find the length and width of a rectangle whose
Length is 5cm longer than it’s width
Whose area is 50cm
Step-by-step explanation:
width= x (let)
length= x+5
Area=50 cm
Now ,
area = l ×b
50 = (X×X+5)
50 = (2X + 5)
50÷ 2= X+5
25 -5 = X
X=20
LENGTH = X+5
20+5
=25
there are 6 members of a board of supervisors for a park district they need to form a subcommittee of 3 people to study expanding a park how many different committees could be formed from the members
What is the correct way to write 0.000000056
meter in scientific notation?
Answer:
[tex]5.6 \times 10^{-8}~ m[/tex]
Step-by-step explanation:
[tex]0.000000056\\\\=\dfrac{56}{1000000000}\\\\\\=\dfrac{56}{10^9}\\\\\\=56 \times 10^{-9}\\\\\\=56 \times 10^{-1} \times 10^{-8}\\\\\\=5.6 \times 10^{-8}~[/tex]
Using the digits 0 to 9
Supplementary Angles:
[tex]\boxed{100°} and \boxed{80°}[/tex]
Arithmetically speaking, the closest 2 supplementary angles can get (in 3 and 2 digits respectively) is the upwritten.
Complementary Angles:
[tex]\boxed{45°} and \boxed{45°}[/tex]
Simply, in this case, for angles to be numerically as close as possible - make both the angles 45°.
A membership at a yoga studio costs $35 per month.
Write an equation for the cost of the membership,that you pay if you keep your membership for months.
Answer:
35×(m)=c
Step-by-step explanation:
m=months
c=cost
What is the measure of angle B in the figure below?
A
3
B
D
3√√2
C
O 30°
O 45°
O 60°
O 90°
Two large numbers of the fibonacci are F(51) = 20,365,011,074 and F(52) = 32,951,280,099 if these two numbers are added together what number results
If these two numbers F(51) and F(52) are added together. Then the number of results will be 53,316,291,173.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Two large numbers of the Fibonacci are given below.
F(51) = 20,365,011,074 and F(52) = 32,951,280,099.
The sum of the F(51) and F(52) will be
20, 365, 011, 074
+ 32, 951, 280, 099
53, 316, 291, 173
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In which two of these numbers does the digit
6 have a value of 0.6?
16.7
61.28 14.63 28.16 96.77 85.62
Answer:
Step-by-step explanation:
In this numbers:
14.63
85.62
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
To determine in which two numbers the digit 6 has a value of 0.6, we need to examine the place value of 6 in each number.
Let's go through each number:
1. 16.7: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
2. 61.28: The digit 6 is in the ones place, so its value is 6 (not 0.6).
3. 14.63: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
4. 28.16: The digit 6 is in the hundredths place, so its value is 6 * 0.01 = 0.06.
5. 96.77: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
6. 85.62: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
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How many grams are there in 28 kilograms
Graph the equations to find the solution(s) to the system.
y=x+3y=13(x+5)(x−1)
Use the Line tool to graph the line.
Use the Parabola tool to graph the parabola. Choose maximum or minimum point first and then a point on the parabola.
By graphing both equations, we see that the solutions of the system of equations are (1.05, 4.05) and (-4.97, - 1.97)
How to solve the system of equations?Here we have the system of equations:
y = x + 3
y = 13*(x + 5)*(x - 1).
To solve this system graphically, we need to graph both equations and see where the curves intercept.
The graph of the two equations can be seen below.
There are two solutions, one is (1.05, 4.05) and the other is (-4.97, - 1.97)
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Please help me thank you :3
Quadrilaterals are angles that has 4 sides and angles. The measure of the angle m<SPQ is 110 degrees
Angles in a quadrilateralQuadrilaterals are angles that has 4 sides and angles. The given quadrilateral is a rhombus with equal opposite sides.
Given the following angles
m<SPR = 2x + 15
m<QPR = 3x - 5
From the figure
m<SPR = m<QPR
Substitute
2x+ 15 = 3x - 5
2x - 3x = -5 - 15
x = 20
Determine the measure of <SPQ
m<SPQ = 3x - 5 +2x +15
m<SPQ = 5x + 10
m<SPQ =5(20) + 10
m<SPQ = 110 degrees
Hence the measure of the angle m<SPQ is 110 degrees
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please help me im just really slow
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Explain.
Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). Explain.
For both problems, we can use the section formula.
1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]
What is the scale factor for XYZ TO UVW?
Answer:
D. 2
Step-by-step explanation:
If you multiply any side from XYZ by 2 it will equal the same length of one of the sides of UVW.
