Answer:
Perimeter, P = 112 meters
Step-by-step explanation:
Let the length of the rectangle be L.Let the width of the rectangle be W.Translating the word problem into an algebraic expression, we have;
L = 6W ...... equation 1
Given the following data;
Area of rectangle = 384 m²To find the perimeter of the rectangle;
First of all, we would determine the dimensions of the rectangle using its area.
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = LW ..... equation 2
Substituting eqn 1 into eqn 2, we have;
384 = 6W(W)
384 = 6W²
Dividing both sides by 6, we have;
W² = 384/6
W² = 64
Taking the square root of both sides, we have;
W = √64
Width, W = 8 meters
Next, we would find the length;
L = 6W
L = 6 * 8
Length, L = 48 meters
Lastly, we would determine the perimeter of the rectangle using the above dimensions;
Mathematically, the perimeter of a rectangle is given by the formula;
Perimeter = 2(L + W)
Substituting the values into the formula, we have;
Perimeter, P = 2(48 + 8)
Perimeter, P = 2(56)
Perimeter, P = 112 meters
What is the degree of this polynomial?
5 + 2s
=====================================================
Explanation:
We can rewrite 5 as 5s^0, since s^0 = 1 where s is nonzero.
Think of 2s as 2s^1
With those ideas in mind, the original polynomial turns into 5s^0 + 2s^1
Sorting the terms so that the largest exponent is first gets us the standard form 2s^1 + 5s^0
The largest exponent is the degree, so the degree is 1.
Side note: This trick only works for single variable polynomials.
Find the indicated angle or side. Give an exact answer.
Find the exact length of side a.
A. 1
B. √61
C. √73
D. √13
Answer:
√13
Step-by-step explanation:
To get the side a, we will use the cosine rule as shown;
a² = b²+c²-2bcCosθ
Substitute the given values
a² = 5²+(3√2)²-2(5)(3√2)Cos45
a² = 25+18-30√2*1/√2
a² = 25+18-30
a² = 13
a = √13
Hence the value of a is √13
None of the multiple choice add up to 102 degrees any help?
Answer:
26
Step-by-step explanation:
Let x = the third angle in the triangle
x = 102 because they are vertical angles
The sum of the angles in the triangle are 180
b+2b+102 =180
3b+102 =180
3b = 180-102
3b = 78
Divide by 3
3b/3 = 78/3
b = 26
Answer:
Its is 26 aka E
Step-by-step explanation:
So we know that a triangle has 180 degrees in total. So we know one side is 102 degrees. 180-102=78. we can do 78 divide by 3 since there is 3b's in total. 78/3=26. Therefore, it is 26 which is E. I hope this helped ^^.
Triangle LMN is dilated by a factor of 1.25 to create triangle PQR what is the length of PQ A 20 cm B 18.75 cm C 17 cm di 12 cm
Answer:
See explanation
Step-by-step explanation:
Given
[tex]\triangle LMN \to \triangle PQR[/tex]
[tex]k = 1.25[/tex]
Required
The length of PQ
[tex]\triangle LMN \to \triangle PQR[/tex] means that the side lengths of LMN are multiplied by 1.25 to get the side lengths of PQR
And it implies that the following sides are corresponding
[tex]LM \to PQ[/tex]
[tex]MN \to QR[/tex]
[tex]LN \to PR[/tex]
So, we have:
[tex]PQ = k * LM[/tex]
[tex]PQ = 1.25* LM[/tex]
The question is incomplete.
Assume LM = 16, then:
[tex]PQ = 1.25* 16[/tex]
[tex]PQ = 20[/tex]
HELPPP!!
Rate the following bank accounts from most to least liquid: CD, savings account, checking account, money market
account
a. CD, savings account, checking account, money market account
b. Savings account, checking account, CD, money market account
C. CD, money market account, savings account, checking account
d. Checking account, savings account, money market account, CD
Please select the best answer from the choices provided
OA
OB
О С
OD
Answer:
C
Step-by-step explanation:
There isn’t one
Instructions: Find the measure of the missing angles in the kite
Answer:
m∠1 = 90º
m∠2 = 25º
Step-by-step explanation:
m∠1
diagonals of a kite are perpendicular by definition
m∠2
the 65º angle, the angle to the right of ∠1, and ∠2 form a triangle
we know that triangles are 180º
65º + 90º + m∠2 = 180º
m∠2 = 25º
PLEASE SOMEONE HELP ME ANSWER THIS !!!!
Write the equations of the linear and exponential functions that pass through the points (0, 15) and (1, 5)
Linear Equation, y = mx+b
Exponential Equation, y = a(b)^x
PLEASE ANSWER IT I HAVE AN IMAGE ATTACHED IF NEEDED !!!!
Step-by-step explanation:
Part A: Linear Equation.
