13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.
What are dimensions?Height, length, and width are the three dimensions that all of the places we dwell and things we utilize on a daily basis have.
Height, depth, and other dimensions are examples of dimensions.
The dimensions of a line, a square, and a cube are each one, two, and three, respectively.
However, we consider the Universe to have one temporal dimension and three spatial dimensions (north-south, east-west, and up-down).
So, we have the area (A):
A = (54 – 2x)x
A = 54x - 2x²
Differentiate to obtain: dA/dX = 54 - 4x
We shall differentiate and equate to zero for a maximum Area, so dA/dx = 0.
54 – 4x = 0
x = 54/4
x = 13.5 m
It covers 280 m². Consequently, the other potential dimension:
w = 280/13.5
w = 20.74 m
Therefore, 13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.
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Find the length of the third side. If necessary, write in simplest radical form.
Answer: 5
Step-by-step explanation:
Pythagorean theorem a^2 + b^2 = c^2
5^2 + x^2 = 5sqrt(2) ^ 2
25 + x^2 = 50
x^2 = 25
x = 5 square root both sides
Mr. Hill also teaches gym. He has 20 soccer balls and 3 teams of
students. He gives the same number of balls to each team.
Can Mr. Hill divide 20 balls into 3 equal groups?
»)
>>>
>>)
Yes
No
I am not sure.
Answer: No
Step-by-step explanation:
No, Mr.Hill can not divide 20 balls into 3 equal groups because 20/3 does not get you a whole number, and you can not have 0.66666667 of a ball.
Answer:
No.
Step-by-step explanation:
20/3 = 5 balls per team and five are left over. No he cannot, this is because Mr. Hill would need to have twenty one balls and he only has 20. So there is not enough. It’s because there are going to be leftovers.
Greg purchased a prepaid phone card for $40.25 calls cost 5 cents a minute using this card. the credit left in the card after it is used for x minutes of calls is given by the following function
Answer: C= 40.25 - 0.05x
Step-by-step explanation:
C is the credit left
We know that the original is 40.25, so we put it as the beginning number.
Each minute costs $0.05x
where x is each minute
, so the equation is C= 40.25 - 0.05x
Sofia bought a package of 20 bottles of water. Each bottle contains w ounces. Write an
expression that shows the total number of ounces.
Answer:
20w
Step-by-step explanation:
If you have 20 bottles, and each contains w ounces, we can use the following example to solve.
If there were 4oz per bottle,
20 * 4 = 80
80oz
We have w oz per bottle,
20 * w = ?
20w
Mrs. Chu is ordering senior portraits of her son to send to their relatives. A medium photo
costs $22 and a large photo costs $42. She wants to spend less than $400 in total.
Select the inequality in standard form that describes this situation. Use the given numbers
and the following variables.
x = the number of medium photos
y = the number of large photos
The inequality which represents the situation is 22x + 42y < 400.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Cost of medium photos = 22x
Cost of large photo = 42y
Total cost < 400
22x + 42y < 400
Hence "The scenario is represented by the inequality 22x + 42y < 400.".
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consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area?
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
what is perimeter ?The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.
calculation
In order to construct a hog pen, I have 800 feet of fencing.
Assume that "l" represents the rectangle's length and "w" its width.
One of your properties borders a river that I own.
I can secure my property with fencing on its three sides.
because of this, the fencing's necessary perimeter p = l + 2w
The fencing's perimeter is now equal to
⇒ l + 2w = 800
= l = 800 - 2w
now the rectangle's area = A = lw
Therefore, A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]
By diffusing the area equation, we can figure out the rectangle's greatest area.
Therefore, A' = 800 - 4w
Again, A" = -4
The rectangle has the largest area since the second order differentiation is constant negative.
Put simply, we obtain: A' = 0 , A' = 800- 4w
⇒800- 4w = 0
⇒ 4 w = 800
⇒ w = 200
So the rectangle has a 200-foot width.
The rectangle's length is currently:
l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
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Determine which of the lines, if any, are
parallel. Explain.
Line a passes through (-2,5) and (2,1)
Line b passes through (-4,3) and (3,4)
Line c passes through (-3,4) and (2,-6)
Please, help. Simplify the expression in positive exponents.
