An architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house? Enter your answer in the box.
A rectangle has a length of 6 inches and a width of 3 inches.
What is the effect on the perimeter when the dimensions are multiplied by 8?
The perimeter is increased by a factor of 8.
The perimeter is increased by a factor of 24.
The perimeter is increased by a factor of 64.
The perimeter is increased by a factor of 256.
This figure is made up of a triangle and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round only your final answer to the nearest tenth.
Enter your answer, as a decimal, in the box.
Answers
the area is 7 square feet
when calculating the area the scale factor is squared as well.
since the scale factor is 16, to find out area the scale should be squared that is,
16*16 = 256
then the new area is 7 square feet * 256
actual area = 256 * 7 = 1792 square feet
Q2. the rectangle with length 6 inches and width 3 inches.
the perimeter of the rectangle before changing dimensions are;
=(6*2) + (3*2)
= 12 + 6 = 18 inches
after multiplying the dimensions by 8,
new length = 6*8 = 48 inches
new width = 3*8 = 24 inches
new perimeter = (48*2) + (24*2)
= 96 + 48
= 144 inches
the perimeter ratio from new to old = 144:18
the perimeter has increased by (144/18) times
= 144/18 = 8
answer is perimeter increased by a factor of 8
q3)
area of the triangle
= 1/2 * height * base
= 1/2 * (5-2) *(4-(-3))
= 1/2 * 3 * 7
= 10.5 units²
area of semicircle
=pi*r2
r = 2-(-1.5)
= 3.5
area = 3.14 * (3.5)²
= 38.465 units²
total area = area of triangle + area of semicircle
= 10.5 + 38.465
= 48.965
round it off to the closest tenth
area = 49 units²
Related Questions
find the measures of two angles one positive and negative that are coterminal with pi/2
Answers
Answer: The required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]
Step-by-step explanation: We are given to find measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}.[/tex]
Let x and y represents the positive and negative co-terminal angles respectively.
We know that
the measures of any two co-terminal angles differ from each other by a multiple of [tex]2\pi.[/tex]
So, the values of x and y can be found as follows :
[tex]x=\dfrac{\pi}{2}-2\pi=-\dfrac{3\pi}{4},\\\\\\y=\dfrac{\pi}{2}+2\pi=\dfrac{5\pi}{2}.[/tex]
Thus, the required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]
Final answer:
The positive coterminal angle with π/2 is 5π/2, and the negative coterminal angle is -3π/2; both angles are found by adding and subtracting 2π radians from the original angle.
Explanation:
To find the measures of two angles, one positive and one negative, that are coterminal with π/2, we need to add and subtract 2π (360 degrees) to the original angle since the angles are coterminal when they share the same initial and terminal sides and differ by a full circle (360 degrees) or a multiple thereof. The angle π/2 radians is equivalent to 90 degrees, so adding 2π radians (360 degrees) gives us a positive coterminal angle, and subtracting 2π radians (360 degrees) gives us a negative coterminal angle.
Positive coterminal angle: π/2 + 2π = 5π/2.
Negative coterminal angle: π/2 - 2π = -3π/2.
(HURRY!!! GET 24 PTS) The residential colony has a population of 5400 requires 60 liters of water is per person per day. For the effective utilization of rain water, a group of people decided for WATER HARVESTING. They constructed a water reservoir measuring 49mx27mx25m to collect the rain water. It this water reservoirs is full of water then for how many days it will last for the colony?
Answers
[tex]60\times5400=324000L[/tex]
Transform the above amount to m^3:
[tex]324000\times0.001=324\,m^3[/tex]
Compute the volume of the reservoir:
[tex]49\times27\times25=33075\,m^3[/tex]
Now compute the number of days covered by the amount of water like this:
[tex] \frac{33075}{324}=102\,\,\,\text{days.} [/tex]
what he said hope it helped
Step-by-step explanation:
Are the two expressions equivalent when x = 20?
8(12x + 4)
96x + 32
Answers
The solution of the two expressions for x = 20 will be equivalent.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two expressions are 8(12x + 4) and 96x + 32. The expressions will be solved as,
8(12x + 4) = 8[12(20) + 4 ] = 1952
96x + 32 = 96 (20) + 32 = 1952
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Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. 2x + y < 0 y ≥ -4 - 2x
Answers
The graph for these inequalities intersects at point (0,0).
The graph displays the solution to the system of inequalities: 2x + y < 0 and y ≥ -4 - 2x. Here's a breakdown:
First Inequality (2x + y < 0):
This translates to a blue line with a negative slope. Points like (0, -2) and (3, -6) lie on this line.
