Answers
a) The length of the roof for the actual house is given as follows: 25 ft.
b) The measure of the angle for the actual house is also of 37º.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The scale factor for the dilation in this problem is given as follows:
40 ft/24 in = 1.67 ft/inch.
Hence the length of the roof for the actual house is obtained as follows:
15 x 1.67 = 25 ft.
The angle measures remain constant, as the dilation preserves the similarity of the figures.
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Related Questions
Graph the image of the given triangle, reflected across the y-axis. Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
Answers
The image of the transformation are (2, -9), (-9, -7), (-7, -4)
How to perform the transformation?The coordinates of the triangle are given as
(-2, -9), (9, -7), (7, -4)
The transformation is given as
Reflection across the y-axis
This is represented as
(x, y) ⇒ (-x, y)
This means that the transformation is (-x, y)
When this rule is applied on the coordinates, we have
(2, -9), (-9, -7), (-7, -4)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
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The triangular pyramid needs square inches of construction paper to make. The square pyramid needs square inches of construction paper to make. The pyramid will need square inches more construction paper to make than the other pyramid. Need help ASAP
Answers
Answer:
Please post the figure
Step-by-step explanation:
What does (Y) equal?
2(5 + y) = 18
Answers
Answer:
y = 4
Step-by-step explanation:
distribute
10 + 2y = 18
minus 10 from both sides
2y = 8
divide by 2
y = 4
Answer: y=4
Step-by-step explanation:
2(5+y)=18
youre going to start by distributing the 2 to (5+y)
10+2y=18
then subract 10 from 18
2y=8
and then divide 2 on both sides
y=4
An office manager orders one calculator or one calendar for each of the office's 60 employees. Each calculator costs $15, and each calendar costs $10. The entire order totaled $800.
Part A: Write the system of equations that models this scenario. (5 points)
Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps. (5 points)
Answers
The system of equations is.
\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)
And the solutions are y = 50 and x = 10.
How to write and solve the system of equations?Let's define the two variables:
x = number of calculators.y = number of calendars.With the given information we can write two equations, then the system will be:
\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)
Now let's solve it.
We can isolate x on the first to get:
\(\text{x} = 60 - \text{y}\)
Replace that in the other equation to get:
\(15\times(60 - \text{y}) + 10\text{y} = 800\)
\(-2\bold{y} = 900 - 800\)
\(-2\bold{y} = 100\)
\(\text{y} = \dfrac{100}{-2} = \bold{50}\)
Then \(\bold{x=10}\).
Therefore, the solutions are y = 50 and x = 10.
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Jane evaluates x2-3x+5 for x=-2 below.
Step 1: (-2)²-3(-2)+5
Step 2: -4+6+5
=
Step 3: = 7
What, if any, was Jane's mistake?
Jane made no mistakes.
O Jane incorrectly evaluated (-2)² in step 2.
Jane incorrectly added the terms in step 3.
O Jane incorrectly substituted in x=-2 in step 1.
K
Answers
Answer: Jane incorrectly evaluated (-2)² in step 2.
Step-by-step explanation:
\((-2)^{2}=4\), not -4.
Arrange the steps in order to simplify the expression
Answers
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
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What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
Answers
Answer:
2.5
Step-by-step explanation:
the length has increased by 7.5/3 = 2.5.
so the scale factor is 2.5
In the 2006 World cup, circles of cloth were used to cover the centre circle at the start of each match . The radius of a centre circle is 9.15m and 12 football pitches were used . Estimate the total area of cloth used .
Please answer with clear explaination.
Answers
The total area of clothes used is 12627m².
How to calculate the area?It is important to note that a football is in the shape of a sphere. Therefore, the area of a ball will be:
= 4πr²
In this case, the radius which is represented by r is given as 9.15m.
The area will be:
= 4πr²
= 4 × 3.142 × 9.15²
= 1052.22
Therefore, since there are 12 pitches, the area will be:
= 1052.22m² × 12
= 12627m²
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On a team, 3 girls and 2 boys scored a total of 41 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 13. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answers
Answer:
each girl scored 9 points
each boy scored 7 points
Step-by-step explanation:
41-13=28
28/2=14
14 is the number scored by boys
14/2
one boy scored 7 points
14+13=27
27 is the number scored by girls
27/3=9
each girl scored 9 points
Maria practiced the piano for 2 1/2 hours last week and 1 3/4 hours this week.Use the bar diagram sections to construct a bar diagram that represents how many hours Maria practiced in the past 2 weeks.
