The width of the door is [tex]37.8ft[/tex] and the height of the door is [tex]39.6ft[/tex]
Let
[tex]A=\text{the front area of the door}\\h=\text{the height of the door}\\w=\text{the width of the door}[/tex]
From the question
[tex]A=w\times h=1496.9\\h=w+1.8[/tex]
We are to find both the width and the height of the door. To proceed, we have to eliminate the height, and solve for the width. Later, we calculate the value of the height from the width.
Eliminate the height;
[tex]A=w\times h\\A=w\times(w+1.8)\\w^2+1.8w-A=0[/tex]
substitute the value of the front area into the equation and solve for the width
[tex]w^2+1.8w-1496.9=0\\w\approx 37.8\text{ or }w\approx-39.6[/tex]
the width can only take positive value. Now, to get the height
[tex]h=w+1.8\\=37.8+1.8\\=39.6[/tex]
the width and height of the door are [tex]37.8ft[/tex] and [tex]39.6ft[/tex] respectively.
Another example can be found in the link: https://brainly.com/question/18625465
A student downloaded a new game on her phone that was recommended by her friend. She wanted to show her friend how good
she was doing, so she wrote down all her scores on the game. Her first five scores on the game were 432, 543, 348, 788, and 823.
On the two questions below, round to the nearest whole number when relevant.
a. What is her mean, or average, score on the game?
b. What is her median score on the game?
Answer:
a. 587
b. 543
Step-by-step explanation:
a. Mean = sum / number of numbers
To find the sum, we can add the numbers up.
432 + 543 + 348 + 788 + 823 = 2934
There are 5 numbers. Our mean is thus
2934/5 = 586.8, or 587 when rounding up. We round up because we have a .8 at the end, and 8 ≥ 5
b. To find the median, we first must order the numbers. The numbers ordered are this:
348 , 432 , 543 , 788 , 823
To find the median, we can cross off one number on each side until we are left with one or two numbers.
348 , 432 , 543 , 788 , 823
cross out one number from each endpoint
432 , 543 , 788
cross out one number from each endpoint
543
Which of the following function pairs are inverses?
(64/8/ 4 + 7 – 2) • 5 =
Answer:
35
Step-by-step explanation:
Let me know if I got it right
Need help with math problem 5 stars and good rating if do
Answer:
Bottom right
Explanation:
visualize both triangle connected to the middle rectangle, and that's a triangular prism
Solve
[tex]\frac{a-1}{a-3} =\frac{a+1}{a-4}[/tex]
Answer:
[tex]a=\frac{7}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a-1}{a-3}=\frac{a+1}{a-4}[/tex]
[tex](a-1)(a-4)=(a-3)(a+1)[/tex]
[tex]a^2-5a+4=a^2-2a-3[/tex]
[tex]-5a+4=-2a-3[/tex]
[tex]-3a+4=-3[/tex]
[tex]-3a=-7[/tex]
[tex]a=\frac{7}{3}[/tex]
Two increased by five times a number is twenty two
What is the equation
Answer:
2 + 5 x a = 22
Step-by-step explanation:
Find the slope of an equation f(x)=-3sqrt(x) at the point (9,-9)
Answer:
Slope is [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-3\sqrt{x}[/tex]
Find the derivative using the product rule:
[tex]f'(x)=\frac{d}{dx}(-3)*\sqrt{x}+-3*\frac{d}{dx}\sqrt{x}[/tex]
[tex]f'(x)=-3*\frac{1}{2\sqrt{x}}[/tex]
[tex]f'(x)=\frac{-3}{2\sqrt{x}}[/tex]
Plug in coordinates to find slope at that point:
[tex]f'(9)=\frac{-3}{2\sqrt{9}}=\frac{-3}{2(3)}=\frac{-3}{6}=-\frac{1}{2}[/tex]
Therefore, the slope of the equation at the point (9,-9) is [tex]-\frac{1}{2}[/tex].
Answer:
Step-by-step explanation:
f(x) = -3√x
f'(x) = -1.5/√x
f'(x) = -1.5/√9
f'(x) = -1.5/3
f'(x) = -0.5
Estimate the product of 54 X 68.
Answer:
54 X 68=3672
Step-by-step explanation:
PLEASE HELPP MEE ASAPP!!
Answer:
Step-by-step explanation:
each zero of the function will have a factor of (x - x₀)
h(x) = a(x + 3)(x + 2)(x - 1)
h(x) = a(x + 3)(x² + x - 2)
h(x) = a(x³ + 4x² + x - 6)
or the third option works if a = 1
however this equation gives us the points (0, -6) and (-1. -4), so "a" must be -2
h(x) = -2x³ - 8x² - 2x + 12
to fit ALL of the given points as it fits the three zeros and also h(0) and h(-1) so I guess that is why the given group is a partial set of solution sets
Which table of ordered pairs represents a proportional relationship?
Answer:
C)
Step-by-step explanation:
Because Its equivalent
The population of New York state can be modeled by: 19.71 P(t) =
1 + 61.22e-0.03513tP is the population in millions
and t is the number of years since 1800
What was the population in 2020?
P(220) = [?] million
Round your answer to the nearest thousandth.
Answer:
19.193 million
Step-by-step explanation:
Put the given value in the formula and do the arithmetic.
P(220) = 19.71/(1 +61.22e^(-0.03513·220))
P(220) = 19.71/(1 +61.22e^-7.7286) = 19.71/(1 +0.02694046)
P(220) ≈ 19.193 . . . million
19.19293355
Nearest thousandth is 19.193
solve for Y 3y =2(4-2y)+6
Answer:
HOLA MATE HERE IS UR ANSWER:-
Step-by-step explanation:
3y=2(4-2y)+63y=8-4y+63y=14-4y3y+4y=147y=14y=14/7y=2Line f has a slope of -9/7. Line g is perpemdicular to f. What is thr slope of line g
Given that y = 11 cm and θ = 34°, work out x rounded to 1 DP.
Check the picture below.
James joins Club One which charges a monthly membership of $19.99. In 6 months, will he spend less than $120 in all?
Answer:
120
Step-by-step explanation:
round 19.99 to 20 and do 20 times 6
Can someone help me with his I will mark u brilliant
Answer: 1260 books
Step-by-step explanation:
2/5=0.4
19000x0.4=7600
12500x0.4=5000
7600+5000=12600
1/10=0.1
12600x0.1 = 1260
/Answer:
1,260 books (or C)
Step-by-step explanation:
1. 2/5 of fiction (12,500) are out, so 5,000 are out
2. 2/5 of non-fiction (19,000) are out, so 7,600 are out
3. Total books checked out are 12,600
4. 1/10 of checked out books are due this week, so 1,260 books (10%)
Joel can do 20 math problems in 90 seconds How many seconds would it take him to do 32 problems?
HELP ME ITS SUPER HARD
Answer:
Joel can do 20 math problems in 90 seconds
He can do 1 math problem in 90/20 = 4.5 seconds
Now, Joel can do 32 math problems in
4.5×32
= 144 seconds
= 2 minutes 24 seconds
Step-by-step explanation:
Here I used the unitary method to sovle the question
The length of a rectangle is 2.3 inches more than the width. Find the dimensions of the
rectangle if the perimeter is 28.6 inches. Show work.
Answer:
See image
Step-by-step explanation:
Let w=width
And let l=length
Perimeter is the distance all the way around the outside of the shape. Add up all the sides to find it.
Step-by-step explanation:
let the width of the rectangle=x
the length=x+2.3
Since perimeter=28.6
We know that perimeter of a rectangle is given by
P=2(l+w)
28.6=2(x+2.3+x)
28.6=2(2x+2.3)
28.6=4x+4.6
28.6-4.6=4x
4x=24
x=24/4=6
Therefore width is 6inches and length is 8.3inches
0.03249 in standard form to 3 significant figures is
(A) 3.24 × 10−1
(B) 3.24 × 10−2
(C) 3.25 × 10−2
(D) 3.25 × 10−3
A convention center is in the shape of a rectangular pyramid with a height of 332 m. Its base measures 475 m by 571 m. Find the volume of the convention center. If necessary, round your answer to the nearest tenth
Answer:
30,015,566.7 m³ OR 3.0 x 10⁷ m³
Step-by-step explanation:
The formula for finding the volume of a rectangular pyramid is:
V = lwh/3
where l = length
w= width
h = height
(475)(571)(332)/3 = 30,015,566.7 m³ = 3.0 x 10⁷
Solve the given equation.
An angle measures 152° more than the measure of its supplementary angle. What is the measure of each angle?
° and
°
Answer:
14° and 166°
Step-by-step explanation:
Ok, so a supplementary angle is 180°.
Let's say one angle is x and the other angle is x+152.
We know these angles add up to a supplementary angle (180°) so...
x+(x+152)=180
x+x+152=180
2x+152=180
2x=28
x=14
So now we know one angle is 14°, we also know the other angle is x+152, knowing that x=14 we can plug it in 14+152= 166° for the other angle.
Hope this helps :)
Gabe has a savings account at the local bank. He deposits $150 in his account every 2 months. Which equation models the relationship between the months that deposits are made, x, and the amount of money deposited in the account, y?
Answer:
y=150(x/2)
Step-by-step explanation:
y = 150(x/2)
y represents the amount of money that is deposited into Gabe's account. x represents the amount of time he is adding money for.
x is divided by 2 because however long gabe has been adding money into his account, he does it every 2 months. This means that if x = 12 (time = 12 months) , then Gabe has only made (12/2) = 6 deposits of $150. If x = 4 (time = 4 months), then Gabe would have only made (4/2) = 2 deposits of $150.
With this being said, 150 is being multiplied by the number of deposits (x/2) to find the total amount of money deposited (y).
Answer all of them plzz
Answer:
a) (2x+3) (x+4)
b) (5x-3) (x-1)
c) (-2x-3) (x-3)
d) 3(x-1) (3x-8)
e) -2(3x+5) (x-2)
f) h(4x-3) (3x-4)
g) -(x-3) (x+7)
h) (3x-2) (x+3)
i) 2(2x+1) (x-2)
j) (3h+2) (h-7)
Step-by-step explanation:
your welcome :)
Answer:
a)
(x+4)(2x+3)
b)
(x-2)(5x-3)
c)
(-x+3)(2x-3)
d)
3(x-1)(3x-8)
e)
2(-x+2)(3x+5)
f)
h(3x-4)(4x-3)
g)
(x+7)(-x+3)
h)
(x+3)(3x-2)
i)
2(x-2)(2x+1)
j)
(h-7)(3h+2)
Hope this helps!
the hoover dam is 725 feet tall. how long would it take an object to fall from the top to the base of the dam? round the answer to two decimal places
Answer:
45.05 seconds
Step-by-step explanation:
Use the formula: d = v[tex]i[/tex] t + [tex]\frac{1}{2}[/tex] a[tex]t^{2}[/tex]
d = distance v[tex]i[/tex] = initial velocity (m/s)
t = time (s) a = acceleration (m/[tex]s^{2}[/tex])
m is meters and s is seconds. They are units of measurement so leave them be.
Assuming the object is simply dropped, the initial velocity is 0 since the object was not moving before it was dropped.
The distance is 725 feet, which is 220.98 meters.
The acceleration is 9.81m/[tex]s^{2}[/tex] since that is the acceleration of Earth's gravity, aka free fall.
Time is what we are trying to find so just leave it as the variable t.
So plug the values into the equation:
220.98m = (0)(t) + [tex]\frac{1}{2}[/tex] (9.81m/[tex]s^{2}[/tex])(t)
220.98m = (4.905m/[tex]s^{2}[/tex])(t)
45.0519877676s = t
t = 45.05s
Remember to pay attention to units because your answer will be wrong otherwise
Solve the following for x. Show all work. x+3/5 =2
Answer:
x+3/5=2
or,x+0.6=2
or,x=2-0.6
x=1.4
A car travels at an average speed of 60 km/h for 2.1 hours.
How far did the car travel in km?
Answer:
15 km
Step-by-step explanation:
What is 1 1/2 divided by 8
Answer:
3/16
Step-by-step explanation:
start by converting 1 1/2 to an improper fraction by multiplying the 1 by the denomerator and then adding the 1 from teh numerator. Then place that all over the denomantor two. so you get 3/2
then set up your equation:
3/2 x 1/8
you do the resipricol of one of the numbers so instead of 8/1 we do 1/8
3 times 1= 3
2 times 8 is 16
3/16 does not simplify so thats your answer
Answer:
3/16
Step-by-step explanation:
((1 1/2)/8)=(3/2)/8
8 times 2(demoninator)=16
numerator stays same so the answer is 3/16
Find the value of x .
K
M
(2x – 10) (2x + 40)º
-
N
Answer:
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7(2+3x)+8, 12+3(8+x), and (7x+2)3+8x
Answer:
The first answer is 21x+22.
Second answer is 36+3x.
Third answer is 29x+6.
Step-by-step explanation:
I just simplified