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:
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Mike traveled from the school to the mall and then from the mall to the library. Henry traveled from the school to the library. How many more miles did Mike travel than Henry?
Answer:
12 miles
Step-by-step explanation:
From the graph given :
Mike's travel :
School to Mall= 16 miles
Mall to Library = 30 miles
Total travel = 16 + 30 = 46 miles
Henry's travel :
From school to Library = Hypotenus :
Distance can be obtained using Pythagoras :
Hypotenus = √(opposite² + adjacent²)
Hypotenus = √(30² + 16²)
Hypotenus = √1156
Hypotenus = 34 miles
Difference in Distance covered :
(46 miles - 34 miles) = 12 miles
Solve for a. HELPPppppppppppppppp
Answer:
a = -24
Step-by-step explanation:
[tex]30=26-\frac{a}{6}\\(6)4=-\frac{a}{6}(6)\\24=-a\\-24=a[/tex]
Answer:
-24 = a
Step-by-step explanation:
30 - 26 - a/6
Subtract 26 from each side
30 -26 = 26 - a/6 - 26
4 = -a/6
Multiply by -6 on each side
-6 *4 = -a/6 *-6
-24 = a
If 150° and 3a are supplementary angles, find the value of a.
Answer:
a = 10
Step-by-step explanation:
Supplementary angles sum to 180° , so
150 + 3a = 180 ( subtract 150 from both sides )
3a = 30 ( divide both sides by 3 )
a = 10
Choose the model that correctly illustrates the division problem 2 3 ÷ 3 4 3 2 ÷ 4 3 .
23÷34÷32÷43
= 0.0001558519
Must click thanks and mark brainliest
In the figure below, triangle ABC is similar to triangle PQR:
A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.
What is the length of side PQ?
48
24
40
18
Answer:
24
Step-by-step explanation:
Since the triangles are similar the side lengths must be proportional
2/12 = 4/PQ cross multiply expressions
2PQ = 48 divide both sides by 2
PQ = 24
Which is the graph of y = [x]-2?
PLEASE HELP TIMED PLEASE 20points
Answer:
3rd graph
Step-by-step explanation:
Answer:
it depends on the equation thats given
Step-by-step explanation:
you put the value of x in the brackets and then solve it so that u get the coordinates of y, then u can put the point on whichever values u get for x and y and continue like that until you get all the points (you can join them if the question asks)
Help pls this is really hard
9514 1404 393
Answer:
see attached
Step-by-step explanation:
√2 ≈ 1.414 ≈ 1.4 +0.1(1/7)
The dot will be about 1/7 of the way between 1.4 and 1.5.
2, Nine people fit comfortably in a 3 ft. by 3 ft. area. Use this value to
estimate the size of a crowd that is 8 yards deep and 1 mile long.
Determine the Ratio? A
Ratio = 9 x (3x3). B
O Ratio = 9/3
C
Ratio = 9/(3x3)
D Ratio = 8/5280
The ratio for Nine people fit comfortably in a 3ft by 3ft area is [tex]\frac{9}{3X3}[/tex]
Option C [tex]Ratio =\frac{9}{3X3}[/tex]
Size of crowd: [tex]\frac{9}{3 \cdot 3} \cdot 24 \cdot 5280[/tex]
Given :
Nine people fit comfortably in a 3 ft. by 3 ft. area
To find : we need to estimate the size of a crowd that is 8 feet deep and 1 mile long. we need to determine the ratio as well
Ratio = number of people / total area
[tex]Raio=\frac{9}{3X3}[/tex]
To find the size of the crowd , convert yards into feet and mile into feet
1 yard = 3 miles
8 yards= 3 times 8 = 24 feet
1 mile = 5280 feet
Now we find the area in feet
[tex]24 \cdot 5280[/tex]
size of the crowd=ratio times the area in feet
[tex]\frac{9}{3 \cdot 3} \cdot 24 \cdot 5280[/tex]
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Write each decimal as a fraction or mixed number in simplest form -0.4
Answer:
-2/5
Step-by-step explanation:
What is the explicit formula for this sequence?
-9, - 3, 3, 9, 15, ...
Answer:
-15+6d
Step-by-step explanation:
The common difference of the sequence is -3+9=6
The formula is an=a+(n-1)d, an=-9+(n-1)*6=-15+6d
If the nth term of A.P. are 7, 12, 17, 22.....is equal to the nth term of another A.P. 27, 30, 33, 36. Find the value of n?
Answer:
[tex]n = 11[/tex]
Step-by-step explanation:
We are given two arithmetic sequences:
7, 12, 17, 22... and 27, 30, 33, 36...
And we want to determine n such that the nth term of each sequence is equivalent.