How many hours did Maria practice the piano in the past 2 weeks?
Answers
The number of hours that Maria practiced in the past 2 weeks will be 4 1/4 hours.
How to illustrate the fraction?From the information, Maria practiced the piano for 2 1/2 hours last week and 1 3/4 hours this week.
Therefore, the number of hours that Maria practiced in the past 2 weeks will be:
= 2 1/2 + 1 3/4
= 2 2/4 + 1 3/4
= 4 1/4 hours
The number of hours that Maria practiced in the past 2 weeks will be 4 1/4 hours.
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Megan made a paper chain that was 4m long. Mason’s chain was 479 cm long. Who’s was the longest? By how much?
Answers
Answer:
Look below
Step-by-step explanation:
Let's start by converting 4 m into cm:
\(4m * \frac{10^{2}cm}{1m} \)\(= 4*10^{2}cm=400cm\)
Since Megan's chain is only 400 cm long, Mason's chain is longer by 79 cm.
Answer:
Masons is longer
Step-by-step explanation:
4m=400 cm
479cm=4.79 m
I'm pretty sure you could answer the rest.
using the disk method, determine the volume of a solid formed by revolving the region bounded above by the line , on the left by the line , on the right by the curve , and below by the line the about the -axis.
Answers
The volume of a solid formed by revolving the region bounded above by the line is (932π/15)
To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.
The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:
\(r = y^2 - 1\)
The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:
h = 3 - 1 = 2
The volume of each disk is then:
\(dV = \pi r^2h dy\)
Substituting r and h, we have:
\(dV = \pi (y^2 - 1)^2 (2) dy\)
To find the total volume, we integrate over the range of y from 1 to 3:
\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)
This integral can be simplified by expanding the squared term:
\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)
V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)
V = 2π [(1/5)(242) - (2/3)(26) + 2]
V = 2π [(242/5) - (52/3) + 2]
V = 2π [(726/15) - (260/15) + 30/15]
V = 2π [(466/15)]
V = (932π/15)
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Note: The full question is
Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.
Factor completely: 5x2 - 2x
Answers
X(5x-2) thats how you factor
Dertermine the quotient of 3/7 divided by 2/3 pls help
Answers
= 3/7 * 3/2 = 9/14
Answer: 9/14
Answer: 9/14
Step-by-step explanation:
hope this helps!
A town has a population of 17000 and grows at 3% every year. What will be the population after 10 years, to the nearest whole number?
Answers
Answer:
22847
Step-by-step explanation:
17000(1.03^x)=f(x)
f(x)=22847
Find the 20 % trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Lengths of Longest 3-Point Kick for NCAA Division 1-A Football 30 32 34 40 41 43 43 4445 45 461% 47 521 5153t 56t 56 57 60 Copy Data Answer How to enter your answer TablesKeypad
Answers
46.53 is the Trimmed mean after removing, 20% of the trimmed mean from all the given lengths of 3-Point Kick for NCAA Division 1-A Football.
The given data is:
Lengths of 3-point kicks = 30 32 34 40 41 43 43 44 45 45 46 47 52 51 53 56 56 57 60.
Trimmed mean = 20%
The trimmed mean is defined as the statistical measure of central tendency. That means calculating the mean value of the given tendency of observations.
Trimmed observations = 20 x (20/100) = 4
These, trimmed observations denote that 2 observations must be trimmed from both sides when they are arranged in ascending order.
Ascending order of lengths = 30 32 34 40 41 43 43 44 45 45 46 47 51 52 53 56 56 57 60.
The trimmed Mean = (34 40 41 43 43 44 45 45 46 47 51 52 53 56 56)/ 15
Trimmed mean = 698/15 = 46.53
Therefore, we can conclude that 46.53 is the Trimmed Mean after removing, 20% of the trimmed mean.
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If the function f(x)=Mx+b has an inverse function , which statement must be true
Answers
m≠0, m must not be zero. I hope this helps!
Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number.)
Rolling an even number or doubles
Answers
The probability of the Doubles" means both dice show the same number is 36.
What is probability?When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.
The likelihood of rolling an even number or doubles is thus:
The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.
The odds of rolling an even number or two doubles are 19/36.
Therefore, the probability of the Doubles" means both dice show the same number is 36.
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please asap help im desperate.......................
Answers
Answer:
D
Step-by-step explanation:
What effect does Mathilde's losing the necklace have on the plot in "The Necklace"? It creates doubt in the mind of Madame Forestier' as to Mathidle's honesty. It helps extinguish Mathilde's longing for a life of luxury and wealth. It leads Mathilde and her husband into a life of debt, hard work, and poverty.
What is the decimal value of the hex number ABE?
Answers
Answer:
The value of HEX ABE in decimal is 2750.
Step-by-step explanation:
Hex ABE to decimal explained:
The value of HEX ABE in decimal is 2750.
The value of HEX ABE in binary is 101010111110.
E 14 X 160 = 14
B 11 X 161 = 176
A 10 X 162 = 2560
HEX ABE = 2750
the binary value is: 101010111110
I'm not gonna put the list anymore just look on your other questions XD
HOPE THIS HELPS!
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the sum of a number and 8 is 22. find the number
Answers
Answer:
x = 14
Step-by-step explanation:
Let's solve for the value of x,
→ x + 8 = 22
→ x = 22 - 8
→ [ x = 14 ]
Hence, the number is 14.
Answer:
the number can be represented by x.
so x=7.
Step-by-step explanation:
• if the area of a square is 100cm ^2, what is the perimeter? • if the perimeter of a square is 116cm, what is it's area?
Answers
1) Given data:
Area of square = 100 cm square
\(A=a^2\)\(\begin{gathered} a^2=100 \\ a=10\operatorname{cm} \end{gathered}\)The perimeter of square is,
\(\begin{gathered} P=4a \\ P=4\times10 \\ P=40\operatorname{cm} \end{gathered}\)2) Given data:
Perimeter of square = 116 cm
\(P=4a\)\(\begin{gathered} 4a=116 \\ a=29 \end{gathered}\)The area os square is,
\(\begin{gathered} A=a^2 \\ A=29\times29 \\ A=841\operatorname{cm}\text{ square} \end{gathered}\)Two cones are mathematically similar.
The total surface area of the smaller cone is 270 cm².
The total surface area of the larger cone is 480 cm².
The volume of the larger cone is 960 cm³.
Calculate the volume of the larger cone.
Answers
The volume of larger coin is 2,275.5cm³
What is volume of cone?
The volume of a cone is defined as the amount of space or capacity a cone occupies. The volume of cone is measured in cubic units like cm3, m3, in3, etc. A cone can be formed by rotating a triangle around any of its vertices. A cone is a solid 3-D shape figure with a circular base. It has a curved surface area.
Let the Slant height of smaller cone =l
Let the Slant height of larger cone =L
Let the radius of smaller cone =r
Let the radius of larger cone =R
Let height of smaller cone =h
Let height of larger cone =H
When cones are mathematically similar ,then
H/h=L/l=R/r=K(say)…
T.S.A of a smaller cone=πr(l+r)
T.S.A of a larger cone = πR(L+R)
Divide T.S.A of larger cone to Smaller cone
r(l+r)/R(L+R)
= 270/480 = 9/16
r(l+r)/k²r(l+r)=9/16
1/k²=9/16
k=3/4
Also, it is given that
volume of smaller cone is 960cm³
1/3πr²h=960
1/3π(3/4R)²(3/4H) =960
27/64×1/3π(R)²(H)= 960
Volume of larger cone = 960×64/27
=2,275.5cm³
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Find the area of the irregular figure. Round to the nearest hundredth.
Answers
Answer:
137.5 in^2
Step-by-step explanation:
So, this is basically a rectangle and two right-sides triangles.
First the rectangle: Formula is A=wl
Replace the Values: A = 14*7 98 in^2
Then we solve for the two right-sides triangles.
A= 1 /2a h= 1 /4 b ^2 sin (2 θ )
Top trinangle= A = 25.5 in^2 (height 7 in base 7 in)
Bottom Trinagle A = 14 in^2 (height 7 in base 4 in)
Add results:
98+25.5+14 = 137.5 in^2
please help me with this please i need the amswers for today,
Answers
The coordinates of each points are:
A = (-0.5, -5)
B = (0.8, -1.8)
C = (-2.6, -2.2)
D = (-1.5, -8.9)
E = (2.5, -6.5)
F = (-1.5, 3.1)
G = (-2.4, 4.1)
H = (1.5, 3)
I = (2.7, 1.5)
J = (-1.5, 0)
K = (-6.5, 0)
We have,
The coordinates of each point are in an ordered form.
i.e
(x, y)
x is the x-axis value.
y is the y-axis value.
Thus,
A = (-0.5, -5)
B = (0.8, -1.8)
C = (-2.6, -2.2)
D = (-1.5, -8.9)
E = (2.5, -6.5)
F = (-1.5, 3.1)
G = (-2.4, 4.1)
H = (1.5, 3)
I = (2.7, 1.5)
J = (-1.5, 0)
K = (-6.5, 0)
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et us address the final position of the fish first. the position of the fish will be given by the equation below. we substitute numerical values into this equation to find the final position of the fish.
Answers
The direction of the acceleration with respect to the unit vector is 346º
The fish starts at coordinates (-10, 4) with an initial velocity of 25i - 5j based on the information provided. There is never a need to calculate the consequent velocity or acceleration because it is never requested. With the components, all the work is finished. There will be two solutions for each equation, one for I and one for j. Using the following formula, we can determine the components of acceleration given the final velocity of 25i - 5j after 23 seconds:
V0 + a*t = Vf
4 + 23ax = 25 and -4 + 23ay = -5
ax = 21/23 m/s2 ay = -1/23 m/s2
arctan ((1/23)/(21/23)) = 2.73º ∴ 360 - 2.73 = 357º (3 sig figs)
The equation: can be used to determine the final position.
X = X0 + 1/2axt2 + Vx0t and Y = Y0 + 1/2ayt2 + Vy0t
X = -10 + 1/2(21/23)332 + 4*33 Y = 4 + 1/2(-1/23)332 + (-4)*33
X = 619 Y = -152
By using the arctan of the displacements, we may determine the direction of travel:
619 - (-10) = 629 -152 - 4 = -156
arctan(156/629) = 13.9º ∴ 360 - 13.9 = 346º
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The full question:
A fish swimming in a horizontal plane has velocity vi = (4.00 i - 4.00 j) m/s at a point in the ocean where the position relative to a certain rock is ri = (-10.0 i + 4.00 j) m. After the fish swims with constant acceleration for 23.0 s, its velocity is v = (25.0 i - 5.00 j) m/s
What is the direction of the acceleration with respect to unit vector i?
° (counterclockwise from the +x-axis is positive)
8 ( x + 7 ) = 32 + 2x
Answers
Answer:
8x (x+7) =32+2x :x=-4
Step-by-step explanation:
best i got i had someone help me lol
Answer:
x = - 4Step-by-step explanation:
8 ( x + 7 ) = 32 + 2x
8x + 56 = 32 + 2x
8x - 2x = 32 - 56
6x = - 24
x = - 24/6
x = - 4
using the basic definition show that {3n-2/n}n=1 converges
Answers
The sequence (3n-2/n)n=1 converges to 1.
How to determine if the series convergesTo show that (3n-2/n)n=1 converges, we need to find the limit as n approaches infinity.
Using algebraic manipulation, we have the following steps
lim (3n-2/n)n = lim (3-2/n)^n
lim (3n-2/n)n = (3-2/∞)^∞
lim (3n-2/n)n = 1^∞
lim (3n-2/n)n = 1
The basic definition of convergence states that a sequence converges if the limit of the sequence as n approaches infinity is equal to a finite number
Since the limit of (3n-2/n)n as n approaches infinity is 1, we can conclude that the sequence converges to 1.
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Find the algebraic form g(x) of the function g whose graph is produced by the following transformations on thegraph of f(x) = ×: The graph of f is reflected vertically, expanded horizontally by a factor of 2, shifted right 6 units, and shifteddown 4 units. Include graphs off and g as a part of your answer.
Answers
Given the function f(x) = x
We will find the function g(x) whose graph is produced by the following transformations on the graph of f(x)
First, The graph of f is reflected vertically
So,
\(\begin{gathered} f(x)\rightarrow f(-x) \\ g(x)=-x \end{gathered}\)Second, expanded horizontally by a factor of 2
So,
\(\begin{gathered} f(-x)\rightarrow f(-2x) \\ g(x)=-2x \end{gathered}\)Finally, shifted right 6 units, and shifted down 4 units.
So,
\(\begin{gathered} f(-2x)\rightarrow f(-2(x-6))-4 \\ g(x)=-2(x-6)-4 \end{gathered}\)Simplifying the function g(x):
\(g(x)=-2x+8\)The graph of the function (f) and (g) will be as shown in the following figure:
The average monthly salary of a worker is ₹8200. If there are 45 workers in a factory, then total expenditureincurred on expenditure is:
Answers
Answer: \(Rs.3,69,000\)
Step-by-step explanation:
Given
average monthly salary of a worker is \(Rs.8200\)
If there are 45 workers in a factory
Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory
\(\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000\)