The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool? w ≤ 10 â€" l 2l 2w ≥ 62 w ≤ 10 â€" l 2l 2w > 62 w ≤ l â€" 10 2l 2w ≥ 62 w ≤ l â€" 10 2l 2w > 62.
Answers
The inequalities is given by l - w > 10 and l + w > 62
Let the possible length in meters, l, and the possible width in meters, w, of the pool.
Since the perimeter of a rectangular pool is more than 62 meters:
2(l + w) > 62
l + w > 62 (1)
Also, the width is at least 10 meters less than the length. hence:
l - w > 10 (2)
The inequalities is given by l - w > 10 and l + w > 62
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Answer:
Step-by-step explanation:
the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.
Let the length of the pool be x.
So, ATQ, the width will be represented by the inequality:
x - 10 ≥ width
w ≤ x - 10
w ≤ l - 10
Also, it is given that, the perimeter of the pool is more than 62 m
So, we get that:
P > 62
Also, we know that:
P = 2 l + 2 w
So, we get that:
2 l + 2 w > 62.
Therefore, the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.
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Related Questions
I need this answered!
Simplify the following expression:
5s + 72 - 6
use s = -8 and z = -3
I Record your answer in this box:
Answers
Answer:
I believe its -82
Step-by-step explanation:
5 × -8 + 7 × -3 = -82
Middle school math adding decimals Help please
Answers
Answer:
31514
Step-by-step explanation:
Answer:
2654 (from left to right)
Step-by-step explanation:
8.5 + 27.64 = 36.14
What is the area of this shape?
Answers
Answer:
1360cm
Step-by-step explanation:
34x40=1360
Answer:
1360\(cm^{2}\)
Step-by-step explanation:
Since this is a parelelorgram. We can find the area by mulitlying the base and the height. and so we get....
base x height = 40 x 34 = 1360\(cm^{2}\)
Write an equation, of the slope intercept form, of the line with slope −2 and passing through the point (−4,−5)
Answers
Equation for the given slope intercept -2 and passing through the point
(-4, -5) is y = -2x -13.
Given that
slope intercept = -2
passing through the point (-4, -5)
General equation formula
y = mx + b
where, b = y value of the y intercept point.
m = slope
x , y = points
substitute the given values in general formula , we get
-5 = -2 × 4 + b
-5 = 8 + b
b = -5 -8
b =-13
Equation in the slope intercept form
y = mx + b
y = - 2x - 13
Therefore, equation for the given slope intercept -2 and passing through the point (-4, -5) is y = -2x -13.
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Assume that A is row equivalent to B. Find bases for Nul A and Col A. 106 4 A2-63 2B0 2 5 2 -24 2 11-6 -3 8 A basis for Col A is ! (Use a comma to separate vectors as needed.) A basis for Nul Ais (Use a comma to separate vectors as needed.)
Answers
the null space of A is the span of the vector:
(-2, 3, 1)
A basis for Nul A is:
{(-2, 3, 1)}
To find bases for Nul A and Col A, we can use the fact that A is row equivalent to B. This means that we can perform a sequence of elementary row operations on A to obtain B. Since elementary row operations do not change the null space or column space of a matrix, the null space and column space of A will be the same as the null space and column space of B.
To find a basis for Col A, we can find the pivot columns of A (or B, since they have the same column space). The pivot columns are the columns of A that contain a leading non-zero entry in the row reduced form of A. In this case, the row reduced form of A is:
1 0 0 -1
0 1 0 2
0 0 1 3
The pivot columns are columns 1, 2, and 3. Therefore, a basis for Col A is the set of corresponding columns from A:
{(1, 0, 2), (4, 2, 5), (2, -6, -3)}
To find a basis for Nul A, we can solve the homogeneous system Ax = 0. Since A is row equivalent to B, we can use the row reduced form of B to solve for x. The row reduced form of B is:
1 0 -2/53 0
0 1 3/53 0
0 0 0 1
The solution to the system Ax = 0 can be written in parametric form as:
x1 = 2/53 s
x2 = -3/53 s
x3 = s
where s is a scalar. Therefore, the null space of A is the span of the vector:
(-2, 3, 1)
A basis for Nul A is:
{(-2, 3, 1)}
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The price of an item has been reduced by 95%. The original price was $33.
Answers
Answer:
25%
Step-by-step explanation:
See a solution process below: Explanation: We can use this formula to solve this problem: s=p−(d×p). Where: s is the sales price: what we are
suppose that you are dealt 5 cards from well shuffled deck of cards. what is proability that you recieve hadn with at least 3 suits
Answers
The probability that you receive a hand with at least 3 suits if you are dealt 5 cards from a well-shuffled deck of cards is 0.45.
What is a deck of cards?A standard deck of cards has 52 cards.
Each card belongs to one of four suits: diamonds, hearts, clubs, and spades.
There are thirteen cards in each suit: ace, two, three, four, five, six, seven, eight, nine, ten, jack, queen, and king.
Calculation:
The total number of hands that can be drawn from a deck of 52 cards is given by 52C5 or (52 × 51 × 50 × 49 × 48) / (5 × 4 × 3 × 2 × 1) = 2,598,960.
There are 4 ways to choose 3 suits out of 4.
If we select 3 suits, each suit is represented by 13 cards, so the number of ways to select 3 suits is
\(13C_5 × 13C_5 × 13C_5 = 5,531,120.\)
Ways to select 4 suits:
There are 4 ways to select 4 suits, each with 13 cards, so the number of ways to select 4 suits is
\(13C_5 × 13C_5 × 13C_5 × 13C_5 = 13,842,900.\)
Total ways of selecting a hand of 5 cards with at least 3 suits = 5,531,120 + 13,842,900 = 19,374,020
Therefore, the probability of getting a hand with at least 3 suits is 19,374,020 / 2,598,960 = 0.45.
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What is the equation of the line in slope-intercept form 
Answers
The slope-intercept formula is one of the formulas used to determine a line's equation. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.
What is slope-intercept form?Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope intercept form.
One of the formulas used to get a line's equation is the slope-intercept formula. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.
The variables we'll use in our function will be as follows:
m = slope, and b = y-intercept.
It is written as y = mx + b. The m and b variables are changed to numbers, while the x and y variables stay as letters (for example, y = 2x + 4, slope = 2, and y-intercept = 4).
The slope and intercept from an equation are used in the following video through a few examples.
y = mx + b
The slope and intercept are the two integers that make up this equation, which is why it is known as the slope-intercept form.
Remember, the slope (m) is the amount being multiplied to x and the intercept (b) is the number being added or subtracted
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The height of a plant in centimeters is recorded each day for 14 days. The function y = 1.44x + 1.55 is determined to be a good fit for the data. On day 7, the recorded height was 12.32 centimeters. How close is the predicted height to the actual height of the plant (the residual)? A) 0.63 cm B) 0.69 cm C) 1.38 cm Eliminate D) −0.69 cm
Answers
The predicted height is close to the actual height of the plant by 0.69 cm
How to determine the closeness in the heights?The equation of the height function of the plant is given as:
y = 1.44x + 1.55
The height on day 7 is calculated as:
y = 1.44 * 7 + 1.55
Evaluate
y = 11.63
The recorded height is given as 12.32
The residual is calculated as:
Residual = Recorded - Predicted
So, we have:
Residual = 12.32 - 11.63
Evaluate
Residual = 0.69
Hence, the predicted height is close to the actual height of the plant by 0.69 cm
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a feature was created using a triangle and a semicircle . use the ruler provided to measure the dimensions of the triangle and semicircle to the nearest centimeter . which measurement is closest to the area of the feature in square centimeters .
Answers
The area of a circle is given by:
\(\begin{gathered} A=r^2\pi \\ \text{Where:} \\ r=\frac{8}{2}=4 \\ \text{ Since it is a semicircle, the area is:} \\ A=\frac{4^2\pi}{2}=8\pi \end{gathered}\)And the area of the triangle is:
\(\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{where:} \\ b=8 \\ h=7 \\ A=\frac{8\cdot7}{2}=28 \end{gathered}\)Therefore, the total area is:
\(A_T=8\pi+28\approx53.13\operatorname{cm}\)Suppose that, from measurements in a microscope, you determine that a certain bacterium covers an area of 1. 50μm2. Convert this to square meters.
Answers
Converting 1. 50μm² to square meters gives 1. 5 × 10 ^-11
What is conversion of units?Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.
From the information given, we are to convert micrometers to square meters
Note that:
1 micrometer ( μm²) = 10^-12m²
Given 1. 50μm² = xm²
cross multiply
x = 1. 50 × 10^-12
x = 1. 50 × 10^-12
x = 1. 50 × 10^-12
x = 1. 5 × 10 ^-11 square meters
Thus, converting 1. 50μm² to square meters gives 1. 5 × 10 ^-11
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f the concentrations of a weak acid and its conjugate base are decreased from 0.5 m and 0.2 m, respectively, to 0.3 m and 0.04 m, the solution's buffer capacity will _________. increase
decrease
remain constant
decrease then increase
Answers
Therefore, when their concentrations decrease from 0.5 m and 0.2 m to 0.3 m and 0.04 m, respectively, the buffer capacity decreases as well.
The solution's buffer capacity will decrease with the decrease in concentrations of the weak acid and its conjugate base. Buffer capacity is the ability of a buffer solution to resist changes in pH when small amounts of acid or base are added. A higher concentration of the weak acid and its conjugate base leads to a higher buffer capacity. Therefore, when their concentrations decrease, the buffer capacity decreases as well. When the concentrations of a weak acid and its conjugate base decrease, the solution's buffer capacity decreases. Buffer capacity is the ability of a buffer solution to resist changes in pH when small amounts of acid or base are added. A higher concentration of the weak acid and its conjugate base leads to a higher buffer capacity.
Therefore, when their concentrations decrease from 0.5 m and 0.2 m to 0.3 m and 0.04 m, respectively, the buffer capacity decreases as well.
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Which of the following integrals represents the area of the region bounded in the first quadrant by x = pi/ 4 and the functions f(x) = sec^2(x) and g(x) = sin(x)? O π/4 (sec²(x)+sin(x))dx
O π/4 (sec²(x)-sin(x))dx
O π/4 (sin(x)-sec² (x))dx
O (sec²(x)-sin(x))dx
Answers
The integral that represents the area of the region bounded in the first quadrant by x = π/4 and the functions f(x) = sec^2(x) and g(x) = sin(x) is π/4 (sec^2(x) - sin(x))dx.
To find the area of the region bounded by the curves, we need to subtract the integral of the lower curve from the integral of the upper curve. In this case, the upper curve is f(x) = sec^2(x) and the lower curve is g(x) = sin(x).
The integral representing the area is given by:
Area = ∫[a,b] (f(x) - g(x))dx
Substituting the given functions, we have:
Area = ∫[0,π/4] (sec^2(x) - sin(x))dx
This integral represents the area bounded by the x-axis, the curve y = sec^2(x), the curve y = sin(x), and the vertical line x = π/4. The integral of (sec^2(x) - sin(x))dx over the interval [0,π/4] calculates the area between the two curves within the specified region.
Therefore, the correct integral that represents the area of the region in the first quadrant is π/4 (sec^2(x) - sin(x))dx.
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. Six times a number diminished by 7
comes out to be 41. The number is
Answers
Answer:
x = 8
Step-by-step explanation:
let x = a number
6x - 7 = 41
+7 +7
6x = 48
divide by 6
x = 8
Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!
-Lil G
Which point on the number line represents the product (-4X=28-02 O W Point A W Point B 0 Point C Point D
Answers
Answer:
tfcfgcvghvgh h hg hjjhnkjknjkhnukj
Step-by-step explanation:
Write and solve a proportion to answer the question.
48 is what percent of 160?
Answers
Answer:
30%
Step-by-step explanation:
\(\frac{48}{160} = 0.3 = 30%\)
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10.
Answers
Answer:
UW = 36 units
Step-by-step explanation:
The question is incomplete. Here is the complete question
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10. If UW = 9x – 9, what is UW in units?
If a point V lies between points U and W on line segment UW, then based on vector notation, UV + VW = UW.
Given parameters
The length between U and V i.e UV = 2x-4
The length between V and W i.e VW= 4x + 10.
UW = 9x – 9
Required
The length between U and W in units
Since UW = UV+VW, we will substitute the given functions into the formula as shown;
9x-9 = 2x-4+4x + 10.
9x-9 = 2x+4x-4+10
9x-9 = 6x+6
collect like terms on both sides;
9x-6x = 6+9
3x = 15
x = 15/3
x = 5
Substitute x = 5 into the function UW = 9x-9 to ge the length of UW in units.
UW = 9(5)-9
UW = 45-9
UW = 36 units
Hence the required length between line segment U and W in units is 36units.
Answer:
36 units, edge 2020-21
Step-by-step explanation:
aka D/last answer
John went to the store and bought 4 pencils
and 10 binders and spent $64. Carmen went
to the same store and bought 7 pencils and 4
binders and spent $31. If Lisa wants to buy
pencils and binders from the same store,
how much should they tell her each item
costs?
Answers
X= pencils and Y= binders
4x + 10y = 64
7x + 4y= 31
Pencils are $1 each and binders are $6 each.
I need help with this question plsss
Answers
Answer: maybe its 6
Step-by-step explanation:
i think its 6 because it has +3 so maybe adding 3+3
sometimes true, always true, or never true?
Answers
===========================================
Explanation:
I'll use x in place of n
Let y = x^2 - 4x + 5
If we complete the square, then,
y = x^2 - 4x + 5
y = (x^2 - 4x) + 5
y = (x^2 - 4x + 4 - 4) + 5
y = (x^2 - 4x + 4) - 4 + 5
y = (x-2)^2 + 1
The quantity (x-2)^2 is never negative as squaring any real number value is never a negative result. Adding on 1 makes the result positive. So y > 0 regardless of whatever x is. Replace x with n, and this shows how n^2 - 4n + 5 is always positive for any integer n.
------------
You could also use the quadratic formula to find that x^2 - 4x + 5 = 0 has no real solutions, so there are no x intercepts. Either the graph is entirely above the x axis or it is entirely below the x axis.
Plug in any x value you want, say x = 0, and the result is positive. Meaning that whatever x value you plug in will be positive (as the graph can't cross the x axis to go into negative territory)
What is the actual length of the living space if the length in the scale drawing is 16. 8 in the scale
Answers
The actual length of the living area is 134.4 feet if the length in the scale drawing is 16.8 in the scale.
To determine the actual length of the living space from a scale drawing, we need to use the scale factor, which is the ratio of the length in the drawing to the actual length. If the length in the scale drawing is 16.8 inches and the scale is given as a ratio of 1 inch in the drawing to 8 feet in actual size, we can set up a proportion:
1 inch (drawing) / 8 feet (actual)
= 16.8 inches (drawing) / x (actual)
We can cross-multiply and simplify to find x's value:
1 inch × x = 8 feet × 16.8 inches
x = (8 feet × 16.8 inches) / 1 inch
x = 134.4 feet.
Therefore, the actual length of the living space is 134.4 feet.
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please check the image !!! WORTH 40 POINTS!
Answers
4. 1<x<5
5. 23<y
6. x=y÷2+1
Can someone help me asap? It’s due tomorrow.
Answers
Answer: C
Step-by-step explanation:
A. is wrong, only 6 students liked pineapple and 12 bacon, so they did not prefer pineapple to bacon
B. is wrong, the most students liked was not cheese, it was pepperoni
C. is correct, pineapple is the least liked at 6 student
D. is wrong, not all the students liked pepperoni, some students liked other things
What is the critical angle between two mystery transparent materials, in degrees? na = 1.65 and nB = 2.12. Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.
Answers
The critical angle between these two materials does not exist.