We can write a direct formula for each sequence. Recall that the direct formula for an arithmetic sequence is given by:
[tex]\displaystyle x_n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The first sequence has an initial term of 7 and a common difference of 5. Hence:
[tex]\displaystyle x_n = 7 + 5(n-1)[/tex]
The second sequence has an initial term of 27 and a common difference of 3. Hence:
[tex]x_n = 27 + 3(n-1)[/tex]
Set the two equations equal to each other:
[tex]7 + 5 (n-1) = 27 + 3(n-1)[/tex]
Solve for n. Distribute:
[tex]7 + (5n - 5) = 27 + (3n - 3)[/tex]
Combine like terms:
[tex]5n + 2 = 3n + 24[/tex]
Isolate:
[tex]2n = 22[/tex]
Divide. Hence:
[tex]n = 11[/tex]
In conclusion, the 11th term of the first A.P. is equivalent to the 11th term of the second.
inWrite the equation of the line that passes through (7, - 4) and (- 1, 2) slope- intercept form.
Answer:
General Equation of a Line
[tex]General Equation \\(y - y_{1} )= m (x-x_{1}) \\Slope=m= \frac{x_{2}-x_{1} }{y_{2}-y_{1} } \\\\Given:\\p_{1}=(7,-4)\\p_{2}=(-1,2)\\Solution:\\m=(\frac{-1-7}{2-(-4)}) =\frac{-8}{6}\\y-(-4) = (\frac{-8}{6} )(x-7)\\y+4=\frac{-8x}{6} + 56\\y=\frac{-8x}{6} + 52 \\\\The\\ equation \\ is \\ y=\frac{-8x}{6} + 52[/tex]
Step-by-step explanation:
Find the slope first and then place the values on the general formula. The final step is to solve for y
Find the missing side of the triangle.
A. √226 ft
B. √17 ft
C. √329 ft
D. √346 ft
15^2 = x^2 + 11^2
225 = x^2 + 121
Subtract both sides 121
225 - 121 = x^2 + 121 - 121
104 = x^2
x = √104
x = √4 × 26
x = √4 × √26
x = 2 × √26
x = 2 √26
Simplify the following equation
4−8÷2+3
Hi there!
»»————- ★ ————-««
I believe your answer is:
3
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying...}}\\\\4-8\div2+3\\\\---------------\\\text{Follow PEMDAS:}\\\\\\\rightarrow4-8\div2+3\\\\\rightarrow 4 - 4 + 3\\\\\rightarrow 0 + 3\\\\\rightarrow \boxed{3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
g(x) = x3 + 2x2 - x - 2 to answer all the questions in Part II. 1. Use synthetic division to show that x = -2 is a zero of the polynomial.
Answer:[tex]x^{2} -1[/tex]
Step-by-step explanation:
Given :[tex]g(x)=x^{3} +2x^{2} -x-2[/tex]
Factor x+2,x=-2
Using synthesis division:
-2 ) 1 2 -1 -2
-2 0 2
1 0 -1 0
[tex]x^{2} +0x-1[/tex]
Yes, x = -2 is a zero of the polynomial.
Given that,
The function g(x) = x³ + 2x² - x - 2 is divided by (x + 2)
Now apply the synthetic division to show that x = -2 is a zero of the polynomial.
When we divide by using synthetic division as shown in the attached image.
Remainder = 0
Hence, this shows that x = -2 is a zero of the polynomial.
Therefore, x = -2 is a zero of the polynomial.
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The expression 8x2 − 176x + 1,024 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998. Choose the equivalent expression that is most useful for finding the year where the population was at a minimum.
B
Step-by-step explanation:
Might be wrong
Pls help. I really suck at math.
Determine whether the following polygons are similar.
Answer:
They are not similar.
To easily check if they are similar, you only need to look at the degrees angles, since if the angles are the same, the lengths of the sides will always come out to be similar somehow.
Those triangles possess right angles as you can see the little square thingie in the corners.
Those are 90 degrees, and you can add the 30 degrees in the left shape to 90 to get 120.
There are 180 degrees in a triangle, so 180 - 120 = 60.
Therefore, the unknown angle is 60.
A 30 60 90 triangle is called a special right triangle since there are many useful ratios hidden inside.
The other triangle has a 55 degree angle which is not on the first, so they must not be similar.
Pls brainly dont delete this link, its useful.
https://blog.prepscholar.com/30-60-90-triangle-ratio-formula
This helps you understand the special triangles.
You don't suck at math, you suck at geometry imo, though only in this unit of geometry, probably good at others.
