Given:
[tex]\frac{1}{3}[/tex]To write the given fraction into two other notations, we use "to" for word notation while ":" for number notation.
Therefore, the answers are:
1 to 3
1:3
Hi I have a meeting at my house in about
The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.
The function is given to be:
[tex]T(t)=Ate^{-kt}[/tex]where A and k are positive constants.
We can find the derivative of the function as follows:
[tex]T^{\prime}(t)=\frac{d}{dt}(Ate^{-kt})[/tex]Step 1: Pull out the constant factor
[tex]T^{\prime}(t)=A\cdot\frac{d}{dt}(te^{-kt})[/tex]Step 2: Apply the product rule
[tex]\frac{d(uv)}{dx}=u \frac{dv}{dx}+v \frac{du}{dx}[/tex]Let
[tex]\begin{gathered} u=t \\ v=e^{-kt} \\ \therefore \\ \frac{du}{dt}=1 \\ \frac{dv}{dt}=-ke^{-kt} \end{gathered}[/tex]Therefore, we have:
[tex]T^{\prime}(t)=A(t\cdot(-ke^{-kt})+e^{-kt}\cdot1)[/tex]Step 3: Simplify
[tex]T^{\prime}(t)=A(-kte^{-kt}+e^{-kt})[/tex]QUESTION A
At t = 0, the instantaneous rate of change is calculated to be:
[tex]\begin{gathered} t=0 \\ \therefore \\ T^{\prime}(0)=A(-k(0)e^{-k(0)}+e^{-k(0)}) \\ T^{\prime}(0)=A(0+e^0) \\ Recall \\ e^0=1 \\ \therefore \\ T^{\prime}(0)=A \end{gathered}[/tex]The rate of change is:
[tex]rate\text{ }of\text{ }change=A[/tex]QUESTION B
At t = 30, the instantaneous rate of change is calculated to be:
[tex]\begin{gathered} t=30 \\ \therefore \\ T(30)=A(-k(30)e^{-k(30)}+e^{-k(30)}) \\ T(30)=A(-30ke^{-30k}+e^{-30k}) \\ Collecting\text{ }common\text{ }factors \\ T(30)=Ae^{-30k}(-30k+1) \end{gathered}[/tex]The rate of change is:
[tex]rate\text{ }of\text{ }change=Ae^{-30k}(-30k+1)[/tex]QUESTION C
When the rate of change is equal to 0, we have:
[tex]0=A(-kte^{-kt}+e^{-kt})[/tex]We can make t the subject of the formula using the following steps:
Step 1: Apply the Zero Factor principle
[tex]\begin{gathered} If \\ ab=0 \\ a=0,b=0 \\ \therefore \\ -kte^{-kt}+e^{-kt}=0 \end{gathered}[/tex]Step 2: Collect common terms
[tex]e^{-kt}(-kt+1)=0[/tex]Step 3: Apply the Zero Factor Principle:
[tex]\begin{gathered} e^{-kt}=0 \\ \ln e^{-kt}=\ln0 \\ -kt=\infty \\ t=\infty \end{gathered}[/tex]or
[tex]\begin{gathered} -kt+1=0 \\ -kt=-1 \\ t=\frac{-1}{-k} \\ t=\frac{1}{k} \end{gathered}[/tex]The time will be:
[tex]t=\frac{1}{k}[/tex]use a power reducing formula to to simplify 20cos^4x
We can replace trigonometric terms in formulas with trigonometric terms of smaller powers using the trigonometric power reduction identities. This is significant for using calculus to integrate the powers of trigonometric expressions, among other applications.
Explain about the power reducing?2cos2 will be equal to 1 plus cos 2. We arrive at an equation for cos2 by dividing by 2. Because they enable us to reduce the power on one of the trig functions when the power is an even integer, these are commonly referred to as "power reduction formulae."
An integral problem can be solved using a reduction formula by first breaking it down into simpler integral problems, which can then be broken down into simpler problems, and so on.
P = E/t is the equation, where P stands for power, E for energy, and t for time in seconds. According to this equation, power is defined as the amount of energy consumed per unit of time.
The Equivalent expression for Cos 4x= 8cos4(x) - 8 cos2(x) + 1.
