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
97. An elevator in a tall building goes up 7 floors, then
down 9 floors, down 4 floors, up 8 floors, and
down 2 floors. Now it is on floor 14. On what
floor did the elevator start?
so, start floor = x
x + 7 - 9 - 4 + 8 - 2 = 14
x = 14
the elevator started on the 14th floor.
to verify: 14 + 7 = 21 - 9 = 12 - 4 = 8 + 8 = 16 - 2 = 14
Find the value of x-8 when x=16.
Answer:
8
Step-by-step explanation:
x=16
x(16)-8=8
In the first quadrant, you start at 2, 6 and move 2units rights and 3 units down what point will you end up on?
Answer:
[tex]End = (4, 9)[/tex]
Step-by-step explanation:
Given
[tex]Start = (2,6)[/tex]
Transformation: 2 units right and 3 units down
Required
The new point
First, we take the right translation;
When a point is translated right by 2 units, the rule is:
[tex](x,y) \to (x + 2, y)[/tex]
So, we have:
[tex](2,6) \to (2 + 2, 6)[/tex]
[tex](2,6) \to (4, 6)[/tex]
Next, we take the down translation;
When a point is translated down by 3 units, the rule is:
[tex](x,y) \to (x, y + 3)[/tex]
So, we have:
[tex](4,6) \to (4, 6+3)[/tex]
[tex](4,6) \to (4, 9)[/tex]
Hence, the endpoint is:
[tex]End = (4, 9)[/tex]
simplify : 5y-2y+4=10
Answer:
[tex]3y = 6,=> y=2[/tex]
Step-by-step explanai
on:
i need help with this one please
Answer:
A
Step-by-step explanation:
a geometric sequence is where we multiply a factor from element to element.
a1 = $900
a2 = 981 = a1 × f = 900 ×
a3 = 1069.29 = a2 × f = a1 × f × f = s1 × f²
[tex]an = 900 \times {f}^{n - 1} [/tex]
so, now let's try and get f.
remember, 981 = 900 × f
f = 981/900 = 109/100 = 1.09
just to control, we check for s3 :
900 × (1.09)² = 900 × 1.1881 = 1069.29
correct.
so,
a13 = 900 × (1.09)¹² = 2,531.398304
s13 is then the sum of all a1, ..., a13
there is a nice formula for sums of finite sequences
s13 = 900 × (1-f¹³) / (1-f) = 900×(1-(1.09)¹³) / (1-1.09) =
= 900×(1-3.065804612) / (-0.09) =
= 900×(-2.065804612) / (-0.09) = 20,658.04612
.
Solve for n. 1/ n-4 - 2/n = 3/ 4 - n
Answer:
The answer is n = - 4.. I hope it will help :)
Solve the equation √2 – 1 = 3.
Question 5 options:
A)
x = 4
B)
x = 16
C)
x = 8
D)
x = 2
Answer:
C x=8
Step-by-step explanation:
Chúc bạn ngày mới tốt lành
Determine the measure of the angle theta to the nearest degree
Answer: B. θ = 36°
Step-by-step explanation:
Concept:
Here, we need to know the idea of the Law of sines.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
The Law of sines: a / sinA = b / sinB = c / sinC
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
a = 10 m
c = 11.2 m
C = 41°
Given formula
a / sinA = c / sinC
Substitute the value into the formula
10 / sinA = 11.1 / sin (41)
Cross-multiply to simplify the equation
sinA × 11.1 = 10 · sin (41)
Divide 11.1 on both sides
sinA × 11.1 / 11.1 = 10 · sin (41) / 11.1
sinA = 10 · sin (41) / 11.1
Apply arcsine or the inverse of sine (basically representing the division of sine)
A = sin⁻¹ (10 · sin (41) / 11.1)
A = 36°
Hope this helps!! :)
Please let me know if you have any questions
A chef cooked 7kg of mashed potatoes for a banquet. If guests only ate 3/4 of the amount he cooked, how much of the potatoes were eaten?
Answer:
5.25 kg of the mashed potatoes were eaten.
Step-by-step explanation:
(3/4) * 7 = 5.25
I hope this is helpful :)
What is the remainder when 4x2 - 2x + 6 is divided by x - 2?
Answer:
18
Step-by-step explanation:
Find the zeros of the divisor
x-2=0
x=2
Plug 2 into the polynomial
4(2)²-2(2)+6
=16-4+6
=18
A number line is divided into fifths. How many equal segments are there between the point at zero and the point 4/5?
Answer:
3?
Step-by-step explanation:
A little confused by the question but is it just
1/5 2/5 3/5 4/5
1 2 3 4
so theres 3 in between
Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{4}{3}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find $\frac{A}{[XYZ]}.$
The area divided by XYZ is 16/9
i.e. [tex]\frac{A}{[XYZ]} = \frac{16}{9}[/tex]
The given parameters can be represented as:
[tex]r = -\frac{4}{3}[/tex] --- the ratio of dilation
The area of the second triangle is as follows:
[tex]A =r^2 * \triangle XYZ[/tex]
Make [tex]r^2[/tex] as subject
[tex]r^2 = \frac{A}{\triangle XYZ}[/tex]
Substitute value for [tex]r^2[/tex]
[tex](\frac{4}{3})^2 = \frac{A}{\triangle XYZ}[/tex]
[tex]\frac{16}{9} = \frac{A}{\triangle XYZ}[/tex]
Rewrite as:
[tex]\frac{A}{\triangle XYZ} = \frac{16}{9}[/tex]
Read more at:
https://brainly.com/question/19305981
Answer:
Step-by-step explanation:
Let each side of triangle XYZ have length s. We therefore have:
s = YZ = YQ + QR + RZ = x + 2y
Since each side of triangle X1 Y2 Z2 is 3/4 the length of the corresponding side of triangle XYZ, we have:
3/4s = X1 Z1 = X1 Q + QP + P Z1 = 2x +y.
The system of equations:
x + 2y = s
2x + y = 3/4s
Multiply the second equation by 2, then subtract the first equation.
3x = 1/2s, so x = 1/6s.
Now we have y = 3/4s-2x = 5/12s.
A/[XYZ] = [XYZ] - 3[YPQ]/[XYZ]
= {[XYZ] - 3[(25)/144] * [XYZ]} / [XYZ]
={23/48* [XYZ]} / [XYZ]
= 23/48
Solve for x: 9(3x+3)=10(3x+9)
Answer:
-21 =x
Step-by-step explanation:
9(3x+3)=10(3x+9)
Distribute
27x +27 = 30x +90
Subtract 27x from each side
27x+27 -27x = 30x-27x +90
27 = 3x+90
Subtract 90 from each side
27-90 = 3x +90-27
-63 = 3x
Divide by 3
-63/3 = 3x/3
-21 =x
Answer:
x = -21
Step-by-step explanation:
9(3x+3) = 10(3x+9)
27x + 27 = 30x + 90
-30x + 27x = 90 - 27
-3x = 63
x = -21
Which expression is equivalent to 1/4y−1/2?
( ignore the highlighted answer i don’t know if it’s right or not)
Answer:
1/4( y -2)
Step-by-step explanation:
1/4 y -1/2
Rewriting
1/4 * 1 y - 1/4*2
Factor out the 1/4
1/4( y -2)
Two neighbors in a rural area want to know the dsitance between their homes in miles what should the mneighbors us as a conversion factor to convert this distance to miles? 4,224 feet
They should use the conversion factor
1 mile = 5280 feet
To go from feet to miles, you divide by 5280
So,
4224 ft = 4224/5280 = 0.8 miles
The distance between their homes is exactly 0.8 miles
What
is the value of In e^4
Answer:
[tex]\displaystyle lne^4 = 4[/tex]
General Formulas and Concepts:
Algebra II
Natural Logarithms ln and Euler's number e
Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle lne^4[/tex]
Step 2: Evaluate
Rewrite [Logarithmic Property - Exponential]: [tex]\displaystyle 4lne[/tex]Simplify: [tex]\displaystyle 4(1)[/tex]Determine the measure of the interior angle at vertex E.
Answer:
135
Step-by-step explanation:
(n−2) × 180° = sum of the interior angles where n is the number of sides
There are 6 sides
(6 -2) * 180
4*180
The sum is 720
2x+2x+3x+3x+3x+3x = 720
16x = 720
Divide by 16
16x/16 = 720/16
x = 45
Angle E = 3x= 3(45) = 135
If x = 2y + 3 and 4x – 5y = 9, what is the value of y?
A. 2
B. 1
C. -1
D. -2
Answer:
Steps shown in picture provided
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)
Answer:
Step-by-step explanation:
Total amount in cents (unsimplified): 5N +17(10-N)
Simplified: 170-5N
On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9.5), (negative 2, 6), (0, 2), (1, 1.5), (2, 2), (4, 6), (5, 9.5), (6, 14).
