56,619/$8,100) cash payback period
cash payback period = 6.66 years.
To calculate the PVF at 8% below is the formula
P = (1/[tex](1+r)^{n}[/tex])
Where,
P = the Present Value Factor.
r = the interest rate
n = the number of periods over which payments are made.
To calculate the Present Value = PVF at 8% x Amount.
Hence, As the Net Present Value is positive, Tamarisk corporation should purchase the truck.
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Determine whether the pair of polygons is similar using properties of similar polygons. Explain your reasoning.
The polygons are similar
What is a polygon?
A polygon (/pln/) in geometry is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain (or polygonal circuit). A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides. The vertices (plural: vertex) or corners of a polygon are the spots where two edges meet. A solid polygon's interior is sometimes referred to as its body. A polygon having n sides is known as an n-gon. A simple polygon is one that does not cross itself. Mathematicians are frequently interested simply in the bounding polygonal chains of simple polygons, and they frequently define a polygon in this manner.
The sides ratio is same in both polygons i.e. 1:2
and all the angles of the two polygons are congruent
So, the polygons are similar
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What is a polygon with 10 sides called?dodecagonoctagontarragondecagon
which function can be used to find y, total amount saved in, x weeks
Input data
Points
A = (0, 50)
B = (30,110)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
[tex]\begin{gathered} m=\frac{110-50}{30-0} \\ m=\frac{60}{30} \\ m=2 \end{gathered}[/tex]Now, what about b, the y-intercept?
[tex]\begin{gathered} b=y-mx \\ b=50-2\cdot0 \\ b=50 \end{gathered}[/tex]The equation of the line that passes through the points
[tex]y=2x+50[/tex]Yaritza finds some nickels and pennies in her change purse. How many coins does she have if she has 140 nickels and 130 pennies? How many coins does she have if she has nn nickels and pp pennies?
As per given by the question,
There are given that 140 nickels and 130 pennies.
Now,
The number of nickels is 140 and number of pennies is 130.
So,
The total number of coin is:
[tex]140+130=270[/tex]Hence, 270 coins does she have if she has 140 nickels amd 130 pennies.
And,
The total coint that have n nickels and p pennies is:
[tex]n+p[/tex]The asnwer is:
[tex]\begin{gathered} (a)\text{ 270 coins} \\ (b)\text{ n+p coins} \end{gathered}[/tex]Write the correct equation for the following statement.
The quotient of x and seven is twelve
To get quotient we divide
in this case we divide x by 7 to get the quotient 12 as A RESULT
[tex]x \div 7 = 12[/tex]
HOPE THIS HELPS.
What does the dashers part of the figure represent
The figure represents : Line
What is a Line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
from the figure we have to find that whether its a line, line segment, vertex or ray
Line: A line is a perfectly straight, one-dimensional shape that extends infinitely in both directions and has no thickness. Sometimes a line is referred to as a straight line or, more formally, a right line.
Line segment: In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters or conventional measures like feet or inches.
Ray: A ray is a vector from a point to another point when seen as a vector. A ray is typically viewed in geometry as a half-infinite line, or half-line, with one of the two points and assumed to be at infinity.
Vertex: A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
The figure represents a Line
Hence, The dashers part of the figure represent a Line
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A poster is 3 feet wide and 12 feet long. What are the dimensions if the poster is enlarged by a factor of 5/2?
To be able to get the enlarged dimensions, we will multiply the dimension of the poster by the given scale factor 5/2.
We get,
[tex]\text{Width = 3 ft. x }\frac{5}{2}\text{ = }\frac{15}{2}\text{ ft. or 7.5 ft.}[/tex][tex]\text{Length = 12 ft. x }\frac{5}{2}\text{ = }\frac{60}{2}\text{ ft. or 30 ft.}[/tex]Therefore, the enlarged dimension of the poster will be 7.5 ft. x 30 ft.
A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is r=5.4 ft, the height of the cylindrical portion is h=7.7 ft, and the overall height is H=16.7 ft?
The Volume of a Compound Solid
The figure consists of a cylinder and a cone, both with the same radius of r=5.4 ft. The height of the cylinder is h=7.7 ft and the total height (of cone and cylinder) is H = 16.7 ft. This means the height of the cone is hc = 16.7 - 7.7 = 9 ft.