One of the points is (0,15). This means 0,15 is the y intercept so b=15.We can find the slope
[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]
So our equation is
[tex]y = - 10x + 15[/tex]
Part B: Exponential Equation
We know that
[tex]15 = a \times b {}^{0} [/tex]
B to the zero power is 1 so
[tex]15 = a[/tex]
This means a =15. Now let find b.
[tex]5 = 15 \times b {}^{1} [/tex]
[tex] \frac{1}{3} = b[/tex]
So the equation is
[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]
what is the length of side s of the square
Answer:
since each side of a square is the same it can simply be the length of one side squared. if a square has one side of 4 inches ,the area would be 4 inches times 4 inches,or 16 square inches
tìm 2 phân số có tử số bằng 1 mẫu số là 2 số tự nhiên liên tiếp sao cho 7/59 ở giữa 2 phân số
Answer:
Bajaj Pulsar of a great time in the 7th century there where you will have the gall the subcontinent the
Helpo pleasssse
On my hw I have a parabola that opens down with its vertex at (-3,-6)......
For the range would I say that {yER | y > -6} OR {yER | y < -6} ????
I'm just confused from the negative numbers
Answer: The range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
Explanation:
The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.
The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.
Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
This translates to "y is a real number such that y is -6 or smaller".
So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.
See below for a visual example of what's going on.
I need help make sure to round it to the nearest 10th
Answer:
10.52
Step-by-step explanation
One of the factors of x² + y² + 2xy - z² is ?
Answer:
x + y + z.
Step-by-step explanation:
x² + y² + 2xy - z²
= (x + y)^2 - z^2
This is the difference between 2 squares so the factors are:
(x + y + z) and (a + y - z).
Answer: The factors are (x+y+z) and (x+y-z)
In other words, it factors to (x+y+z)*(x+y-z)
=====================================================
Work Shown:
[tex]x^2 + y^2 + 2xy - z^2\\\\(x^2 + 2xy + y^2) - z^2\\\\(x+y)^2 - z^2\\\\(x+y+z)(x+y-z)\\\\[/tex]
Notes:
In the third step, I used the rule (A+B)^2 = A^2+2AB+B^2. For this, A = x and B = y.In the last step, I used the difference of squares factoring rule A^2-B^2 = (A+B)(A-B). In this case, A = x+y and B = z.What are the domain and range of f(x) = |x + 6|? Domain: (negative infinity, infinity); range: f(x) > 0 domain: x < -6; range: (negative infinity, infinity) domain: x > -6; range: (negative infinity, infinity) domain: (negative infinity, infinity) ; range: f(x) < 0
Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex]f(x) \ge 0[/tex]
Step-by-step explanation:
Given
[tex]f(x) = |x + 6|[/tex]
Required
The domain and the range
First, we calculate the domain
[tex]f(x) = |x + 6|[/tex]
The above function does not have roots or fraction, where x is the denominator. This means that the domain is all real numbers, i.e. [tex](-\infty,\infty)[/tex]
The range
The function is an absolute function; So, the minimum value is 0.
Hence, the range is:
[tex]f(x) \ge 0[/tex]
Answer:
A
Step-by-step explanation:
on edge
8.
The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.
A. quadratic; y = 0.79x2 + 98
B. linear; y = 0.79x + 98
C. quadratic; y = 98x2 + 0.79
D. exponential; y = 98 • 0.79x
Answer:
D. exponential; y = 98 • 0.79x
Step-by-step explanation:
Answer:
Option D is correct.
Exponential model are the data best represented.
Equation:
Step-by-step explanation:
An exponential function is in the form of .....[1] where a is the initial value and b≠0 , b > 1.
Consider any two points from the table;
(0, 98) and ( 1, 77)
Then substitute these in [1];
For (0, 98)
x = 0 and y = 98 substitute in [1] we get;
98 = a
Similarly, For (1, 77)
we have;
77 = ab
Substitute the value of a =98 we get;
Divide both sides by 98 we get;
⇒ b = 0.79
We get an equation;
Therefore, the data represent here is, Exponential function.
also, an equation to model the data is;
...............................................................................................................................................
All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx
The solution is D
...............................................................................................................................................
Exponential would be the correct answer I believe...
...............................................................................................................................................
For a better understanding of the explanation provided here please find the attachment.
The solution will employ the use of the trial and error method and basic math.
As can be see from the given data, the deer population keeps on falling from the year zero. Thus, we can safely conclude that the quadratic and the linear models will not represent the situation at all.
We are left with the exponential model and since we have in it we can see that the deer population will fall as the years pass.
We have checked it in the table that has been provided and we have concluded that the data is best represented by the exponential model because when the exponential formula is applied it is almost equal to the actual number of deers.
Please check the attached table for a better understanding.
I rlly need help like pleasee
The parallelogram in Quadrant III is the image of the parallelogram in Quadrant II after a counterclockwise rotation about the origin. What is the angle of rotation?
A.) 90 B.) 180 C.) 270 D.) 360
Answer:
A. 90
Step-by-step explanation:
Correct on EDGE
Answer:
maybe 90
Step-by-step explanation:
what's the answer for this?