We shade the region below this line because the inequality specifies "less than." Points there, like (1, -5), satisfy the inequality.
Second Inequality (y ≥ -4 - 2x):
This translates to a green line with a negative slope as well. Points like (0, -4) and (2, -8) lie on the line.
Unlike the first, we shade the region above this line because the inequality specifies "greater than or equal to." Points like (1, -3), above the line, satisfy the inequality.
Combined Solution:
The solution space is the overlap where both inequalities hold true. This is the triangular region shaded in both blue and green. Points within this region, like (1, -5), satisfy both inequalities.
Checking Points:
If unsure about shading, test points outside the shaded region. For example, point (0, 0) lies above both lines, satisfying both inequalities. This confirms the shading is correct.
Sara left home and drove East 12 miles to Bakersville for her friends birthday cake then she drove 10 miles south to a friends house how far apart is Sarah's friends house and Sarah's house
Answers
Therefore, using Pythagoras's theorem The distance from Sarah's home to her friend's house will be;
=√ 12²+10²
= √244
= 15.62 miles
Fifty people are surveyed at a state fair. Of the 50 people, 30 like funnel cake and 25 like fried oreos. Twenty people like both funnel cakes and fried oreos. Use a Venn Diagram to organize the data and answer the questions. How many people like either funnel cake or fried oreos?
Answers
55
When using a Venn diagram to determine how many people like either funnel cake or fried Oreos out of a survey of 50, after subtracting the 20-person overlap from each individual preference to avoid double counting, the total number liking either is found to be 35 people.
To determine how many people like either funnel cake or fried Oreos, we need to use the concept of set union from Venn diagrams. First, we draw two overlapping circles, one for people who like funnel cake and another for those who like fried Oreos.
The overlapping area represents people who like both. Given that 30 people like funnel cake and 25 like fried Oreos, with a 20-person overlap liking both, we add the individual preferences and subtract the overlap to avoid double counting.
The representation is:
Number liking funnel cake only: 30 - 20 = 10
Number liking fried Oreos only: 25 - 20 = 5
Number liking both: 20
Adding these, the total number liking either funnel cake or fried Oreos is 10 + 5 + 20 = 35 people.
The equation shown below involves a perfect square trinomial.
9x2 - 24x + 16 = 11
Which of the following is a step in solving this equation?
A. Divide both sides by 8
B. Subtract 16 from both sides
C. Square both sides
D. Take the square root of both sides
Answers
What is the value of x in the quadrilateral shown below?
A. 80°
B. 70°
C. 60°
Answers
85+150+55=290
360-290= 70
X= 70 degrees
Darlene's Caillou's 8 gallons of gasoline to travel 340 miles at mechanic work on the car and use 7 gallons of gasoline to travel 350 miles if the price of gasoline was approximately $4 per gallon how much less to the nearest cent per get a smile that it cost to run after the mechanic work on it
Answers
340 miles with 8 gallons.
A gallon costs $4, so 8 gallons cost 8 * $4 = $32.
$32 per 340 miles = $32/340 = $0.0941/mile = 9.4 cents/mile
After mechanic:
350 miles with 7 gallons.
7 gallons cost 7 * $4 = $28.
$28 per 350 miles = $28/350 = $0.08/mile = 8 cents/mile
The difference is 9.4 - 8 = 1.4.
To the nearest cent, round 1.4 to 1.
Answer: After the mechanic, it cost 1 cent per mile less to run the car.
How can one 1/4x − 3 = 1/2x + 8 be set up as a system of equations?
a. 4y + 4x = −12
2y + 2x = 16
b.4y − x = −12
2y − x = 16
c.4y + x = −12
2y + x = 16
d.4y − 4x = −12
2y − 2x = 16
Answers
Left side:
.. y = 1/4x -3
.. 4y = x -12 . . . . multiply by 4
.. 4y -x = -12 . . . subtract x
Right side:
.. y = 1/2x +8
.. 2y = x +16 . . . multiply by 2
.. 2y -x = 16 . . . subtract x
These equations correspond to selection B.
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
How mach is deducted from her paycheck for retirement plan?
A) $26.11
B) $52.22
C) $104.44
D) $522.24
Answers
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
So the deduction will be given as
[tex]\rm Deduction = \dfrac{4}{100} *1305.6\\\\Deduction = 0.04 * 1305.6\\\\Deduction = 52.224 \approx 52.22[/tex]
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
More about the percentage link is given below.