The volume of a cylinder of height h and radius r is:
[tex]V_{\text{cyl}}=\pi\cdot r^2\cdot h[/tex]The volume of a cone of height hc and radius r is:
[tex]V_{\text{cone}}=\frac{\pi\cdot r^2\cdot h_c}{3}[/tex]Calculate the volume of the cylinder:
[tex]\begin{gathered} V_{\text{cyl}}=\pi\cdot(5.4ft)^2\cdot7.7ft \\ V_{\text{cyl}}=705.388ft^3 \end{gathered}[/tex]Calculate the volume of the cone:
[tex]V_{\text{cone}}=\frac{\pi\cdot(5.4ft)^2\cdot9}{3}=274.827ft^3[/tex]Now we add both volumes:
V = 705.388 + 274.827 = 980.215 cubic feet
Rounding to the nearest tenth:
V = 980.2 cubic feet
How long ago, to the nearest year, was the artifact made?
Let's use the following formula:
[tex]A=A_0(0.5)^{\frac{t}{h}}[/tex]where:
Ao= Initial amount
t = time
h = half-life
[tex]\begin{gathered} A=0.2A_0 \\ so\colon \\ 0.2A_0=A_0(0.5)^{\frac{t}{5730}} \end{gathered}[/tex]solve for t:
[tex]\begin{gathered} 0.2=0.5^{\frac{t}{5730}} \\ \ln (0.2)=\frac{t}{5730}\ln (0.5) \\ t=5730\cdot\frac{\ln (0.2)}{\ln (0.5)} \\ t\approx13305 \end{gathered}[/tex]Final Grade An instructor gives four 1-hour exams and one final exam, which counts as three 1-hour exams. Find a student's grade if she received 66, 81, 99 and 86 on the 1-hour exams and 85 on the final exam. Round your answer to one decimal place if necessary.
Answer:
83.9
Explanation:
The final exam counts as three 1-hour exams. Therefore, the student's scores written in terms of 1-hour exams will be:
• One-Hour Exam: 66, 81, 99 and 86
,• Final Exam: (85 x 3)
We take the average to find the student's grade:
[tex]\begin{gathered} \text{Final Grade}=\frac{66(1)+81(1)+99(1)+86(1)+85(3)}{1+1+1+1+3} \\ =\frac{332+255}{7} \\ =\frac{587}{7} \\ =83.857 \\ \approx83.9 \end{gathered}[/tex]The student's grade will be 83.9 correct to one decimal place.
I believe you start with 2.4 million has initial start value? Not sure cause it worded weirdly and English not very good
2,466,000
Here, we want to know what is to be used as the initial value
The general exponential equation should be in the form;
[tex]P=I(1+R)^n[/tex]where P is the population at a certain year
I is the initial population which is 2,466,000 in this case
R is the rate of increase
n is the number of years
1. What would the slope of a line that is parallel to the line in the graph be?
(4,3)
X
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above, since a parallel line will have the same slope anyway
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -3 } \implies {\Large \begin{array}{llll} \cfrac{ 4 }{ 3 } \end{array}}[/tex]
Help me asp please!!
The measures of the angles of a triangle are 2x, 3x, and 4x. What is the degree measure of the largest angle of the triangle?o 20°o 60°o 80°o 100°
ANSWER
[tex]80\degree[/tex]EXPLANATION
We want to find the measure of the largest angle of the triangle.
The sum of angles in a triangle is 180 degrees. This means that:
[tex]2x+3x+4x=180[/tex]Simplify the equation and solve for x:
[tex]\begin{gathered} 2x+3x+4x=180 \\ 9x=180 \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]The largest angle is 4x. Therefore, the measure of the largest angle is:
[tex]\begin{gathered} 4\cdot20 \\ 80\degree \end{gathered}[/tex]find the surface area of a square pyramid with side length 3km and slant height 5km
Explanation
the surface area of a square pyramid is given by:
[tex]\begin{gathered} sa=A+\frac{1}{2}ps \\ \text{where A is the area of the base} \\ p\text{ is the perimeter of the base} \\ s\text{ is the }slant\text{ heigth} \end{gathered}[/tex]so
Step 1
area of the base
the baseis a square, so the area is
[tex]\begin{gathered} Area=side^{^2} \\ Area_{base}=3km\cdot\text{ 3}km \\ Area_{base}=\text{ 9(}km^2) \end{gathered}[/tex]Step 2
perimeter of the base
the perimeter of a square is given by:
[tex]\begin{gathered} \text{Perimeter}=\text{ 4}\cdot side \\ sp \\ \text{Perimeter}=\text{ 4}\cdot3km\text{ =12 }km \\ \text{Perimeter}=12km \end{gathered}[/tex]Step 3
finally, let
[tex]\text{slant heigth=5}km[/tex]now, replace in the formula
[tex]\begin{gathered} sa=A+\frac{1}{2}ps \\ sa=9(km^2)+\frac{1}{2}(12km)(5km) \\ sa=9(km^2)+30(km^2) \\ sa=39(km^2) \end{gathered}[/tex]therefore, the answer is
[tex]\text{ 36 }km^2[/tex]I hope this helps you
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 67°C, it is cooling at a rate of 1°C per minute.