Answer:
(r⁶s³t¹⁰)/uStep-by-step explanation:
= r⁻¹st⁻¹u⁻¹/(r⁽¹⁺¹⁻⁹⁾s⁽⁻²⁺⁰⁺⁰⁾t⁽⁻¹⁻⁹⁻¹⁾u⁽⁻⁶⁺⁰⁺⁶⁾)= r⁻¹st⁻¹u⁻¹/r⁻⁷s⁻²t⁻¹¹u⁰= r⁻¹⁺⁷s¹⁺²t⁻¹⁺¹¹/u⁰⁺¹= r⁶s³t¹⁰/uThe circle graph shows how a typical household spends money on energy. Use the graph to find the measure of each arc.
mPQ
MUPT
Converting the percentage to degree in the pie chart, angle PQ and UPT are 162° and 25.2° respectively
Pie ChartThis is a statistical tool used to represent data in a chart. It is often represented using angles or percentage.
To find the value of the respectively angles, we have to convert the values from percentage to degree.
The formula to do this is given as
Percentage = angle * (100 / 360)
A)
Angle PQ = ?
Substituting the values;
45 = angle * (100 / 360)
45 = angle * (5/18)
angle = 45 / (5/18)
angle = 162°
B) Angle UPT = ?
7 = angle * (5/18)
angle = 7 / (5/18)
angle = 25.2
The angle PQ is 162 degrees, the angle UPT is 25.2 degrees
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Find the additive inverse of 2x+5 .
Answer: -5-2x
Step-by-step explanation:
factorise x squared + 3x
Answer:
x(x + 3)
Step-by-step explanation:
x² + 3x ← factor out x from each term
= x(x + 3)
Refer to the equation 2x - 6y = 12.
(a) Create a table of values for at least 4 points. Show your work.
(b) Use the table of values to graph
the line.
The points on the line 2x - 6y = 12 is
x y
0 -2
6 0
9 -1
12 2
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
a)The equation is 2x - 6y = 12
For x = 0,
[tex]2 \times 0- 6y = 12\\6y = -12\\y = -\frac{12}{6}\\y = -2[/tex]
For x = 6,
[tex]2 \times 6 - 6y = 12\\6y = 0\\y = 0[/tex]
For x = 9
[tex]2 \times 9 -6y = 12\\18 - 6y = 12\\6y = 12 - 18\\6y = -6\\y = -\frac{6}{6}\\y = -1[/tex]
For x = 12
[tex]2 \times 12 - 6y = 12\\-6y = 12 - 24\\-6y = -12\\y = \frac{12}{6}\\y = 2[/tex]
x y
0 -2
6 0
9 -1
12 2
b) The graph has been attached
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Which type of graph would best compare the number of school days in California, Kansas, Alabama, and Rhode island?
Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.
What is Bar graph?
A bar chart or bar chart is a chart or graph that represents categorical data in rectangular bars whose height or length is proportional to the value they represent. Bars can be drawn vertically or horizontally. Column charts are sometimes called vertical bar charts.
Bar charts show comparisons between discrete categories. One axis of the chart shows the specific category to be compared and the other axis represents the measured values. Some bar charts represent bars grouped into multiple groups to show values for multiple measurement variables.
Therefore, Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.
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If $\frac{x}{2} \frac{y}{3} = 1$ and $\frac{x}{4} \frac{2y}{3} = -1$, what i the value of the um of $x$ and $y$?
Help Pl
If x² /y³ = 1 and x^4/2y³ = -1, the value of the sum of x and y would be y^(3/2).
What are different operations in maths?The fundamental procedures for altering and combining mathematical objects, such as integers and functions, are known as operations in mathematics. These operations, which are used to carry out mathematical computations on numbers, generally include sum, subtraction, multiplication, and division. Operations may also be applied to other types of mathematical objects, like as vectors, matrices, and sets, to execute more sophisticated operations such as vector addition, matrix multiplication, and set intersection. The outcome of an operation is referred to as an operand, and the procedures for combining operands are referred to as the operation's laws. A basic idea in mathematics, operations are applied in many different areas of science and math.
How to solve?
