Here we need to use what we know about rectangles to make a system of equations.
By solving that system we found that the tile has a length of 36 inches and a width of 21 inches.
Remember that for a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = W*L
Here we know that the perimeter is 114 inches, then we can write:
114in = 2*(L + W)
We also know that the area is 756 in^2, then we can write:
756 in^2 = L*W
So we found two equations, which means that we have a system of two equations with two variables:
114in = 2*(L + W)
756 in^2 = L*W
To solve this, the first step is to isolate one of the variables in one of the equations, we can isolate L in the first equation:
114in = 2*(L + W)
114in/2 = (L + W)
57in = L + W
57in - W = L
Now that we have an expression equivalent to L, we can replace it in the other equation to get:
756 in^2 = L*W
756 in^2 = (57in - W)*W
Now we can solve this for W.
756 in^2 = W*57in - W^2
W^2 - W*57in + 756 in^2 = 0
The solutions are given by the Bhaskara's formula:
[tex]W = \frac{57in \pm \sqrt{(-57in)^2 - 4*1*(756in^2)} }{2*1} = \frac{57in \pm 15in}{2}[/tex]
Then the two possible values of the width will be:
W = (57in + 15in)/2 = 36 in
W = (57in - 15in)/2 = 21 in
Suppose that we choose the second solution, W = 21in
Now using the equation 57in - W = L we can find the value of L
L = 57in - W = 57in - 21in = 36in
L = 36in
Then we found that the tile has a length of 36 inches and a width of 21 inches.
If you want to learn more, you can read:
https://brainly.com/question/11137975
Given the function g(x) = x^2 + 5x + 14, determine the average rate of change
of the function over the interval 1 < x < 7.
Answer:
13
Step-by-step explanation:
The average rate of change is
f(7) - f(1)
---------------
7-1
f(7) = 7^2 + 5*7 +14 = 49 +35 +14=98
f(1) = 1^2 +5(1)+14 = 1+5+14=20
98-20
--------
7-1
78/6
13
need help with this!!
A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist
Answer:
one third (1/3)
Step-by-step explanation:
we have 5 provinces.
Each province contains the same number of Traditionalists, let's say that there are T traditionalists per province, thus, there are:
5*T in the country.
now we know that in each province, the number of traditionalists is equal to 1/10 of the total number of progressives in the entire country.
If there are a total of P progressives in the entire country, we will have that:
T = P/10
Then the total number of traditionalists in the entire country is:
5*T = 5*(P/10) = P/2
So in the whole country, there are P progressives and P/2 traditionalists.
So the total population is:
total = P + P/2 = (3/2)*P
We want to know what fraction of the country is traditionalist, this is equal to the quotient between the traditionalist population, P/2, and the total population, (3/2)*P
This is:
[tex]c = \frac{P/2}{(3/2)*P} = 1/3[/tex]
So one third of the country is traditionalist.
f The difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 37 vedanta Excel in Mathematics
Answer:
15
Step-by-step explanation:
first find f which is (8-3) × ( 1/4 × 7 + 5)
simplify
5 × (1/4 ×12)
5 × 3
15 is thw answer
b) Tìm ba cách viết số hữu tỉ -11/25 dưới dạng tổng của hai số hữu tỉ dương.
The temperature is 45°F The temperature will decrease by 2°F each hour. Let
h be the number of hours.
When will the temperature be below 32°F?
Write an inequality for this problem.
A. 45 + 25 = 32
B. 45 - 2.32
C. 45 + 25 32
D. 45 - 253
Can someone help me I don't understand
Answer:
Okay,So lines of symmetry are basically how many different ways you can fold that shape without any hanging out etc.
Answer:
There are 3 lines of symmetry
Step-by-step explanation:
The lines of symmetry are
horizontal
vertical.
diagonal
Hope this helped! Please tell me if there is something wrong with my answer.
Statement Reason
Check Answers
Answer:
Question?
Step-by-step explanation:
Sally spent half of her allowance going to the movies. She washed the family
car and earned 6 dollars. What is her weekly allowance if she ended with
17 dollars ?
does it give the answer choice or is it a blank space?
If the amount of waking time 4 year old children spend with their fathers each day is 42 minutes while the daily waking time spent in daycare is 6 hours, what is the ratio of time with father to time in daycare?
Answer:
7/60
Step-by-step explanation:
Because the question is phrased such that it asks "the ratio of time with father to....", we know to put the time with father on top, or first. Similarly, since it is asked to put the ratio of time with the father to the time in daycare, we can put the daycare amount second/on the bottom. Therefore, we can write the ratio as
(42 minutes)/(6 hours)
To make both of these in terms of minutes to simplify it, we know that 60 minutes = 1 hour, so 1 hour / 60 minutes =1 . Since multiplying something by 1 keeps it the same, we can multiply our ratio by this amount. We want to multiply with the hour on top so the hours cancel out, as so:
[tex]\frac{42 minutes}{6 hours} * \frac{1 hour}{60 minutes} = \frac{42 minutes * hours}{360 minutes * hours} = \frac{42}{360}[/tex]
To simplify this even further, we can note that 6 is a factor of both 42 and 360*, so we can multiply this fraction by (1/6) / (1/6) to get
(42/360) * (1/6)/(1/6) = 7/60 as our final answer
If this doesn't come up immediately, you can always find the greatest common factor by listing the factors of each number and finding the highest one that fits both, e.g.
for 42: 42, 21, 14, 7 , 6...
for 360: 360,180, ... 6,5....
Find the value of x for which (4/5)-4 x (4/5)-7 =(4/5)2x-1 Can some1 say this ans fast plz
Answer:
Fraction form: x = -21/4
Decimal Form: x = -5.25
Step-by-step explanation:
See the picture for steps :)
help me please and thank youu
Answer:
-3
Step-by-step explanation:
The shape on the left is translated to the shape on the right which statement about transformation is true?
A kindergarten class had a total of 15 boys 9 girls , what is the ratio of girls to boys in that class ?
Answer:
9:15
girls : boys
Step-by-step explanation:
Answer:
9:15
Or 3:5 when reduced
Step-by-step explanation:
HELP HURRY PLEASE i dont understanddd
Answer:
see image
Step-by-step explanation:
put a point on .5 on the x axis and a point on -3 on the y axis draw a line through them and shade the space under the line
In a survey of women in a certain country the mean height was 62.9 inches with a standard deviation of 2.81 inches answer the followinv questions about the specified normal distribution
The question is incomplete. The complete question is :
In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 99th percentile? (b) What height represents the first quartile? (Round to two decimal places as needed)
Solution :
Let the random variable X represents the height of women in a country.
Given :
X is normal with mean, μ = [tex]62.9[/tex] inches and the standard deviation, σ = [tex]2.81[/tex] inches
Let,
[tex]$Z=\frac{X - 62.9}{2.81}$[/tex] , then Z is a standard normal
a). Let the [tex]99th[/tex] percentile is = a
The point a is such that,
[tex]$P(X<a)=0.99$[/tex]
[tex]$P \left( Z < \frac{a-62.9}{2.81} \right) = 0.99$[/tex]
From standard table, we get : [tex]P( Z < 2.3263) =0.99[/tex]
∴ [tex]$\frac{(a-62.9)}{281} = 2.3263$[/tex]
[tex]$a= (2.3263 \times 2.81 ) +62.9$[/tex]
= 6.536903 + 62.9
= 69.436903
= 69.5 (rounding off)
Therefore, the height represents the [tex]99th[/tex] percentile = 69.5 inches.
b). Let b = height represents the first quartile.
It is given by :
[tex]P( X < b) =0.25[/tex]
[tex]$P \left( Z < \frac{(b-62.9)}{2.81} \right) = 0.25$[/tex]
From the standard normal table,
[tex]P( Z < -0.6745) =0.99[/tex]
∴ [tex]$\frac{(b-62.9)}{2.81}= 0.6745$[/tex]
[tex]$b=(0.6745 \times 2.81) +62.9$[/tex]
= 1.895345 + 62.9
= 64.795345
= 64.8 (rounding off)
Therefore, the height represents the 1st quartile is 64.8 inches.
What is the distance between (1, 9) and (1, -4)? Use the distance formula.
D=(x2-x1)2+(y2-y1)2
Answer:
D. 13
Step-by-step explanation:
You just have to plug in numbers then solve.
(1,9) and (1,-4). Every coordinate is placed as (x,y)
(1,9) is labeled as (x1, y1)
(1,-4) is labeled as (x2,y2)
Now plug in the numbers.
d= Square root of (1-1)^2 + (-4-9)^2
d= Square root of 1^2 +-13^2
d= Square root of 1+169
d= Square root of 170
d= 13.04
Rounded to a whole number, the answer is 13
Answer:
D
Step-by-step explanation:
you have to substitute the values in the distance formula,in this case x2 is 1,x1 is 1,y2 is -4 and y1 is 9
d=√(x2-x1)²+(y2-y1)²
=√(1-1)²+(-4-9)²
=√(0)²+(-13)²
=√169
=13
I hope this helps
Please hurry I will mark you brainliest
Answer:
q = 1/4
Step-by-step explanation:
-5/4 - (-1/4) = -1
-1/(q-1/2) = 4
-1 = 4(q-1/2)
-1 = 4q - 2
1 = 4q
q = 1/4
The present age of Madison's Mother is 3 time that of Madison. After 6 1/4 years, the sum of their age will be 53 3/4 years. Find their present ages. (Estimate to the nearest whole number)
Answer: [tex]10, 31\ \text{years}[/tex]
Step-by-step explanation:
Given
The present age of Madison's Mother is three time that of Madison
Suppose the Present age of Madison is [tex]x[/tex], so age of her mother is [tex]3x[/tex]
After [tex]6\dfrac{1}{4}\ \text{years}[/tex], the sum of their age will be [tex]53\dfrac{3}{4}\ \text{years}[/tex]
[tex]\therefore (x+6\dfrac{1}{4})+(3x+6\dfrac{1}{4})=53\dfrac{3}{4}\\\\\Rightarrow 4x+2\times \dfrac{25}{4}=\dfrac{53\times 4+3}{4}\\\\\Rightarrow 4x+\dfrac{50}{4}=\dfrac{215}{4}\\\\\Rightarrow 4x=\dfrac{215-50}{4}\\\\\Rightarrow x=\dfrac{165}{16}\\\\\Rightarrow x= 10.31\approx 10[/tex]
Madison mother's age [tex]3x=30.93\approx 31\ \text{years}[/tex]
You tried to get every semi truck to honk but only 7 did what fraction if semi trucks you saw honked
Answer:
I am so lost but if it's how many honk out of how many you saw I would assume 7/7
** I NEED HELP PLEASE AND THANK YOU***
Instructions : X,Y,and Z are midpoints. Find the length of each segment.
Answer:
MZ = 10
ZO = 10
MO = 20
XZ = 9
YZ = 7
Step-by-step explanation:
Triangles are all the same, proportionally.
X is midpoint of 14, so 7
Y for 18, so 9
Triangle with 10 is 7, 9, 10
Full triangle is double at 14, 18, MO
Since angle N is same angle, MO is double 10, so 20
Z is midpoint, so both halves are 10
Because of midpoints, XZ and YZ with 10 form same triangle as half triangle at 9, 7, and 10 respectively.
pls help in question no 10. a)
Find the multiples of 7 which is greater than 56 but less than 77
Answer:
63,70
Step-by-step explanation:
7 x 8 = 56
7 x 11 = 77
multiples of 7 and 9, 7 x 10
63 and 70
7×9 = 63
7×10 = 70
Answered by Gauthmath must click thanks and mark brainliest
solve y+1/2-2y-1/2=4
Answer:
y+1/2-2y-1/2=4
y-2y=4
-y=4
y=-4
Let me know if this helps!
answer all of the following please.
Answer:
Front = 30
Back = 30
Right = 30
Left = 30
Bottom = 25
Top = 16
Total = 161
Let me know if this helps!
hdndnndndndndnndndndndnbd
Answer:
Hshushahhahaa
Hdhddjkddjdkjd
A boat goes 24 miles at a constant speed in 4 hours against a river current. It takes the boat 3 hours to go the same distance at the same speed with the current of the river. What is the speed of the boat and what is the current of the river?
Boat speed: Speed of Current:
Answer: 7 miles/h and 1 miles/h
Step-by-step explanation:
With the speed of current = x + 1
Against the speed of current = x - 1
ATQ
4(x-1) = 3(x+1)
4x-4 = 3x+3
4x - 3x = 3+4
x = 7
Speed of boat = 7miles/h
Current of river = 1 miles/h
please click thanks and mark brainliest if you like :)
Answer:
Hello,
Boat speed=7 miles/h
Current speed = 1 mile/h
Step-by-step explanation:
I am going to try to explain.
Let say V the speed of the boot (V like vitesse in french)
Let say v the speed of the current.
distance=24 miles
[tex]\left\{\begin{array}{ccc}V-v&=&\dfrac{24}{4} \\V+v&=&\dfrac{24}{3} \\\end{array}\right.\\\\\left\{\begin{array}{ccc}V-v&=&6 \\V+v&=&8 \\\end{array}\right.\\\\Adding\ the\ 2\ equations\ and\ substracting\ them \\\\\\\left\{\begin{array}{ccc}2V&=&14 \\2v&=&2 \\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}V&=&7 \\v&=&1 \\\end{array}\right.\\\\[/tex]
Boat speed=7 miles/h
Current speed = 1 mile/h
what is the value of the smallest of five consecutive integers if the least minus twice the greates equals -3
A. -9
B. -5
C. -3
D. 5
Answer: (b)
Step-by-step explanation:
Given
There are five consecutive integers and the least minus twice the greatest equals to -3
Suppose [tex]x,x+1,x+2,x+3,x+4[/tex] are the five consecutive integers
According to the question
[tex]\Rightarrow x-2(x+4)=-3\\\Rightarrow x-2x-8=-3\\\Rightarrow -x=8-3\\\Rightarrow x=-5[/tex]
option (b) is correct.
find the missing side lengths answered in the simplest radical form with the denominator rationalized
9514 1404 393
Answer:
u = 7√2; v = 7
Step-by-step explanation:
The ratios of side lengths in an isosceles right triangle are ...
1 : 1 : √2 = 7 : v : u
Then v = 7 and u = 7√2.
Find the area of the triangle.
Answer:
B
Step-by-step explanation:
area=1/2×32×6.1=16×6.1=97.6 yd²
Answer:
Choice B. 97.6 yd^2
Step-by-step explanation:
B×W×.5= A