Answer:
A
Step-by-step explanation:
Observe the coordinates of C, it's (5,2). Now observe C' which is (2, - 5). Hence the rule is (x, y) -> (y, - x)
Round off all these
1) 378811,
2) 267988,
3) 250260,
4) 196596,
5) 193171
to the nearest ten thousand
Answer:
1. 380,0002. 270,0003. 250,0004. 200,0005. 190,000[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Which of the following is an example of exponential growth?
A. Investing $1,000 at an annual interest rate of 3%, compounded monthly
B. A bacterial culture increases by 1,000 bacteria per day
C. The height of a tree increases by 2 feet each year
D. Water drips into a bucket at a rate of 2 pints each minute
An example of an exponential function is given as follows:
A. Investing $1,000 at an annual interest rate of 3%, compounded monthly.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.As we saw above, the rate of change is a percent, and in this problem, only option A has a rate of change as a percent, hence it is an exponential function.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Help anyone can help me do the question,I will mark brainlest.
Answer:
a)11cm
b)49.5cm²
Step-by-step explanation:
to find the perimeter you use the formula
o/360×2piR
since 2pi R=18pi cm,to find the radius you cancel pi from both sides 2r/2=18/2...so the radius is 9cm
therefore the perimeter will be:
70/360×2×22/7×9
27720/2520
=11cm
then to find the area you say
o/360×pi R²
70/360×22/7×9²
124740/2520
=49.5cm²
I hope this helps
Solve the system of equations and choose the correct ordered pair.
4x - 2y = -2
6x + 3y = 27
A. (2,5)
B. (3,7)
C. (0, -1)
D. (0,9)
Answer:
(2,5)
Step-by-step explanation:
4x - 2y = -2
6x + 3y = 27
Divide the first equation by 2 and the second equation by 3
2x - y = -1
2x + y = 9
Add the equations together
2x - y = -1
2x + y = 9
-------------------
4x = 8
Divide by 4
4x/4 = 8/2
x =2
2x+y = 9
2(2) +y = 9
4+u = 9
y = 9-4
y=5
(2,5)
Solve the equation by finding square roots. x2-1/4=0
Answer:
x = ±1/2
Step-by-step explanation:
x^2-1/4=0
Add 1/4 to each side
x^2 -1/4+1/4 = 0+1/4
x^2 = 1/4
Take the square root of each side
sqrt(x^2) = sqrt(1/4)
x = ±1/2
2. Given the function f : x -> |x+8|, find the possible values of x when the image is 3.
Answer:
f (x)=11
Step-by-step explanation:
f (x)= x + 8
f (3)= (3 +8)
=f(x) =11
**replace the x with a variable which is 3
How can we write an algebraic expression to describe a two-digit number whose unit's digit is 5 less than the ten's digit?
Answer:
Let x= the ones digit
Then x+5=the tens digit
Hence the equation is: 10(x+5)+x=x+5+x+63
10(x+5)+x=x+5+x+63
10x+50+x=2x+68
11x+50=2x+68
-2x-50 -2x-50
---------------------
9x=18 Divide both sides of the equation by 9
x=2
Hence the number is 10(2+5)+2=10(7)+2=70+2=72.
Find the perimeter of the sector of a circle of radius 14cm with an angle of 72 degree
Answer:
the area sector is 123.2
School is stressful.
Also, I don't know what I am supposed to put in this text box.
Answer: A) 4
Explanation:
For any 30-60-90 triangle, the short leg is half as long as the hypotenuse.
The short leg is opposite the smallest angle (30 degrees), so we see that
x = 8/2 = 4.
(2x2 + 1) + 3/2x2=1=4
Answer:
3(2×2+1)+3×(2×2)/3=1×3=4×3
36+3+4=3=12
36+3+4-3-12
43-15
28
what do you mean by trigonometry
Answer:
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle
If 12(x - a)(x - b) = 12x² - 7x - 12 , then ab =
Answer choices :
1
-1
7
12
-12
Answer: -1
Step-by-step explanation:
12x^2-7x-12 = (4x+3)(3x-4)
4x+3=0. X = -3/4
3x-4=0. X = 4/3
(-3/4) (4/3) = -1
In parallelogram ABCD, what is BDC?
Answer:
25
Step-by-step explanation:
<ABD=<BDC
Check it out
Answer:
∠ BDC = 25°
Step-by-step explanation:
Since ABCD is a parallelogram , then
AB and DC are parallel , so
∠ BDC = ∠ ABD = 25° ( alternate angles )
A pole that is 2.7 m tall casts a shadow that is 1.56 m long. At the same time , a nearby building casts a shadow that is 38.25 m long. How tall is the building ? Round your answer to the nearest meter.
Set up a ratio of height/ shadow
2.7/1.56 = x/38.25
Cross multiply:
1.56x = 103.275
Divide both sides by 1.56
X = 66.2
Round to nearest meter = 66
Answer: 66 meters