Step-by-step explanation:
choose the equation below that represents the line passing through the point (1,-4) with a slope of 1/2
Need help with 1 and 2
Answer:
1a. 128
1b. 81
1c. 64
1d. 25
1e. 343
1f. 100000
1g. 64
1h. 0
1i. 13
1j. 1
2a. 243
2b. 64
2c. 36
2d. 625
2e. 1331
2f. 10000000
2g. 81
2h. 0
2i. 17
2j. 1
Which situation is best represented using a negative integer?
Answer:
a
Step-by-step explanation:
fine the area ABC triangle
Answer:
48 cm²
Step-by-step explanation:
A(Triangle) = 1/2bh
b = baseh = heightA(Triangle) = 1/2(12)(8) = 48 cm²
Answer:
area of triangle = 1/2 * b* h
=1/2 ×12 ×8
=48 cm^2
PLZ HELP! I WILL PUT BRAINLIEST!
Find the three digit numbers which have the the following properties: all three digits are different, the first digit is the square of the second digit and the third digit is one more than twice the second digit.
Answer:
Step-by-step explanation:
1^2 = 1 This one is impossible. The digits have to be different.
2^2 = 4
3^2 = 9
so the first two digits can either be
4 and 2
9 and 3
The third clue is the one that decides. The third digit is odd and and 1 more than twice the second
The third digit can be 2 * 2 + 1 = 5 or 2*3 + 1 = 7. There is no way to choose between them.
So the answer is either 425 or 937. We cannot decide which. If there is another clue that will break the log jam, post it and I'll come back.
These are the only two answers possible. If the second digit is more than 3 then the first digit is no longer a single digit. It is more than 9.
raise s to the 7th power, then find the sum of the result and 3
Answer:
s^7 + 3
Step-by-step explanation:
Brainliest, please!
At age 20, to save for retirement, Rebecca decides to deposit 80$ at the end of each month in an IRA that pays 6.2% compounded monthly. Use the formula for the value of an annuity.
A=P[(1+r/n)^nt-1]/(r/n)
How much money will be in the IRA when Rebecca retires?
How much interest will the IRA have gained?
Answer:
159319.26 I Don't know the interest
The cost of hat, pants, and sweater is $225. The pant cost $10 more than hat, and the sweater cost $10 more than the pants. What is the cost of the hat ?
Answer:
$65
Step-by-step explanation:
Let x represent the cost of the hat.
Since the pants cost $10 more than the hat, the cost can be represented by x + 10.
Since the sweater cost $10 more than the pants, the cost can be represented by x + 20.
Create an equation adding these all together and setting it equal to 225, then solve for x:
(x) + (x + 10) + (x + 20) = 225
3x + 30 = 225
3x = 195
x = 65
So, the hat cost $65
Simplify 7 to the 6th power ⋅ 7 to the fifth power.
49 to the 11th power
49 to the 35th power
7 to the 11th power
7 to the 35th power
Answer:
7 to the 11th power
Step-by-step explanation:
7⁶×7⁵=7¹¹
because a¹×a¹=a¹+¹
Solve for p.
–
19p–2p+16p+12=
–
18
p=
Answer:
6
BRAINLIEST, PLEASE!
Step-by-step explanation:
-19p - 2p + 16p + 12 = -18
-5p + 12 = -18
-5p = -30
p = 6
Answer:
p = 6
Step-by-step explanation:
Given
- 19p - 2p + 16p + 12 = - 18 ( simplify left side )
- 5p + 12 = - 18 ( subtract 12 from both sides )
- 5p = - 30 ( divide both sides by - 5 )
p = 6
Find the volume of a rectangular solid that
is 9 ft. by 12 ft. by 8 ft.
Help please
Answer:
864 ft³ is the volume
Step-by-step explanation:
Volume = width · height · length
= 12 · 9 · 8
= 864
Answer:
Step-by-step explanation:
Volume of rectangular solid = length * width * height
= 9 * 12 * 8
= 864 ft³
Please help for brainliest!!
Answer:
108
Step-by-step explanation:
3(6*3*2)
Answer:
L x W x H is the formula to solving this problem.
It looks like 6 is the length, 3 is the width and 2 is the height!
6 x 3 x 2 = 36
BUT WAIT!
It seems like the 2 is on one of the tissues, if it isn't 36, the other answer is definitely something else...
2 + 2 + 2 = 6
6 x 3 x 6 = 108!
_ _ _ _ _
The answers could either be 36 or 108!
1)a)write any three rational numbers .
Answer : 3/4,-2/6,1/2 is are called rational
number.
b)Explain rational numbers in your own words .
Answer: A number which can be written in the form p/q , where p and q are integers and q = 0 is called a rational number
Step-by-step explanation:
1)1/2,1/5 and 0
2)In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer
