The inequality expression of the volume of the balloon is V < 4,400
How to determine the inequality expression?From the question, we have the following statement:
The initial volume of the balloon is 4,400 cubic centimeters
Also, we understand that:
The balloon leaks out over time
This means that the volume of air in the balloon decreases over time.
So, we have the following representation
V = Less than the initial volume
Rewrite as
V < 4400
Hence, the volume of the balloon at any time after it starts leaking is V < 4,400
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can someone answer this question really quick
c = 2.97r is the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost
How to write an equation that describes proportional relationships?Two variables have a proportional relationship if all the ratios of the variables are equivalent
In order to write an equation that describes the proportional relationship r, the number of reams purchased and c, the total cost, we need to write a proportional equation using the variables:
c α r (Note: α is the proportion symbol)
c = kr
k = c/r
Where k is the constant of proportionality
As shown in the image, you can see that 4 reams cost $11.88 and 6 reams cost $17.82
k = c/r
k = 11.88/4 = 2.97 or 17.82/6 = 2.97
c = kr
c = 2.97r
Therefore, the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost is c = 2.97r. Enter c = 2.97r in the box
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domain of "-x^4-x^3+3x^2+2x+6"
The domain of the given function is -∞ < x < ∞.
What is a domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, the function is:
-x⁴-x³+3x²+2x+6Now, the domain of the given function is:
The set of input or argument values for which the function is actual and defined is known as the function's domain.Neither the function's domain constraints nor its undefined points exist.The domain will therefore be -∞ < x < ∞.
Therefore, the domain of the given function is -∞ < x < ∞.
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I need this by tonight would be appreciated. :) I know this is basic stuff I'm in Middle School but when I signed up for this there wasn't a middle school option.
The area of the floor of the convenience store would be = 212.5 ft²
What is the area of an object?The area of an object is defined as the total space that is being occupied by that object.
To calculate the area of the convenience store is to find the area of the shaded part which would be = area of square - area of the triangle.
Area of square = l ×w = 15 × 15 = 225ft²
Area of triangle= 1/2 base ×height
= 1/2 × 5 × 5
(Note: 15 - 10 = 5 ft from the diagram used as base and height)
= 25/2
= 12.5 ft²
The area of the convenience store;
= 225 - 12.5
= 212.5 ft².
Therefore, the area that is covered by the convenience store should be = 212.5ft².
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help i have no clue what this even means
Case 1: largest surface area: 2120 sq. in.
Case 2: smallest surface area: 1380 sq. in. of the wooden block.
What is defined as the cuboid?A three-dimensional shape called a cuboid is described as having six rectangular face, eight vertices, and twelve edges.Twelve edges plus eight vertices and corners to up a cuboid.For the given question, the dimensions of the wooden block are given.
Length l = 50 inchesWidth w = 5 unitsHeight h = 2 unitsSurface area of a cuboid is = 2lw + 2lh + 2 hw
Case 1: largest surface area.
To get the largest surface area, join the wooden cube along length 50 cm.
Total length = 50 + 50 + 50 = 150 inches.
Put in formula.
Surface area = 2×150×5 + 2×5×2 + 2×2×150
Surface area = 2120 sq. in.
Case 2: smallest surface area.
To get the smallest surface area, join the wooden cube along height 2 cm.
Total length = 2 + 2 + 2 =8 inches.
Put in formula.
Surface area = 2×8×50 + 2×50×5 + 2×5×8
Surface area = 1380 sq. in.
Thus, the smallest surface area of the wooden cube is found as 1380 sq. in.
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The correct question is-
There are 3 identical wooden blocks that are 50 inches long, 5 inches wide and 2 inches thick. If you glue them together , what is the largest and smallest outer surface area can get?
Please, can someone help me with this math? I would greatly appreciate it!
The proof that shows that lines DC and AB are parallel is shown below.
What is the SSS Congruence Theorem?The SSS congruence theorem states that two triangles that have three corresponding congruent sides are congruent to each other.
When two triangles are proven to be congruent triangles, invariably, we can state that the corresponding parts of both triangles are also equal to each other by CPCTC.
The following proof shows lines DC and AB are parallel lines:
Statement Reasons
1. AB = CD 1. Given
AD = CB
2. Line AC = Line AC 2. Reflexive property
3. Triangle ADC ≅ Triangle ABC 3. SSS
4. Angle 1 ≅ Angle 4 4. CPCTC
5. DC║AB 5. Converse of alternate interior ∠s theorem
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CORE
SKILL
ADVANCED
If a is inversely related to the square of b, and a = 3 when bis
8, which of the following is another possible value for a and b?
(A) a = 4, b = 12
(B) a = 12, b = 4
(C) a = 8, b = 3
(D) a = 2, b = 4
(E) a = 6, b = 4
Another possible values for a and b are a = 12 and b = 4
How to find another possible value for a and b?
A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: a is inversely related to the square of b, and a = 3 when bis
8.
This can be written as:
a α 1/b²
a = k/b² (where k is a constant)
k = ab²
since a = 3 and b = 8.
Thus, k = 3 × 8² = 3 × 64 = 192
For a value to be another possible value for a and b, they must give k = 192 when substituted into the equation k = ab²:
a = 4, b = 12: k = 4 × 12² = 576
a = 12, b = 4: k = 12 × 4² = 192
a = 8, b = 3: k = 8 × 3² = 72
a = 2, b = 4: k = 2 × 4² = 32
a = 6, b = 4: k = 6 × 4² = 96
The values that produce k = 192 are a = 12 and b = 4. Therefore, another possible value for a and b is a = 12 and b = 4. So option B is the answer
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The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -9 ≤ x ≤ -4?
Answer:
2.4
Step-by-step explanation:
You want the average rate of change on the interval [-9, -4] for the graphed function.
Average rate of changeThe average rate of change (m) is the slope of the line between the points at the ends of the interval. For function f(x) on interval [a, b], this is ...
m = (f(b) -f(a))/(b -a)
ApplicationFor the function f(x) on the interval [-9, -4], the average rate of change is ...
m = (f(-4) -f(-9))/(-4 -(-9)) = (-4 -(-16))/5 = 12/5 = 2.4
The average rate of change of f(x) on [-9, -4] is 2.4.
PLEASE ANSWER
there are no choises
The relation between angle 1 and angle 2 is they are equal and corresponding angle.
What are parallel lines?
Two lines are said to be parallel when they do not intersect each other. We can also say that two lines that run along and meet at infinity are called parallel lines.
What are corresponding angles?
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines and the transversal.
Given, m and l are parallel line.
Hence, m and l satisfy the condition of parallel lines.
Therefore, the angle 1 and angle 3 are equal.
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The front elevation of a solid shape is a triangle. The side elevation of the solid shape is a triangle. The plan view of the solid shape is a circle. Write the name of the shape.
Answer:
Cone
Step-by-step explanation:
The Angles are all triangle-shaped, but the bottom is circle-shaped.
The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 45° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
The measure of each angle of this isosceles triangle is equal to 27°, 27°, and 126°.
What is an isosceles triangle?An isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles that have the same measure or are equal in magnitude.
Let the variable x represent the angles that have the same measure or are equal in magnitude. Therefore, the sum of the measures of the angles of this isosceles triangle is given by this mathematical expression:
x + x + (45° + 3x) = 180°.
5x + 45° = 180°.
5x = 180° - 45°
5x = 135°
x = 135°/5
x = 27°
Therefore, the measure of each angle of the isosceles triangle is given by:
First angle = 27°.
Second angle = 27°.
Third angle = 45° + 3(27) = 126°.
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402 students were surveyed about their preferences of sports. 140 students like football, 144 students like baseball, and 42 students like both sports. how many students like exactly one of the two sports? a) 200 b) 140 c) 284 d) 98 e) 102 f) none of the above.
The students that will like exactly one of the two sports out of football and baseball is 200.
What is set theory?These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).