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What are the roots of the function represented by the table?
From the table, the root of the function is a point where y = 0.
Therefore,
The root of the function are ( 4, 0 ) and ( -3, 0 )
Final answer
I and III only Option B
Use this information to answer the following two questions. Mathew finds the deepest part of the pond to be 185 meters. Mathew wants to find the length of a pond. He picks three points and records the measurements, as shown in the diagram. Which measurement describes the depth of the pond? Hide All Z between 13 and 14 meters 36 m 14 m between 14 and 15 meters between 92 and 93 meters Х ag between 93 and 94 meters
it's letter A. Between 13 and 14 meters
Because one side measure 14, and the height (depth) could not be
higher than 14 meters .
The length of the pond can be calculated using the Pythagorean theorem
length^2 = 36^2 + 14^2
length^2 = 1296 + 196
length^2 = 1492
length = 38.6 m
Write this ratio as a fraction in simplest form without any units.75 minutes to 1 hourYou can use the table below to help convert the units.1 minute = 60 seconds1 hour = 60 minutes-1 day = 24 hours1 week = 7 days0
To get an unitless ratio, both of our quantities have to be in the same units. Let's convert that hour into minutes:
[tex]1h\rightarrow60\min [/tex]Thereby, our ratio would be:
[tex]\frac{75\min }{60\min }\rightarrow\frac{5}{4}[/tex]a box of cereal states that there are 75 calories in a 3/4 serving what is the unit rate for calories cup how many calories are there in 2 cups
We know that a box of cereal states that there are 75 calories in a 3/4 cup.
To find the unit rate for calories cup we must represent the the situation with an equation
[tex]\frac{75\text{ calories}}{\frac{3}{4}\text{ cup}}=\frac{x\text{ calories}}{1\text{ cup}}[/tex]Then, to find the unit rate for calories we need to solve the equation for x
[tex]x\text{ calories}=\frac{75\text{ calories}\cdot1\text{ cup}}{\frac{3}{4}\text{ cup}}=100\text{ calories}[/tex]Now, to find how many calories there are in 2 cups we must multiply the unit rate for calories by 2
[tex]x\text{ calories=100 calories}\cdot2=200\text{ calories}[/tex]Finally, the answers are:
- The unit rate for calories is 100 calories/cup.
- In 2 cups there are 200 calories.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-6, -6); y=-2x+4
Answer:
y = 2x + 6
Step-by-step explanation:
Parallel lines have the same slope, so the slope is 2.
y = mx + b
When need the slope which is given to be 2
We will use the point given (-6,-6) for an x and y on the line
m= 2
x -= -6
y = -6
y=mx+ b
-6 = 2(-6) + b Sole for b
-6 = -12 + b Add 12 to both sides
6 = b
y = 2x + 6
I have a calculus question about related rates, pic included
ANSWER
40807 cm³/min
EXPLANATION
The tank has the shape of a cone, with a total height of 9 meters and a diameter of 3.5 m - so the radius, which is half the diameter, is 1.75 m. As we can see, the relationship between the height of the cone and the radius is,
[tex]\frac{r}{h}=\frac{1.75m}{9m}=\frac{7}{36}\Rightarrow r=\frac{7}{36}h[/tex]So the volume of water will be given by,
[tex]V(h)=\frac{1}{3}(\pi r^2)h=\frac{1}{3}\cdot\pi\cdot\frac{7^2}{36^2}h^2\cdot h=\frac{49\pi}{3888}h^3[/tex]Where h is the height of the water (not the tank).
If we derive this equation, we will find the rate at which the volume of water is changing with time,
[tex]\frac{dV}{dt}=\frac{49\pi}{3888}\cdot3h^{3-1}=\frac{49\pi}{3888}\cdot3h^2=\frac{49\pi}{1296}h^2[/tex]We want to know what is the change of volume with respect to time, and this is,
[tex]\frac{dV}{dt}=\frac{dV}{dt}\cdot\frac{dh}{dt}[/tex]Because the height also changes with time. We know that this change is 24 cm per minute when the height of the water in the tank is 1 meter (or 100 cm), so we have,
[tex]\frac{dV}{dt}=\frac{49\pi}{1296}h^2\cdot\frac{dh}{dt}=\frac{49\pi}{1296}\cdot100^2cm^2\cdot\frac{24cm}{1min}\approx28507cm^3/min[/tex]This is the rate at which the water is increasing in the tank. However, we know that there is a leak at a rate of 12300 cm³/min, which means that in fact the water is being pumped into the tank at a rate of,
[tex]28507cm^3/min+12300cm^3/min=40807cm^3/min[/tex]Hence, the water is being pumped into the tank at a rate of 40807 cm³/min, rounded to the nearest whole cm³/min.
Which of the binomials below is a factor of this trinomial?x^2 - 13x + 42A. x + 84B. x - 7C. x^2 +12D. x + 7
Given the following trinomial:
[tex]x^2-13x+42[/tex]To factor the trinomial, we need two numbers the product of them = 42
And the sum of them = -13
Two of the numbers of factors of 42 = -6, and -7
So, the factor of the trinomial will be as follows:
[tex]x^2-13x+42=(x-6)(x-7)[/tex]So, the answer will be option B. x - 7
How long can you lease the car before the amount of the lease is more than the cost of the car
ANSWER:
48 months
STEP-BY-STEP EXPLANATION:
According to the statement we can propose the following equation, where the price of the car is more than or equal to the amount of the lease. Just like this:
Let x be the number of months
[tex]16920\ge600+340x[/tex]We solve for x, just like this:
[tex]\begin{gathered} 600+340x-600\le16920-600 \\ \frac{340x}{340}\le\frac{16320}{340} \\ x\le48 \end{gathered}[/tex]Therefore, for 48 months, the car rental will be lower
What is the median of the data set 4 7 9 10 5 12 6
The median is the value of the data set that separates the sample in halves.
To determine the median of a determined data set, you have to calculate its position.
The given sample has n=7 elements, to determine the position of the median given that the data set is odd, you have to use the following formula:
[tex]\text{PosMe}=\frac{1}{2}(n+1)[/tex]Replace it with n=7
[tex]\begin{gathered} PosMe=\frac{1}{2}(7+1) \\ \text{PosMe}=\frac{1}{2}\cdot8 \\ \text{PosMe}=4 \end{gathered}[/tex]This result indicates that the media is the fourth observation of the data set.
Next, you have to order the data set from least to greatest:
Original data set: 4, 7, 9, 10, 5, 12, 6
Ordered from least to greatest: 4, 5, 6, 7, 9, 10, 12
Once the data set is ordered, you have to count starting from the left until you reach the fourth observation:
O4, 5, 6, 7, 9, 10, 1
The fourth value of the data set is 7, which means that the median of the data set is 7.
Median=7
2
which of the following lines are parallel, skew, intersection, or none of these.
Parallel lines are lines that have the same direction and there is always the same distance between them
Skew lines are lines that are not on the same plane (they are not coplanar) and also they do not intersect.
Intersecting lines are lines that cross at a point, they can be on the same plane or on different planes.
Let's analyze the parts of this problem.
DE and AB.
These two lines are shown in red and blue in the following diagram:
These are not parallel lines because one line is vertical and the other line is horizontal. They are also not intersecting lines because they do not cross at any point. Lines DE and AB are skew lines because they do not intersect and they are on different planes.
--> DE and AB --> skew
CB and
A circle has a radius of .10 in. Find
the increase in area when the radius is increased by 2 in. Use
3.14 for
The increase in area of the circle when the radius is increased by 2 is 13.8 in.
How to calculate area of circle?Area of a circle can be described as the region that is been taken by the circle.
The area of the circle can be expressed as A=πr^2
We were told that the radius of the circle is been given as 0.10 in.
Then we can calculate the are of the circle by input the given radius into the formula above as:
A=πr^2
r= radius of the circle
A= area of the circle
A=3.14 (0.10)^2 =0.0314 in.
Then we were told that the radius is increased by 2 in.
Then the area of the circle will now be A=3.14* (2.10)^2 =13.85 in.
Then the the increase in area can be calculated as : (13.85 in. - 0.0314 in.) = 13.8 in.
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Which of the following represents the set of possible rational roots for thepolynomial shown below?2x3 + 5x2 - 8x - 20 = 0oa{=}, +2, +1, +2, +3, +3 + 1}O B. {+1, +2, +4, +5, +10, 20}O a {, +1, +2 +3 +4, + 3, +10, +20)02 (1.1,2,3,4,5,10,20)
We will have that the set of rational roots for the expression will be:
[tex]\mleft\lbrace\pm\frac{1}{2},\pm1,\pm2,\pm\frac{5}{2},\pm4,\pm5,\pm10,\pm20\mright\rbrace[/tex][Option C].
Mathematics literacy Finance Break-even analysis homework (1.1 and 1.2 only)
We are given a set of data with the employee number and the corresponding weekly wage.
Part 1.1 To determine the wage per hour we need to find the quotient between the weekly wage and the number of hours worked per week.
In the case of employee 1, we have that his weekly wage was 1680, therefore, the weekly payment per hour is:
[tex]p=\frac{1680}{42}=40\text{ per hour}[/tex]The weekly payment is $40 per hour.
Part 1.2 We have that employee number 4 work a total of 6 hours each day of the week. Since there are 7 days per week we have that the total number of hours during the week is:
[tex]h_4=(6day)(7)=42\text{ }hours[/tex]Now, we multiply by the rate of payment per week, therefore, his weekly pay must be:
[tex]p_4=(42hours)(40\text{ per hour\rparen}=1680[/tex]Therefore, the weekly wage of 4 is 1680.
Part 1.3 To determine the number of hours that employee 8 we must have into account that the number of hours per week by the rate of pay per hour is the total weekly wage, therefore:
[tex](40\text{ per hour\rparen}h_8=2000[/tex]Now, we divide both sides by 40:
[tex]h_8=\frac{2000}{40}=50hours[/tex]Therefore, employee 8 worked 50 hours.
Part 1.4 Since the weekly payment is proportional to the number of hours this means that the employee that worked the least number of hours is the one with the least weekly wage.
We have that employee 5 has the smaller wage, therefore, employee 5 worked the least number of hours.
Part 1.5 we are asked to identify the dependent variable between weekly wage and the number of hours worked.
Since the number of hours does not depend on any of the other considered variables this means that this is the independent variable. Therefore, the dependent variables is the weekly wage. The correct answer is A
Part 1.6 The modal value of a set of data is the value that is repeated the most. We have that the weekly wage that is repeated the most is 1600 since it is the wage of employees 2 and 7. Therefore, the modal value is 1600
Part 1.7 The range of a set of data is the difference between the maximum and minimum values. The maximum wage is 2000 and the minimum is 1160, therefore, the range is:
[tex]R=2000-1160=840[/tex]The range is 840
when doing right triangle trigonometry how do you determine which sine you use like sin, cos etc?
Let's draw a right triangle to guide us:
Every right triangle will have one hypotenuse side and two leg sides. The hypotenuse is always the bigger one and it is always opposite to the right angle, so in this triangle the hypotenuse is a (the letter can change from exercise to exercise, but it is always the opposite to the rignt angle).
The legs can be classified as adjancent or opposite legs, but this is with respect to the angle we are using.
So, if we are using angle C, the opposite leg is the leg that is opposite to angle C, that is, c.
Thus, the adjancent leg is the leg that is touching the angle C, that is, b.
So, with respect to angle C, we have:
Hypotenuse - a
Opposite leg - c
Adjacent leg - b
The sine is the ratio between the opposite leg and the hypotenuse, always.
The cosine is the ratio between the adjacent leg and the hypotenuse, always.
The tangent is the ratio between the opposite leg and the adjacent leg, always.
For, for angle C, we have:
[tex]\begin{gathered} \sin C=\frac{c}{a} \\ \cos C=\frac{b}{a} \\ \tan C=\frac{c}{b} \end{gathered}[/tex]For angle B, we do the same, however now, the legs are switched, because the leg that is opposite to angle B is b and the leg that is adjance to angle B is c, so, for angle B:
Hypotenuse - a
Opposite leg - b
Adjacent leg - c
And we follow the same for sine, cosine and tangent but now for angle B and with the legs switched:
[tex]\begin{gathered} \sin B=\frac{b}{a} \\ \cos B=\frac{c}{a} \\ \tan B=\frac{b}{c} \end{gathered}[/tex]Questions regaring these ratios normally will present 2 values and ask for a third value. One of the values will be an angle, the other will be side (usually). So, we need to identify which angle are we working with and which sides are the hypotenuse, the opposite leg and adjancent leg with respect to the angle we will work with. Then we identify which of the side we will use and pick the ratio thet relates the sides we will use.
keisha is an avid reader. One day she read for 8 hours. She read a total of 600 pages during that time. How many pages did keisha read per minute?
To find the number of page she read per minute
First let's chenge the 8 hours to minute
8 hours = 8 x 60 = 480 min
Since she read 600 pages
Number of pages read per min = 600/ 480
=1.25 pages
An actor invests some money at 7%, and $24000 more than three times the amount at 11%. The total annual interest earned from the investment is $27040. How much did he invest at each amount? Use the six-step method.
0.07x+0.11(3x+24000)=27040
we will solve for x
x=61,000 [ investment at 7%]
Investment at 11% = 3x + 24000
= 3(61000)+24000
= 207000 [ investment at 11%]
Cassie’s latest financial goal is to eliminate her credit card debt
Based on Cassie's financial goal to eliminate her credit card debt, the graph that would best model her situation in terms of scale and label is B. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)
How to model a graph?When modeling a graph, the time period is often the independent variable. This means that the time period which are in months (months that Cassie makes monthly payments) need to be on the x-axis and will be labelled from 0 to 12 months for the months of the year.
The amount of credit card debt would then be on the y-axis. It is best to have a scale that is larger than the maximum debt Cassie has to that the data can be included properly. So a limit of 0 - 8,000 is best and would properly incorporate the $5,000 she already owes.
Full question is:
Cassie's latest financial goal is to eliminate her credit card debt. She has about $5,000 in credit card debt. She determines that she can afford to make
monthly payments of about $500. To track her progress, she plans to create a graph to model her situation. How should Cassie label and scale her
graph?
A.X-axis scale, 0-8; label, Total Debt ($) y-axis scale, 0-5,000; label, MonthsB. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)C. X-axis scale, 0-8; label, Years y-axis scale, 0-5,000; label, Total Debt ($)D. x-axis scale, 0-12; label, Total Debt ($) y-axis scale, 0-8,000; label, YearsFind out more on models at https://brainly.com/question/22049822
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Consider the line segment porque shown. For which of the following transformations would the image porque be contained entirely in Quadrant II?
We will have the following:
In order to have PQ entirely in the quadrant II, the transformation must be:
*Translate PQ up 4 units and to the left 3 units. [Option K]
Which two ratios are NOT equal? 1:6 and 3:18 OB. 2:14 and 3:42 OC. 12:6 and 2:1 OD 3:11 and 6:22
Let's check the ratios:
[tex]\begin{gathered} \frac{1}{6} \\ \text{and} \\ \frac{3}{18} \\ \end{gathered}[/tex]First one is already reduced. Let's reduce the 2nd fraction by dividing top and bottom by 3, so
[tex]\frac{3}{18}=\frac{1}{6}[/tex]So, they are equal.
Next ratio:
[tex]\begin{gathered} \frac{2}{14}\text{and}\frac{3}{42} \\ \end{gathered}[/tex]Let's divide both top and bottom by 2 (1st fraction) and top and bottom by (3) in 2nd fraction:
[tex]\begin{gathered} \frac{2}{14}=\frac{1}{7} \\ \text{and} \\ \frac{3}{42}=\frac{1}{14} \end{gathered}[/tex]They aren't equal. So, we have already found our answer.
OB. 2:14 and 3:42 --- is our answer.
4)Describe the difference between a sampling error and non-sampling error .
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
sampling error and non-sampling error
Step 02:
statistics:
Sampling error:
It is the error that arises in a data collection process as a result of taking a sample from a population rather than using the whole population.
Non-sampling error:
It is the error that arises in a data collection process as a result of factors other than taking a sample.
non-response errors, coverage errors, interview errors, and processing errors
A tourist from the U.S. is vacationing in China. One day, he notices that has cost 6.84 yuan per liter. On the same day, 1 yuan is worth 0.14 dollars. How much does the gas cost in dollars per gallon? Fill in the two blanks on the left side of the equation using two of the ratios. THEN WRITE THE ANSWER ROUNDED TO THE NEAREST HUNDREDTH. Will send pic of question.
Solve:
[tex]\frac{6.84\text{ yuan}}{1\text{ L}}\times\frac{0.14\text{ dollars}}{1\text{ yuan}}\times\frac{3.79\text{ L}}{1\text{ gal}}=3.63\frac{dollars}{gal}[/tex]find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
A square has side length (2x+3). The perimeter is 60cm. Find the length of one side in centimetres
As given by the question
There are given that the side length is (2x+3) and perimeter is 60 cm.
Now,
From the formula of perimeter:
[tex]\text{Perimeter =4}\times side[/tex]So,
[tex]\begin{gathered} \text{Perimeter =4}\times side \\ 60=4\times(2x+3) \\ 60=8x+12 \\ 8x=60-12 \\ 8x=48 \\ x=\frac{48}{8} \\ x=6 \end{gathered}[/tex]Then,
Put the value of x into the given side length (2x+3)
So,
[tex]\begin{gathered} 2x+3=2\times6+3 \\ =12+3 \\ =15 \end{gathered}[/tex]Hence, the one side of length is 15 cm.
Solve for "x":3x - 5 < -14 or 2x - 1 > 7
We are given the following inequalities:
[tex]\begin{gathered} 3x-5<-14,(1)\text{ or} \\ 2x-1>7,(2) \end{gathered}[/tex]First, we will solve for inequality 1. To do that we will add 5 to both sides:
[tex]3x-5+5<-14+5[/tex]Solving the operations:
[tex]3x<-9[/tex]Now we divide both sides by 3:
[tex]\frac{3x}{3}<-\frac{9}{3}[/tex]Solving the operations:
[tex]x<-3[/tex]Now we solve for "x" in inequality (2). To do this we will add 1 to both sides:
[tex]2x-1+1>7+1[/tex]Solving the operations:
[tex]2x>8[/tex]Now we divide both sides by 2:
[tex]\frac{2x}{2}>\frac{8}{2}[/tex]Solving the operations:
[tex]x>4[/tex]Therefore, the solution to the system is:
[tex]x<-3\text{ or x > 4}[/tex]What is the value of the expression below when z6?9z + 8
Hello!
Let's solve your expression:
[tex]9z+8[/tex]Let's replace where's z by 6, look:
[tex]\begin{gathered} (9\cdot z)+18 \\ (9\cdot6)+18 \\ 54+18 \\ =72 \end{gathered}[/tex]So the value of this expression when z=6 is 72.
Find the equation of the line parallel to the line y=-1, going through point (-5,4)
In this problem, want to find the equation of a line that will be parallel to a given function through a point.
Recall that parallel lines have the same slope.
We are given the line
[tex]y=-1[/tex]and the point
[tex](-5,4)[/tex]Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:
[tex]y=0x-1[/tex]Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.
Using the form
[tex]y=mx+b[/tex]we can substitute the point and the slope to solve for b:
[tex]\begin{gathered} 4=0(-5)+b \\ \\ 4=b \end{gathered}[/tex]So, the equation of our line is:
[tex]y=0x+4\text{ or }\boxed{y=4}[/tex]the measure of angle is 15.1 what is measure of a supplementary angle
we get that measure of the supplemantary angle is:
[tex]180-15.1=164.9[/tex]Please show formula and explain work in 6th grade format
The surface area of a pyramid is given as:
[tex]SA=\frac{1}{2}pl+B[/tex]where p is the perimeter of the base, l is the slant height and B is the area of the base.
In this case the slant height is 4 in.
Now, since the base is a square which sides that has length 5 in. then the perimeter is:
[tex]p=4\cdot5=20[/tex]The area of the base is the length of the side squared, then we have:
[tex]B=5^2=25[/tex]Once we know the values we plug them in the formula, then we have:
[tex]\begin{gathered} SA=\frac{1}{2}(20)(4)+25 \\ SA=40+25 \\ SA=65 \end{gathered}[/tex]Therefore the surface area is 65 squared inches.