53, 13, 34, 41, 26,61, 34, 13,69 mean median mode and range
Answer:
mean 38.22
median 34
mode 13 & 34
range 56
Step-by-step explanation:
mean- add all values together and divide by number of values
median- order from least to greatest find the middle value
mode- the value that appears most often, can be more than one value
range- smallest value subtracted from the largest
In ΔOPQ, o = 500 cm, p = 600 cm and q=380 cm. Find the measure of ∠P to the nearest 10th of a degree.
The measure of ∠P to the nearest 10th of a degree is 84.8°
Law of CosinesFrom the question, we are to determine the measure of ∠P
From the law of cosines, we can write that
[tex]cos \ P=\frac{o^{2}+q^{2}-p^{2} }{2oq}[/tex]
From the given information,
o = 500 cm
p = 600 cm
q = 380 cm
Putting the parameters into the formula, we get
[tex]cos \ P=\frac{500^{2}+380^{2}-600^{2} }{2\times 500 \times 380}[/tex]
[tex]cos \ P =\frac{34400}{380000}[/tex]
[tex]cos \ P =0.0905[/tex]
P = cos⁻¹(0.0905)
P = 84.8076
P ≅ 84.8°
Hence, the measure of ∠P to the nearest 10th of a degree is 84.8°
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On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 3, 3), (1, 4), (1, negative 4), (2, negative 4), (2, negative 2).
How many points need to be removed from this graph so that it will be a function?
1 point
2 points
3 points
0 points
Three points must be removed from this graph so that it will be a function
How to determine the number of points?The points are given as:
(-3, 2), (-3, 3), (1, 4), (1, -4), (2, -4), (2, -2).
For a set of point to represent a function;
Each x coordinate must point to only one y coordinate
From the given points, we have the following highlights:
The x value -3 has two y values (2 and 3)The x value 1 has two y values (4 and -4)The x value 2 has two y values (-4 and -2)In the above highlights, one point each must be removed.
This means we have a total of 3 points
Hence, three points must be removed from this graph so that it will be a function
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Answer:
C. 3 points
Step-by-step explanation:
Select the correct answer from each drop-down menu.
veronica wants to cut a sheet of paper into squares with an area of 12 square inches. for the best approximation, the length of each side o
the square pieces of paper must be approximately equal to
inches. if each side were exactly this length, the area of each square
would be _____
square inches
Answer:3.46
Step-by-step explanation:i dont know the other one
Find the equation that is parallel to 2x-y=7
Answer:
Below
Step-by-step explanation:
Lines that are parallel have the same slope, so all lines parallel to the one given have the same slope as it does. That slope value is most easily seen by transforming the given equation to slope-intercept form
(y = mx + b).
This line would be y = 2x -7, so the slope of any line parallel to it must have a slope value of 2.
Hi there.
[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]
First of all, we can't find the equation of the line that is parallel to the line we are provided with in this problem, which is [tex]\bf{2x-y=7}[/tex], until we convert this equation into another form.
.
.
This form has a name, and it's called "[tex]\bf{Slope-Intercept\:Form}[/tex].
.
.
So first, what we need to do is subtract 2x from both sides:
.
[tex]\bf{-y=7-2x}[/tex]
.
It's not mandatory, but we can re-arrange the terms "7" and "-2x":
.
[tex]\bf{-y=-2x+7}[/tex]
.
Last step: Divide both sides of the equation by -1:
.
[tex]\bf{y=2x-7}[/tex]
.
"-2x" turned into "2x" because a negative number multiplied or divided by a negative number equals a positive number.
.
"7" turned into "-7" because a positive number multiplied or divided by a negative number equals a negative number.
.
Now, our equation is in "Slope-Intercept Form".
.
Remember that "Slope-Intercept Form" looks like this:
.
[tex]\bf{y=mx+b}[/tex].
.
Now what we need to find is the equation of the line.
.
Let's skim through the provided information to see whether or not there's some information that can help us find the equation.
.
We're also provided with the fact that these lines, or equations, are parallel.
.
What that means is if two lines are parallel, their slopes are the same.
.
The slope of the line whose equation we just found is -2 (it's the number next to "x").
.
I hope that this helped clear your doubts; if any are left, please ask.
.
I wish you a nice rest of your day.
.
[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\sf{n}\bf{g}\:\sf{A}\:\bf{L}\sf{e}\bf{t}\sf{t}\bf{e}\sf{r}.[/tex]
--
given lim x→0 f(x)=4. what is lim x→0 1/4 [f(x)]^4?
Given that
[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]
we can use the properties of limits to show
[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]
[tex]\\ \rm\Rrightarrow 64[/tex]
You are building a brick patio. the length of the patio is (x+11) feet.
the total area of the patio can be represented by x^2+14x+33. write an expression for the width of the patio
The expression that represents the width of the patio is (x+3) feet
Calculating areaFrom the question, we are to determine the width of the patio
The area of the patio = Length of the patio × Width of the patio
From the given information,
Length of the patio = (x+11) feet
Area of the patio = x^2+14x+33 = x²+14x+33
Putting the parameters into the formula,
x²+14x+33 = (x+11) × Width of the patio
∴ Width of the patio = (x²+14x+33) / (x+11)
First, we will factor x²+14x+33
x²+14x+33
x²+11x+3x+33
x(x+11) +3(x+11)
(x+3)(x+11)
Thus,
Width of the patio = [(x+3)(x+11)] / (x+11)
∴ Width of the patio = (x+3) feet
Hence, the expression that represents the width of the patio is (x+3) feet
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What is the diameter of a hemisphere with a volume of 458 ft³, to the nearest tenth
of a foot?
Answer:
12.0 ft
Step-by-step explanation:
Mr. Addison is building a sandbox shaped like a rectangular prism. The sandbox is 9ft long, 5ft wide, and 2.5 ft deep. How many cubic ft of sand will the sandbox hold?
if 6 men. 8 women and 16 boys together can do a piece of work in 288 days by working 6 hours each day in how many days can 12 men, 18 women and 28 boys complete the same & work by working 8 hours each day? The work efficiency of men, women and boys proportion 3:2:1 respectively?
Answer:
144 days
Step-by-step explanation:
Let's put the efficiency in terms of b
m = 3b w = 2b b=b
starting with 6 m = 18 b
8w = 16 b
16b = 16 b total 50 b
then increase 12m = 36b
18w = 36b
28b = 28 b total = 100 b
You doubled 'b' workers so work time will be halved to 144 days
which 2 numbers have a mean of 10 and a range of 12
Answer:
Step-by-step explanation:
16 - 4 = 12
16 + 4 = 20
then 20 ; 2 = 10
Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.
given that y= 6 cm and θ= 32 °, work out x rounded to 1 dp.
(not drawn to scale)
X=7.1cm
The solution is in the attached file
A stainless steel patio heater is a square pyramid. The length of one side of the base is 23.4 in. The
slant height of the pyramid is 93.2 in. What is the height of the pyramid?
The height of the pyramid is aboutin.
(Round to one decimal place as needed.)
The height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
We have a square pyramid.
Length of the pyramid = 23.4 in
The slant height of the pyramid = 93.2 in
From the figure:
Base length CB = DC = 23.4 in
In a right-angled triangle, BCD
Applying Pythagoras theorem:
DC² + CB² = DB²
23.4² + 23.4² = DB²
DB = 33.092 in
OB = (1/2)DB
OB = (1/2)33.092 = 16.546 in
In the right-angle triangle AOB, again applying Pythagoras theorem:
AO² + OB² = AB²
h² + 16.546² = 93.2²
AO = h (height of the square pyramid)
AB = slant height = 93.2 in
After calculating, we get:
h = 91.719 ≈ 91.72 in
Thus, the height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.
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Write an equation for the line through the point (1,3) parallel to
the line y =
1/2x + 10.
Answer:
y=1/2x+5/2
Step-by-step explanation:
The slope will not change if the line is parallel.
So start with 1/2x and plug in 1.
You will get 1/2 and you need to get a total of 6/2 to get a y of 3.
since you already have 1/2 the remanding value needed is 5/2 and once you add the two you will get 6/2 which equals a y of 3.
Maria is on a hike. If she hikes to the scenic lookout on the following map first, she will have to hike farther than if she
went straight to the end of the hike.
Y
end
scenic lookout
5 6 7
1
765
4
6+
5+
432
23
-2+
-3+
-4+
-5+
67
7-6-5-4-3-2
Maria
Coordinate values on the map are in kilometers.
1
1
N
HE
Based on the distance to the end of the hike and the distance to the scenic lookout, we can calculate that the straight route is 2 km shorter than the scenic lookout route.
Which route is shorter for Maria?If Maria took the straight route to the end of the Hike from the coordinates, (4, -4) to (-5, 5), she would have to walk 13 km.
If she went the scenic lookout route, she would have to first go to (2,3) before going to (-5,5) which is 15 km.
The difference is:
= 15 - 13
= 2 km
A more readable version of the question is:
Maria is on a hike. If she hikes to the scenic lookout on the following map first, she will have to hike farther than if she went straight to the end of the hike.
3 connected points on a coordinate plane. The point labeled, "Maria," is at 4, -4. The point labeled, "end," is at -5, 5.
A solid line connect the points "Maria" and "end." The point labeled, "scenic lookout," is at 2, 3. Dashed lines connect "Maria" to "scenic lookout" and connect "scenic lookout" to "end."
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Answer:
2KM
Step-by-step explanation:
Derrick grows vegetables on a circular patch of land. The radius of the patch is 16 meters. What is the approximate area of the patch of land?
Answer:
A≈804.25m²
Step-by-step explanation:
A=πr2=π·162≈804.24772m²