1. The expressionx^3+3x^2+x-5 represents the total length across the front of the mansion. Find the length of side I. Show all work. X will stay a variable and your answer will be a polynomial
2. 2. The owners of the mansion want to install a new security system to protect the outside of their house. To get an estimate for the cost of the new security system they need to know the total distance around the outside of the mansion.
a. How many sides does the Mansion have?
b. What side would be the same length as side L?
c. What side would be the same length as side D?
d. Find an expression for the perimeter of the mansion. Show all work. X will stay a variable and your answer will be a polynomial.
3. The owners of the mansion also want to install new AC units. You must know the amount of air on the first floor of the mansion to determine the size of AC units necessary to function properly. The first floor of the mansion covers, or has a base, 15x^4+20x^2+45x+590 square feet. If the height of the ceilings on the first floor is 5x-3, find the total volume of air on the first floor. Use the formula V=Bh where Bis the area of the base and his the height. Show all work. X will stay a variable and your answer will be a polynomial.
4. The area of the Gothic Room in the mansion’s layout is2x^3+25x^2+169, what are the dimensions (length and width) for the room? Side E is x + 13. Use synthetic division to find the other side width. Show all work. X will stay a variable and your answer will be a polynomial.
Answers
Given that the expression [tex]x^3+3x^2+x-5[/tex] represents the total length across the front of the mansion. Let the length of side I be a, then
[tex]x^4-2x^3+x-10+a-x^3+5x^2+2=x^3+3x^2+x-5 \\ \\ \Rightarrow a=x^3+3x^2+x-5-x^4+2x^3-x+10+x^3-5x^2-2 \\ \\ =\bold{-x^4+4x^3-2x^2+3}[/tex]
Part 2:
From the given figure it can be seen that the mansion has 12 sides labelled A - L.
Side F will be of the same length as side L.
Side B will be of the same length as side D.
The perimeter of figure is the sum of all the lengths of the outlines of the figure.
The perimeter is given by:
[tex]P=2(x^3+3x^2+x-5)+2(-2x^4+24x^2-10)+2(4x)+x^2-x+6 \\ \\ =2x^3+6x^2+2x-10-4x^4+48x^2-20+8x+x^2-x+6 \\ \\ =\bold{-4x^4+2x^3+55x^2+9x-24}[/tex]
Part 3:
The volume of an object is given by: V = Area of base x height.
Given that the first floor of the mansion has a base, [tex]15x^4+20x^2+45x+590\ square\ feet[/tex]. If the height of the ceilings on the first floor is 5x-3, then, the total volume of air on the first floor is given by:
[tex]V=(5x-3)(15x^4+20x^2+45x+590) \\ \\ =75x^5+100x^3+225x^2+2950-45x^4-60x^2-135x-1770 \\ \\ =\bold{75x^5-45x^4+100x^3+165x^2-135x+1180}[/tex]
Part 4:
Given that the area of the Gothic Room in the mansion’s layout is [tex]2x^3+25x^2+169[/tex], with the length of one of the sides of the room as x + 13. Then, the length of the other side is given by:
-13 | 2 25 0 169
|
| -26 13 -169
|______________
2 -1 13 0
Therefore, the length of the other side of the length is [tex]-26x^2+13x-169[/tex]
Related Questions
Explain how finding 4x 384 can help you find 4 x 5,384. Then find both products
Answers
so the answer is 21,536
"isotherms are drawn at regular intervals; on this map, the interval between successive isotherms is ______ fahrenheit degrees."
Answers
An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.
Basing from the graph, we can actually see that the interval is:
10 Fahrenheit degrees
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks she needs to sell to earn $100.
1.25x + 1.49 = 100
What error did Barbara make in writing the equation?
Answers
Pascal wants to find the sum of the measures of the interior angles of a polygon that has n sides. How could he do this?
Answers
multiply by 180 (n-2)
count how many sides you have.. subtract the sides by the number 2. then multiply tht by 180
Answer with explanation:
Smallest Polygon = Triangle , which has 3 sides
Sum of angles of triangle = 180°→→, Using the angle sum property of triangle.
We can find the Sum of angles of triangle, using the formula
= (n-2)×180°
= (3-2)×180°
= 1 × 180°
= 180°
A Quadrilateral has four sides.
Sum of angles of Quadrilateral = 360°
Or , using the formula
=(4-2)×180°
=2 × 180°
=360°
For, n sided Polygon
Sum of it's Interior angles = (n-2) × 180°
To prove this, we should divide that polygon into triangles, and multiply number of triangles by angle of 180°.
For, example, Quadrilateral can be divided into two triangles , sum of interior angles of Quadrilateral =2 × 180°=360°
The isosceles triangle has a perimeter of 7.5m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
Answers
2x=7.5-2.1
2x=5.4
x=2.7
Answer:
2.1 +2x=7.5
Step-by-step explanation:
A bag contains 450 blue and yellow marbles. The probability of drawing a yellow marble is 46%. How many blue marbles are in the bag?
Answers
Hope this helps! :)
50 points and brainliest
(3^8 x 2^-5 x 9^0) ^-2 x (2^-2 / 3^3) ^4 x 3^28
Write your answer in simplified form. Show all the steps
Answers
(3^8 *2^-5 *9^0)^-2 * (2^-2/3^3)^4 * 3^28 =
(6561 * 0.03125 * 1)^-2 * (0.25/27)^4 * 2.287679245x10^13 =
0.0000237881 * 0.00000000073503 * 2.287679245x10^13 =
0.40000008, round to 0.4
= 3^-16 2^10 x 1^-2 x 2^-8 x 3^-12 x 3^28
= 3^0 x 2^10 x 1^-2 x 2^-8
=1 x 2^2 x 1
= 1 x 4 x 1
= 4
the ratio of girls to boys in the math club was 3.5. if there were 120 children altogether, how many girls were there?
Answers
3 girls to 5 boys
3+5 =8
120/8 = 15
3 *15 = 45 girls
a right triangle has one angle that measures 23 degress.The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle?Round to the nearest tenth.Area of a triangle =1/2bh
Answers
Answer:
Area of the triangle will be 162.3 cm²
Step-by-step explanation:
From the figure attached,
In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm
Now we have to calculate the area of the given right angle triangle.
Since area of a right angle triangle is represented by
Area = [tex]\frac{1}{2}\times b\times h[/tex]
Where b = adjacent side
h = opposite side
To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.
AC² = AB² + BC²
AB² = AC² - BC²
AB² = (30)² - (27.6)²
= 900 - 761.76
= 138.24
AB = √138.24
= 11.76
Area of the triangle = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(11.76)(27.6)[/tex]
= 162.28 cm² ≈ 162.3 cm²
Can someone help me with 2 and 4
Answers
First write down what we know:
Number of papers delivered per year
(1) 31
(2) 55
(3) 60
(4) 78
Now add 31,55,60,78 and then divide by 4
[tex] \frac{31 + 55 + 60 + 78}{4} = 56[/tex]
Answer:
For the four years Alexis delivered 56 papers per week
Number 4:
Thomas caught 24 fish in total. He then gave 6 to his mother and then divided the rest of the fish between his two aunts. It want to know how many fish did each aunt get.
He had 24 the he gave 6 away so we have 24 - 6 = 18 fish left. Now he divide the rest 18 between his two aunts so 18 / 2 = 9. This mean each aunt received 9 fish each.
A grocery store's receipts show that sunday customer purchases have a skewed distribution with a mean of $3030 and a standard deviation of $2121. suppose the store had 304304 customers this sunday. a) estimate the probability that the store's revenues were at least $9 comma 6009,600. b) if, on a typical sunday, the store serves 304304 customers, how much does the store take in on the worst 11% of such days?
Answers
a) The probability is approximately 0.9973.
b) The store takes in at most [tex]$\$ 15,600.00$[/tex].
a) To estimate the probability that the store's revenues were at least [tex]$\$9,500$[/tex], we need to find the z-score corresponding to this revenue value and then find the probability associated with that z-score in the standard normal distribution.
First, we calculate the z-score:
[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{9500 - 3200}{2000} = \frac{6300}{2000} = 3.15 \][/tex]
Using a standard normal distribution table or a calculator, we find that the probability corresponding to [tex]$z = 3.15$[/tex] is approximately 0.9987.
So, the estimated probability that the store's revenues were at least [tex]$\$9,500$[/tex] is approximately 0.9987.
b) To find out how much the store takes in on the worst [tex]$10\%$[/tex] of such days, we need to find the revenue value corresponding to the [tex]$90\%$[/tex] percentile of the distribution.
Using the standard normal distribution table or a calculator, we find that the [tex]$90\%$[/tex] percentile corresponds to a z-score of approximately 1.28.
Now, we can find the revenue value:
[tex]\[ X = \mu + z \times \sigma = 3200 + 1.28 \times 2000 = 3200 + 2560 = 5760 \][/tex]
So, on the worst [tex]$10\%$[/tex] of such days, the store takes in at most [tex]$\$5,760.00$[/tex].
The correct question is:
A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of [tex]$\$ 32$[/tex] and a standard deviation of [tex]$\$ 20$[/tex]. Suppose the store had 294 customers this Sunday.
a) Estimate the probability that the store's revenues were at least [tex]$\$ 9,500$[/tex].
b) If, on a typical Sunday, the store serves 294 customers, how much does the store take in on the worst [tex]$10 \%$[/tex] of such days?
a) The probability is [tex]$\square$[/tex].
b) The store takes in at most [tex]$\$ \square$[/tex].
The mean height of a group of students is 65.4 inches. A student joins the group who is 73 inches tall. How does this student’s height affect the mean?
A. The new mean height will still be 64.5 inches.
B. The new mean height will be greater than 65.4 inches.
C. The new mean height will be less than 65.4 inches.
D. The new mean height will be 73 inches.
Answers
Answer:
The new mean height will be greater than 65.4 inches.
Step-by-step explanation:
The mean height of a group of students is 65.4 inches. A student joins the group who is 73 inches tall.
Mean is 65.4 inches
A student joins the group who is 73 inches tall.
73 is greater than the means 64.4 inches
So mean will increase definitely
Mean will vary depends on the total number of students
The new mean height will be greater than 65.4 inches.
You take a trip by air that involves three independent flights. if there is an 76% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time?
Answers
Nine fewer than half a number is a five more than a four times the number.define a varible, write an equation, and slove to find the number
Answers
0.5x-9 = 4x+5
add 9 to both sides
0.5x = 4x+14
subtract 4x from each side
-3.5x =14
x = 14/*3.5
x = -4
Gina works at a diner. Earns $6.00 hour + $43.00 tips how much does she make all together?
Answers
Explain in a minimum of 2 sentences how to graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½.
Answers
To graph an absolute value function with a given vertex and 'a' value, first plot the vertex. Then use the 'a' value to find and plot other points. Connect the points to create the graph.
Explanation:To graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½, you first plot the vertex on the graph. This point will be the lowest (if 'a' is positive) or highest (if 'a' is negative) point on the graph. The vertex of the absolute value function is the point of reflection. Next, create a table to find extra points on the graph. Because 'a' is ½, count over 1 and up (or down depending on if 'a' is positive or negative) half the distance. Similarly, count over 2 and up (or down) the distance to find more points. Once you've plotted these points, you'll see the absolute value function starting to take shape. Connect the dots to create the two arms of the absolute value function that point upwards or downwards depending on the value of 'a'. This will result in a 'V' shaped graph if 'a' is positive or an upside-down 'V' shape if 'a' is negative.
Learn more about Absolute Value Function Graphing here:https://brainly.com/question/14758059
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Which value of b will cause the quadratic equation x2 + bx + 5 = 0 to have two real number solutions?
Answers
The Correct Answer is A:-5 :)
if Chelsea has 11 times as many art. Brushes and they have 60 art brushes altogether how many brushes does Chelsea have
Answers
What is the Measure Of arc WX in the diagram below?
Answers
Answer:
The correct option is A.
Step-by-step explanation:
Given information: Length of Arc TR is 116° and the measure of ∠WSX is 45°.
According to the angle of Intersecting Secants Theorem,
[tex]\text{Angle of Intersecting Secants}=\frac{1}{2}(\text{Major arc - Minor arc})[/tex]
Using this property we get
[tex]45^{\circ}=\frac{1}{2}(Arc(TR)-Arc(WX))[/tex]
[tex]45^{\circ}=\frac{1}{2}(116^{\circ}-Arc(WX))[/tex]
Multiply 2 on both the sides.
[tex]90^{\circ}=116^{\circ}-Arc(WX)[/tex]
[tex]Arc(WX)=116^{\circ}-90^{\circ}[/tex]
[tex]Arc(WX)=26^{\circ}[/tex]
The measure of arc WX is 26°. Therefore the correct option is A.
After a concert for 1,200 people, only 9 people said they would not go to see the band again. What percent of the people who went to the concert said they would not go to see the band again? 0.75% 9% 75% 133%
Answers
divide 9 by 1200
9 / 1200 = 0.0075 = 0.75%
may i please have some help?
Answers
notice the tickmarks, thus TP = PU and TQ = QS, so the PQ segment is then a midsegment of the larger triangle, and thus the angles it makes on the small one, are exactly the same.
HELP QUICK!!! 3. There is a special sale at the pet store. You can buy a fish bowl and get 6 free goldfish. Carlos and Olivia each buy a bowl and get 6 fish. They want to keep track of their fishes’ growth, so they carefully measure each fish and record these lengths:
1 ¼ in
1 7/8in.
1 1/4in.
1 3/4in.
1 3/8 in.
1 7/8 in.
1 3/8 in.
1 1/4in.
1 4/8in.
1 6/8in.
1 7/8in.
1 3/4in.
(a) Plot the lengths of each of the 12 goldfish on the line plot.
(b) Which is greater: the amount of fish that measure less than 1 1/2 inches in length or the amount of fish with a length greater than 1 1/2 inches?
Answers
for a, make a dot on the line plot at each of the given lengths
b) there are more fishes greater than 1 1/2
I HAVE 2 QUESTIONS:
1. if y = x^2 - x find the value of y when x = 3
2. if y = x^3 + x find the value of y when x = 5
Answers
1. y=6
2. =130
The length of the base of a rectangle is 6 less than 3 times the width. The perimeter of the rectangle is 52 inches. What is the length of the base?
Answers
what's the length? well, length = 3w - 6.
Please help! (Picture included)
Answers
1 _______=5,280 feet
Answers
hope this helps
One book costs 95p. How much do five books cost?
Answers
If one book costs 95p, then 5 must cost 5 times 95p.
95*5
=475
Five books would cost 475p.
Hope this helps.
-Benjamin
Heather purchased an iPad mini on sale 20% off for 263.20 what's the original price of the iPad mini
Answers
$328.99 - $65.79 = $263.20
so divide 263.20 by .8
this equals 329
to check your work multiply 329 by .2 and then subtract the answer from 329.
it equals 263.2
so the answer is $329.00
A rectangular table is 4 times as long as it is wide. If the area is 100ft^2, find the width and length of the table.
Answers
find the sum of all 3 digit whole numbers that arw divisible by 13 ?
Answers
a0 = 1st 3-digit number divisible by 13
a0 = 104
d = 13 (why?)
last term is largest divisible by 13 = 988
how many terms? (988-104)/13 + 1 = 69
S = 69/2(104+988) = 37674
The sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
To find the sum of all 3-digit whole numbers that are divisible by 13, we can use the arithmetic series formula.
1. Identify the first and last 3-digit numbers divisible by 13:
- The smallest 3-digit number divisible by 13 is 104 (since [tex]\( 13 \times 8 = 104 \)[/tex]).
- The largest 3-digit number divisible by 13 is 988 (since [tex]\( 13 \times 76 = 988 \)[/tex]).
2. Calculate the number of terms in the series:
- Use the formula for the number of terms n in an arithmetic sequence:
[tex]\[ n = \frac{\text{last term} - \text{first term}}{\text{common difference}} + 1 \][/tex]
Here, the common difference d = 13:
[tex]\[ n = \frac{988 - 104}{13} + 1 = \frac{884}{13} + 1 = 68 + 1 = 69 \][/tex]
3. Find the sum of the arithmetic series:
- The sum [tex]\( S_n \)[/tex] of the first n terms of an arithmetic series is given by:
[tex]\[ S_n = \frac{n}{2} \times (\text{first term} + \text{last term}) \][/tex]
Substitute the values:
[tex]\[ S_{69} = \frac{69}{2} \times (104 + 988) \][/tex]
Simplify the calculation:
[tex]\[ S_{69} = \frac{69}{2} \times 1092 = 34.5 \times 1092 = 37674 \][/tex]
Thus, the sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].