The critical angle θc is given by the equation sin θc = nB/na, where na and nB are the refractive indices of the two materials. Substituting na = 1.65 and nB = 2.12 into this equation, we get sin θc = 2.12/1.65 = 1.2848. However, since the sine function is only defined between -1 and 1, this means there is no real value of θc that satisfies this equation. Therefore, the critical angle between these two materials does not exist.
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Find the area of a circle with a circumference of 50.24 units.
Answers
Answer:
200.96
Step-by-step explanation:
have a good day:D
Which equation can be solved to find x, the measure of BD in the diagram
below?
C
53
AB
D
E
2330
O A. *- 53 = 233
B. }(233 + x) = 53
C. (233 - x) = 53
D. x+ 53 = 233
=
Answers
The value of x is equal to 127 degrees.
Data;
Outer angle = 233Inner angle = 53unknown angle = xAngle tangent to a circleTo find the angle x which is related to angle 233 to form the outer angle 53, the equation
\(\frac{1}{2} (233 - x) = 53\)
We can proceed to solve for x by simplifying the equation which will give us
\(\frac{1}{2}(233-x) = 53\\2 * 53 = 233 - x\\106 = 233 - x\\x = 233 - 106\\x = 127^0\)
The value of x is equal to 127 degrees.
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Answer:
Step-by-step explanation:
just took the quiz
help is appreciated
Which is the graph of the inequality 2 - (x+3) <4- 2x?
OA
-5
0
5
OB
-5
0
5
OC
-5
0
5
OD
-5
0
5
+
OE.
-5
0
5
Answers
Answer:
C
Step-by-step explanation:
hope this help Im pretty sure it's right
The graph for the inequality given is graph 1.
What is an inequality?An inequality is a relation between two numbers or expressions that are not equal. It can show which of them is greater or smaller by using symbols like < or >. It can also be a statement of fact about the order relationship of quantities.
Given that an inequality, 2-(x+3) < 4 -2x, we need to determine its graph,
For the same solving the inequality,
2-(x+3) < 4 -2x
2-x-3 < 4 - 2x
Add x to both sides,
2-3 < 4-x
-1 < 4-x
Subtract 4
-1-4 > -x
x > 5
Since, the x is greater than 5 so the graph will be the numbers that greater than 5,
Hence, the graph is 1.
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there are 6 large bags and 4 small bags of stones.Each bags hold the same number of stones as the other bags of the same size .how could you represent the total number of the stones with a polynomial
Answers
Answer:
Let's represent the number of stones each bag holds by the variable x.
Then the total number of stones in the 6 large bags is 6x, and the total number of stones in the 4 small bags is 4x.
Therefore, the total number of stones can be represented by the polynomial:
6x + 4x = 10x
So the polynomial is 10x, which represents the total number of stones.
Answer:
Step-by-step explanation:
large bags = x
small bags = y
6x + 4y
A process in which a number is changed, such as by adding, subtracting, dividing, or multiplying.A. operation.B. smart.C. super cool.
Answers
Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.
The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.
The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.
Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.
Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.
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To prove the following statement by contradiction: The average of three real numbers is greater than or equal to at least one of the numbers. What would be assumed to be true? A)The average of three real numbers is greater than or equal to at least one of the numbers, B) The average of three real numbers is greater than or equal to all of the numbers. C) The average of three real numbers is less than at least one of the numbers. D) The average of three real numbers is less than all of the numbers. E) The average of three real numbers is less than or equal to at least one of the numbers. F) The average of three real numbers is less than or equal to all of the numbers.
Answers
To prove the statement by contradiction, we assume that option C) The average of three real numbers is less than at least one of the numbers is true.
Then, we can use a counterexample to disprove this assumption.
For example, let's consider the numbers 1, 2, and 3.
Their average is (1+2+3)/3 = 2, which is greater than all of the numbers.
This counterexample shows that the assumption is false, and therefore, option C) is not correct.
Hence, the correct assumption to prove the statement by contradiction is option A) The average of three real numbers is greater than or equal to at least one of the numbers.
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