Let y = T − Ts, where T(t) is the temperature of the coffee in degrees Celsius at time t and Ts is the temperature of the surroundings in degrees Celsius. Find the values of A (in °C) and k for y(t) = Aekt.
Find: A and k
After how many minutes is the temperature of the coffee 67°C? (Round your answer to two decimal places.)
Answer:
The temperature of coffee will reach 67 °C
The rate of temperature change is most directly related to the difference between the body temperature and room temperature.
[tex]\frac{dT}{dt} =-k(T-T1)[/tex]
This equation's solution using the initial condition
T(0) = T0
T(t) = Tr + (T0 - Tr)
At the moment, the cooling rate
k × (T(t) - Tr)
We can write that according to the text
T1 = Tr + (T0 - Tr)
Solving the system of equations generates the unknown time:
t = [tex]\frac{69-20}{1} (ln\frac{95-20}{69-20})[/tex]
t = 21 min.
Hence the coffee will reach the temperature 67°C in 21 minutes.
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find the height of a square pyramid with V of 60 cm3 and base side length S of 6cm
Using Volume formula, the height of the square pyramid is 5 cm.
What is volume of a square pyramid?If the side of the square base of the pyramid is b and height of the pyramid be h
Volume of the square pyramid , V is given by the below formula.
V = 1/3(b²h)
Given
Volume of the square pyramid, V = 60 cm³
base side is given , b = 6 cm
let Height of the square pyramid be h
⇒ V = 1/3(b²h)
⇒ 3V = b²h
⇒3V/b² = h
⇒ 3(60)/ 6² = h
⇒ h = 180/36 = 5
Therefore, the height of the given square pyramid id 5 cm.
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Middle School Debate Club 30% members are in 6th grade. If there are 12 6th graders in The Debate Club, how many total members are there ?
We know that 30% of the members are in 6th grade, and add up to 12 members.
Lets X be the total members.
Then 0.3*X are in 6th grade, and this is equivalent to 12 members.
NOTE: 0.3 is the decimal form of 30%.
We can write:
[tex]\begin{gathered} 0.3\cdot X=12 \\ X=\frac{12}{0.3} \\ X=40 \end{gathered}[/tex]Answer: there are 40 members in the Debate Club.
which of the following graphs match the indicated rotation? Point “R” Rotated 90 degrees about the origin.
The rule for a 90° rotation about the origin is:
[tex](x,y)\rightarrow(-y,x)[/tex]then, if we select one of the points of the figure, A(-2,1), and apply the transformation,
[tex]A(-2,1)\rightarrow A^{\prime}(-1,-2)[/tex]do the same for the other three points,
[tex]\begin{gathered} B(3,3)\rightarrow B^{\prime}(-3,3) \\ C(4,0)\rightarrow C^{\prime}(0,4) \end{gathered}[/tex]select the graph with all three points.
Answer:
The correct answer is option 4.
Ana has two plants. From Monday to Tuesday, plant A grew 5 cm more than plant B. If the sum of the length of the two plants on Tuesday is 41 cm, how long is each plant on Tuesday?
Write a system of equations using A and B as the variables
The first equation is the sum of the lengths of the plants
[tex]A+B=41[/tex]The second equation is the relation of growth that plant A grew 5cm more than plant B
[tex]A=B+5[/tex]Insert the second equation into the first one to solve for B
[tex]\begin{gathered} A+B=41 \\ (B+5)+B=41 \end{gathered}[/tex]Solve the equation for B
[tex]\begin{gathered} 2B+5=41 \\ 2B=41-5 \\ 2B=36 \\ B=\frac{36}{2} \\ B=18 \end{gathered}[/tex]Use the value of B in the second equation to find the value of A
[tex]\begin{gathered} A=B+5 \\ A=18+5 \\ A=23 \end{gathered}[/tex]Plant A is 23 cm long on Tuesday and plant B is 18 cm long on Tuesday.
a realtor make 6% commission on each sale how much commission will the realtor earn for selling a $140,000 home
Answer:
1&3239282882819&;&39303847
Answer:
$8,400
Step-by-step explanation:
6%x140,000