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-(5)^-1
-1/5
-5
5
1/5
Answers
= −1/5
Answer = −1/5 (A)
The two figures are similar. What is the value of the marked angle?
A. 108
B. 72
C. 90
D. 162
Answers
When two figures are similar, they always have the same angles.
I think its b
Hope this helps
how many triangles have the following measurements? A=38, a=432, b=382
Answers
_____
You know this because the given angle is opposite the longest given side. You only have ambiguous cases if the given angle is opposite the shorter of two given sides.
Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.
To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.
First, let's use the Law of Sines which states that:
sin(A)/a = sin(B)/b = sin(C)/c
Given:
A = 38° (angle)a = 432 (side opposite to angle A)b = 382 (side opposite to angle B)We can calculate angle B using:
sin(B) = (b × sin(A)) / a
sin(B) = (382 × sin(38°)) / 432 ≈ 0.556
Finding the arc sine of 0.556, we get:
B ≈ 33.8°
Now, we find angle C:
C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°
Using the Law of Sines again to find side c:
c = (a × sin(C)) / sin(A)
c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85
Thus, it's possible to form one such triangle with the given conditions.
What's the difference between residential heating and cooling systems and commercial/industrial heating, cooling, or refrigerating facilities? A. The amount of energy the building or facility uses B. The location of the system—in a home or a business C. The number of people that occupy the building or facility D. The size of the building or facility
Answers
If the radius of a circle is 18 yd, then the diameter of the circle is 9 yd
TRUE OR FALSE
Answers
Answer:
Step-by-step explanation: False.
highest value on the domain of the function is called what.
Answers
Suppose a - b = 0.
Which one of these expressions equals ab?
a. a^2
b. 0
c. 2b
d. 2a
e. a/b
Answers
a-b=0-----------------> a=b
b=a
therefore
a.b--------> substituting---------> a*(a)=a² or b*b=b²
the answer is the option A) a²
Which of the following is not a classification of the number given below? -3
Answers
I know for a fact that -3 classifies as an integer and a rational number for sure. So, that leaves us two options, real number, and whole number.
Given this information I think the correct answer is whole number, but it might also be real number. So sorry if I am wrong! : )
I hope this helps!
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Have a wonderful day! : )
Why does a negative number times a negative number equal a positive number?
Answers
17 POINTS. Find the x and y intercepts and show work please.
It’s number 2. y=x^4+2x^2-1
Answers
The first think I always do in such a question is get the graph.
Go to wolfranalpha.com and see the graph to tell me what I'm looking for.
Put y = x^4 + 2x^2 - 1 into the input bar. You find out that there are only 2 answers.
Use the Quadratic Formula
a = 1
b = 2
c = - 1
Then let z = x^2
So the new equation is
y = z^2 + 2x - 1
You solve for z and you get
z1 = 0.4142 and z2 = - 2.4142 You can go no further with z2 because the square root of a minus number can't be graphed on the coordinate system.
z = x^2
0.4142 = x^2
x = +/- 0.6435
Note to moderator
When I send a student to wolframalpha, the work is mine and I'm not copying and pasting anything that isn't allowed by wolfram
Find the value of x and the value
A: x=20,y=45
B:x=45,y=20
C:x=60,y=120
D:x=90,y=60
Answers
[3y°+6y°+2x°+90°]=360°
9y°+2x°=270°
but we know that
2x°=90°------------------ > x=45°
therefore
9y°+2x°=270°--------> 9y°+2(45°)=270°
9y°=270°-90°------------------> y=20°
the answer is
x=45°
y=20°
the option B:x=45°,y=20°
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?
A ) f(x) = (x - 1)(x + 1)^11
B ) f(x) = (x + 2)^3(x^2 -7x +3)^4
C ) f(x) = (x^5 + 7x + 14)^6
D ) f(x) = 11x^5 + 5x + 25
I originally chose A, but that was incorrect on my quiz.
Answers
F(x) = (x+2)^3 = the highest power for this type turn out will be x^3
the other part is (x^2 - 7x + 3)^4, the highest power for this part will be x^8
since (x+2)^3(x^2-7x +3)^4 = the highest power of first part x^3 second part x^8
x^3 * x^8 = x^11 that result in 11 roots
This type of math, you don't need to configure the whole problem, you just need to know the basic rules of power of a number. For example, (x^2)^3, then 2*3 = 6 make x^6.
or x^2 * x^3 = x^2 + 3 = x^5.
Answer:
The correct answer is B
Step-by-step explanation:
Hannah has $1000 in her savings account. During 1 month , she withdraws $25. Each successive month, she withdraws $10 more than the previous month . How much remains in her savings account after 10 months ?
Answers
The total she withdrawn after ten months was $700.00. So $1000 - $700 = $300. That is how much that is left after ten months
Answer: A-$300 is correct
picking a multiple of 5 from the integers between 1 and 40
Answers
5,10,15,20,25,30,35,40 are all multiples of 5
What is the x-coordinate for the minimum point in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?
Answers
[tex]cos(2x- \pi )=-1[/tex]
[tex]2x- \pi=\pi[/tex]
[tex]2x=2\pi[/tex]
[tex]x=\pi[/tex]
The x-coordinate for the minimum point of the function f(x) must be π.
f(x) = 4 cos(2x − π)
using a graph tool
see the attached graph
the x-coordinate for the minimum point from x = 0 to x = 2π
if the interval is [0,2π]
there are 3 minimal points
(0,-4) (π,-4) (2π, -4)
if the interval is (0,2π)
there is 1 minimal point
(π,-4)
Which is an equivalent expression for 14+10x+6−8x?14+10x+6−8x?
Answers
= 2x +20
If 2a+3b=12 and ab=6 find the value of 8a^3+27b^3
Answers
B) ab = 6 solving for a
B) a = 6 / b then we substitute this into equation A)
A) 12 / b + 3b = 12 multiplying this by "b"
A) 12 + 3b^2 = 12b
A) 3b^2 -12b +12= 0 dividing by "3"
A) b^2 -4b + 4 = 0
Factoring
(b-2) * (b-2) = 0
b = 2
Since b = 2 then a = 3
NOW, we put these numbers into:
8a^3 +27b^3
8*3*3*3 + 27*2*2*2
216 + 216
The answer is 512
a = 6/b
2 *6/b + 3b = 12
12/b + 3b = 12
12 + 3b^2 = 12b
3b^2 - 12b + 12 = 0
b^2 - 4b +4 = 0
(b - 2)^2 = 0
b = 2
a will = 3
8*3^3 + 27*2^3
8*27 + 27*8
I'm getting 432
I thought perhaps I could do this a shorter way. Turns out I can't. If you give out a Brainly Please give it to the other responder.
What is a simpler form of the radical expression square root of 36g^6?
Answers
What is the measure of AC ? Enter your answer in the box. ° Circle with inscribed angle A B C. Angle A B C is 3 x minus 1.5 degrees. The intercepted arc A C is 3 x plus 9 degrees.
Answers
[tex](3x-1.5)=\frac{1}{2}(3x+9)[/tex]. Distribute the 1/2:
[tex]3x-1.5=\frac{1}{2}*3x+\frac{1}{2}*9 \\3x-1.5=\frac{1}{2}*\frac{3x}{1} + \frac{1}{2}*\frac{9}{1} \\3x-1.5=\frac{3x}{2}+\frac{9}{2} \\3x-1.5=1.5x+4.5[/tex]
We cannot have a variable on both sides of the equation, so cancel the 1.5x to avoid negatives:
[tex]3x-1.5-1.5x=1.5x+4.5-1.5x[/tex]
Combine like terms:
[tex]1.5x-1.5=4.5[/tex]
Cancel the -1.5 by adding:
[tex]1.5x-1.5+1.5=4.5+1.5 \\1.5x=6[/tex]
Divide both sides by 1.5:
[tex]\frac{1.5x}{1.5}=\frac{6}{1.5} \\x=4[/tex]
Since AC is 3x+9, we substitute 4 in for x:
3*4+9=12+9=21°
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is [tex]21^{\circ}[/tex].
Given,
The inscribed angle [tex]\angle ABC[/tex] is [tex]3x-1.5[/tex].
And the Intercepted arc AC is [tex]3x+9[/tex].
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
So,
[tex]3x-1.5=\frac{1}{2} (3x+9)[/tex]
[tex]2 (3x-1.5)=3x+9[/tex]
[tex]6x-3.0=3x+9[/tex]
[tex]6x-3x=9+3[/tex]
[tex]3x=12\\x=4[/tex]
Since the intercepted arc AC is [tex]3x+9[/tex], putting the value of [tex]x=4[/tex] we get,
intercepted arc AC is [tex]21^{\circ}[/tex].
Hence the intercepted arc AC is [tex]21^{\circ}[/tex].
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