Which is the rate of change for the interval between 2 and 6 on the x-axis?
Answer:
Step-by-step explanation:
The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:
by finding the slope. Remember, that slope is the same thing as rate of change.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:
[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]
Find the area of the regular polygon. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.
Use the tan of the angle so formed (which is 30 degrees)
Tan(30)= opposite / height (which is the line you just drew).
Tan(30) = 3.5 / h
Tan(30) = 0.5774
Tan(30) = 3.5 / h multiply both sides by h
h*Tan(30) = 3.5 Divide by tan30
h = 3.5 / Tan(30)
h = 3.5 / 0.5774
h = 6.062
Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.
Area of 1 triangle = 1/2 * b * h
area of 1 triangle = 1/2 * 7 * 6.062
Area of 1 triangle = 21.2176
There are 6 such triangles so multiply that number by 6
Answer: 6 * 21.2176
Answer: 127.31
could someone help me with these questions please i’m really confused
Answer:
C
Step-by-step explanation:
c
Sin(2x+30°)=1
Tìm x
Cảm ơn vì giúp đỡ
Answer:
Step-by-step explanation:
This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):
[tex]sin^{-1}[sin(2x+30)]=sin^{-1}(1)[/tex]
On the left, the inverse sin "undoes" or cancels the sin, leaving us with
2x + 30 = sin⁻¹(1)
The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:
2x + 30 = 90 and
2x = 60 so
x = 30
You're welcome!
whats the perimeter and area of this shape?
Answer:
(4x4) + (6x11) = 82 for area
4+4+10+11+7+6= 42
Step-by-step explanation:
You can calculate this by calculating the two squares separately, and on the bottom line, it is 10, so just subtract 4 to make the rectangle on the right, separate from the square on the left. (for area)
Ai đó giúp mình với. Bài này mình không nghĩ ra cách giải
Answer:
-3 -2. 1 0 2 3 -2 3Step-by-step explanation:
please make it a brainliest answer.
What is the volume of the rectangular prism?
Answer:
94.5 yd^3
Step-by-step explanation:
The volume of a rectangular prism is given by the formula:
A = lwh
Where:
l = length
w = width
h = height
Volume is how much space a 3d figure occupies.
USE THE FORMULA WITH THE GIVEN DIMENSIONS:
A = (7)(4.5)(3)
= (31.5)(3)
= 94.5
Volume is measured in cubic yards, in this case.
Therefore your answer is 94.5 yd^3
I hope I helped!
Answer:
Step-by-step explanation:
length = 7 yd
Width = 4.5 yd
height = 3 yd
Volume of rectangular prism = length * width * height
= 7 * 4.5 * 3 = 94.5 yd³
It takes 3 identical water pumps 8 hours to fill a pool. How long would it take 4 of
these same pumps to fill the pool?
Answer:
Step-by-step explanation:
We have 3 identical pumps working to fill a pool. If it takes them working together 8 hours to fill the pool, the equation is:
[tex]\frac{1}{x}+\frac{1}{x}+\frac{1}{x}=\frac{1}{8}[/tex] and
[tex]\frac{3}{x}=\frac{1}{8}[/tex] . Cross multiply to get
x = 24, which is the number of hours it will take one pump to do the job all alone. If this be the case, and we have 4 pumps WORKING AT THE SAME TIME, filling the pool will be the number of hours it takes one pump divided by 4.
4 pumps can do the job in 6 hours.
assume abc=def. if ab=5, ac=9 and ef=7, what is the length of bc?
Answer:
bc= 7
Step-by-step explanation:
56 = h/9
k/5 - 10 = 3
3t + 5 =2
Answer:
h = 504, k = 65, t = -1
Step-by-step explanation:
56 = h/9
h = 56 x 9
h = 504
k/5 - 10 = 3
k/5 = 3 + 10
k/5 = 13
k = 13 x 5
k = 65
3t + 5 = 2
3t = 2 - 5
3t = -3
t = -3/3
t = -1
HELP PLEASE IM GONNA FAIL
21. Identify as a function or not a Function
Answer:
First one: function
Second one: not a function
Step-by-step explanation:
A function is a relationship where each input has it's own unique output. If an input has more than one output then the relationship is not a function
For the first one no x value repeats meaning each input has it's own output therefore it is a function
For the second one the x value 8 has more than 1 output therefore the second one is not a function