Here,
F=140
B=144
F∩B=42
F-B=n(F)-n(F∩B)
=140-42
F-B=98
B-F=n(B)-n(F∩B)
=144-42
=102
So, the students that will like exactly one of the two sports,
=102+98
=200
There are 200 students who will only enjoy one of the two sports—football or baseball.
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you wish to survey people who have brought in their cars for service during the past month. you decide to choose a random sample of gas stations in the city and then survey all customers from those stations who had work done during the past month. this procedure is an example of which type of sampling?
An illustration of "Cluster sampling" is the practice of selecting a random sample of the city's gas stations, and then surveying every station's patrons.
Define the term Cluster sampling?In cluster sampling, a population is divided into clusters, which have been smaller groups. They but choose a sample at random from these clustersOften employed to investigate huge populations, typically those that are substantially geographically distributed, cluster sampling is a probability sampling technique. Often, clusters used by researchers have been groups like cities or schools.As per the given question.
People who brought their autos in for service over the past month should be surveyed. You make the decision to selecting a haphazard sample of the city's petrol stations, after which you interview all of their patrons whom have work done on their vehicles well within previous month.Thus, an implementation of "Cluster sampling" is the practice of randomizing sample of the city's gas stations, and thereafter surveying every station's patrons.
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Part A: Timothy said that triangle KLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy correct? Explain your answer or show your work by listing the coordinates of the primage and image and showing the scale factor
Part B: Are the two triangles similar? Explain.
a. Timothy is correct regarding the dilation, considering the vertices of each triangle.
b. The two triangles are similar, as they have congruent angle measures.
What is a dilation?A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor.
The effects of a dilation are given as follows:
Congruence is lost, as the side lengths will be different due to the multiplication by the scale factor.Similarity is kept, as the side lengths are proportional, hence the angles remain constant.The vertices of each triangle in this problem are given as follows:
Triangle KLM: K(-1,3), L(8,4) and M(10,-3).Triangle K'L'M': K'(-1.5, 4.5), L'(12, 6) and M'(15, -4.5).The scale factor is obtained by the division of any of the equivalent factors, hence:
k = 4.5/3 = 1.5.
Confirming that Timothy's statement regarding the scale factor of the dilation is correct.
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Which values of aand b make the following equation true?
(5x²y²){-4xªy³) =−20xªy°
O
a = 11, b = 7
O a = 11, b = 10
O a=28, b = 7
O a= 28, b = 10
The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.
Expression:
An expression is set of numbers or variables combined using the operations +, -, * and /.
Given,
Here we have the expression (5x²y²){-4xªy³) =−20xªy°.
Now, we have to the value of a and b which make both equation as equal.
In order to get the value a and b, first, we have to solve the expression in the left hand side,
To solve this type of equation, the first step is to combine the like terms, then we get,
=> (5x²y²){-4xªy³)
=> (5 x -4) (x² xᵃ) (y² y³)
Now, we have to do the multiplication on it, then we get,
=> -20 xᵃ⁺² y²⁺³
=> -20xᵃ⁺²y⁵
Now, we have to equate both LHS and RHS, then we get,
=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ
While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.
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The table shows the side
lengths and perimeters of
regular hexagons. Is the
relationship between the
perimeter and the side
length of the hexagons
proportional? Explain.
The relationship between the perimeter and the side length of the hexagons is proportional.
What is a proportional relationship?A proportional relationship is one that illustrates the constant between the data that are given.
In this case, when the side length is 2, the perimeter is 12. The constant is:
= Perimeter / Length
= 12 / 2
= 6
Also, when the length is 3, the perimeter is 18. The constant will be:
= 18 / 3
= 6
Since they have 6 as constant, it's a proportional relationship.
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One share of kimcos common stock pays an annual dividend of 1. 43. Today kimco closed at 19. 09 with a net cahnge of +0. 72. The stock yield yesterdays closing price is about 8
With a net change of +0.72 yesterday's closing price was 19.81 and stock dividend yield for yesterday's closing price is 7.2%.
How to calculate the Dividend Yield?
To calculate dividend yield, all you have to do is divide the annual dividends paid per share by the price per share.
Dividend Yield = Annual Dividends Paid Per Share / Price Per Share
According to the given question:
Net change = today's price - yesterday's price
0.72 = 19.09 - yesterday's price
∴ Yesterday's price = 19.81
Stock dividend yield
= (1.43/19.81) x 100
= 7.2%
Therefore the stock yield of yesterday's closing price is 7.2%
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What is the slope of a line parallel to the line whose equation is 3x+4y=36
Answer:
3/4
Step-by-step explanation:
Get into y=mx+b
Subtract 3x
4y=3x+36
Divide by 4
y=3/4x+9
Parallel= 3/4
Perpendicular= -4/3
Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=2x5−x3+x2+4; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down
The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11
How to determine the transformation of the function?The equation of the function is given as
f(x) = 2x⁵ - x³ + x² + 4
The sequence of transformations is given as follows:
Reflection across the y-axisVertically stretched by a factor of 3Translate down by 1 unitWhen the above transformations are combined, we have:
g(x) = 3f(-x) - 1
So, we have
3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1
This gives
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1
Expand
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11
So, we have
g(x) = -6x⁵ + 3x³ + 3x² + 11
Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11
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the area of a rectangle shown is 44m2
3 2/3 m
x?
work out the missing length x
can someone solve this?
Find the values of the variables and the measures of the angles.
Answer:
x = 52°
y = 25°
z = 90°
Step-by-step explanation:
We know there are 180 degrees in a triangle. The box represents 90 degrees.
90° + x + 38° = 180°
x + 128° = 180°
x = 52°
Next, we know that a straight line is equal to 180 degrees. Again, the box represents 90 degrees.
90° + z = 180°
z = 90°
Lastly, we will use the same process for angle x, but for angle y.
y + z + 65° = 180°
y + 90° + 65° = 180°
y + 155° = 180°
y = 25°
Alyssa misses 2% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 63?
Answer: 3150
Step-by-step explanation:
We know that 50×2%s is 100%, so 50×63 should result in the total amount of throws she attempts, which is 3150.
will give you brainliest!! ASAP
Answer:
686 cm^2
Step-by-step explanation:
4(7)=28
7(7)=49
49 x 28= 1372
1372/2=686
hopes this helps
Find the x- and y-intercepts of the graph of 4x - 9y = 20. State each answer as an
integer or an improper fraction in simplest form.
Calculation
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's x-intercept: x= 5
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's y-intercept: y = [tex]-\frac{20}{9}[/tex]
The chart for : 4x-9y = 20
see the attachment
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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4
What is meant by fraction?A fraction is a portion of a whole. In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator. In a simple fraction, both are integers.A complex fraction has a fraction in either the numerator or denominator. In a proper fraction, the top number is less than the lowest common.A fraction pretty much tells us how many parts of a whole we have. A fraction is identified by the slash that is written between the two numbers. Designers have a top number, the quaternion, and a bottom number, the denominator. For instance, 1/2 is a fraction.Given
x, 4x - 9y = 20
x = 20 + 9 /4 y
Steps
4x - 9y = 20
Add 9 y to both sides
4x - 9y + 9y = 20 + 9y
Simplify
4x = 20 + 9y
Divide both sides by 4
4x/4 = 20/4 + 9y/4
Simplify
x = 20 + 9y /4
Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.
x = 20 + 9y /4
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“Find the requested information based on the given facts.
Total sales is $55,000
The commission is 3.5%
Determine the commission.”
Can someone please help?
Answer:
$1925
Step-by-step explanation:
So your problem is $55,000 x 3.5%
You can rewrite this as:
55,000 x 3.5/100 or 55,000 x 35/1000
Now multiply. I will remove the /1000 for now.
55,000x35=1925000
Now, divide 1925000 by 1000.
1925/1000=$1,925
solve the equation 8-3(x + 4)= 2x +1
Answer:
x = -1
Step-by-step explanation:
8 - 3x - 12 = 2x + 1
-3x - 4 = 2x + 1
-5 = 5x
x = -1
The value of x in the equation 8-3(x+4)=2x+1 is -1.
Given equation 8-3(x+4)=2x+1
= 8-3x-12 = 2x+1
= -3x-4 = 2x+1
= -5x = 5
= x = -1
We will first solve the bracket which is -3(x+4) which will give us -3x-12 and then we will add this to 8 which will give us -3x-4. Next, we will move all the constants to one side and the terms with x to one side which will give us -5x=5. Finally, we will divide the whole equation by -5 and we will get the answer of x as -1.
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x represents the number
of comic books Priya buys
at the store, all at the same
price, and y represents the
amount of money (in
dollars) Priya has after
buying the comic books.
By using the concept of equation of line in slope intercept form, it can be obtained that
a) x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
y- intercept is 20
This means, Priya had $20 before buying any comics
b) Slope = -4
This means Priya's money has been decreasing by $4 after buying one comics
c) Equation of line
y = -4x + 20
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.
x represents the number of comic books Priya buys at the store
y represents the amount of money (in dollars) Priya has after buying the comic books.
a)From the figure, it is clear that x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
From the figure, it is clear that y- intercept is 20
This means, Priya had $20 before buying any comics
b) The line passes through (5, 0) and (0, 20)
Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4
This means Priya's money has been decreasing by $4 after buying
one comics
c) Equation of line
y - 0 = -4(x - 5)
y = -4x + 20
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Complete Question
The figure has been attached-
Larissa is standing at point L Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
If LR equals 12 and PR equals 4, then: LP = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
What is the Segment Addition Postulate?The Segment Addition Postulate states that when there are two endpoints on a line segment (L) and (C), a third point (P) would lie on the line segment (LR), if and only if the magnitude of the distances between the endpoints satisfy the requirements of this equation LP + PR = LR.
This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.
By applying the Segment Addition Postulate to the given endpoints, the value of LP is given by:
LP + PR = LR
LP = LR - PR
Substituting the given parameters into the formula, we have;
LP = 12 - 4
LP = 8.
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Complete Question:
Larissa is standing at point L. Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
LP = 16 because 12 + 4 = 16 according to the addition property of equality.
LP = 8 because 12 - 4 = 8 according to the subtraction property of equality.
PR = 16 because LR + LP = PR according to the Segment Addition Postulate, and 12 + 4 = 16 using substitution.
PR = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
Answer: Lp = 8
Step-by-step explanation:
Got it right
HELP ASAP !!!! Use the equation one fourth plus s equals 18 over 20 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
a. The two numbers between which the solution to the equation lies are 0 and 1.
b. The value of the variable "s" is 13/20.
How to solve Algebra Word Problems?The equation given to us is one fourth plus s equals 18 over 20. This can be expressed as;
¹/₄ + s = ¹⁸/₂₀
s = ¹⁸/₂₀ - ¹/₄
s = (18/20) - (5/20)
s = (18 - 5)/20
s = 13/20
The solution is a rational number. A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
We can determine two rational numbers such that the solution is in between them. A rational number smaller than the solution is 0. A rational number larger than the solution is 1. Hence, the solution lies between 0 and 1.
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Work out the length of x if one of the lengths is 9.7cm.Give your answer rounded to 3 significant figures.
Tysm if u can work this out correctly.
Considering the figure of a right angle triangle, the given length is the hypotenuse,. The unknown side x is calculated to be 6.86 cm
How to find xinformation given in the question
hypotenuse = 9.7 cm
opposite = x
adjacent = x
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
opposite = adjacent
plugging the values as in the problem
let x be the required distance
9.7² = x² + x²
94.09 = 2x²
47.045 = x²
x² = 47.045
x = √47.045
x = 6.8589
x = 6.86 to 3 significant figures
side x is 6.86 cm
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lins bike travels 100 meters when her wheels rotate 55 times . whats the circumferences of her wheels
Answer:
Using formula to calculate the circumference of wheel: c=d/n
where
D is the distance bike travel
n is the number of times rotation
C is the circumference of the wheel
As per the statement:
Lin’s bike travels 100 meters when her wheels rotate 55 times.
here, n = 55 rotation and D = 100 meter.
then by definition:
meter c=100/55=20/11
Therefore, the circumference of her wheel is 1 9/11