Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.She needs to find the approximate surface area of the attic, including the walls, floor, andceiling. The attic is in the shape of a triangular prism. Linda draws the net and writesthe expression below to represent the surface area of the attic. Are Linda's net andexpression correct?15 ft45 ft25 ft40 ft25 ft25 ft25 ft- 15 ft45 ft40 ft15 ftExpression for Surface Area of Attic:45 (40 + 25 + 25) + ] (40 x 15)
Answers
We can formulate an expression for the surface area of the attic like this:
The area of a triangle is given by the following formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the base and h is the height of the triangle.
The area of a rectangle is given by the following formula:
[tex]A=w\times l[/tex]Where w is the width and l is the length of the rectangle.
In this case, the attic has three rectangular faces, all of them have a width of 45 ft. two of them have a length of 25 ft and one has a width of 40 ft, then we can calculate the areas of these faces like this:
[tex]\begin{gathered} A1=45\times40 \\ A2=45\times25 \\ A3=45\times25 \end{gathered}[/tex]By summing up these areas, we get the area of the rectangular faces:
[tex]A=45\times40+45\times25+45\times25[/tex]From this expression, we can factor 45 to get:
[tex]A=45\times(40+25+25)[/tex]For the two triangular faces, their height equals 15 ft and the length of the bases equals 40 ft, then their areas are:
[tex]\begin{gathered} A1=\frac{15\times40}{2} \\ A2=\frac{15\times40}{2} \end{gathered}[/tex]By summing them up, we get the area of the triangular faces:
[tex]A=\frac{15\times40}{2}+\frac{15\times40}{2}=15\times40[/tex]By summing the area of the rectangular faces and the area of the triangular faces, we get the expression to calculate the total surface area of the attic, like this:
[tex]A=45(40+25+25)+40\times15=4650[/tex]Then, the net Linda draw is correct. The first term of Linda's expression 45(40+25+25) is correct. The second term of Linda's equation missing a factor of 2. The surface area of Linda's attic is 4650 square feet
Related Questions
What is the Y intercept of 8X plus 4Y equals -48
Answers
the given equation is,
[tex]8x+4y=-48[/tex]Now, we will solve it further,
[tex]\begin{gathered} 8x+4y=-48 \\ 4y=-8x-48 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{-8x-48}{4} \\ y=-2x-12 \end{gathered}[/tex]Now, we will put x=0 to get the intercept of the line on the Y axis,
[tex]\begin{gathered} y=-2x-12 \\ y=-2\times0-12 \\ y=-12 \end{gathered}[/tex]So, the Y-intercept of the given line equation is -12.
There are a total of 50 questions worth 130 points on Chenille's history exam. Someof the questions are worth five points each, and the other questions are worth twopoints each. Which of the following systems of equations could be used todetermine F, the correct number of five point questions, and t, the correct numberof two point questions answered correctly?
Answers
Since F represents the number of five point questions and t represents the number of two point questions, and the total amount of questions is 50, then:
[tex]F+t=50[/tex]F correct answers would give us 5F points, and t correct answers would give us 2t points, for a total of 130 points. Then:
[tex]undefined[/tex]Find the missing angle:
FRT=________
Answers
Using the secant-secant theorem,
[tex]m\angle FRT=\frac{140^{\circ}-50^{\circ}}{2}=\boxed{45^{\circ}}[/tex]
Answer: 45 degrees
Step-by-step explanation:
Using the secant-secant theorem
You bought a magazine for $7 and some notepads for $5 each. You spend a total of $27 how many notepads did you buy.
Answers
From the information available, some magazines (m) and some notepads (n) were bought.
If you bought a magazine for $7, then mathematically that would be;
[tex]\begin{gathered} 1\times m=7 \\ m=7 \end{gathered}[/tex]Also, if you bought some notepads for $5 each, that would be expressed as;
[tex]5\times n=5n[/tex]This represents 5 dollars times every given number of notepads, hence we would have;
[tex]\begin{gathered} m+5n=27 \\ \end{gathered}[/tex]Note that one magazine was bought which is why we have m = 7. We shall now substitute for thw value of m;
[tex]\begin{gathered} m+5n=27 \\ 7+5n=27 \\ \text{Subtract 7 from both sides;} \\ 7-7+5n=27-7 \\ 5n=20 \\ \text{Divide both sides by 5;} \\ \frac{5n}{5}=\frac{20}{5} \\ n=4 \end{gathered}[/tex]The value of n = 4
ANSWER:
This means you bought 4 notepads
Which of the following is the graph of f(x)= x² +3x-4?
Answers
Given the function
[tex]f(x)=x^2+3x-4[/tex]To determine which graph corresponds to this function you have to determine the coordinates of the vertex and the roots of the function.
Vertex
To determine the coordinates of the vertex you have to calculate the x-coordinate using the formula:
[tex]x=-\frac{b}{2a}[/tex]a is the coefficient of the quadratic term
b is the coefficient of the x-term
The term of the quadratic term, in this case, is a=1 and the term of the x-term is b=3
[tex]\begin{gathered} x=-\frac{3}{2\cdot1} \\ x=-\frac{3}{2}=-1.5 \end{gathered}[/tex]Replace the x-coordinate in the function to calculate the corresponding value of f(x):
[tex]\begin{gathered} f(x)=x^2+6x-4 \\ f(-3)=(-\frac{3}{2})^2+3\cdot(-\frac{3}{2})-4 \\ f(-3)=\frac{9}{4}-\frac{9}{2}-4 \\ f(-3)=-\frac{25}{4}=-6.25 \end{gathered}[/tex]The coordinates of the vertex are (-1.5,-6.25)
Roots of the function
To determine the roots of the function you have to use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant of the function
For a=1, b=3, and c=-4
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\cdot1\cdot(-4)}}{2\cdot1} \\ x=\frac{-3\pm\sqrt[]{9+16}}{2} \\ x=\frac{-3\pm\sqrt[]{25}}{2} \\ x=\frac{-3\pm5}{2} \end{gathered}[/tex]Solve the addition and the subtraction separately
Addition
[tex]\begin{gathered} x=\frac{-3+5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]Subtraction
[tex]\begin{gathered} x=\frac{-3-5}{2} \\ x=\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]The roots of the function are (1,0) and (-4,0)
The graph that corresponds to this function is
Which of the following things is not contained at the plane B?
Answers
Related with the picture and your question, you should notice that an element is not contained in a set, that in your case is the plane B, when any of its points is outside of this one.
Then by the picture we could notice that the line q is not contained at the plane B, because the point G is inside q but it is not in B.
write an inequality for the graph using x for the variable.
Answers
Given:
There are given that the inequality graph.
Explanation:
In the given question, there are given number line graphs, in which the arrow has been shown in a negative direction.
Also,
There are given that the number 2 has not been included in the given graph.
So,
The inequality will be:
[tex]x<2[/tex]Final answer:
Hence, the inequality is shown below:
[tex]x\lt2[/tex]
Convert 15 gal to quarts
Answers
The conversion rate for a gallon to quart is given as
[tex]1\text{ ga }\to4\text{ quart}[/tex]This means that to get the number of quarts in a given measure in gallons, we multiply the number by 4.
The question asks us to convert 15 gallons to quarts.
This can be calculated as
[tex]\begin{gathered} 15\times4 \\ =60\text{ quarts} \end{gathered}[/tex]Therefore,
[tex]15\text{ gal }\to60\text{ quarts}[/tex]Evaluate the determinant.7 3 28 2 76 8 5A) 212B) -464© -212D860
Answers
| 7 3 2|
8 2 7
6 8 5
7(10 - 56) - 3(40 - 42) + 2(64 - 12)
7(-46) - 3(-2) + 2( 52)
-322 + 6 + 104
= -212
Identify the units you would expect for the given quantity.The price of a bottle of French perfume, found by multiplyingthe unit price of the perfume in euros per milliliter by thevolume of the bottle in milliliters.
Answers
Given:
The price of a bottle of French perfume, found by multiplying
the unit price of the perfume in euros per milliliter by the volume of the bottle in milliliters.
the unit of the unit price is: euros per milliliter
And the unit of the volume is: milliliters
By multiplying the two units: the unit of the result will be euros
Devin owes $26,000 in students loans for college. The interest rate is 8.75% and the loan will be paid off over 15 years. How much will Devin pay altogether?$60,125$72,123$3,412,500$8,125
Answers
Answer:
$60,125
Explanation:
We'll use the below formula to determine how much Devin will pay altogether;
[tex]A=P(1+rt)[/tex]where A = final amount = ?
P = principal amount = $2600
r = interest rate in decimal = 8.75/100 = 0.0875
t = time in years = 15 years
Substituting the given values into our formula and solving for A, we'll have;
[tex]\begin{gathered} A=26000(1+0.0875\times15) \\ =26000(2.3125) \\ =60,125 \end{gathered}[/tex]Therefore, Devin will pay $60,125 altogether.
find the first five terms of the recursive sequence. aₙ = -6aₙ₋₁ where a₁ = 45
Answers
The first terms is
[tex]undefined[/tex]Substitute 2, 3, 4, and 5 for n in the equation to find first four next terms.
In AFGHFH.GF +40, HF 3x - 20, and GH find the value of 21 20
Answers
You have the next triangle:
As the triangle has two angles that are congruent, then it is a isisceles triangle. The opposite sides of the equal angles have the same measure.
Sides FG and GH have the same measure:
[tex]FG\cong GH[/tex][tex]x+40=2x+20[/tex]Use this equation to find the value of x:
- Substract in both sides of the equation 2x:
[tex]\begin{gathered} x-2x+40=2x-2x+20 \\ -x+40=20 \end{gathered}[/tex]- Substract in both sides of the equation 40:
[tex]\begin{gathered} -x+40-40=20-40 \\ -x=-20 \end{gathered}[/tex]- Multiply both sides of the equation by -1:
[tex]\begin{gathered} (-1)(-x)=(-1)(-20) \\ \\ x=20 \end{gathered}[/tex]Answer x=204p-9=2p+21solve the equation
Answers
The given equation is,
[tex]4p-9=2p+21[/tex]The equation can be solved as,
[tex]\begin{gathered} 4p-9=2p+21 \\ 4p-2p=21+9 \\ 2p=30 \\ p=\frac{30}{2} \\ p=15 \end{gathered}[/tex]Thus, the requried value of p is 15.N
Type the correct answer in the box. Use numbers instead of words.
The number 392,000 is divided by 10.
What is the value of the digit 2 in the quotient?
Answers
The value of 2 in the quotient is 200.
What is division?
One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.
The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups.
Let, the number 392,000 is divided by 10.
That means, [tex]\frac{392000}{10}[/tex]
Here, 392000 is the numerator and 10 is the base.
Simplifying the fraction, we get 39200.
39200 is the quotient.
Here 2 is on the hundredth place.
Therefore, the value of 2 in the quotient is 200.
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The Fishers ate out at a restaurant and paid a total of $68.22, including the tip. If the Fishers tipped 20%, what was the cost of the meal?
Answers
Explanation:
Multiply 68.22 by 1.2 to get 81.864 or $81.86
Dave started at the black dot and traveled the distance shown on the map on his bike. The length of the section in red is not known.
About how far did Dave travel on his bike?
Answers
Answer: 9,00
Step-by-step explanation:
I am right.
Answer:
1,402
Step-by-step explanation
the red line is further than the 1,396
find the value of x then find the measure of both angles
Answers
According to the given graph, the angles are linear pairs because they are on a straight angle, so the must sum 180°. Having said that, we express the following.-
[tex](4x+20)+(x-10)=180[/tex]We reduce like terms
[tex]5x+10=180[/tex]Then, we subtract 10 on each side.
[tex]\begin{gathered} 5x+10-10=180-10 \\ 5x=170 \end{gathered}[/tex]At last, we divide the equation by 5.
[tex]\begin{gathered} \frac{5x}{5}=\frac{170}{5} \\ x=34 \end{gathered}[/tex]We use this value to find the angles.
[tex]\begin{gathered} 4x+20=4(34)+20=136+20=156 \\ x-10=34-10=24 \end{gathered}[/tex]Therefore, x is equal to 34, and the angles are 156° and 24°.1-58. Copy the number line below and place the following probabilities on it
Answers
Considering the following:
a) 1/4 chance that you will be the team member who gets supplies tomorrow
b) A 25% chance of snow tomorrow
c) A 0.8 probability of eating vegetables with dinner
d) P(blue marble) = 5/8
e) A 0.10 probability that it will be 85º on Saturday
Then:
1/4 =0.25 and 25% represents the same amount
A 0.8 probability is equivalent to 80% of probability of eating vegetables.
P (blue marble) = 5/8 5: 8 =0.625 what is equivalent to 62.5 if we multiply it by 100
And Finally 0.10 probability is a probability of 10% of 85ºF on Saturday
Placing all this values on a line by increasing order
Roughly sketched.
Remember that Probability is always represented within an interval between 0 and 1
Wich expression is equivalent to a+(c+7)
Answers
Given the expression:
[tex]a+(c+7)[/tex]To determine an equivalent expression, the first step is to open the bracket.
Therefore:
[tex]undefined[/tex]Determine the area of the base of a cone with a volume of 36 cubic inches and a height of 9 inches?
Answers
the are of a base cone, while we have the volume and the height
V= pi*r^2*(h/3)
36=pi*r^2*3
we can find out now the r, radius
r=sqrt(3*36/pi*9)=1.95
Area, A= pi*r^2=
we can look at the Volume formula
36=pi*r^2*3
and if we divide both sides by 3 we get
12=pi*r^2, which is area
A= 12
suppose s and t are mutually exclusive events. find p (s or t) if p(s)=29% and p(t)=49%
Answers
Given:
P(s) = 29%
P(t) = 49%
For us to be able to determine P(S or T), we will be using the following formula:
[tex]\text{ P\lparen S or T\rparen = P\lparen S\rparen + P\lparen T\rparen}[/tex]We get,
[tex]\text{ P\lparen S or T\rparen = 29\% + 49\% = 78\%}[/tex]Therefore, the answer is CHOICE A: 78%
What are the coordinates of point w? 5 Z 3 2 Y 3 0 2 2. 4 -1 -2 W -3 -5 Х
Answers
the point W is positioned 3 units to the right (the x-coordinate is 3) and 2 units down (the y-coordinate is -2), thus the coordinates of W are (3,-2)
Which of the following is equal to ? 1/5^-2
Answers
25
1) Let's evaluate this expression making use of one exponent property:
[tex](\frac{1}{5})^{-2}=(\frac{5}{1})^2=(5)^2=25[/tex]2) Note that negative exponents reciprocate the base.
3) Hence, the answer is 25
Question 4 please . Using a graphing utility (geogebra) to graph the function
Answers
Problem N 4
we have the function
[tex]f\mleft(x\mright)=x^4-3x^2+2x-1[/tex]Interval (-2,2)
using a graphing tool
Local minimum value at (1,-1)
Local maximum value at (0.37,-0.65)
Increasing functionIntervals (-1.37,0.37) U (1, infinite)
Decreasing functionIntervals (-infinite, -1.37) U (0.37,1)
107. Cranky mower To start her old lawn mower, Rita has
S to pull a cord and hope for some luck. On any partic-
ular pull, the mower has a 20% chance of starting.
(a)
Find the probability that it takes her exactly 3 pulls to
start the mower.
(b) Find the probability that it takes her more than 6
pulls to start the mower.
108. 1-in-6 wins Alan decides to use a different strategy for
the 1-in-6 wins game of Exercise 90. He keeps buying
one 20-ounce bottle of the soda at a time until he gets
a winner.
Find the probability that he buys exactly 5 bottles.
(b) Find the probability that he buys at most 6 bottles.
Show
your work.
Answers
According to the binomial distribution, there is a 0.128 = 12.8% chance that it will take her precisely 3 pushes to start the mower.
she will need to start the mower more than 10 times.There are just two possible results for each pull. The lawnmower either starts or it doesn't. The binomial distribution is employed to answer this question since the likelihood that the mower will start on a pull is independent of all other pulls.Binomial distribution of probabilitiesThe conditions are: x is the total number of victories.The number of trials is n.P represents the likelihood that a trial will be successful.It has a 20% chance of starting on any given pull, therefore
Item
a:This probability is P(X = 0) when n = 2, multiplied by 0.2, which is the probability that it starts on the third, and it is that it doesn't start on the first two. Hence:
It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.
Item b:When n = 10, this probability is none on the first 10 and is hence P(X = 0):
Her chances of needing more than 10 pushes to start the mower are 0.1074, or 10.74%.
It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.
Item b:On the first, there is no chance in this.
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MAH ~ WCF what is the value of x?picture will be sent in messages
Answers
Since both triangles are congruent, the proportion between their sides is the same, so we can write:
[tex]\frac{MA}{MH}=\frac{WC}{WF}\Longrightarrow\frac{62}{92}=\frac{15.5}{x}\Longrightarrow62x\text{ = 92 }\cdot\text{ 15.5 = }1426\Longrightarrow\text{ x = 1426/62 =}23[/tex]x = 23
Answer:
x = 23
25. Ally is making a replica of a building that is at ascale of 4 m. to 3 in.The model is 84 in tall. How tallis the building?
Answers
We know that in our model 3 inches represent 4 m, to determine how tall the building is with the knowledge that the model is 84 in we can use a rule of three:
[tex]\begin{gathered} 4\text{ m}\rightarrow3\text{ in} \\ x\rightarrow84\text{ in} \end{gathered}[/tex]then:
[tex]x=\frac{84\cdot4}{3}=112[/tex]Therefore, the building is 112 meters tall.
A small pool can hold 72.5 gallons of water . The pool is currently 3/4full how many gallons are in the pool ?
Answers
If we have that the pool is currently 3/4 full, we need to multiply this fraction by the total the small pool can hold. That is (with no units):
[tex]T=72.5\Rightarrow\frac{3}{4}T=\frac{3}{4}\cdot72.5=54.375[/tex]Therefore, the pool currently has 54.735 gallons (3/4 of its total capacity) (we multiply 3 times 72.5, and then we divide this result by 4).
Express the following as an algebraic function of x.sin(sin-'(x) – cos-'(x))
Answers
Hello there. To solve this question, we'll have to remember some properties about inverse trigonometric functions.
Given the expression:
[tex]\sin (\sin ^{-1}(x)-\cos ^{-1}(x))[/tex]We want to express it as an algebraic function of x.
For this, imagine the following triangle:
Now, we find the missing leg of the triangle applying Pythagoras theorem:
[tex]\begin{gathered} 1^2=x^2+?^2 \\ 1-x^2=?^2 \\ ?^{}=\sqrt[]{1-x^2} \end{gathered}[/tex]Now, finding the sine and cosine of the angles alpha and beta, we get:
First, remember the sine of an angle is equal to the ratio between the opposite side to the angle and the hypotenuse of the triangle. The cosine of the same angle is equal to the ratio between the adjacent side to the angle and the hypotenuse of the triangle.
Therefore, we have:
[tex]\begin{gathered} \sin (\alpha)=\frac{x}{1}=x \\ \cos (\beta)=\frac{x}{1}=x \\ \sin (\beta)=\frac{\sqrt[]{1-x^2}}{1}=\sqrt[]{1-x^2} \\ \cos (\alpha)=\frac{\sqrt[]{1-x^2}}{1}=\sqrt[]{1-x^2} \end{gathered}[/tex]This means that:
[tex]\begin{gathered} \alpha=\sin ^{-1}(x) \\ \beta=\cos ^{-1}(x) \end{gathered}[/tex]Now, the expression we had earlier turns into:
[tex]\sin (\alpha-\beta)[/tex]For this, we'll use the angle sum formula:
[tex]\sin (u-v)=\sin (u)\cos (v)-\sin (v)\cos (u)[/tex]Which gives us:
[tex]\sin (\alpha)\cos (\beta)-\sin (\beta)\cos (\alpha)_{}[/tex]Plugging the results we got earlier, this is simply:
[tex]x\cdot x-\sqrt[]{1-x^2}\cdot\sqrt[]{1-x^2}[/tex]As x > 0, because we're using it as a triangle side (but it could be negative considering inverse sine and cosine as functions), we get:
[tex]\begin{gathered} x^2-(1-x^2) \\ x^2-1+x^2 \\ 2x^2-1 \end{gathered}[/tex]