If x² /y³ = 1, then x² = y³
If x^4/2y³ = -1, then x^4 = -2y³
The sum of x and y is x + y = (x²)^1/2 + (y³)^1/3 = y^(3/2) + y
x + y = (x^4)^1/4 + (y³)^1/3 = (-2y³)^1/4 + y^(3/2) = -y + y^(3/2)
x + y = 0 + y^(3/2) = y^(3/2)
The sum of x and y is y^(3/2)
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Christina and Spencer have 120 baseballs together. Spencer has 28 more baseballs than Christina. How many baseballs are in Spencer's collection? How many baseballs are in Christina's collection?
Christina has 46 baseballs and Spencer has 74 baseballs in their collections.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Christina and Spencer have 120 baseballs together.
Let christina has x baseballs
Spencer has 28 more
than Christina
x+28 has Spencer
So x+x+28=120
2x+28=120
Subtract 28 from both sides
2x=120-28
2x=92
Divide both sides by 2
x=46
Hence, Christina has 46 baseballs and Spencer has 46+28=74 baseballs in their collections.
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answer pls with work
The solution is Option C.
4cm , 6cm , 10 cm does not form a right angle triangle
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be ABC which is a right angle triangle
Now , the sides of the triangle is given as
a)
6cm , 8cm , 10cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
10² = 8² + 6²
100 = 64 + 36
100 = 100
Therefore , it is a right angle triangle
b)
12 cm , 35 cm , 37 cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
37² = 35² + 12²
1369 = 1225 + 144
1369 = 1369
Therefore , it is a right angle triangle
c)
4 cm , 6 cm , 10 cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
10² = 6² + 4²
100 = 36 + 16
100 ≠ 52
Therefore , it is not a right angle triangle
d)
10 cm , 24 cm , 26 cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
26² = 24² + 10²
676 = 576 + 100
676 = 676
Therefore , it is a right angle triangle
Hence , the triangle with sides 4cm , 6cm , 10 cm does not form a right angle triangle
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write in slope-intercept form of the line that passes through the points (-2,-2) and (5,12)
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).
We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Plugging in the values for the given points and solving for m, we get:
m = (12 - (-2)) / (5 - (-2))
= 14 / 7
= 2
Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):
y = mx + b
-2 = 2(-2) + b
-2 = -4 + b
b = -2 + 4
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = 2x + 2
This is the equation of the line that passes through the points (-2,-2) and (5,12).
how can you graph point with rational coordinates on a coordinate plane
Answer:
Locate the given point in the coordinate plane: for example; (−9,4)
Ans: Given that the x and y coordinate of the point are −9 and 4, respectively.
Here, the given point (−9,4) is located in the coordinate plane. It will be located on the top left side of the coordinate plane if you drew it out.
Step-by-step explanation:
1. You have to draw two perpendicular lines, \ (x-\)axis and \ (y-\)axis.
2. From the point of origin, you have to move 5 units to the right side along the positive \ (x-\)axis.
3. Now, you have to move \ (6\) units up, parallel to the positive \ (y-\)axis
4. Here, you mark the point of intersection and mark it as \ ((-9, 4).\)
In △QRS , point A is between points Q and R, point B is between points R and S, and AB∥QS .
QA=23 cm , QR=41 cm , and RS=123 cm .
What is RB ?
Answer:
the length of RB is 18 cm.
Step-by-step explanation:
In △QRS, since point A is between points Q and R, and point B is between points R and S, we have that QR > QA > 0 and RS > RB > 0. Additionally, since AB∥QS, we know that the segment AB is parallel to the segment QS.
We can use this information to set up an equation to solve for RB. Since AB∥QS and QA = 23 cm, we have that QR = RB + 23. We can substitute this expression into the equation QR = 41 cm to get:
RB + 23 = 41
Solving this equation for RB, we get:
RB = 41 - 23
Therefore, the length of RB is 18 cm.
The function f(x)f(x) is graphed below. How many points on the graph represent a relative minimum?
A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³,y = sinx.
As per the given graph,
The point where the slope is zero and the smallest among its neighborhood points then it will be relative minima.
In the given graph the point b is the smallest among its neighborhood thus b will be the relative minimum.
Hence "A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima".
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The standard deviation provides insight into the distribution of values around the mean. If the standard deviation is small, in general, the more narrow the range between the lowest and highest value. That is, values will cluster close to the mean. From your descriptive statistics, describe the standard deviations of salary, hrly rate, yrs worked, education, and age. What does this tell you about the variables
The standard deviation gives information about how values are distributed around the mean. The range between the lowest and highest number is more constrained when the standard deviation is low. Values will so tend to group together around the mean.
What is explained by the standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30.
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I don’t understand need help please. Calculate the line of best fit for the data in the table. The table below gives the number of hours spent studying for a science exam and the final exam grade. Show work
Study hours: 2 5 1 0 4 2 3
Grade: 77 92 70 63 90 75 84
Answer:
y = 6.08871x + 63.9274
Step-by-step explanation:
You can use Desmos a free graphing calculator to do this.
Help me pls , I don’t understand this
21 miles per hour is the speed of boat still in water and 9 miles per hour is the speed of current.
What is downstream speed and upstream speed?Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream.
Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The term "upstream speed" in this context refers to the boat's net speed.
13) Given that, a boat traveled 280 miles downstream and back.
Time taken by boat in downstream is 7 hours and in upstream is 14 hours.
Let the speed of a boat be x miles per hour and the speed of a current be y miles per hour.
So, the total speed in downstream is x+y miles per hour and the total speed in upstream is x-y miles per hour.
We know that, Distance = Speed × Time
Now, 280=(x+y)×7
⇒ x+y=40 ------(I)
Here, 280=(x-y)×14
⇒ x-y=20 ------(II)
Add equation (I) and (II), we get
x+y+x-y=40+20
⇒ 2x=60
⇒ x=30 miles per hour
So, x+y=40
⇒ y=10 miles per hour
14) Given that, a boat traveled 252 miles downstream and back.
Time taken by boat in downstream is 12 hours and in upstream is 84 hours.
Let the speed of a boat be p miles per hour and the speed of a current be q miles per hour.
So, the total speed in downstream is p+q miles per hour and the total speed in upstream is p-q miles per hour.
We know that, Distance = Speed × Time
Now, 252=(p+q)×12
⇒ x+y=21 ------(I)
Here, 252=(p-q)×84
⇒ p-q=3 ------(II)
Add equation (I) and (II), we get
p+q+p-q=21+3
⇒ 2p=24
⇒ p=12 miles per hour
So, p+q=21
⇒ q=9 miles per hour
Therefore, the speed of boat still in water is 21 miles per hour and the speed of current is 9 miles per hour.
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function rule to find f(72)
Answer:
-10
Step-by-step explanation:
When a problem asks you to find f("a number"), it's just telling you to replace x with "a number." So, substitute x with 72 to get the equation [tex]f(72)=-12+\frac{72}{36}[/tex]. The fraction simplifies to 2, and -12 plus 2 is just -10.
can you help me thank you
0.09 (100n + 1) = 0.3 (n +9)
Answer:
n = 0.3
Step-by-step explanation:
0.09(100n + 1) = 0.3(n + 9) ← distribute parenthesis on both sides
9n + 0.09 = 0.3n + 2.7 ( subtract 0.3n from both sides )
8.7n + 0.09 = 2.7 ( subtract 0.09 from both sides )
8.7n = 2.61 ( divide both sides by 8.7 )
n = 0.3
6x^2+60x+144 factor and is the first polynomial prime
Step-by-step explanation:
[tex]6x^2+60x+144\\\\6(x^2+10x+24)[/tex]
You are looking for two numbers that add to 10 and multiply to 24:
6 + 4 = 10
6 * 4 = 24
so [tex]x^2 + 10x + 24 = (x+6)(6+4)[/tex]
factored: [tex]6(x+6)(x+4)[/tex]
if f(x) = 2x + 7, what is the value of f(-10) and f(5)?
if f(x)= 2x+7
f(x)= two points
-10 and +5
the solution is : A,,,,f(-10)=2(-10)+7
= -20+7
= -13
and
B,,,,, f(5)= 2(5)+7
= 10+7
= 17
Which number line represents the solution to the inequality 3x−8≥7?
Answer:
Look at the attached image below
Step-by-step explanation:
[tex]\tt 3x-8\ge \:7[/tex]
Add 8 to both sides:-
[tex]\tt 3x\ge 7+8[/tex]
Add 7 and 8 to get 15:-
[tex]\tt 3x\ge 15[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3x}{3}\ge \cfrac{15}{3}[/tex]
[tex]\tt x\ge \:5[/tex]
Find the measure of the missing angles.
Answer: To find the missing angle, subtract the given angle from 180°.
Step-by-step explanation: